storage systems for high-speed railway traction …...energies article optimized sizing and...

energies

Article

Optimized Sizing and Scheduling of Hybrid EnergyStorage Systems for High-Speed RailwayTraction Substations

Yuanli Liu 1, Minwu Chen 1,*, Shaofeng Lu 2 ID , Yinyu Chen 1 ID and Qunzhan Li 1

1 School of Electrical Engineering, Southwest Jiaotong University, Chengdu 611756, China;[email protected] (Y.L.); [email protected] (Y.C.); [email protected] (Q.L.)

2 Department of Electrical and Electronic Engineering, Xi’an Jiaotong-Liverpool University, Suzhou 215123,China; [email protected]

* Correspondence: [email protected]; Tel.: +86-028-6636-6930

Received: 23 July 2018; Accepted: 18 August 2018; Published: 22 August 2018��

Abstract: The integration of hybrid energy storage systems (HESS) in alternating current (AC)electrified railway systems is attracting widespread interest. However, little attention has beenpaid to the interaction of optimal size and daily dispatch of HESS within the entire project period.Therefore, a novel bi-level model of railway traction substation energy management (RTSEM) systemis developed, which includes a slave level of diurnal HESS dispatch and a master level of HESS sizing.The slave level is formulated as a mixed integer linear programming (MILP) model by coordinatingHESS, traction load, regenerative braking energy and renewable energy. As for the master levelmodel, comprehensive cost study within the project period is conducted, with batteries degradationand replacement cost taken into account. Grey wolf optimization technique with embedded CPLEXsolver is utilized to solve this RTSEM problem. The proposed model is tested with a real high-speedrailway line case in China. The simulation results of several cases with different system elementsare presented, and the sensitivity analyses of several parameters are also performed. The obtainedresults reveal that it shows significant economic-saving potentials with the integration of HESS andrenewable energy.

Keywords: railway traction substation energy management; hybrid energy storage systems;mixed integer linear programming; bi-level model; battery degradation

1. Introduction

The dramatic increase of carbon emissions is driving global climate change and poses risks forhuman and natural systems [1,2], and a worldwide consensus on reducing atmospheric greenhousegases (GHGS) has been reached [3,4]. As for China, the government committed a reduction ofcarbon emission intensity by 18% during the 13th Five-Year Plan period (2015–2020) [5]. A jointreport from the International Energy Agency (IEA) and the International Union of Railways (UIC)shows that the transport sector accounted for 24.7% of global carbon emissions and the rail sectoraccounted for 4.2% of total transport carbon emission in 2015, while the corresponding proportionin China is 10.6% and 15.3% [6]. Most noteworthily, the railway-related energy consumption andcarbon emissions per passenger-km increased by 44.1% and 96.8% between 2005 and 2015 in Chinarespectively, largely as a result of the rapid expansion of the high-speed railway (HSR) network [6].Consequently, energy savings in railway systems and in HSR systems have received considerablecritical attention.

A few approaches provide insights for energy saving, such as the use of regenerative brakingenergy and renewable energy techniques. Due to the high speed and colossal traction power

Energies 2018, 11, 2199; doi:10.3390/en11092199 www.mdpi.com/journal/energies

http://www.mdpi.com/journal/energies

http://www.mdpi.com

https://orcid.org/0000-0001-5361-2463

https://orcid.org/0000-0002-9792-3834

http://www.mdpi.com/1996-1073/11/9/2199?type=check_update&version=1

http://dx.doi.org/10.3390/en11092199

http://www.mdpi.com/journal/energies

Energies 2018, 11, 2199 2 of 29

of high-speed trains (HSTs) with pulse width modulation-based four-quadrant converters [7],considerable regenerative braking power (RBP) is produced in their braking mode. For instance,the maximum braking power of a CRH-380AL electric multiple unit (manufactured by China RailwayRolling Stock Corporation, Qingdao, China) can be up to 20 MW. Therefore, there is a growingapplication of energy storage systems (ESSs) in railway systems to store this massive braking energy [8].Currently, industrial applications of onboard ESS for braking energy recovery include the Sitras SES ofSiemens, the MITRAC energy saver of Bombardier and the STEEM project of Alstom [9–11]. However,the limitations of size and weight have presented an obstacle to the application of onboard ESSs inHSRs. By comparison, wayside ESSs can be a better solution. Moreover, the intersections of railwaynetworks and renewable energy sources (RES) are propitious to the utilization of local renewableenergy. For instance, the Lanzhou-Xinjiang HSR line crosses the north-western regions of China withrich solar and wind energy, while there is no access to local RES consumption. With regard to the waythat RBP and RES are used, aside from supplying to the HSTs, they can also be utilized to charge theenergy storage devices, e.g., HESS, for further usage. Therefore, increasing the utilization rate of RBPand RES via HESS helps achieve the energy saving goals.

Moreover, cost savings for rail operators can also be implemented from another point of view.In the current railway power systems, the dramatic stochastic volatility of traction loads and the harshrequirements for overload capacity of traction transformers result in the extremely low utilization rateof traction transformers and high demand charge. Besides, the RBP fed back to the grid contains alarge number of harmonic components and negative sequence components because of the single-phaseasymmetry of traction loads, seriously jeopardizing the safety and stabilization of the utility powersystem [12]. Consequently, a resulting penalty bill is charged. To this end, there is great potential forcost saving through the application of HESS and management of energy flows.

Smart grid technologies present the potential of energy management in railway power supplysystems. The battery sizing and energy management in smart grids have been extensively studied inrecent years, such as grid-tied photovoltaic (PV) systems [13,14], wind farms [15], active distributionsystems [16] and microgrids in stand-alone mode or grid-connected mode [17–22]. However,the characteristic of traction loads differ significantly from conventional loads. Therefore, the sizingand dispatch strategy of HESS need to be re-examined when applied to electrified railway systems.

Numerous researchers have focused on solving the above problems in the railway systems.Khayyam et al. [23] developed a railway energy management system (REM-S) architecture bycoordinating loads, regeneration, storage, and distributed energy resources for optimal energy use.It offers the inspiration of applying the research achievements of smart grids to railway systems.Generic hybrid railway power substation (HRPS) architectures for DC and AC systems were proposedin [24] by integrating RES and storage units with railway systems. Based on the HRPS system in [24],corresponding fuzzy logic energy management strategies were developed in [25,26] for feasibilityanalysis. However, the battery degradation and replacement were ignored. A hierarchical structure,including on-route trains energy consumption optimization and traction substation energy flowsmanagement, was identified in [27,28] to minimize the electricity bill. However, no capital cost ofstorage devices was considered. In [29] a smart railway station energy management system model wasformulated for the utilization of braking energy, and the initial state of charge (SOC) was highlighted inparticular as the uncertain factor. Unfortunately, it merely concentrated on the reduction of electricitybill of power consumption and paid little attention to the comprehensive cost analysis. In [30] anoptimization model of battery energy storage system (BESS) operation strategy was developed for themaximization of owner’s net benefit. However, the evaluation of degradation cost was off-line, i.e.,it was not included in the optimization model. Furthermore, regenerative braking energy of metrotrains was not considered. In [31] the author proposed a methodology for optimal dispatch of railwayESS with RES and braking energy, while the investment cost was not taken into consideration. In [32]the optimal sizing of HESS for braking energy utilization was studied, yet the battery lifetime was

Energies 2018, 11, 2199 3 of 29

estimated simply based on the cycles, and the depth of discharge (DOD) of each cycle was ignored,thus the estimation of battery lifetime and daily cost need to be further improved.

The aforementioned studies and many other studies not referred here give approaches to sizingof energy storage devices or energy management in railway systems from different perspectives,while the comprehensive cost study within the time scope of project period is ignored, and a moreaccurate on-line methods for battery lifetime estimation are not considered. Accordingly, this paperaims at addressing this problem. The highlights of this paper can be outlined as follows:

• The interaction of HESS sizing and daily scheduling of HESS within the time scope of projectservice period considering battery degradation are formulated via a bi-level model.

• The electricity bill for rail operators is largely reduced through peak shaving of traction loads,utilization of braking power and the mitigation of bill penalties for power fed back to theutility grid.

• The impact of different electricity pricing schemes, length of project service period and initialSOC of HESS are also analyzed.

The rest of this paper is structured as follows: Section 2 introduces the general architecture ofRTSEM system and descriptions of all the elements included. Sections 3 and 4 present the problemformulations of the master level and slave level respectively. In Section 5, a grey wolf optimizationapproach with CPLEX solver embedded is proposed. In Section 6 the case study is performed andrelevant results are given. Finally the conclusions are reached in Section 7.

2. System Description

2.1. Block Diagram of the System and Model

In conventional electrified railway systems, the 25 kV traction network supplies single-phaseAC at the power frequency for HSTs. As the phases of adjacent power supply sections are different,all sections must be kept strictly isolated to prevent the risk of mixing out-of-phase supplies, which isachieved by neutral sections. In this study, a scheme of RTSEM system is illustrated in Figure 1, which isbased on the architecture of hybrid railway power substation proposed in previous studies [24,27].The power direction and corresponding symbol convention are presented as well. The RTSEMsystem is mainly composed of utility grid, PV generator, battery storage system, ultracapacitor (UC)storage system and HSTs. It is important to highlight that HSTs have dual properties of “load” and“power source”, depending on whether the train is in traction mode or regenerative braking mode.This special feature of HSTs differs from conventional power load greatly, increasing the diversity ofoperation mode and the complexity of energy management though, yet nevertheless showing quiteeconomic-saving potentials.

Energies 2018, 11, x FOR PEER REVIEW 3 of 29

The aforementioned studies and many other studies not referred here give approaches to sizing of energy storage devices or energy management in railway systems from different perspectives, while the comprehensive cost study within the time scope of project period is ignored, and a more accurate on-line methods for battery lifetime estimation are not considered. Accordingly, this paper aims at addressing this problem. The highlights of this paper can be outlined as follows:

• The interaction of HESS sizing and daily scheduling of HESS within the time scope of project service period considering battery degradation are formulated via a bi-level model.

• The electricity bill for rail operators is largely reduced through peak shaving of traction loads, utilization of braking power and the mitigation of bill penalties for power fed back to the utility grid.

• The impact of different electricity pricing schemes, length of project service period and initial SOC of HESS are also analyzed.

The rest of this paper is structured as follows: Section 2 introduces the general architecture of RTSEM system and descriptions of all the elements included. Sections 3 and 4 present the problem formulations of the master level and slave level respectively. In Section 5, a grey wolf optimization approach with CPLEX solver embedded is proposed. In Section 6 the case study is performed and relevant results are given. Finally the conclusions are reached in Section 7.

2. System Description

2.1. Block Diagram of the System and Model

In conventional electrified railway systems, the 25 kV traction network supplies single-phase AC at the power frequency for HSTs. As the phases of adjacent power supply sections are different, all sections must be kept strictly isolated to prevent the risk of mixing out-of-phase supplies, which is achieved by neutral sections. In this study, a scheme of RTSEM system is illustrated in Figure 1, which is based on the architecture of hybrid railway power substation proposed in previous studies [24,27]. The power direction and corresponding symbol convention are presented as well. The RTSEM system is mainly composed of utility grid, PV generator, battery storage system, ultracapacitor (UC) storage system and HSTs. It is important to highlight that HSTs have dual properties of “load” and “power source”, depending on whether the train is in traction mode or regenerative braking mode. This special feature of HSTs differs from conventional power load greatly, increasing the diversity of operation mode and the complexity of energy management though, yet nevertheless showing quite economic-saving potentials.

Note that a study of the entire HSR line containing plenty of traction substations (TSSs) and power supply sections may lead to a large-scale problem. As different power supply sections of an HSR line are electrically disconnected via neutral sections, this paper concentrates on each power supply section individually.

Utility Grid

Traction Substation

Neutral Section

A B C

βα~

=

Battery

PV Generator

Traction mode

==

Regenerative braking mode

DC busPower Flow Communication Flow

Control Center

Meter

Signal Tower

…

==

Ultracapacitor

HESS, 0gridt sP > , 0fed

t sP >

, 0loadt sP > , 0brake

t sP >

, 0pvt sP >

,, 0bat dist sP >

,, 0bat cht sP >

,, 0uc dist sP >

,, 0uc cht sP >

=~

Figure 1. Structure diagram of the RTSEM system. Figure 1. Structure diagram of the RTSEM system.

Energies 2018, 11, 2199 4 of 29

Note that a study of the entire HSR line containing plenty of traction substations (TSSs) and powersupply sections may lead to a large-scale problem. As different power supply sections of an HSRline are electrically disconnected via neutral sections, this paper concentrates on each power supplysection individually.

Figure 2 illustrates the block diagram of the bi-level model proposed in this paper. The upperblocks of computer simulation and scenarios are the pretreatment process, which offers inputparameters for the following model. In this study, the sizing of HESS and comprehensive costcalculation are implemented within the time scope of the project service period. A bi-level modelis thus proposed in order to reflect the close association between the total project cost and diurnalscheduling of HESS. The master level model concentrates on the optimal sizing of HESS and theslave level model involves the diurnal scheduling of HESS. As the decision variables of master levelmodel, the power rating and capacity of battery and UC are regarded as the boundary parameters ofslave level model. Battery lifetime, HESS operation hours and daily electricity cost calculated in theslave level model are returned to the master level model for the assessment of certain types of costaccordingly. The diurnal operation of HESS is regarded as repeated within the project service period.Energies 2018, 11, x FOR PEER REVIEW 5 of 30

Figure 2. Overview of proposed bi-level model optimization.

2.2. Traction Load and Regenerative Braking Power

As the input parameters of the proposed model, railway traction load and RBP profile should be determined in an accurate and efficient way. Two common methods for traction load prediction include [31]:

• Computer simulation method based on traction and power supply calculation. • Statistical model or sampling method based on measurement data from the meter installed in

the traction substation.

For ease of the analysis of different operation conditions, the computer simulation method is adopted here. A lot of parameters of HSTs and HSR lines are required in advance in the computer simulation method, e.g., the traction force, running resistance and braking force of HSTs, slope, curve radius and speed limitation of HSR lines, and the equivalent impedance and admittance of traction power systems [31]. Normally, these required parameters can be obtained from the railway investigation and design institutes. Benefitting from the great advances of simulation software for the load processes of traction power supply systems, forecasting of railway traction loads and regenerative braking power can be easily implemented based on the aforementioned parameters and timetables preset by railway operators. In this study the traction simulation is performed via the commercial software ELBAS WEBAnet v3.121 (SIGNON Group, Berlin, Germany) [33].

On account of the computational resource limitations and for saving computation time, sampling and processing of the simulation results should be designed appropriately. The sampling time interval in [29] is determined as 1 min considering the short braking time. A time period reduction method is applied in [31,32] via combining short 30 s time periods to form longer time periods, yet with the defect

Figure 2. Overview of proposed bi-level model optimization.

2.2. Traction Load and Regenerative Braking Power

As the input parameters of the proposed model, railway traction load and RBP profile shouldbe determined in an accurate and efficient way. Two common methods for traction load predictioninclude [31]:

Energies 2018, 11, 2199 5 of 29

• Computer simulation method based on traction and power supply calculation.• Statistical model or sampling method based on measurement data from the meter installed in the

traction substation.

For ease of the analysis of different operation conditions, the computer simulation method isadopted here. A lot of parameters of HSTs and HSR lines are required in advance in the computersimulation method, e.g., the traction force, running resistance and braking force of HSTs, slope,curve radius and speed limitation of HSR lines, and the equivalent impedance and admittance oftraction power systems [31]. Normally, these required parameters can be obtained from the railwayinvestigation and design institutes. Benefitting from the great advances of simulation software for theload processes of traction power supply systems, forecasting of railway traction loads and regenerativebraking power can be easily implemented based on the aforementioned parameters and timetablespreset by railway operators. In this study the traction simulation is performed via the commercialsoftware ELBAS WEBAnet v3.121 (SIGNON Group, Berlin, Germany) [33].

On account of the computational resource limitations and for saving computation time, samplingand processing of the simulation results should be designed appropriately. The sampling time intervalin [29] is determined as 1 min considering the short braking time. A time period reduction methodis applied in [31,32] via combining short 30 s time periods to form longer time periods, yet with thedefect of unequal duration between different time periods. The sampling time of power profile and thescheduling time interval of HESS are determined as 1 min in this study, based on the fact that powerprofiles of traction load and HESS do not change much during this short period.

2.3. Uncertainty Representation of PV Generation

When we focus on the sizing configuration and long-term planning of HESS within the time scopeof project period, the stochastic characteristics of weather conditions have to be included. Typically,a series of scenarios and corresponding probabilities are used to describe the stochastic process anddata process [34], thus the scenario-based technique is adopted in this section.

Renewable energy represented by PV generation is taken into account in this paper for the nearbyconsumption of renewable energy. With regard to the scenarios generation, in order to describe theuncertainty of PV generation as far as possible, the annual solar irradiance profile is used here togenerate 365 different scenarios.

Significant computational resources and time cost are required when all the scenarios are includedin the stochastic bi-level model, thus a tradeoff between the solution accuracy and computation speedshould be achieved [35–37]. Aiming at dealing with the contradiction of computational complexityand time limitation, scenario reduction method is developed in previous studies [34,38,39]. In [34] thescenario reduction algorithms reject the low-probability scenarios and aggregate those that approximateto each other in light of probability metric, forming a scenario subset that represents a relatively goodapproximation to the initial scenario set in terms of statistic metric:

s ∈ {1, 2, 3, 4} (1)

Various algorithms can be applied for scenario reduction, including the fast backward method,fast backward/forward method and fast backward/backward method [34,38]. In view of the differentcomputation performance and accuracy between these algorithms, they are applicable for differentoccasions, such as the problem size and target precision [35,40,41]. For example, the forward methodprovides the best solution accuracy with the largest computational resource consumption, while the fastbackward method requires the least computational effort at the cost of lower accuracy [35,41]. Thereforethe forward method is utilized to generate four representative scenarios for scenario reduction in thisstudy, as shown in Equation (1), considering a small number of scenarios need to be reduced.

Energies 2018, 11, 2199 6 of 29

2.4. Hybrid Energy Storage Systems

Energy storage systems play a key role in the cost-saving benefits of RTSEM by means ofdischarging during peak traction load periods and charging during regenerative braking periods.Two types of widely applied energy storage systems include the high energy density type, representedby batteries, and high power density type represented by UC. Batteries have good performance interms of high energy density and mature manufacturing process, whereas lifetime cycles and powerdensity are limited [42]. By contrast, UC have advantages of high power density, fast response,lower maintenance cost and extremely long cycle life [8], while low energy density and quite highenergy capacity cost are the main obstacles to the spread application of UC. HESS is proposed with theintention of combining the batteries and UC to obtain both high energy and power density, and thushas an obvious advantage over the single type of energy storage system, especially for the applicationof peak load shaving and regenerative braking power absorbing in the high-speed railway system.In general, the UC’s advantage of long cycle life and fast response make it suitable to capture therailway power peaks and valleys in high frequency, while batteries are more suited for low frequencyoperation [31,32]. Accordingly, HESS is adopted in this study for the better energy saving performance.

3. Master Level: HESS Sizing Problem Formulation

3.1. Battery Degradation Analysis

When applied into the electrified railway systems, HESSs are operated to coordinate with thetraction loads, a kind of shock load with dramatic stochastic volatility. It is assumed that UC can servefor the entire project period and the batteries degradation analysis is considered, as a result of the factthat the lifetime of UC is less affected by the cycles, while batteries are more likely to suffer from thefrequent fluctuations and plenty of cycles of traction load in view of the limited life cycles [42].

As the key connection between the master and slave level model, battery lifetime indicates thefact that the diurnal operation strategies of HESS have a great impact on the replacement cost, thus anoptimal balance should be achieved between the performance of HESS and the replacement cost,and that is the problem this paper tries to solve.

The disadvantage of limited lifetime cycles results in a more severe aging of batteries duringthe operation of HESSs, thus an appropriate method should be utilized to evaluate the aging rate ofbatteries within the considered time scope. There are lots of approaches for batteries lifetime estimation,in which the number of battery cycles calculation method is utilized in this study. Generally, batterycycles can be divided into two types, including full cycles and partial cycles [43]. A full cycle is definedas a combination of a charge half cycle and a discharge half cycle with equal starting SOC and endingSOC. Accordingly, a partial cycle is defined as a charge or discharge progress with unequal startingSOC and ending SOC. By means of the rainflow counting method, full cycles and half cycles can beextracted from a series of charge or discharge sequences. For further knowledge of counting methodsreaders may refer to [44].

The flow chart of the rainflow counting method is presented in Figure 3. The functions of thismethod include the extraction of two types of cycles and the determination of corresponding DODof each cycle. According to manufacturer’s data, number of battery cycles to failure as a functionof depth of discharge D is presented in Equation (2), by applying interpolation with least squaremethod. The coefficient α1, α2, α3 and α4 are 24,090, −9.346, 6085 and −1.319 respectively in this studyaccording to [45]:

NC(D) = α1eα2·D + α3eα4·D (2)

Each cycle corresponds to an aging rate. In order to establish the association between the lifetimeand aging rate of each cycle, accumulated aging rate AR is derived in Equation (3) by adding up thetotal aging rate based on the total cycles (Ntotal) of batteries within a day, where 1/[αi · NC(Di)] is theaging rate for each cycle i. Coefficient αi is 1 when cycle i is a full cycle and 0.5 when cycle i is a half

Energies 2018, 11, 2199 7 of 29

cycle, since it is regarded that the effect of a half cycle is the half of a full cycle. Therefore the expressionof lifetime in years can be derived in Equation (4):

AR =Ntotal

∑i=1

1αi · NC(Di)

(3)

Tbat = 1/(365AR) (4)

Note that according to [45], an adverse effect is on the lifetime once the operating temperatureis over 20 ◦C. A constant operating temperature of 20 ◦C is assumed in this study for the sake ofsimplicity and the related cost is included in the Balance of Plant (BOP) cost that is introduced inSection 3.2.1.Energies 2018, 11, x FOR PEER REVIEW 7 of 29

SOC profiles of batteries from the optimal scheduling in the slave

model

Peaks and valleys extraction from the considered SOC profile

Full cycles and half cycles counting

Determination of DoD of each cycle

Number of cycles versus DoD according to manufacturers’data

Evaluation of aging rate and lifetime

Rainflow counting method

Read 3 successive points of peak and valley from starting point S

Out of data?

X denotes the considered peak-valley range

Y denotes the previous peak-valley range adjacent to X

|X|<|Y| ?

Y contains S?

Count Y as a half cycle

Abandon the first point in Y and set the starting point as the second

point in Y

Count Y as a full cycle

Abandon both the peak and valley points in Y

Read the next peak or valley to form 3 successive points

Count remaining peak-valley ranges as half cycles

start

End

Lifetime calculation

Input profile

Cycle counting algorithm

Yes

No

No

Yes

No

Yes

Figure 3. Flow chart of batteries lifetime estimation.

Figure 4 shows the identification of full cycles and half cycles from the input signal via the process of the rainflow counting method.

(a)

(b)

Figure 4. Demonstration of the rainflow counting algorithm: (a) Extraction of peaks and valleys from the input signal; (b) Identification of full cycles and half cycles.

3.2. Objective Function of the Master Level Model

In the following Equation (5)

( )1 −min bat bat uc uc HESS bat HESStotal rate rate rate rate cap rep om e salf = C P ,E ,P ,E = C + C + C + C C (5)

where batrateP and bat

rateE are the rated power and total capacity of battery; ucrateP and uc

rateE are the rated power and total capacity of UC. Note that the investment cost of PV is not considered within the scope of this paper. Each cost in this study is expressed as the daily cost.

3.2.1. Capital Cost

The HESS is mainly composed of battery banks, UC banks, power conversion systems (PCS), and other devices related to BOP [46,47], such as protective devices, monitoring and control systems

Valu

e

0 2 4 6 8 10 12 14Number of peaks and valleys

-2

-1

0

1

2

peaks and valleys of signal

Full cycles

Half cycles


Figure 4 shows the identification of full cycles and half cycles from the input signal via the processof the rainflow counting method.


SOC profiles of batteries from the optimal scheduling in the slave

model

Peaks and valleys extraction from the considered SOC profile

Full cycles and half cycles counting

Determination of DoD of each cycle

Number of cycles versus DoD according to manufacturers’data

Evaluation of aging rate and lifetime

Rainflow counting method

Read 3 successive points of peak and valley from starting point S

Out of data?

X denotes the considered peak-valley range

Y denotes the previous peak-valley range adjacent to X

|X|<|Y| ?

Y contains S?

Count Y as a half cycle

Abandon the first point in Y and set the starting point as the second

point in Y

Count Y as a full cycle

Abandon both the peak and valley points in Y

Read the next peak or valley to form 3 successive points

Count remaining peak-valley ranges as half cycles

start

End

Lifetime calculation

Input profile

Cycle counting algorithm

Yes

No

No

Yes

No

Yes


Figure 4 shows the identification of full cycles and half cycles from the input signal via the process of the rainflow counting method.

(a)

(b)

Figure 4. Demonstration of the rainflow counting algorithm: (a) Extraction of peaks and valleys from the input signal; (b) Identification of full cycles and half cycles.



( )1 −min bat bat uc uc HESS bat HESStotal rate rate rate rate cap rep om e salf = C P ,E ,P ,E = C + C + C + C C (5)

where batrateP and bat

rateE are the rated power and total capacity of battery; ucrateP and uc

rateE are the rated power and total capacity of UC. Note that the investment cost of PV is not considered within the scope of this paper. Each cost in this study is expressed as the daily cost.

3.2.1. Capital Cost

The HESS is mainly composed of battery banks, UC banks, power conversion systems (PCS), and other devices related to BOP [46,47], such as protective devices, monitoring and control systems

Valu

e


-2

-1

0

1

2

peaks and valleys of signal

Full cycles

Half cycles

Figure 4. Demonstration of the rainflow counting algorithm: (a) Extraction of peaks and valleys fromthe input signal; (b) Identification of full cycles and half cycles.

Energies 2018, 11, 2199 8 of 29



min f1 = Ctotal

(Pbat

rate, Ebatrate, Puc

rate, Eucrate

)= CHESS

cap + Cbatrep + CHESS

om + Ce − Csal (5)

where Pbatrate and Ebat

rate are the rated power and total capacity of battery; Pucrate and Euc

rate are the rated powerand total capacity of UC. Note that the investment cost of PV is not considered within the scope of thispaper. Each cost in this study is expressed as the daily cost.

3.2.1. Capital Cost

The HESS is mainly composed of battery banks, UC banks, power conversion systems (PCS),and other devices related to BOP [46,47], such as protective devices, monitoring and control systemsand so on. The PCS cost is associated with the designed power level of PCS, which is considered as thepower rating of battery and UC respectively in this paper. BOP cost is typically related to the ratedpower, thus the diurnal capital cost of HESS can be expressed as:

CHESScap = 1

Tday·[kBp · Pbat

rate + kBe · Ebatrate + kCp · Puc

rate + kCe · Eucrate + kbop

(Pbat

rate + Pucrate

)]· CRF

(r0, Tproj

)(6)

CRF(r0, Tproj

)=

r0 · (1 + r0)Tproj

(1 + r0)Tproj − 1

(7)

where Tday is the operation days of HESS within a year (365 in this paper); kBp (CNY/MW),kBe (CNY/MWh) are the specific cost of per unit of power rating and capacity of battery respectively;kCp (CNY/MW), kCe (CNY/MWh) are the specific cost of per unit of power rating and capacity of UCrespectively; kbop (CNY/MW) refers to the unit cost associated with BOP; CRF denotes capital recoveryfactor, which is the ratio of a constant annuity to the present value of receiving that annuity for a givenlength of time [16,48]. Tproj is the project service period in years and r0 is the annual discount rate.The definition of capital recovery factor can be described using Equation (7).

3.2.2. Replacement Cost

As the master level concentrates on the long-term planning and the lifetime of battery is normallyfar less than the project service period due to the limitation of total number of cycles until end-of-life,thus battery needs to be replaced every specific period. From this point of view, diurnal operationstrategies of battery not only affect the performance of traction load peak shaving and penalty billavoidance in the short term, but also impact the life cycle cost and replacement of battery in the longrun. It is assumed that UC and devices related to BOP can serve all through the project period and noreplacement is taken into consideration, considering its extremely long cycle life. The total replacementcost per day is expressed in Equation (8):

Cbatrep =

1Tday· CRF

(r0, Tproj

)·

Nrep

∑k=1

[krep

Be · Ebatrate · PVF(r0, k · Tbat)

](8)

where krepBe (CNY/MWh) is the replacement cost of the capacity of battery. Tbat denotes the battery

lifetime, of which the calculation method is introduced in Equation (4); PVF denotes the present valuefactor which is used to derive the present value of a receipt of cash in the future. Present value factor isdefined as Equation (9); Nrep is the total times of battery replacement during the project period and krepresents the index of replacement. Nrep is defined in Equation (10):

PVF(r0, k · Tbat) = (1 + r0)−k·Tbat (9)

Energies 2018, 11, 2199 9 of 29

Nrep =

⌈Tproj

Tbat

⌉− 1 (10)

where d e represents the rounding up operand.

3.2.3. Operation and Maintenance (O&M) Cost

The diurnal O&M cost is divided into fixed O&M cost and variable O&M cost in [47], it can beexpressed as:

CHESSom = CHESS

om, f + CHESSom,v (11)

CHESSom, f =

1Tday·(

kbatom, f · P

batrate + kuc

om, f · Pucrate

)(12)

CHESSom,v = Tbat

hr · kbatom,v · Pbat

rate + Tuchr · k

ucom,v · Puc

rate (13)

where kbatom, f and kuc

om, f are fixed O&M cost per unit of power rating associated with battery and UC,

in CNY/MW; kbatom,v and kuc

om,v are variable O&M cost per unit of power rating associated with batteryand UC, in CNY/MW; Tbat

hr and Tuchr represent the operation time of battery and UC during a day,

in hours, which can be obtained from the Equations (44) and (45) in the slave model of diurnalHESS scheduling.

3.2.4. Salvage Value

Salvage value is the estimated resale value of an asset at the end of its useful life. In the final yearof the project service period, the salvage value of the system primarily depends on the recovery valueof batteries that have not reached the failure of their lifetime:

Csal = λdep ·(

Nrep + 1)· Tbat − Tproj

Tday · Tbatkrep

Bp · Pbatrate · SFF

(r0, Tproj

)(14)

where λdep is the depreciation coefficient for the recovery of battery storage banks. SFF denotes thesinking fund factor which is used to calculate the future value of a series of equal annual cash flows.The definition of sinking fund factor can be presented as follows:

SFF(r0, Tproj

)=

r0

(1 + r0)Tproj − 1

(15)

3.3. Constraints of the Master Level

The sizing of the HESS involves finding the optimal power rating and energy capacities ofbatteries and UCs aiming at minimizing the total cost within the time horizon of project serviceperiod. Equations (16)–(19) state that these decision variables are limited by upper and lower bounds,which can be determined according to the types of ESS and the traction load of traction substations.Besides, Equations (2)–(4) performing the battery lifetime estimation are also a part of the constraintsin the master level model:

Pbat ≤ Pbatrate ≤ Pbat (16)

Ebat ≤ Ebatrate ≤ Ebat (17)

Puc ≤ Pucrate ≤ Puc (18)

Euc ≤ Eucrate ≤ Euc (19)

4. Slave Level: Diurnal Dispatch Problem Formulation

Under the restrictions of power capacity and energy capacity of HESS and power balance amongthe RTSEM system, slave model focuses on the optimal scheduling of HESS during a day, aiming

Energies 2018, 11, 2199 10 of 29

to minimize the electricity cost via traction load peak shaving and avoiding penalty bill for therailway operators.

4.1. Objective Function of the Slave Level Model

As a major role of commercial and industrial (C&I) electricity consumer, electrified railwayoperators are primarily charged based on two aspects in China: energy consumption and demand, i.e.,with a two-part tariff [49]. In addition, other regulations and tariff rules imposed by the State GridCorporation of China should be considered. The composition of electricity charge can be expressedas follows:

1. Energy consumption charge. Electric utilities installed in the traction substation meter the energyconsumption supplied by utility grid, and this charge is obtained through the energy consumptionand corresponding energy price.

2. Capacity charge or demand charge. This part of charge is associated with the construction costof power plant, transmission lines and other facilities. Typically two options are offered to theC&I consumers: transformer-capacity-based charge or peak-demand-based charge. The formeris related to the capacity of transformers, and the latter depends on the maximum value of theaveraged active power consumption in successive 15 min time intervals, during a billing month(or a day in this study, as the diurnal operation of the elements in RTSEM system is regarded asrepeated within the project service period). The latter option is applied in this paper.

3. Penalty charge. HSTs have been widely put into service in HSR lines in China. Part of the RBP isabsorbed by HSTs running in the same power supply section, and the rest returns to utility powersystem. However, the RBP fed back to the grid contains a large number of harmonic componentsand negative sequence components, bring potential threats to the utility power system. Therefore,a bill penalty is charged for the traction power fed back to the utility grid.

According to aforementioned tariff rules, objective function of slave model is the diurnal electricitybill for railway operators, including energy consumption charge (ECC), demand charge (DC) andpenalty charge (PC). They are calculated as follows:

minCe = ECC + DC + PC (20)

• The energy consumption charge can be expressed as:

ECC = ∑s

πs ·(

T

∑t=1

ρt,s · Pgridt,s · ∆t

)∀t, s (21)

• The demand charge is derived as:

DC = ∑s

πs · ρbases ·max

(Pdemand

t,s

)∀s, t = 1, 2, · · · , T − 14 (22)

Pdemandt,s =

t+14

∑t

Pgridt,s /15 ∀t = 1, 2, · · · , T − 14 (23)

• The penalty charge is as follows:

PC = ∑s

πs ·(

T

∑t=1

ρpent,s · P

f edt,s · ∆t

)∀t, s (24)

where πs is the probability of PV generation scenario; Pgridt,s (MW), ρt,s (CNY/MW) are active

power supplied by the utility grid and corresponding electricity price signal; Pfedt,s (MW) and

Energies 2018, 11, 2199 11 of 29

ρpent,s (CNY/MW) represent the regenerative braking power fed back to utility grid and the

penalty charge; ρbases (CNY/MW) denotes the electricity price of peak demand power; ∆t is

the discretization time interval; Pdemandt,s is the average active power consumption during each

15-min interval and T refers to the total number of time intervals during a day.

Due to the nonlinearity of the maximum function in Equation (22), linearization is applied inEquations (25) and (26) in order to formulate the diurnal scheduling problem as a mixed-integer linearprogramming (MILP) model.

DC = ∑s

πs · ρbases · Ppeak

s ∀s (25)

Ppeaks ≥ Pdemand

t,s ∀s, t = 1, 2, · · · , T − 14 (26)

where Ppeaks is an additional time-independent variable representing the peak demand power during

a day.

4.2. Constraints of the Slave Level Model

4.2.1. Power Balance

All participants in the RTSEM system are constrained by the active power balance, whichis presented in Equation (27). It states that the active power supplied by the utility grid (Pgrid

t,s ),

PV generator (Ppvt,s ), battery (Pbat,dis

t,s ), UC (Puc,dist,s ) and regenerative braking power (Pbrake

t ) must meet

the requirement of railway traction load (Ploadt ), battery charging (Pbat,ch

t,s ), UC charging (Puc,cht,s ), or even

feed superfluous power back to grid (Pfedt,s ), inevitably resulting in penalty charge of course.

Pgridt,s + Ppv

t,s + Pbat,dist,s + Puc,dis

t,s + Pbraket = Pload

t + Pbat,cht,s + Puc,ch

t,s + Pfedt,s ∀t, s (27)

4.2.2. HESS Constraints

The charging or discharging power and stored energy of the HESS are constrained by thephysical characteristics of battery and UC at any time interval. All the inequality and equalityconstraints related to the operation of HESS in this proposed diurnal dispatch problem are organizedas follows. Equations (28) and (29) imply the relationship between discharging or charging power andremaining energy at adjacent time intervals with efficiency and self-discharging rate taken into account.Generally a limitation of state of charge is set so as to avoid over-discharge and extend the lifetime ofbattery [50–52], so Equations (30) and (31) indicate that the stored energy in battery and UC must bebounded by a predefined upper and lower bounds according to the actual parameters of selected typeof storage systems. Equations (32)–(35) set up the limitation of discharging and charging power, whichmeans that both the power rating and available energy variation at time interval can decide the upperbound of power. Equations (36) and (37) state that stored energy at initial stage equals that at finalstage for the convenience of scheduling in the next day, as the diurnal operation of HESS is regardedas repeated within the project service period. Equations (38)–(43) demonstrate the fact that chargingstatus cannot coexist with discharging status simultaneously. Equations (44) and (45) are applied tocalculate the operation hours of batteries and UCs during a day.

Ebat,storedt+1,s = (1− εb) · Ebat,stored

t,s − 1ηbat

dis· Pbat,dis

t,s · ∆t + ηbatch · P

bat,cht,s · ∆t ∀t, s (28)

Euc,storedt+1,s = (1− εc) · Euc,stored

t,s − 1ηuc

dis· Puc,dis

t,s · ∆t + ηucch · P

uc,cht,s · ∆t ∀t, s (29)

SOCbatmin · Ebat

rate ≤ Ebat,storedt,s ≤ SOCbat

max · Ebatrate ∀t, s (30)

Energies 2018, 11, 2199 12 of 29

SOCucmin · Euc

rate ≤ Euc,storedt,s ≤ SOCuc

max · Eucrate ∀t, s (31)

0 ≤ Pbat,dist,s ≤ min

(Pbat

rate,Ebat,stored

t−1,s − SOCbatmin · Ebat

rate

∆tηbat

dis

)∀t, s (32)

0 ≤ Pbat,cht,s ≤ min

(Pbat

rate,SOCbat

max · Ebatrate − Ebat,stored

t−1,s

ηbatch · ∆t

)∀t, s (33)

0 ≤ Puc,dist,s ≤ min

(Puc

rate,Euc,stored

t−1,s − SOCucmin · Euc

rate

∆tηuc

dis

)∀t, s (34)

0 ≤ Puc,cht,s ≤ min

(Puc

rate,SOCuc

max · Eucrate − Euc,stored

t−1,s

ηucch · ∆t

)∀t, s (35)

Ebat,storedt=1,s = Ebat,stored

t=T,s = SOCbat0 · Ebat

rate ∀s (36)

Euc,storedt=1,s = Euc,stored

t=T,s = SOCuc0 · Euc

rate ∀s (37)

Pbat,dist,s ≤ Pbat

rate · ubat,dist,s ∀t, s (38)

Pbat,cht,s ≤ Pbat

rate · ubat,cht,s ∀t, s (39)

Puc,dist,s ≤ Puc

rate · uuc,dist,s ∀t, s (40)

Puc,cht,s ≤ Puc

rate · uuc,cht,s ∀t, s (41)

ubat,opet,s = ubat,dis

t,s + ubat,cht,s ≤ 1 ∀t, s (42)

uuc,opet,s = uuc,dis

t,s + uuc,cht,s ≤ 1 ∀t, s (43)

Tbathr = ∑

s∑

tπs · ubat,ope

t,s · ∆t (44)

Tuchr = ∑

s∑

tπs · uuc,ope

t,s · ∆t (45)

where εb and εc are the self-discharging rate of battery and UC; ηbatdis , ηbat

ch , ηucdis and ηuc

ch are dischargingand charging efficiency of battery and UC; ∆t is duration of time interval in hours (1 min in this paper);SOCbat

min, SOCbatmax and SOCbat

0 denote the minimum, maximum and initial state of charge of batteryrespectively; SOCuc

min, SOCucmax and SOCuc

0 represent the minimum, maximum and daily initial stateof charge of UC respectively; binary variable ubat,dis

t,s and uuc,dist,s are 1 if battery or UC is in discharging

state, and 0 otherwise; binary variable ubat,cht,s and uuc,ch

t,s are 1 if battery or UC are in charging state, and 0

otherwise; binary variable ubat,opet,s and uuc,ope

t,s equal 1 if battery or UC are in operation mode (chargingor discharging) and 0 otherwise.

It is noted that the rated power Pbatrate and capacity Ebat

rate of battery, and the rated power Pucrate and

capacity Eucrate of UC in this HESS constraints of slave level are transferred from master level. Besides,

operation time Tbathr and Tuc

hr obtained in this model are delivered to the master level model.

4.2.3. PV Generation Constraints

Typically, the PV output power (Ppvt,s ) can be expressed in Equation (46), which is constrained by

the maximum available active power of PV plant (Ppvt,s ) and PV converter capacity (Spv). Note that in

order to make full utilization of the PV active power, PV converter is not allowed to participate in thereactive power exchanges in this paper:

Ppvt,s = 10−3 · ηpv · Apv · spv

t,s ∀t, s (46)

Energies 2018, 11, 2199 13 of 29

Ppvt,s ≤ Ppv

t,s ∀t, s (47)

Ppvt,s ≤ Spv ∀t, s (48)

where ηpv is the efficiency of PV generation; Apv is the total area of PV panels (m2), spvt,s is the solar

irradiance at time interval t for scenario s (kW/m2), and 10−3 is used to convert the unit kW into MW.

4.2.4. Power Exchange Constraints

The massive requirement for railway traction load is mainly met by the receiving power fromthe utility grid, and exceeded regenerative braking power that cannot be absorbed by HESS is fedback to the utility power system under exceptional circumstances. A binary variable ugrid

t,s is usedhere to make sure that both the above situation will not take place at the same time interval [29].Equations (49) and (50) state that ugrid

t,s equals 1 if grid supplies power to HSTs, and 0 if RBP is fed backto grid:

Pgridt,s ≤ Pgrid

limit · ugridt,s ∀t, s (49)

Pfedt,s ≤ P f ed

limit ·(

1− ugridt,s

)∀t, s (50)

where Pgridlimit is the maximum limit for active power imported from the utility grid, Pfed

limit denotes themaximum limit for exceeded regenerative braking power fed back to the utility grid.

5. Proposed Approach

With regard to the slave problem of diurnal HESS scheduling, a formulation of MILP model makesit suitable to be solved by CPLEX solver considering the large number of time intervals. However,as for the master level problem of HESS sizing, it is the batteries lifetime estimation which makesit a non-convex optimization problem. The relaxation or linearization of batteries lifetime-relatedconstraints is hard to be implemented through regular mathematical planning method, thus theheuristic approach is adopted in this study for its tractability of non-convex problems. Grey wolfoptimizer is applied here for obtaining the optimal sizing of HESS.

5.1. Overview of Grey Wolf Optimizer

As a meta-heuristic optimization technique, grey wolf optimizer (GWO) is proposed by Mirjaliliet al. based on the hunting behavior of grey wolves [53]. Under the leadership of chief wolf, the wolvestrace, approach, surround and attack the prey, which represents the process of candidate solutionsapproaching the global optimal solution in optimization problems. The enhanced performance ofGWO has been verified in previous studies [54,55].

In GWO, the hierarchy of grey wolves (solutions) is determined based on the fitness. Top threebest candidate solutions are represented as α, β and δ and the remaining solutions are represented asω. The ω wolves follow the leadership of α, β and δ throughout the hunting process. Several essentialsteps of GWO are formulated as follows.

5.1.1. Encircling Prey

In the following equationsD = |C ·XP(t) −X(t)| (51)

X(t + 1 ) = XP(t)−A ·D (52)

A = 2a · r1 − a (53)

C = 2 · r2 (54)

Energies 2018, 11, 2199 14 of 29

where X and XP indicate the position vectors of wolves and prey; t is the index of iteration;the components of a are decreased from 2 to 0 linearly along with iteration; r1 and r2 are randomvectors within [0, 1].

5.1.2. Hunting

Under the leadership of wolf α, β and δ, wolves ω keep updating their positions. This huntingprocess can be formulated as follows:

Dα = |C1 ·Xα −X | (55)

Dβ =∣∣C2 ·Xβ −X

∣∣ (56)

Dδ = |C3 ·Xδ −X | (57)

X1 = Xα −A1 · (Dα ) (58)

X2 = Xβ −A2 ·(Dβ

)(59)

X3 = Xδ −A3 · (Dδ ) (60)

X(t + 1 ) = (X1 + X2 + X3)/3 (61)

where Dα, Dβ and Dδ represent the distance between wolf α, β, δ and the hunter; position updating inEquation (61) is implemented based on Equations (58)–(60).

5.1.3. Attacking or Searching for Prey

Coefficient vector A in Equation (53) plays a crucial role in determining whether the wolvesare get diverged or converged. As the components of a is decreased from 2 to 0 linearly along withiteration, the variation range of A is limited gradually. When |A| < 1, the next updated position ofeach ω wolf is within the bounds of its current position and the position of grey, driving the wolves toconverge towards the prey and to attack it finally. On the contrary, |A| > 1 indicates that the wolvesget diverged from the prey with the intention of searching for a fitter prey globally. Furthermore,another coefficient vector C with the random values between [0, 2] helps improve the explorationability of wolves, by means of stochastically determining the weight of considered prey’s effect.

5.2. Application of GWO Approach with CPLEX Solver Embedded

By applying GWO to solve the HESS sizing problem and CPLEX solver to figure out the complexHESS scheduling problem, a GWO with CPLEX solver embedded approach is adopted to deal withthis bi-level problem.

In GWO, given the number of wolf populations N, the position of each search agent can beexpressed as a four-dimensional vector xi = [xi,1, xi,2, xi,3, xi,4] which represents the decision variablesPbat

rate, Ebatrate, Puc

rate and Eucrate in the master level model respectively.

Note that in order to reduce the computational burden in GWO, decision variables are performedas discrete variables within the search domain with fixed step. The step may differs within differentvariables according to their search domain ranges and expected solution precisions. In this paper,the steps for Pbat

rate and Pucrate are both 0.1 MW, for Ebat

rate and Eucrate are 0.1 MWh and 0.01 MWh respectively,

considering the relatively small value of UC’s energy capacity. Toward this end, each element of searchagent vector xi with fixed step within the lower and upper bounds can be initialized as follows:

xi,j =

xminj + 0.1 · ceil

[10 ·

(xmax

j − xminj

)· rand(0, 1)

]for j = 1, 2, 3

xminj + 0.01 · ceil

[100 ·

(xmax

j − xminj

)· rand(0, 1)

]for j = 4

(62)

where the lower and upper bound xminj xmax

j are in accord with the parameters in Equations (16)–(19).

Energies 2018, 11, 2199 15 of 29

In regard to the position update of search agents, an additional operation in Equation (63) isadded to maintain that each component is performed as discrete variable with fixed step and accountsto fixed decimal places:

xi,j =

{xi,j − 0.1 ·

[10 · xi,j − floor

(10 · xi,j

)]for j = 1, 2, 3

xi,j − 0.01 ·[100 · xi,j − floor

(100 · xi,j

)]for j = 4

(63)

It is essential to maintain all search agents are limited within the searching domain duringthe hunting process, thus the adjustment operation for variable beyond the lower/upper bounds isdescribed as Equation (64). The overall flowchart of applying GWO and embedded CPLEX solver tosettle the HESS sizing and diurnal dispatch problems is illustrated in Figure 5.

xi,j =

xmin

j , xi,j < xminj

xmaxj , xi,j > xmax

jxi,j, else

(64)


Read all input data of traction load, PV Generation and price signal

Give the number of search agents (N), Max number of iterations (Itmax)

Initialize the wolf population Xi (i=1,2,…,N) by Equation (62)

Initialize a, A and C by Equation (53) and (54)

Transfer the position of each search agent to the slave model, obtain Ce via embedded CPLEX

solver and calculate the fitness (total cost per day)

Xα, Xβ, Xδ denote top three best search agent positions

Iteration index t =1

Update the position of each search agent by Equation (61)

Adjustment operation for variables beyond the lower/upper bounds by Equation (64)

Additional operation by Equation (63) to maintain each component of search agents accounts to fixed

decimal places

Update a, A and C by Equation (53) and (54)

Transfer the position of each search agent to the slave model, obtain Ce via embedded CPLEX

solver and update the fitness (total cost per day)

Update Xα, Xβ, Xδ

Iteration index t = t + 1

If t >= Itmax ?

Output Xα as optimal HESS sizing, corresponding fitness as optimal total cost per day

End

Start

Yes

No

Figure 5. Flowchart of GWO with CPLEX solver embedded.

6. Case Study

To validate the feasibility of proposed HESS sizing approach, an HSR line with a length of 710 km at the design phase in Xinjiang province is considered for case study. In this section the total cost of different cases within the project service period are compared and the effects of electricity pricing strategies, length of project service time and initial SOC of HESS are also analyzed.

6.1. Cases Description and Input Parameters

As the diurnal operation of HESS is regarded as repeated within the project service period, the simulation period for case study is one day and TSS 2 of the HSR line is selected as an example for detailed cases analysis. Four different scenarios are proposed and they are presented as follows:

• Case 1: conventional railway system with no HESS nor PV generation, as the base case; • Case 2: conventional railway system with HESS only; • Case 3: conventional railway system with battery energy storage systems only; • Case 4: conventional railway system with both HESS and PV generation.

As an illustration, the longitudinal profile of considered HSR line and the location of traction substations are outlined in Figure 6. The designed maximum speed is limited at 250 km/h. It turns out that there are high altitude drops between several adjacent TSSs, which is in favor of the production of RBP.

CRH-3 HST (manufactured by China Railway Rolling Stock Corporation, Qingdao, China) is considered in this HSR line. Physical parameters of CRH-3 HST are listed in Table 1 and the traction and braking characteristics are presented in Figure 7. In regard to timetable, the departure time interval of trains is 30 min for both traveling directions. Based on the above parameters of the trains and the HSR line, the speed and power consumption of each train along the line are obtained by means of the computer simulation software WEBAnet. The simulation results of upward trains are shown in Figure 8 and downward trains are processed in the same manner.

Figure 5. Flowchart of GWO with CPLEX solver embedded.

6. Case Study

To validate the feasibility of proposed HESS sizing approach, an HSR line with a length of 710 kmat the design phase in Xinjiang province is considered for case study. In this section the total cost ofdifferent cases within the project service period are compared and the effects of electricity pricingstrategies, length of project service time and initial SOC of HESS are also analyzed.

Energies 2018, 11, 2199 16 of 29

6.1. Cases Description and Input Parameters

As the diurnal operation of HESS is regarded as repeated within the project service period,the simulation period for case study is one day and TSS 2 of the HSR line is selected as an example fordetailed cases analysis. Four different scenarios are proposed and they are presented as follows:

• Case 1: conventional railway system with no HESS nor PV generation, as the base case;• Case 2: conventional railway system with HESS only;• Case 3: conventional railway system with battery energy storage systems only;• Case 4: conventional railway system with both HESS and PV generation.

As an illustration, the longitudinal profile of considered HSR line and the location of tractionsubstations are outlined in Figure 6. The designed maximum speed is limited at 250 km/h. It turns outthat there are high altitude drops between several adjacent TSSs, which is in favor of the productionof RBP.


For the utilization of RES, PV generation sources are included in RESEM system. It is assumed that PV generation sources are connected to the traction substations. As for PV panels, ηpv = 12%, Apv = 104 m2. PV converter capacity Spv = 1 MVA. The annual profile of solar irradiance can be obtained from [56] and four representative scenarios after using forward reduction algorithm are illustrated in Figure 9b.

With regard to HESS, lead-acid (LA) batteries and UCs are considered in this study. All parameters associated with HESS are presented in Table 2 [31,32,47,57]. It is assumed that the service period of this project is 20 years and all the HESS-related devices can serve for the entire project period except for batteries. The lifetime estimation of LA batteries can be obtained according to the method introduced in previous sections.

100 200 300 400 500 600 700Position in the line (km)

800

1000

1200

1400

1600

1800

2000

2200 Altitude curveTunnelStationTraction substation

TSS1

(DK

47km

)

TSS2

(DK

47km

)

TSS3

(DK

141.

2km

)

TSS4

(DK

180.

51km

)

TSS5

(DK

239.

80km

)

TSS6

(DK

297.

10km

)

TSS7

(DK

357.

8km

)

TSS8

(DK

419.

5km

)

TSS9

(DK

481k

m)

TSS1

0(D

K 54

1.8k

m)

TSS1

1(D

K 60

3.21

km)

TSS1

2(D

K 64

5.71

km)

TSS1

3(D

K 69

1.71

km)

Altit

ude

(m)

Figure 6. Longitudinal profile of HSR line for case study.

0 50 100 150 200 250 300 350Train Speed (km/h)

0

50

100

150

200

250

300

350

Trac

tion

Forc

e(k

N)

Level track

3.0%

2.0%

1.2%

0.6%

Wheel (half worm): 0.830m

6600kW(75% of traction)



(a)

0 50 100 150 200 250 300 350Train Speed (km/h)

0

50

100

150

200

250

300

350

Brak

ing

Forc

e(k

N)





(b)

Figure 7. Traction and braking characteristic of CRH-3 high-speed train: (a) Traction curve; (b) Braking curve.

(a)

(b)

Figure 8. Dynamic speed and power consumption of upward trains versus position: (a) Speed curve; (b) Energy consumption curve, where the negative values indicate regenerative braking power.

0 100 200 300 400 500 600 700Position of the train (km)

0

50

100

150

200

250

300

Spee

d (k

m/h

)


-15

-10

-5

0

5

10

15

20

25

Pow

er c

omsu

ptio

n (M

W)


CRH-3 HST (manufactured by China Railway Rolling Stock Corporation, Qingdao, China) isconsidered in this HSR line. Physical parameters of CRH-3 HST are listed in Table 1 and the tractionand braking characteristics are presented in Figure 7. In regard to timetable, the departure time intervalof trains is 30 min for both traveling directions. Based on the above parameters of the trains and theHSR line, the speed and power consumption of each train along the line are obtained by means ofthe computer simulation software WEBAnet. The simulation results of upward trains are shown inFigure 8 and downward trains are processed in the same manner.





800

1000

1200

1400

1600

1800

2000


TSS1

(DK

47km

)

TSS2

(DK

47km

)

TSS3

(DK

141.

2km

)

TSS4

(DK

180.

51km

)

TSS5

(DK

239.

80km

)

TSS6

(DK

297.

10km

)

TSS7

(DK

357.

8km

)

TSS8

(DK

419.

5km

)

TSS9

(DK

481k

m)

TSS1

0(D

K 54

1.8k

m)

TSS1

1(D

K 60

3.21

km)

TSS1

2(D

K 64

5.71

km)

TSS1

3(D

K 69

1.71

km)

Altit

ude

(m)


0 50 100 150 200 250 300 350Train Speed (km/h)

0

50

100

150

200

250

300

350

Trac

tion

Forc

e(k

N)

Level track

3.0%

2.0%

1.2%

0.6%





(a)

0 50 100 150 200 250 300 350Train Speed (km/h)

0

50

100

150

200

250

300

350

Brak

ing

Forc

e(k

N)





(b)


(a)

(b)



0

50

100

150

200

250

300

Spee

d (k

m/h

)


-15

-10

-5

0

5

10

15

20

25

Pow

er c

omsu

ptio

n (M

W)

Figure 7. Traction and braking characteristic of CRH-3 high-speed train: (a) Traction curve;(b) Braking curve.

Energies 2018, 11, 2199 17 of 29

Table 1. Parameters of CRH-3 HST.

Parameters Value Parameters Value

Unloaded weight 479.36 t Max. traction power 8800 kWAverage load 56.64 t Max. braking power 8000 kW

Power factor (traction) 0.98 Auxiliary power 408 kWPower factor (braking) 0.9 Max. acceleration (traction) 0.65 m/s2

Transmission efficiency 0.9 Max. acceleration (braking) 1.2 m/s2





800

1000

1200

1400

1600

1800

2000


TSS1

(DK

47km

)

TSS2

(DK

47km

)

TSS3

(DK

141.

2km

)

TSS4

(DK

180.

51km

)

TSS5

(DK

239.

80km

)

TSS6

(DK

297.

10km

)

TSS7

(DK

357.

8km

)

TSS8

(DK

419.

5km

)

TSS9

(DK

481k

m)

TSS1

0(D

K 54

1.8k

m)

TSS1

1(D

K 60

3.21

km)

TSS1

2(D

K 64

5.71

km)

TSS1

3(D

K 69

1.71

km)

Altit

ude

(m)


0 50 100 150 200 250 300 350Train Speed (km/h)

0

50

100

150

200

250

300

350

Trac

tion

Forc

e(k

N)

Level track

3.0%

2.0%

1.2%

0.6%





(a)

0 50 100 150 200 250 300 350Train Speed (km/h)

0

50

100

150

200

250

300

350

Brak

ing

Forc

e(k

N)





(b)


(a)

(b)



0

50

100

150

200

250

300

Spee

d (k

m/h

)


-15

-10

-5

0

5

10

15

20

25

Pow

er c

omsu

ptio

n (M

W)

Figure 8. Dynamic speed and power consumption of upward trains versus position: (a) Speed curve;(b) Energy consumption curve, where the negative values indicate regenerative braking power.

For the utilization of RES, PV generation sources are included in RESEM system. It is assumedthat PV generation sources are connected to the traction substations. As for PV panels, ηpv = 12%,Apv = 104 m2. PV converter capacity Spv = 1 MVA. The annual profile of solar irradiance can be obtainedfrom [56] and four representative scenarios after using forward reduction algorithm are illustrated inFigure 9b.


Table 1. Parameters of CRH-3 HST.

Parameters Value Parameters Value Unloaded weight 479.36 t Max. traction power 8800 kW

Average load 56.64 t Max. braking power 8000 kW Power factor (traction) 0.98 Auxiliary power 408 kW Power factor (braking) 0.9 Max. acceleration (traction) 0.65 m/s2

Transmission efficiency 0.9 Max. acceleration (braking) 1.2 m/s2

(a)

(b)

Figure 9. Initial and reduced scenarios: (a) Annual data of solar irradiance; (b) Typical scenarios of solar irradiance after scenario reduction.

Table 2. Parameters of hybrid energy storage systems.

Parameters Unit LA Battery UC PCS costs CNY/kW 2838 2050

Energy capacity costs CNY/kWh 4640 198,000 Replacement costs CNY/kWh 1292 0

BOP costs CNY/kW 674 674 O&M costs (fixed) CNY/kW/year 25.5 0

O&M costs (variable) CNY/MW/h 2.78 0 Efficiency (charge/discharge) - 80%/80% 95%/95%

SOC range - 20~80% 0~100% Initial SOC - 50% 50%

Self-discharging rate /mon 5% 0 Depreciation coefficient - 0.7 0.7

Two different electricity pricing schemes, including fixed tariff and time-of-use (TOU) tariff are considered here. The fixed tariff is 0.782 CNY/kWh for all time periods. As for TOU tariff, electricity price varies at different time periods. The price is 1.252 CNY/kWh for peak time periods of 8:00–11:00 and 18:00–21:00, 0.370 CNY/kWh for valley time periods of 0:00–6:00 and 22:00–0:00, 0.782 CNY/kWh for the rest time periods. The penalty charge price equals to the electricity price. Moreover, the demand charge price is 1.2 CNY/kW and the annual discount rate r0 is 5%. It is assumed that the upper and lower bounds of decision variables of master level model are [ ]∈ 1, 3bat

rateP MW, [ ]∈ 5, 10batrateE

MWh, [ ]∈ 10, 20ucrateP MW and [ ]∈ 0.1, 0.5uc

rateE MWh. The GWO with CPLEX solver embedded approach is implemented under a MATLAB environment on a computer with Intel Core i5-4210M CPU at 2.6 GHz and 8 GB RAM. In GWO the number of search agents is 50 and the maximum number of iterations is 50. CPLEX solver is performed with YALMIP toolbox [58] for the convenience of describing variables and constraints easily and selecting different solvers.

6.2. Cases Results Analysis

Figure 9. Initial and reduced scenarios: (a) Annual data of solar irradiance; (b) Typical scenarios ofsolar irradiance after scenario reduction.

With regard to HESS, lead-acid (LA) batteries and UCs are considered in this study. All parametersassociated with HESS are presented in Table 2 [31,32,47,57]. It is assumed that the service period of thisproject is 20 years and all the HESS-related devices can serve for the entire project period except forbatteries. The lifetime estimation of LA batteries can be obtained according to the method introducedin previous sections.

Energies 2018, 11, 2199 18 of 29

Table 2. Parameters of hybrid energy storage systems.

Parameters Unit LA Battery UC

PCS costs CNY/kW 2838 2050Energy capacity costs CNY/kWh 4640 198,000

Replacement costs CNY/kWh 1292 0BOP costs CNY/kW 674 674

O&M costs (fixed) CNY/kW/year 25.5 0O&M costs (variable) CNY/MW/h 2.78 0

Efficiency (charge/discharge) - 80%/80% 95%/95%SOC range - 20~80% 0~100%Initial SOC - 50% 50%

Self-discharging rate /mon 5% 0Depreciation coefficient - 0.7 0.7

Two different electricity pricing schemes, including fixed tariff and time-of-use (TOU) tariff areconsidered here. The fixed tariff is 0.782 CNY/kWh for all time periods. As for TOU tariff, electricityprice varies at different time periods. The price is 1.252 CNY/kWh for peak time periods of 8:00–11:00and 18:00–21:00, 0.370 CNY/kWh for valley time periods of 0:00–6:00 and 22:00–0:00, 0.782 CNY/kWhfor the rest time periods. The penalty charge price equals to the electricity price. Moreover, the demandcharge price is 1.2 CNY/kW and the annual discount rate r0 is 5%. It is assumed that the upper andlower bounds of decision variables of master level model are Pbat

rate ∈ [1, 3] MW, Ebatrate ∈ [5, 10] MWh,

Pucrate ∈ [10, 20] MW and Euc

rate ∈ [0.1, 0.5] MWh. The GWO with CPLEX solver embedded approach isimplemented under a MATLAB environment on a computer with Intel Core i5-4210M CPU at 2.6 GHzand 8 GB RAM. In GWO the number of search agents is 50 and the maximum number of iterations is50. CPLEX solver is performed with YALMIP toolbox [58] for the convenience of describing variablesand constraints easily and selecting different solvers.

6.2. Cases Results Analysis

6.2.1. Case 1

As the base case, Case 1 demonstrates the scenario of conventional railway system at present, i.e.,no HESS, RES considered. Toward this end, the total cost per day equals to the daily electricity cost.The results are listed in Table 3 and the composition of electricity cost is presented in Figure 10.

Table 3. Results of different cases.

Cases Case 1 Case 2 Case 3 Case 4

Pricing Schemes FixedTariff

TOUTariff

FixedTariff

TOUTariff

FixedTariff

TOUTariff

FixedTariff

TOUTariff

Pbatrate/MW - - 2.9 2.2 2.9 3.0 2.7 2.7

Ebatrate/MWh - - 5.0 5.0 5.1 5.1 5.0 5.0

Pucrate/MW - - 13.0 11.6 - - 16.7 14.5

Eucrate/MWh - - 0.43 0.43 - - 0.49 0.48Tbat/year - - 5.47 3.26 1.21 1.1 3.95 2.84

Ce/k CNY 88.70 99.98 40.84 45.42 70.38 75.83 31.31 33.14CHESS

cap /k CNY - - 26.72 25.75 6.22 6.29 30.18 28.98Cbat

rep/k CNY - - 3.57 7.14 19.42 21.84 5.95 8.33CHESS

om /CNY - - 202.60 153.70 202.60 209.60 188.63 169.52Csal/k CNY - - 0.57 1.43 0.83 1.48 1.55 1.60

Ctotal/k CNY 88.70 99.98 70.76 77.02 95.39 102.69 66.08 69.04

Battery cycles per day(full/half cycles) - - 16/4 21/3 75/4 73/3 25/3 32/5

Electricity Cost Savings - - 53.96% 54.57% 20.65% 24.16% 64.70% 66.85%

Total Cost Savings - - 20.22% 22.96% −7.54% −2.71% 25.50% 30.95%

Energies 2018, 11, 2199 19 of 29


6.2.1. Case 1

As the base case, Case 1 demonstrates the scenario of conventional railway system at present, i.e., no HESS, RES considered. Toward this end, the total cost per day equals to the daily electricity cost. The results are listed in Table 3 and the composition of electricity cost is presented in Figure 10.

Table 3. Results of different cases.

Cases Case 1 Case 2 Case 3 Case 4

Pricing Schemes Fixed Tariff

TOU Tariff

Fixed Tariff

TOU Tariff

Fixed Tariff

TOU Tariff

Fixed Tariff

TOU Tariff

batrateP /MW - - 2.9 2.2 2.9 3.0 2.7 2.7

batrateE /MWh - - 5.0 5.0 5.1 5.1 5.0 5.0

ucrateP /MW - - 13.0 11.6 - - 16.7 14.5

ucrateE /MWh - - 0.43 0.43 - - 0.49 0.48

batT /year - - 5.47 3.26 1.21 1.1 3.95 2.84 eC /k CNY 88.70 99.98 40.84 45.42 70.38 75.83 31.31 33.14

HESScapC /k CNY - - 26.72 25.75 6.22 6.29 30.18 28.98

batrepC /k CNY - - 3.57 7.14 19.42 21.84 5.95 8.33 HESSomC /CNY - - 202.60 153.70 202.60 209.60 188.63 169.52 salC /k CNY - - 0.57 1.43 0.83 1.48 1.55 1.60

totalC /k CNY 88.70 99.98 70.76 77.02 95.39 102.69 66.08 69.04 Battery cycles per day

(full/half cycles) - - 16/4 21/3 75/4 73/3 25/3 32/5

Electricity Cost Savings - - 53.96% 54.57% 20.65% 24.16% 64.70% 66.85% Total Cost Savings - - 20.22% 22.96% −7.54% −2.71% 25.50% 30.95%

88.70

40.84

70.38

31.31

99.98

45.42

75.83

33.14

Case 1 Case 2 Case 3 Case 4

0

25

50

75

100

125

Fixed Tariff

Elec

tricit

y co

st p

er d

ay (k

CNY

)

Energy consumption charge Denmand charge Penalty charge

TOU Tariff Fixed Tariff TOU Tariff Fixed Tariff TOU Tariff Fixed Tariff TOU Tariff

Figure 10. Electricity cost and composition in different cases.

The obtained results are 88.70 k CNY and 99.98 k CNY under fixed tariff and TOU tariff respectively. It shows that rail operators can benefit more under fixed tariff from the perspective of daily cost, which is in line with current situation that fixed tariff is adopted in Chinese railway systems.

6.2.2. Case 2

In this case, HESS is included compared to Case 1. By applying proposed bi-level model combining HESS sizing and daily scheduling, the optimized sizing results are shown in Table 3. It is interesting that there are electricity cost savings of 53.96% under fixed tariff and 54.57% under TOU tariff, and the corresponding percentage for total cost saving are 21.78% and 24.12%, owing to the operation of charging at valley time period with low price and discharging at peak time period with high price under TOU tariff.

Another significant difference we need to pay close attention to is the battery lifetime. As shown in Table 3, the battery lifetime of 3.26 years under TOU tariff is apparently shorter than that of 5.27

Figure 10. Electricity cost and composition in different cases.

The obtained results are 88.70 k CNY and 99.98 k CNY under fixed tariff and TOU tariffrespectively. It shows that rail operators can benefit more under fixed tariff from the perspective ofdaily cost, which is in line with current situation that fixed tariff is adopted in Chinese railway systems.

6.2.2. Case 2

In this case, HESS is included compared to Case 1. By applying proposed bi-level model combiningHESS sizing and daily scheduling, the optimized sizing results are shown in Table 3. It is interestingthat there are electricity cost savings of 53.96% under fixed tariff and 54.57% under TOU tariff, and thecorresponding percentage for total cost saving are 21.78% and 24.12%, owing to the operation ofcharging at valley time period with low price and discharging at peak time period with high priceunder TOU tariff.

Another significant difference we need to pay close attention to is the battery lifetime. As shown inTable 3, the battery lifetime of 3.26 years under TOU tariff is apparently shorter than that of 5.27 yearsunder fixed tariff, primarily arising from the fact that battery performs with a broader range of SOCand larger DOD of cycles so as to take advantage of the pricing signal and minimize the electricity costunder TOU tariff.

In order to demonstrate the operation status of system components in detail, a time horizon of 2 hand a half from 8:00 to 10:30 is highlighted, as shown in Figure 11. As we can observe from Figure 10a,the effects of peak traction load shaving and RBP absorption are significant with the application ofHESS compared to case 1, which gives an explicit explanation of the remarkable reduction of electricitycost. The frequent energizing of UC and relatively smooth energizing of LA battery depicted inFigure 11b,c reveal that, UC takes the responsibility of responding to power peaks rapidly, while LAbattery plays the role of storing massive energy.

Energies 2018, 11, 2199 20 of 29


years under fixed tariff, primarily arising from the fact that battery performs with a broader range of SOC and larger DOD of cycles so as to take advantage of the pricing signal and minimize the electricity cost under TOU tariff.

In order to demonstrate the operation status of system components in detail, a time horizon of 2 h and a half from 8:00 to 10:30 is highlighted, as shown in Figure 11. As we can observe from Figure 10a, the effects of peak traction load shaving and RBP absorption are significant with the application of HESS compared to case 1, which gives an explicit explanation of the remarkable reduction of electricity cost. The frequent energizing of UC and relatively smooth energizing of LA battery depicted in Figure 11b,c reveal that, UC takes the responsibility of responding to power peaks rapidly, while LA battery plays the role of storing massive energy.

(a)

(b)

(c)

Figure 11. Results demonstration of Case 1 and Case 2: (a) Power of utility grid in Case 1 and Case 2, where positive values indicate power imported from grid and negative values indicate power fed back to grid; (b) Charge and discharge power of LA battery and UC in Case 2, where positive values indicate discharge power and negative values indicate charge power; (c) SOC of LA battery and UC in Case 2.

6.2.3. Case 3

In this section we consider the base case with BESS, for the comparison with the performance of HESS. All parameters of LA battery are same with HESS in Case 2. The power and SOC of LA battery during a time horizon of 2 h and a half are illustrated in Figure 12.

As we can observe from Table 3, battery lifetime are 1.21 year and 1.10 year under fixed tariff and TOU tariff in case 3, which is much shorter than that in case 2, and the replacement cost in Case 3 is consequently much larger than that in Case 2. Moreover, negative total cost savings of −10.86% and −1.31% under these two pricing schemes are achieved, which means that the daily total cost is even larger than initial electricity cost in Case 1. In order to explain the difference of battery lifetime in detail, the SOC curve of LA battery in Case 2 and Case 3 are illustrated in Figure 12.

As Figure 13 shows, the SOC curve of LA battery in Case 3 contains more fluctuating components and micro-cycles. For instance, in Figure 13a, SOC of LA battery in Case 2 contains merely a half cycle in a fixed time horizon of two hours. By contrast, SOC of LA battery in Case 3 has five half cycles and seven full cycles, resulting in a significant reduction of battery lifetime and degradation of system applicability. As a result, compared to BESS, a combination of battery and UC cannot only perform in a more flexible manner, but also help prolong the battery lifetime and reduce relevant replacement cost.

-20

0

20

40power of utility grid in Case 2 power of utility grid in Case 1

Figure 11. Results demonstration of Case 1 and Case 2: (a) Power of utility grid in Case 1 and Case 2,where positive values indicate power imported from grid and negative values indicate power fed backto grid; (b) Charge and discharge power of LA battery and UC in Case 2, where positive values indicatedischarge power and negative values indicate charge power; (c) SOC of LA battery and UC in Case 2.

6.2.3. Case 3

In this section we consider the base case with BESS, for the comparison with the performance ofHESS. All parameters of LA battery are same with HESS in Case 2. The power and SOC of LA batteryduring a time horizon of 2 h and a half are illustrated in Figure 12.Energies 2018, 11, x FOR PEER REVIEW 21 of 29

(a)

(b)

Figure 12. Power and SOC of LA battery in Case 3 under TOU tariff: (a) Charge and discharge power, where positive values indicate discharge power and negative values indicate charge power; (b) SOC.

SOC of LA battery in case 2SOC of LA battery in case 3

Upper Limit

Lower Limit

①② ①

②

Cycles identification of LA battery SOC in case 2


0 5 10 15 20Number of peaks and valleys

0.26

0.28

0.3

0.32

0.34

0.36

0.38

Valu

e

1(h)2(f)

3(f)

4(f) 5(f)

6(f)

7(f)

8(h)

9(h)

10(h)

11(h)

12(h)

peaks and valleys of SOC signal

0 1Number of peaks and valleys

0.28

0.3

0.32

0.34

0.36

0.38

0.4

Valu

e

1(h)


(a)

0 4 8 12 16 20 24Time (hr)

0

0.2

0.4

0.6

0.8

1

SOC


Upper Limit

Lower Limit

①② ①

②




0.76

0.77

0.78

0.79

0.8

Valu

e

1(f)

2(f)3(h)



0.74

0.75

0.76

0.77

0.78

0.79

0.8

Valu

e

1(h)

2(f)

3(h)

4(f)5(f)

6(f)

7(f)

8(f)

9(f)

10(f)

11(h) 12(h)peaks and valleys of SOC signal

(b)

Figure 13. SOC curve of LA battery and cycle identification in Case 2 (HESS) and Case 3 (BESS): (a) Under fixed tariff; (b) Under TOU tariff, where (f) denotes full cycle and (h) denotes a half cycle.

6.2.4. Case 4

For the utilization of renewable energy sources, PV generation as well as HESS are included in this case. The power and SOC of LA battery and UC over a time horizon of 2 h and a half are presented in Figure 14. The obtained results show that there are 27.07% and 32.39% of total cost savings under two price schemes, with marked improvements compared to Case 2.

8:00 8:15 8:30 8:45 9:00 9:15 9:30 9:45 10:00 10:15 10:30Time (hr)

0.2

0.4

0.6

0.8

Figure 12. Power and SOC of LA battery in Case 3 under TOU tariff: (a) Charge and discharge power,where positive values indicate discharge power and negative values indicate charge power; (b) SOC.

As we can observe from Table 3, battery lifetime are 1.21 year and 1.10 year under fixed tariffand TOU tariff in case 3, which is much shorter than that in case 2, and the replacement cost in Case 3is consequently much larger than that in Case 2. Moreover, negative total cost savings of −10.86%and −1.31% under these two pricing schemes are achieved, which means that the daily total cost is

Energies 2018, 11, 2199 21 of 29

even larger than initial electricity cost in Case 1. In order to explain the difference of battery lifetime indetail, the SOC curve of LA battery in Case 2 and Case 3 are illustrated in Figure 12.

As Figure 13 shows, the SOC curve of LA battery in Case 3 contains more fluctuating componentsand micro-cycles. For instance, in Figure 13a, SOC of LA battery in Case 2 contains merely a half cyclein a fixed time horizon of two hours. By contrast, SOC of LA battery in Case 3 has five half cyclesand seven full cycles, resulting in a significant reduction of battery lifetime and degradation of systemapplicability. As a result, compared to BESS, a combination of battery and UC cannot only perform in amore flexible manner, but also help prolong the battery lifetime and reduce relevant replacement cost.


(a)

(b)

Figure 12. Power and SOC of LA battery in Case 3 under TOU tariff: (a) Charge and discharge power, where positive values indicate discharge power and negative values indicate charge power; (b) SOC.


Upper Limit

Lower Limit

①② ①

②




0.26

0.28

0.3

0.32

0.34

0.36

0.38

Valu

e

1(h)2(f)

3(f)

4(f) 5(f)

6(f)

7(f)

8(h)

9(h)

10(h)

11(h)

12(h)


0 1Number of peaks and valleys

0.28

0.3

0.32

0.34

0.36

0.38

0.4

Valu

e

1(h)


(a)

0 4 8 12 16 20 24Time (hr)

0

0.2

0.4

0.6

0.8

1

SOC


Upper Limit

Lower Limit

①② ①

②




0.76

0.77

0.78

0.79

0.8

Valu

e

1(f)

2(f)3(h)



0.74

0.75

0.76

0.77

0.78

0.79

0.8

Valu

e

1(h)

2(f)

3(h)

4(f)5(f)

6(f)

7(f)

8(f)

9(f)

10(f)

11(h) 12(h)peaks and valleys of SOC signal

(b)

Figure 13. SOC curve of LA battery and cycle identification in Case 2 (HESS) and Case 3 (BESS): (a) Under fixed tariff; (b) Under TOU tariff, where (f) denotes full cycle and (h) denotes a half cycle.

6.2.4. Case 4

For the utilization of renewable energy sources, PV generation as well as HESS are included in this case. The power and SOC of LA battery and UC over a time horizon of 2 h and a half are presented in Figure 14. The obtained results show that there are 27.07% and 32.39% of total cost savings under two price schemes, with marked improvements compared to Case 2.

8:00 8:15 8:30 8:45 9:00 9:15 9:30 9:45 10:00 10:15 10:30Time (hr)

0.2

0.4

0.6

0.8

Figure 13. SOC curve of LA battery and cycle identification in Case 2 (HESS) and Case 3 (BESS):(a) Under fixed tariff; (b) Under TOU tariff, where (f) denotes full cycle and (h) denotes a half cycle.

6.2.4. Case 4

For the utilization of renewable energy sources, PV generation as well as HESS are included inthis case. The power and SOC of LA battery and UC over a time horizon of 2 h and a half are presentedin Figure 14. The obtained results show that there are 27.07% and 32.39% of total cost savings undertwo price schemes, with marked improvements compared to Case 2.

Energies 2018, 11, 2199 22 of 29


However, it is noteworthy that the battery lifetimes of 3.95 and 2.84 years in this case are evidently decreased compared to the 5.47 and 3.26 years in Case 2. As shown in Figure 15, the difference of LA battery SOC with or without PV integrated occurs at the daytime, particularly from 10:00 to 18:00. Generally, at daytime LA battery SOC curve in Case 4 stays at a higher level, while contains more cycles with larger DOD.

As PV generation is considered here, batteries tend to charge and discharge more frequently to make full use of the available renewable energy and reduce the energy demand from utility grid so as to reduce the electricity cost, which inevitably accelerates the aging of batteries.

(a)

(b)

Figure 14. Power and SOC of LA battery and UC in Case 4 under TOU tariff: (a) Charge and discharge power, where positive values indicate discharge power and negative values indicate charge power; (b) SOC.

Upper Limit

Lower Limit

Figure 15. Comparison of LA battery SOC between Case 2 (without PV integrated) and Case 4 in scenario 2 (with integrated PV).

6.2.5. Convergence Performance of GWO

As GWO algorithm is utilized to solve the master level problem, a comparison of convergence performance between GWO, differential evolution (DE), simulated annealing (SA) optimization and particle swarm optimization (PSO) is conducted, as shown in Figure 16. Note that in this section, these four algorithms with embedded CPLEX solver are used to solve the problem in Case 2 under fixed tariff.

Figure 14. Power and SOC of LA battery and UC in Case 4 under TOU tariff: (a) Charge and dischargepower, where positive values indicate discharge power and negative values indicate charge power;(b) SOC.

However, it is noteworthy that the battery lifetimes of 3.95 and 2.84 years in this case are evidentlydecreased compared to the 5.47 and 3.26 years in Case 2. As shown in Figure 15, the difference of LAbattery SOC with or without PV integrated occurs at the daytime, particularly from 10:00 to 18:00.Generally, at daytime LA battery SOC curve in Case 4 stays at a higher level, while contains morecycles with larger DOD.


However, it is noteworthy that the battery lifetimes of 3.95 and 2.84 years in this case are evidently decreased compared to the 5.47 and 3.26 years in Case 2. As shown in Figure 15, the difference of LA battery SOC with or without PV integrated occurs at the daytime, particularly from 10:00 to 18:00. Generally, at daytime LA battery SOC curve in Case 4 stays at a higher level, while contains more cycles with larger DOD.

As PV generation is considered here, batteries tend to charge and discharge more frequently to make full use of the available renewable energy and reduce the energy demand from utility grid so as to reduce the electricity cost, which inevitably accelerates the aging of batteries.

(a)

(b)

Figure 14. Power and SOC of LA battery and UC in Case 4 under TOU tariff: (a) Charge and discharge power, where positive values indicate discharge power and negative values indicate charge power; (b) SOC.

Upper Limit

Lower Limit

Figure 15. Comparison of LA battery SOC between Case 2 (without PV integrated) and Case 4 in scenario 2 (with integrated PV).


As GWO algorithm is utilized to solve the master level problem, a comparison of convergence performance between GWO, differential evolution (DE), simulated annealing (SA) optimization and particle swarm optimization (PSO) is conducted, as shown in Figure 16. Note that in this section, these four algorithms with embedded CPLEX solver are used to solve the problem in Case 2 under fixed tariff.

Figure 15. Comparison of LA battery SOC between Case 2 (without PV integrated) and Case 4 inscenario 2 (with integrated PV).

As PV generation is considered here, batteries tend to charge and discharge more frequently tomake full use of the available renewable energy and reduce the energy demand from utility grid so asto reduce the electricity cost, which inevitably accelerates the aging of batteries.


As GWO algorithm is utilized to solve the master level problem, a comparison of convergenceperformance between GWO, differential evolution (DE), simulated annealing (SA) optimization andparticle swarm optimization (PSO) is conducted, as shown in Figure 16. Note that in this section,these four algorithms with embedded CPLEX solver are used to solve the problem in Case 2 underfixed tariff.

Energies 2018, 11, 2199 23 of 29Energies 2018, 11, x FOR PEER REVIEW 23 of 29

0 10 20 30 40 50Iteration

7

7.1

7.2

7.3

7.4

7.5

7.6 104

GWODEPSOSA

X=12Y=7.0760e+04

X=16Y=7.0760e+04

X=29Y=7.0783e+04

X=41Y=7.0844e+04

Best

fitn

ess

of to

tal c

ost p

er d

ay (C

NY)

Figure 16. Convergence characteristics of grey wolf optimizer, differential evolution, simulated annealing optimization and particle swarm optimization for Case 2 under fixed tariff.

Figure 16 shows that the optimal solution of GWO equals to that of DE (70.760 k), both of which are better than PSO (70.783 k) and SA (70.844 k). Besides, the optimal solutions of GWO, DE, PSO and SA are achieved at the 12th, 16th, 29th and 41th iterations, respectively, which indicates that GWO algorithm has better convergence performance than the other algorithms for solving the RTSEM problem in this paper. Therefore, the results validate the effectiveness of GWO technique with embedded CPLEX solver.

6.3. Sensitivities Analysis

As the default project service period and daily initial SOC of HESS are set as 20 years and 50% in previous cases analysis, in this section, the sensitivities analysis concerning daily initial SOC of HESS and project service period are performed to evaluate the impact of these two parameters on total cost savings.

As for the sensitivity analysis concerning daily initial SOC of HESS, both LA battery and UC are performed with the same initial SOC so that the considered initial SOC depends on the SOC range of LA battery. A series of initial SOC values of 20%, 30%, 40%, 50%, 60%, 70% and 80% are simulated with default project service period under fixed price tariff and relevant results are shown in Figure 17a. As observed in Figure 17a, a maximum total cost saving of 20.22% is achieved with initial SOC of 50%, as a result of allowing for a more flexible SOC range.

With regard to the project service period, a series of integers from 10 to 20 years are considered for sensitivity study with default initial SOC. Figure 17b reveals that total cost savings keep increasing with the extension of project service period, arising from a more sufficient utilization of UC. It’s worth noting that the project period should be bounded by the UC cycle lifetime.

17.5

18.0

18.5

19.0

19.5

20.0

20.5

20 30 40 50 60 70 800

5

10

15

20

25

30

35

Initial SOC (%)

Capital cost Replacement cost

Tota

l cos

t sav

ing

(%)

Total cost saving (%)

Cos

t per

day

(k C

NY)

(a)

-10

-5

0

5

10

15

20

25

10 11 12 13 14 15 16 17 18 19 200

10

20

30

40

50

Project service period (year)


Tota

l cos

t sav

ing

(%)


Cos

t per

day

(k C

NY)

(b)

Figure 17. Sensitivity studies: (a) The impact of initial SOC of HESS on total cost saving; (b) The impact of project service period on total cost saving.

Figure 16. Convergence characteristics of grey wolf optimizer, differential evolution, simulatedannealing optimization and particle swarm optimization for Case 2 under fixed tariff.

Figure 16 shows that the optimal solution of GWO equals to that of DE (70.760 k), both ofwhich are better than PSO (70.783 k) and SA (70.844 k). Besides, the optimal solutions of GWO, DE,PSO and SA are achieved at the 12th, 16th, 29th and 41th iterations, respectively, which indicatesthat GWO algorithm has better convergence performance than the other algorithms for solving theRTSEM problem in this paper. Therefore, the results validate the effectiveness of GWO technique withembedded CPLEX solver.


As the default project service period and daily initial SOC of HESS are set as 20 years and 50%in previous cases analysis, in this section, the sensitivities analysis concerning daily initial SOC ofHESS and project service period are performed to evaluate the impact of these two parameters on totalcost savings.

As for the sensitivity analysis concerning daily initial SOC of HESS, both LA battery and UC areperformed with the same initial SOC so that the considered initial SOC depends on the SOC range ofLA battery. A series of initial SOC values of 20%, 30%, 40%, 50%, 60%, 70% and 80% are simulatedwith default project service period under fixed price tariff and relevant results are shown in Figure 17a.As observed in Figure 17a, a maximum total cost saving of 20.22% is achieved with initial SOC of 50%,as a result of allowing for a more flexible SOC range.


0 10 20 30 40 50Iteration

7

7.1

7.2

7.3

7.4

7.5

7.6 104

GWODEPSOSA

X=12Y=7.0760e+04

X=16Y=7.0760e+04

X=29Y=7.0783e+04

X=41Y=7.0844e+04

Best

fitn

ess

of to

tal c

ost p

er d

ay (C

NY)

Figure 16. Convergence characteristics of grey wolf optimizer, differential evolution, simulated annealing optimization and particle swarm optimization for Case 2 under fixed tariff.

Figure 16 shows that the optimal solution of GWO equals to that of DE (70.760 k), both of which are better than PSO (70.783 k) and SA (70.844 k). Besides, the optimal solutions of GWO, DE, PSO and SA are achieved at the 12th, 16th, 29th and 41th iterations, respectively, which indicates that GWO algorithm has better convergence performance than the other algorithms for solving the RTSEM problem in this paper. Therefore, the results validate the effectiveness of GWO technique with embedded CPLEX solver.


As the default project service period and daily initial SOC of HESS are set as 20 years and 50% in previous cases analysis, in this section, the sensitivities analysis concerning daily initial SOC of HESS and project service period are performed to evaluate the impact of these two parameters on total cost savings.

As for the sensitivity analysis concerning daily initial SOC of HESS, both LA battery and UC are performed with the same initial SOC so that the considered initial SOC depends on the SOC range of LA battery. A series of initial SOC values of 20%, 30%, 40%, 50%, 60%, 70% and 80% are simulated with default project service period under fixed price tariff and relevant results are shown in Figure 17a. As observed in Figure 17a, a maximum total cost saving of 20.22% is achieved with initial SOC of 50%, as a result of allowing for a more flexible SOC range.

With regard to the project service period, a series of integers from 10 to 20 years are considered for sensitivity study with default initial SOC. Figure 17b reveals that total cost savings keep increasing with the extension of project service period, arising from a more sufficient utilization of UC. It’s worth noting that the project period should be bounded by the UC cycle lifetime.

17.5

18.0

18.5

19.0

19.5

20.0

20.5

20 30 40 50 60 70 800

5

10

15

20

25

30

35

Initial SOC (%)


Tota

l cos

t sav

ing

(%)


Cos

t per

day

(k C

NY)

(a)

-10

-5

0

5

10

15

20

25

10 11 12 13 14 15 16 17 18 19 200

10

20

30

40

50

Project service period (year)


Tota

l cos

t sav

ing

(%)


Cos

t per

day

(k C

NY)

(b)

Figure 17. Sensitivity studies: (a) The impact of initial SOC of HESS on total cost saving; (b) The impact of project service period on total cost saving. Figure 17. Sensitivity studies: (a) The impact of initial SOC of HESS on total cost saving; (b) The impactof project service period on total cost saving.

Energies 2018, 11, 2199 24 of 29

With regard to the project service period, a series of integers from 10 to 20 years are consideredfor sensitivity study with default initial SOC. Figure 17b reveals that total cost savings keep increasingwith the extension of project service period, arising from a more sufficient utilization of UC. It’s worthnoting that the project period should be bounded by the UC cycle lifetime.

6.4. Cost Savings Analysis of TSSs in the HSR Line

Detailed case studies of TSS 2 have been performed in the previous sections. Here we concentrateon the cost-saving study of remaining TSSs in the HSR line and try to evaluate whether each TSSshows satisfactory cost-saving potentials when the HESS is integrated. Note that one of the two powersupply sections that each TSS contains is selected for cost savings analysis.

As observed from Figure 18, almost all TSSs shows different levels of economic-saving potentialsand the best cost saving is achieved at TSS 10, primarily arising from considerable RBP of train at onlong and sharp grade. With regard to TSS 12 and TSS 13, high altitude and relatively gentle slopingtrack result in lower RBP for reuse and inconspicuous cost-saving results. Toward this end, TSSs withnotable cost savings should be given priority to when HESS is applied in the future.


6.4. Cost Savings Analysis of TSSs in the HSR Line

Detailed case studies of TSS 2 have been performed in the previous sections. Here we concentrate on the cost-saving study of remaining TSSs in the HSR line and try to evaluate whether each TSS shows satisfactory cost-saving potentials when the HESS is integrated. Note that one of the two power supply sections that each TSS contains is selected for cost savings analysis.

As observed from Figure 18, almost all TSSs shows different levels of economic-saving potentials and the best cost saving is achieved at TSS 10, primarily arising from considerable RBP of train at on long and sharp grade. With regard to TSS 12 and TSS 13, high altitude and relatively gentle sloping track result in lower RBP for reuse and inconspicuous cost-saving results. Toward this end, TSSs with notable cost savings should be given priority to when HESS is applied in the future.

1 2 3 4 5 6 7 8 9 10 11 12 130

5

10

15

20

25

30

35

40

Tota

l cos

t sav

ing

(%)

TSSs

With HESS and PV generation With HESS

Figure 18. Cost saving results of TSSs in the HSR line.

7. Conclusions

This paper proposes a bi-level model combining long-term HESS sizing and short-term diurnal HESS dispatch strategy for energy management in railway traction substations. The optimized sizing of HESS involving power rating and capacity of LA battery and UC is formulated in the master level model with the intention of minimizing the total cost throughout the project service period, with battery degradation and replacement cost taken into account. While the diurnal HESS scheduling strategy is formulated as a MILP model in the slave level model. The proposed GWO with CPLEX solver embedded approach has been implemented successfully on TSSs of considered HSR line. The case study results reveal that there are significant cost savings with the integration of HESS and RES under both fixed tariff (25.5%) and TOU tariff (30.95%). Besides, a combination of battery and UC, namely HESS, helps prolong the battery lifetime and reduce replacement cost remarkably. Meanwhile, the daily initial SOC of HESS and project service period are found to have significant impacts on total cost savings, and the sensitivity analysis is performed. It is noteworthy that TSSs in the HSR line present different cost-saving potentials under different line geometry, thus it is crucial to evaluate each TSS in advance so as to provide preferences for further application of HESS.

Future work can incorporate the power flow calculation of traction networks into the optimization model and figure out the optimal position and sizing of HESS and RES in the HSR line. Moreover, HESS between adjacent power supply sections for power routing and negative sequence reduction deserves further study.

Author Contributions: Y.L. and M.C. proposed the idea, developed the model, performed the simulation works and wrote the paper. S.L., Y.C. were in charge of review and editing. This work was conducted under the supervision of Q.L.

Funding: This research was funded by the National Natural Science Foundation of China (Grant No. 51877182) and the Science and Technology Plan Project of Sichuan Province (Grant No. 2018FZ0107). The APC was funded

Figure 18. Cost saving results of TSSs in the HSR line.

7. Conclusions

This paper proposes a bi-level model combining long-term HESS sizing and short-term diurnalHESS dispatch strategy for energy management in railway traction substations. The optimized sizingof HESS involving power rating and capacity of LA battery and UC is formulated in the master levelmodel with the intention of minimizing the total cost throughout the project service period, with batterydegradation and replacement cost taken into account. While the diurnal HESS scheduling strategyis formulated as a MILP model in the slave level model. The proposed GWO with CPLEX solverembedded approach has been implemented successfully on TSSs of considered HSR line. The casestudy results reveal that there are significant cost savings with the integration of HESS and RESunder both fixed tariff (25.5%) and TOU tariff (30.95%). Besides, a combination of battery and UC,namely HESS, helps prolong the battery lifetime and reduce replacement cost remarkably. Meanwhile,the daily initial SOC of HESS and project service period are found to have significant impacts on totalcost savings, and the sensitivity analysis is performed. It is noteworthy that TSSs in the HSR linepresent different cost-saving potentials under different line geometry, thus it is crucial to evaluate eachTSS in advance so as to provide preferences for further application of HESS.

Future work can incorporate the power flow calculation of traction networks into the optimizationmodel and figure out the optimal position and sizing of HESS and RES in the HSR line. Moreover,

Energies 2018, 11, 2199 25 of 29

HESS between adjacent power supply sections for power routing and negative sequence reductiondeserves further study.

Author Contributions: Y.L. and M.C. proposed the idea, developed the model, performed the simulation worksand wrote the paper. S.L., Y.C. were in charge of review and editing. This work was conducted under thesupervision of Q.L.

Funding: This research was funded by the National Natural Science Foundation of China (Grant No. 51877182)and the Science and Technology Plan Project of Sichuan Province (Grant No. 2018FZ0107). The APC wasfunded by the National Natural Science Foundation of China and the Science and Technology Plan Project ofSichuan Province.

Acknowledgments: This research was supported by the China Railway Construction Co., Ltd. (CRCC) and theFirst Design and Survey Institute (FDSI) Group Co., Ltd.

Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

AbbreviationsRTSEM Railway traction substation energy managementHESS Hybrid Energy storage systemsPCS Power conversion systemsBOP Balance of plantRBP Regenerative braking powerUC UltracapacitorLA Lead-acidPV PhotovoltaicMILP Mixed-integer linear programmingHSR High-speed railwayHSTs High-speed trainsDOD Depth of dischargeSOC State of chargeParametersPload

t Railway traction load at time interval t (MW)Pbreak

t Regenerative braking power at time interval t (MW)T Total number of operation time intervals during a day∆t The discretization time interval (1 min)ρt,s Electricity price for power imported from the utility grid (CNY/MWh)ρ

pent,s penalty charge for power fed back to the utility grid (CNY/MWh)

Apv Total area of PV panels (m2)πs Probability of PV generation scenariospv

t,s Solar irradiance at time interval t for scenario s (kW/m2)Tproj Project service period (year)r0 Annual discount ratePbat, Pbat Upper and lower bounds of power rating of battery (MW)Ebat, Ebat Upper and lower bounds of capacity of battery (MWh)Puc, Puc Upper and lower bounds of power rating of UC (MW)Euc, Euc Upper and lower bounds of capacity of UC (MWh)ηbat

dis , ηbatch Discharge and charge efficiency of battery

ηucdis, ηuc

ch Discharge and charge efficiency of UCεb ,εc Self-discharging rate of battery and UCSOCbat

min,SOCbat

maxMinimum and maximum SOC limit of battery

SOCbat0 Initial SOC of battery per day

SOCucmin,

SOCucmax

Minimum and maximum SOC limit of UC

Energies 2018, 11, 2199 26 of 29

SOCuc0 Initial SOC of UC per day

Pgridlimit Maximum limit for active power imported from the utility grid (MW)

Pfedlimit Maximum limit for regenerative braking power fed back to the utility grid (MW)

VariablesPbat,dis

t,s , Pbat,cht,s Discharge and charge power of battery at time interval t for scenario s (MW)

Puc,dist,s , Puc,ch

t,s Discharge and charge power of UC at time interval t for scenario s (MW)

Pgridt,s Power supplied by the utility grid at time interval t for scenario s (MW)

Pfedt,s Power fed back to utility grid at time interval t for scenario s (MW)

Ppvt,s PV output power at time interval t for scenario s (MW)

Ebat,storedt,s ,

Euc,storedt,s

The energy stored in battery and UC at time interval t for scenario s (MWh)

ubat,dist,s , uuc,dis

t,s Binary variable: 1 if battery or UC are discharging at time interval t for scenario s, 0 otherwiseubat,ch

t,s , uuc,cht,s Binary variable: 1 if battery or UC are charging at time interval t for scenario s, 0 otherwise

ubat,opet,s , uuc,ope

t,sBinary variable: 1 if battery or UC are in operation mode (charge/discharge) at time interval tfor scenario s, 0 otherwise

ugridt,s Binary variable: 1 if grid supplies power to trains, and 0 if braking power is fed back to grid.

Tbat Battery lifetime (year), as an intermediate variablePbat

rate, Pucrate Rated power of battery and UC (MW)

Ebatrate, Euc

rate Rated capacity of battery and UC (MWh)Tbat

hr , Tuchr Operation time of battery and UC per day (hour), as intermediate variables

References

1. Intergovernmental Panel on Climate Change. Climate Change 2014—Impacts, Adaptation and VulnerabilityPart A: Global and Sectoral Aspects; Cambridge University Press: Cambridge, UK; New York, NY, USA, 2014;ISBN 1-107-05807-4.

2. Intergovernmental Panel on Climate Change. Climate Change 2014—Impacts, Adaptation and VulnerabilityPart B: Regional Aspects; Cambridge University Press: Cambridge, UK; New York, NY, USA, 2014;ISBN 1-107-05816-3.

3. Kyoto Protocol to the United Nations Framework Convention on Climate Change. Available online:https://unfccc.int/process/the-kyoto-protocol (accessed on 11 February 2018).

4. Doha Amendment to the Kyoto Protocol. Available online: https://unfccc.int/process/the-kyoto-protocol/the-doha-amendment (accessed on 11 February 2018).

5. Yan, Q.; Wang, Y.; Baležentis, T.; Sun, Y.; Streimikiene, D. Energy-Related CO2 Emission in China’s ProvincialThermal Electricity Generation: Driving Factors and Possibilities for Abatement. Energies 2018, 11, 1096.[CrossRef]

6. Railway Handbook 2017: Energy Consumption and CO2 Emissions. Available online: https://uic.org/IMG/pdf/handbook_iea-uic_2017_web2-2.pdf (accessed on 2 February 2018).

7. Wang, K.; Hu, H.; Zheng, Z.; He, Z.; Chen, L. Study on Power Factor Behavior in High-Speed RailwaysConsidering Train Timetable. IEEE Trans. Transp. Electrif. 2018, 4, 220–231. [CrossRef]

8. Ratniyomchai, T.; Hillmansen, S.; Tricoli, P. Recent developments and applications of energy storage devicesin electrified railways. IET Electr. Syst. Transp. 2014, 4, 9–20. [CrossRef]

9. Sitras SES of Siemens Transportation Systems: Energy Storage System for Mass Transit Systems. Availableonline: https://w3.usa.siemens.com/mobility/us/Documents/en/rail-solutions/railway-electrification/dc-traction-power-supply/sitras-ses2-en.pdf (accessed on 15 January 2018).

10. MITRAC Energy Saver. Available online: https://www.bombardier.com/en/media/insight/economy-and-rail/eco4-technologies/mitrac-energy-saver.html (accessed on 15 January 2018).

11. Moskowitz, J.P.; Cohuau, J.L. STEEM: ALSTOM and RATP experience of supercapacitors in tramwayoperation. In Proceedings of the 2010 IEEE Vehicle Power and Propulsion Conference, Lille, France,1–3 September 2010; pp. 1–5.

12. Shu, Z.; Xie, S.; Li, Q. Single-Phase Back-To-Back Converter for Active Power Balancing, Reactive PowerCompensation, and Harmonic Filtering in Traction Power System. IEEE Trans. Power Electron. 2011, 26,334–343. [CrossRef]

https://unfccc.int/process/the-kyoto-protocol

https://unfccc.int/process/the-kyoto-protocol/the-doha-amendment

https://unfccc.int/process/the-kyoto-protocol/the-doha-amendment

http://dx.doi.org/10.3390/en11051096

https://uic.org/IMG/pdf/handbook_iea-uic_2017_web2-2.pdf

https://uic.org/IMG/pdf/handbook_iea-uic_2017_web2-2.pdf

http://dx.doi.org/10.1109/TTE.2017.2762474

http://dx.doi.org/10.1049/iet-est.2013.0031

https://w3.usa.siemens.com/mobility/us/Documents/en/rail-solutions/railway-electrification/dc-traction-power-supply/sitras-ses2-en.pdf

https://w3.usa.siemens.com/mobility/us/Documents/en/rail-solutions/railway-electrification/dc-traction-power-supply/sitras-ses2-en.pdf

https://www.bombardier.com/en/media/insight/economy-and-rail/eco4-technologies/mitrac-energy-saver.html

https://www.bombardier.com/en/media/insight/economy-and-rail/eco4-technologies/mitrac-energy-saver.html

http://dx.doi.org/10.1109/TPEL.2010.2060360

Energies 2018, 11, 2199 27 of 29

13. Riffonneau, Y.; Bacha, S.; Barruel, F.; Ploix, S. Optimal Power Flow Management for Grid Connected PVSystems with Batteries. IEEE Trans. Sustain. Energy 2011, 2, 309–320. [CrossRef]

14. Roncero-Sánchez, P.; Parreño Torres, A.; Vázquez, J. Control Scheme of a Concentration Photovoltaic Plantwith a Hybrid Energy Storage System Connected to the Grid. Energies 2018, 11, 301. [CrossRef]

15. Jiang, Q.; Gong, Y.; Wang, H. A Battery Energy Storage System Dual-Layer Control Strategy for MitigatingWind Farm Fluctuations. IEEE Trans. Power Syst. 2013, 28, 3263–3273. [CrossRef]

16. Li, R.; Wang, W.; Chen, Z.; Wu, X. Optimal planning of energy storage system in active distribution systembased on fuzzy multi-objective bi-level optimization. J. Mod. Power Syst. Clean Energy 2018, 6, 342–355.[CrossRef]

17. Fossati, J.P.; Galarza, A.; Martín-Villate, A.; Fontán, L. A method for optimal sizing energy storage systemsfor microgrids. Renew. Energy 2015, 77, 539–549. [CrossRef]

18. Sukumar, S.; Mokhlis, H.; Mekhilef, S.; Naidu, K.; Karimi, M. Mix-mode energy management strategy andbattery sizing for economic operation of grid-tied microgrid. Energy 2017, 118, 1322–1333. [CrossRef]

19. Chen, C.; Duan, S.; Cai, T.; Liu, B.; Hu, G. Optimal Allocation and Economic Analysis of Energy StorageSystem in Microgrids. IEEE Trans. Power Electron. 2011, 26, 2762–2773. [CrossRef]

20. Akram, U.; Khalid, M.; Shafiq, S. Optimal sizing of a wind/solar/battery hybrid grid-connected microgridsystem. IET Renew. Power Gener. 2017, 12, 72–80. [CrossRef]

21. Serpi, A.; Porru, M.; Damiano, A. An Optimal Power and Energy Management by Hybrid Energy StorageSystems in Microgrids. Energies 2017, 10, 1909. [CrossRef]

22. Wang, H.; Wang, T.; Xie, X.; Ling, Z.; Gao, G.; Dong, X. Optimal Capacity Configuration of a Hybrid EnergyStorage System for an Isolated Microgrid Using Quantum-Behaved Particle Swarm Optimization. Energies2018, 11, 454. [CrossRef]

23. Khayyam, S.; Ponci, F.; Goikoetxea, J.; Recagno, V.; Bagliano, V.; Monti, A. Railway Energy ManagementSystem: Centralized–Decentralized Automation Architecture. IEEE Trans. Smart Grid 2016, 7, 1164–1175.[CrossRef]

24. Pankovits, P.; Ployard, M.; Pouget, J.; Brisset, S.; Abbes, D.; Robyns, B. Design and operation optimizationof a hybrid railway power substation. In Proceedings of the 2013 15th European Conference on PowerElectronics and Applications (EPE), Lille, France, 2–6 September 2013; pp. 1–8.

25. Pankovits, P.; Abbes, D.; Saudemont, C.; Abdou, O.M.; Pouget, J.; Robyns, B. Energy managementmulti-criteria design for hybrid railway power substations. In Proceedings of the 11th InternationalConference on Modeling and Simulation of Electric Machines, Converters and Systems (Electrimacs 2014),Valencia, Spain, 20–22 May 2014.

26. Pankovits, P.; Pouget, J.; Robyns, B.; Delhaye, F.; Brisset, S. Towards railway-smartgrid: Energy managementoptimization for hybrid railway power substations. In Proceedings of the IEEE PES Innovative Smart GridTechnologies, Europe, Istanbul, Turkey, 12–15 October 2014; pp. 1–6.

27. Novak, H.; Vašak, M.; Lešic, V. Hierarchical energy management of multi-train railway transport systemwith energy storages. In Proceedings of the IEEE International Conference on Intelligent Rail Transportation(ICIRT), Birmingham, UK, 23–25 August 2016; pp. 130–138.

28. Novak, H.; Lesic, V.; Vasak, M. Hierarchical Coordination of Trains and Traction Substation Storages forEnergy Cost Optimization. In Proceedings of the 2017 IEEE 20th International Conference on IntelligentTransportation Systems (ITSC), Yokohama, Japan, 16–19 October 2017.

29. Sengor, I.; Kilickiran, H.C.; Akdemir, H.; Kekezoglu, B.; Erdinc, O.; Catalão, J.P.S. Energy Managementof A Smart Railway Station Considering Regenerative Braking and Stochastic Behaviour of ESS and PVGeneration. IEEE Trans. Sustain. Energy 2018, 9, 1041–1050. [CrossRef]

30. Kim, H.; Heo, J.H.; Park, J.Y.; Yoon, Y.T. Impact of Battery Energy Storage System Operation Strategy onPower System: An Urban Railway Load Case under a Time-of-Use Tariff. Energies 2017, 10, 68. [CrossRef]

31. Aguado, J.A.; Racero, A.J.S.; de la Torre, S. Optimal Operation of Electric Railways ith Renewable Energyand Electric Storage Systems. IEEE Trans. Smart Grid 2018, 9, 993–1001. [CrossRef]

32. De la Torre, S.; Sanchez-Racero, A.J.; Aguado, J.A.; Reyes, M.; Martianez, O. Optimal Sizing of EnergyStorage for Regenerative Braking in Electric Railway Systems. IEEE Trans. Power Syst. 2015, 30, 1492–1500.[CrossRef]

33. SIGNON SINAnet and WEBAnet. Available online: http://www.elbas.de/sinanetwebanet_e.html (accessedon 8 March 2018).

http://dx.doi.org/10.1109/TSTE.2011.2114901

http://dx.doi.org/10.3390/en11020301

http://dx.doi.org/10.1109/TPWRS.2013.2244925

http://dx.doi.org/10.1007/s40565-017-0332-x

http://dx.doi.org/10.1016/j.renene.2014.12.039

http://dx.doi.org/10.1016/j.energy.2016.11.018

http://dx.doi.org/10.1109/TPEL.2011.2116808

http://dx.doi.org/10.1049/iet-rpg.2017.0010

http://dx.doi.org/10.3390/en10111909

http://dx.doi.org/10.3390/en11020454

http://dx.doi.org/10.1109/TSG.2015.2421644


http://dx.doi.org/10.3390/en10010068



http://www.elbas.de/sinanetwebanet_e.html

Energies 2018, 11, 2199 28 of 29

34. Growe-Kuska, N.; Heitsch, H.; Romisch, W. Scenario reduction and scenario tree construction for powermanagement problems. In Proceedings of the 2003 IEEE Bologna Power Tech Conference Proceedings,Bologna, Italy, 23–26 June 2003; Volume 3, p. 7.

35. Soares, J.; Canizes, B.; Ghazvini, M.A.F.; Vale, Z.; Venayagamoorthy, G.K. Two-Stage Stochastic Model UsingBenders’ Decomposition for Large-Scale Energy Resource Management in Smart Grids. IEEE Trans. Ind. Appl.2017, 53, 5905–5914. [CrossRef]

36. Nasri, A.; Kazempour, S.J.; Conejo, A.J.; Ghandhari, M. Network-Constrained AC Unit Commitment underUncertainty: A Benders’ Decomposition Approach. IEEE Trans. Power Syst. 2016, 31, 412–422. [CrossRef]

37. Wu, H.; Shahidehpour, M.; Alabdulwahab, A.; Abusorrah, A. A Game Theoretic Approach to Risk-BasedOptimal Bidding Strategies for Electric Vehicle Aggregators in Electricity Markets with Variable Wind EnergyResources. IEEE Trans. Sustain. Energy 2016, 7, 374–385. [CrossRef]

38. Dupacová, J.; Gröwe-Kuska, N.; Römisch, W. Scenario reduction in stochastic programming. Math. Program.2003, 95, 493–511. [CrossRef]

39. Razali, N.M.M.; Hashim, A.H. Backward reduction application for minimizing wind power scenarios instochastic programming. In Proceedings of the 2010 4th International Power Engineering and OptimizationConference (PEOCO), Shah Alam, Malaysia, 23–24 June 2010; pp. 430–434.

40. Fotouhi Ghazvini, M.A.; Faria, P.; Ramos, S.; Morais, H.; Vale, Z. Incentive-based demand response programsdesigned by asset-light retail electricity providers for the day-ahead market. Energy 2015, 82, 786–799.[CrossRef]

41. Wu, H.; Shahidehpour, M.; Alabdulwahab, A.; Abusorrah, A. Thermal Generation Flexibility with RampingCosts and Hourly Demand Response in Stochastic Security-Constrained Scheduling of Variable EnergySources. IEEE Trans. Power Syst. 2015, 30, 2955–2964. [CrossRef]

42. Tankari, M.A.; Camara, M.B.; Dakyo, B.; Lefebvre, G. Use of Ultracapacitors and Batteries for Efficient EnergyManagement in Wind Diesel Hybrid System. IEEE Trans. Sustain. Energy 2013, 4, 414–424. [CrossRef]

43. Bordin, C.; Anuta, H.O.; Crossland, A.; Gutierrez, I.L.; Dent, C.J.; Vigo, D. A linear programming approachfor battery degradation analysis and optimization in offgrid power systems with solar energy integration.Renew. Energy 2017, 101, 417–430. [CrossRef]

44. Amzallag, C.; Gerey, J.; Robert, J.; Bahuaud, J. Standardization of the rainflow counting method for fatigueanalysis. Int. J. Fatigue 1994, 16, 287–293. [CrossRef]

45. Layadi, T.M.; Champenois, G.; Mostefai, M.; Abbes, D. Lifetime estimation tool of lead–acid batteries forhybrid power sources design. Simul. Model. Pract. Theor. 2015, 54, 36–48. [CrossRef]

46. Bindner, H.; Cronin, T.; Lundsager, P.; Manwell, J.F.; Abdulwahid, U.; Baring-Gould, I. Lifetime Modelling ofLead Acid Batteries; Risø National Laboratory: Roskilde, Denmark, 2005.

47. Zakeri, B.; Syri, S. Electrical energy storage systems: A comparative life cycle cost analysis. Renew. Sustain.Energy Rev. 2015, 42, 569–596. [CrossRef]

48. Tsikalakis, A.G.; Hatziargyriou, N.D. Centralized Control for Optimizing Microgrids Operation. IEEE Trans.Energy Convers. 2008, 23, 241–248. [CrossRef]

49. Roch-Dupre, D.; Lopez-Lopez, A.J.; Pecharroman, R.R.; Cucala, A.P.; Fernandez-Cardador, A. Analysis of thedemand charge in DC railway systems and reduction of its economic impact with Energy Storage Systems.Int. J. Electr. Power Energy Syst. 2017, 93, 459–467. [CrossRef]

50. Zhao, B.; Zhang, X.; Chen, J.; Wang, C.; Guo, L. Operation Optimization of Standalone MicrogridsConsidering Lifetime Characteristics of Battery Energy Storage System. IEEE Trans. Sustain. Energy 2013, 4,934–943. [CrossRef]

51. Zhao, B.; Zhang, X.; Li, P.; Wang, K.; Xue, M.; Wang, C. Optimal sizing, operating strategy and operationalexperience of a stand-alone microgrid on Dongfushan Island. Appl. Energy 2014, 113, 1656–1666. [CrossRef]

52. Chen, S.X.; Gooi, H.B.; Wang, M.Q. Sizing of Energy Storage for Microgrids. IEEE Trans. Smart Grid 2012, 3,142–151. [CrossRef]

53. Mirjalili, S.; Mirjalili, S.M.; Lewis, A. Grey Wolf Optimizer. Adv. Eng. Softw. 2014, 69, 46–61. [CrossRef]54. Sharma, S.; Bhattacharjee, S.; Bhattacharya, A. Grey wolf optimisation for optimal sizing of battery energy

storage device to minimise operation cost of microgrid. IET Gener. Transm. Dis. 2016, 10, 625–637. [CrossRef]55. Hassan, Z.G.; Ezzat, M.; Abdelaziz, A.Y. Enhancement of power system operation using grey wolf

optimization algorithm. In Proceedings of the 2017 Nineteenth International Middle East Power SystemsConference (MEPCON), Cairo, Egypt, 19–21 September 2017; pp. 397–402.

http://dx.doi.org/10.1109/TIA.2017.2723339



http://dx.doi.org/10.1007/s10107-002-0331-0

http://dx.doi.org/10.1016/j.energy.2015.01.090



http://dx.doi.org/10.1016/j.renene.2016.08.066

http://dx.doi.org/10.1016/0142-1123(94)90343-3

http://dx.doi.org/10.1016/j.simpat.2015.03.001

http://dx.doi.org/10.1016/j.rser.2014.10.011

http://dx.doi.org/10.1109/TEC.2007.914686

http://dx.doi.org/10.1016/j.ijepes.2017.06.022


http://dx.doi.org/10.1016/j.apenergy.2013.09.015


http://dx.doi.org/10.1016/j.advengsoft.2013.12.007

http://dx.doi.org/10.1049/iet-gtd.2015.0429

Energies 2018, 11, 2199 29 of 29

56. National Renewable Energy Laboratory Measurement and Instrumentation Data Center (MIDC). Availableonline: https://midcdmz.nrel.gov/ (accessed on 28 March 2018).

57. Battke, B.; Schmidt, T.S.; Grosspietsch, D.; Hoffmann, V.H. A review and probabilistic model of lifecycle costsof stationary batteries in multiple applications. Renew. Sustain. Energy Rev. 2013, 25, 240–250. [CrossRef]

58. Lofberg, J. YALMIP: A toolbox for modeling and optimization in MATLAB. In Proceedings of the 2004 IEEEInternational Conference on Robotics and Automation (IEEE Cat. No.04CH37508), New Orleans, LA, USA,2–4 September 2004; pp. 284–289.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open accessarticle distributed under the terms and conditions of the Creative Commons Attribution(CC BY) license (http://creativecommons.org/licenses/by/4.0/).

https://midcdmz.nrel.gov/

http://dx.doi.org/10.1016/j.rser.2013.04.023

http://creativecommons.org/

http://creativecommons.org/licenses/by/4.0/.