stefanie aebip l power systems laboratory optimal … · 2017-10-31 · optimal power flow...

P LPower

Systems

Laboratory

Stefanie Aebi

Optimal Power Flow Calculation forUnbalanced Distribution Grids

Semester ProjectPSL

EEH – Power Systems LaboratoryETH Zurich

Examiner: Prof. Dr. Gabriela HugSupervisor: MSc Stavros Karagiannopoulos

Zurich, June 28, 2017

Abstract

New developments in distribution grids including the increased penetra-tion of distributed energy resources require the distribution system oper-ator to apply new planning and operating schemes for cost-effective andsecure power supply. This paper proposes a centralized approach for theoperational planning of unbalanced active distribution grids based on [1],where the algorithm of [1] has been extended to 3-phase unbalanced oper-ation. Optimal set-points of distributed energy resources are determinedwith a multi-period optimal power flow algorithm. An exact power flowcomputation to ensure feasibility of the resulting flows is then done using abackward-forward sweep method as proposed by [2]. The resulting planningscheme is applied to and demonstrated on a low-voltage distribution networkmodel. We see that the efficient use of active control measures helps main-taining currents and voltages under acceptable thresholds. In this thesis, wecompare the symmetrical 1-phase case against the 3-phase representation inorder to identify differences in the control usage arising from the 3-phasecoupling.

iii

Acknowledgements

My special thanks go to Stavros Karagiannopoulos who has supervised thisproject, spent a lot of time helping me to find algorithm bugs, supported mewith his specialist knowledge and motivated and challenged me throughoutthis project. I’m really greatful for your support!

v

Contents

List of Acronyms ix

1 Introduction 11.1 Motivation: New Developments in Distribution Grids . . . . . 11.2 Employed Algorithm . . . . . . . . . . . . . . . . . . . . . . . 11.3 Main Contributions . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Power Flow Calculations in DNs 32.1 Characteristics of Distribution Grids . . . . . . . . . . . . . . 32.2 Backward Forward Sweep Method . . . . . . . . . . . . . . . 32.3 Case Study I: Power Flow Calculations in DNs . . . . . . . . 4

2.3.1 Case Study Setup . . . . . . . . . . . . . . . . . . . . 42.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3.3 Multi-Period PF results . . . . . . . . . . . . . . . . . 5

3 Optimal Power Flow Calculations in DNs 113.1 Optimal Power Flow Fundamentals . . . . . . . . . . . . . . . 11

3.1.1 Objective Function . . . . . . . . . . . . . . . . . . . . 113.1.2 Power Balance Constraints . . . . . . . . . . . . . . . 123.1.3 Power Quality Constraints . . . . . . . . . . . . . . . . 133.1.4 OPF Calculation Specifications in this Project . . . . 13

3.2 Case Study II: OPF . . . . . . . . . . . . . . . . . . . . . . . 133.2.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 17

4 Conclusion 21

vii

viii CONTENTS

List of Acronyms

DG Distribution Grid

DER Distributed Energy Resource

DSO Distribution System Operator

OPF Optimal Power Flow

BFS Backward-Forward Sweep

DN Distribution Network

RPC Reactive Power Control

APC Active Power Curtailment

YALMIP Yet Another Linear Matrix Inequality Parser

PF Power Flow

BIBC Bus Injection to Branch Current [matrix]

BCBV Branch Current to Bus Voltage [matrix]

LV Low Voltage

OLTC On Load Tap Changer

BESS Battery Energy Storage System

ix

x CONTENTS

Chapter 1

Introduction

1.1 Motivation: New Developments in Distribu-tion Grids

The increasing share of distributed energy resources (DERs) in the electricitydistribution network (DN) constitutes new challenges as well as new oppor-tunities. Intermittent renewable energy generators and other DERs lead tointensified power flow (PF) variability, and thus, constantly changing oper-ating conditions [1]. On the other hand, controllable DERs represent newsources of flexibility by providing ancillary services such as reactive powercontrol (RPC) [3] and active power curtailment (APC) [4], whereof RPC isusually preferred to APC for the treatment of voltage or congestion prob-lems because it usually incurs lower cost [1]. These new developments inDNs require the distribution system operator (DSO) to apply new planningand operating schemes to ensure optimal cost-effectiveness and security ofsupply. This project focuses on optimal power flow calculations for balancedand unbalanced distribution grids.

1.2 Employed Algorithm

In this project, a centralized scheme for the operational planning of activeDNs was developed, extending [1] to unbalanced operating situations. Atthe core of the proposed algorithm lies a multi-period centralized optimalpower flow (OPF) calculation, employing optimization under considerationof system-wide information. In a first step, a multi-period OPF algorithmis used to compute the optimal set-points of controllable DERs. To reducecomputational burden, this is approximated based on the first step of abackward-forward sweep (BFS) algorithm. In a second step, an iterativepower flow computation based on BFS is run until convergence to determinethe solution state, and thus, ensure feasibility of the resulting power flowsand tractability of the algorithm. The resulting operational planning scheme

1

2 CHAPTER 1. INTRODUCTION

is tested on the Cigre European low-voltage distribution network [6].

1.3 Main Contributions

A centralized scheme for the operational planning of active distribution gridshas been proposed in [1]. This project extends the algorithm used by [1] tounbalanced operating conditions, which is usually the case in distributionnetworks. Furthermore, this paper uses a case study in order to investigatethe system behaviour under balanced and unbalanced loading operations.

Chapter 2

Power Flow Calculations inDNs

2.1 Characteristics of Distribution Grids

It is well-known that power distribution systems are significantly differentfrom transmission systems. They are usually radial or weakly meshed, showhigh R/X ratios and are operated multiphase and unbalanced. Moreover,DNs contain increasing shares of distributed loads and generation [5]. Allthese factors make traditional power flow methods, e.g. based on NewtonRaphson method, inappropriate for distribution grids due to poor conver-gence features. However, various methods making use of the specific char-acteristics of distribution grids have been proposed and can be summed intothree groups: network reduction methods, backward/forward sweep meth-ods and fast decoupled methods [5]. The algorithm proposed in this projectbuilds upon a direct backward/forward sweep procedure based on [2], whichsolves PF exploiting the radial DN topology.

2.2 Backward Forward Sweep Method

A backward forward sweep method (BFS), in short terms, is carried out byiteratively ”sweeping” the network and updating the variables at each itera-tion. A rough summary of the algorithm is given in Algorithm 1.

3

4 CHAPTER 2. POWER FLOW CALCULATIONS IN DNS

Algorithm 1: Main steps of BFS, based on [2], taken from [1]

Input: BIBC, BCBV , Pinj , Qinj , VslackOutput: Ikbranch, V k

bus

1: initialize: k = 1, V kbus = 1∠0◦

2: do

3: Backward sweep: Ikinj =((Pinj+jQinj)

∗

V k∗bus

)4: Ikbranch = BIBC · Ikinj5: Forward sweep: ∆V k+1 = BCBV · Ikbranch6: V k+1

bus = Vslack + ∆V k+1

7: Update iteration: k+ = 1

8: while max|(|V k

bus| − |Vk−1bus |

)| ≥ η̄

9: return Ikbranch, V kbus

The Bus Injection to Branch Current matrix (BIBC) is a matrix captur-ing the network topology and the Branch Current to Bus Voltage matrix(BCBV) the complex line impedances. The algorithm proposed by [2] wasexpanded to 3-phase systems in order to account for imbalances; BIBC thusin our case contains 3x3 identity matrices and BCBV is made of 3x3 com-plex impedance matrices. During the backward sweep, current injections atall buses are calculated and then used to compute branch currents. Thesebranch currents are then used in the forward sweep to determine the voltagedrops over all branches and thus update the bus voltages.

2.3 Case Study I: Power Flow Calculations in DNs

2.3.1 Case Study Setup

The methods suggested in this project are demonstrated on a benchmarksystem proposed in [6]. CIGRE benchmark systems form a common basisof test systems for the analysis and validation of new methods and tech-niques tackling the integration of DERs and Smart Grid technology in thepower system [6]. In this project, the proposed algorithm was applied tothe CIGRE European low-voltage distribution network, which is depicted inFig. 2.1.All network parameters were taken from [6]. The grid consists of 18 branchesand 19 buses, including loads at buses 12, 16, 17, 18 and 19. In this project,the case of a system with a small battery storage at node 16 and PV gener-ation at nodes 12, 16, 18 and 19 with a share of 30% each on the load wasstudied for a worst-case summer day. The applied load was balanced over allphases, however the algorithm is also supposed to work under unbalancedloading conditions.

2.3. CASE STUDY I: POWER FLOW CALCULATIONS IN DNS 5

Figure 2.1: CIGRE European low-voltage distribution network [6]

2.3.2 Results

A BFS PF calculation was applied to the Cigre LV grid without control.Fig. 2.2 and 2.3 show the resulting voltage magnitudes and angles at allbuses of the system. For a comparison, the states calculated by [1] for1-phase balanced operation (using self-impedances only and symmetricalcomponents) are plotted next to the full 3-phase BFS results. It can beobserved that the two approaches yield very similar results regarding thevoltage magnitudes, yet differ substantially concerning the voltage angles.The 3-phase BFS results in slightly lower voltage magnitudes as an effect of

phase interference (mutual impedance) leading to higher overall impedances.It can be shown that the algorithm results in exactly the same PF resultsfor 3-phase calculation as it does for 1-phase calculation, if the mutualimpedances (i.e. the off-diagonal elements in the line impedance matrices)are left out (Fig. 2.4). This implies that phase interference is responsible forthe differences observed between the 3-phase and 1-phase calculation and -since these differences are not negligible - must be considered if the assump-tion of having balanced loading is not realistic.

2.3.3 Multi-Period PF results

The voltage and current magnitude evolution over a period of 24 hours isdepicted in Fig. 2.5. Regarding the PV injections, we consider the worstsummer day in order to investigate the control behavior under high solarradiation. It can easily be seen that for the given worst-case scenario, thesystem experiences severe overvoltages (up to 10%) and thermal overload-ings. This calls for active control measures, which will be considered in thenext chapter.


0 5 10 15 20

bus

0.9

0.92

0.94

0.96

0.98

1voltage m

agnitude [p.u

.]

BFS 1-phase

Matpower

(a) Voltage magnitudes, 1-phase, according to [1]

0 5 10 15 20

bus

0.9

0.92

0.94

0.96

0.98

1

voltage m

agnitude [p.u

.]

BFS phase A-B

BFS phase B-C

BFS phase C-A

(b) Voltage magnitudes, 3-phase

Figure 2.2: Voltage magnitudes at all the buses for a symmetrical single-phase (top) and a 3-phase (bottom) representation


0 5 10 15 20

bus

-2.5

-2

-1.5

-1

-0.5

0

voltage a

ngle

[deg]

BFS 1-phase

Matpower

(a) Voltage angles, 1-phase, according to [1]

0 5 10 15 20

bus

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

voltage a

ngle

[deg]

BFS phase A-B

BFS phase B-C + 120°

BFS phase C-A - 120°

(b) Voltage angles, 3 phases

Figure 2.3: Voltage angles at all the buses for a symmetrical single-phase(top) and a 3-phase (bottom) representation


0 5 10 15 20

bus

0.9

0.92

0.94

0.96

0.98

1voltage m

agnitude [p.u

.]BFS phase A-B

BFS phase B-C

BFS phase C-A

1-phase reference

(a) Voltage magnitudes, 1 phase and 3 phase without phase interference

0 5 10 15 20

bus

-2.5

-2

-1.5

-1

-0.5

0

voltage a

ngle

[deg]

BFS phase A-B

BFS phase B-C

BFS phase C-A

1-phase reference

(b) Voltage angle, 1phase and 3 phases without phase interference

Figure 2.4: Voltage magnitudes and angles at all the buses, consideringall three phases but without mutual interference, compared to the 1-phasereference of [1]


5 10 15 20time [h]

5

10

15

node

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

(a) Voltage magnitudes (p.u.)

1- 2 2- 3 3- 4 4- 5 5- 6 6- 7 7- 8 8- 9 9-10 10-11 4-12 5-13 13-1414-1515-16 7-17 10-1811-19branch

0

50

100

150

ther

mal

load

ing

[%]

(b) Thermal loadings

Figure 2.5: Voltage magnitudes and thermal loadings for an uncontrolled1-phase system, based on [1]

Chapter 3

Optimal Power FlowCalculations in DNs

To make sure that the network constraints are not violated, the system needsto be controlled. Optimal Power Flow (OPF) is a widely used tool in thiscontext. In this project, an Optimal Power Flow algorithm for unbalanceddistribution grids was set up and investigated. The algorithm is an extensionof [1] and basically consists of two main steps processed in an iterativemanner: First, a multi-period OPF is run to calculate optimal set-points ofDERs in the system. Second, an iterative PF computation using BFS (asdescribed in Chapter 2) is run until convergence to determine the solutionstates of the system (Fig. 3.1). What has been modified as compared to [1]is that 3 phases have been considered in the PF computation, making thealgorithm applicable to unbalanced loading.

3.1 Optimal Power Flow Fundamentals

Optimal Power Flow is a powerful tool which is used to calculate DERsoptimal set-points in the context of this project. It works on the optimizationof an objective function under given constraints. Usually, the objective is acost function and to be minimized:

minuc(x, u)

where u is the control vector (i.e., the DERs set-points) and x is the statevector (i.e. the bus voltage magnitudes and angles). The control vector u isoptimized over the objective function.

3.1.1 Objective Function

In our case, the cost function is based on cost of APC and RPC, which areassumed to account for the overall cost of DER control to guarantee a safe

11

12 CHAPTER 3. OPTIMAL POWER FLOW CALCULATIONS IN DNS

Figure 3.1: Proposed operational planning scheme, based on [1]

grid, and on the network losses [1]. For a multi-period OPF, the objectivefunction is summed over the entire time horizon Nhor and over all busesNbus and branches Nbranch:

minu

Nhor∑t=1

Nbus∑j=1

(cTP · Pcurt,j,t + cTQ ·Qctrl,j,t) +

Nbranch∑i=1

cTP · Ploss,i,t

∆t

where Pcurt,j,t is the curtailed active power at node j and time t and Qctrl,j,t

the reactive power support, cTP and cTQ represent the cost of curtailing activepower and supplying reactive power, respectively. Reactive power control isusually the preferred option. Ploss,i,t accounts for the power losses in branchi at time t.

3.1.2 Power Balance Constraints

Power balance constraints create a relation between injected and withdrawnpowers from the network. They are set up for both active and reactivepower:

P finj,j,t = P f

gen,j,t − Pfflex.load,j,t − (P charge

B,j,t − P dischargeB,j,t )

Qfinj,j,t = Qf

gen,j,t − Pfflex.load,j,t · tan(arcos(pf))

where P finj,j,t is the flexible power injected at node j and time t, P f

gen,j,t

describes generated power, P fflex.load,j,t consumed power and PB the power

charged to or discharged from a battery, respectively. The reactive power

3.2. CASE STUDY II: OPF 13

balance is based on flexibly generated reactive power (Qfgen,j,t) and consumed

reactive power, which is determined from consumed active power via thepower factor.

3.1.3 Power Quality Constraints

Power quality constraints make sure the system parameters stay within ac-ceptable limits. These usually comprise voltage and current constraints:

Vmin ≤ |Vbus,j,t| ≤ Vmax

|Vslack| = 1, θ1 = 0

|Ibr,i,t| ≤ Ii,max

where |Vbus,j,t| is the voltage magnitude at bus j and node t, Vmin and Vmax

are given voltage constraints, |Vslack| and θ1 are the reference voltages at theslack bus and |Ibr,i,t| is the current magnitude in branch i at time t, limitedby a maximal branch current Ii,max.

In addition to the constraints mentioned above, there can also be furtherconstraints such as on load tap changer (OLTC) constraints, controllableload constraints, battery energy storage system (BESS) constraints etc. [1].

3.1.4 OPF Calculation Specifications in this Project

Optimal Power Flow typically considers the full, non-linear AC power flowequations. If the inter-temporal constraints that come with active measuressuch as BESS and controllable loads and the integer variables of OLTCand controllable loads are considered as well, the problem can easily getcomputationally very intensive [1]. To avoid that within the context of thisproject, the full PF equations within the OPF problem are approximatedwith a single BFS iteration. After the OPF solution, which determinesoptimal DERs set-points, an exact BFS power flow computation under theseset-points returns the precise solution state of the system.

3.2 Case Study II: OPF

3.2.1 Results

Using the same setup as presented in section 2.3.1 and employing the algo-rithm introduced in Chapter 3 and depicted in Fig. 3.1, the results illustratedin Fig. 3.2 - 3.4 were obtained.

Comparing these results to the case without control (shown in Fig. 2.5),


5 10 15 20time [h]

5

10

15

node

0.94

0.96

0.98

1

1.02

(a) Voltage magnitudes (p.u.), 1 phase with control

5 10 15 20time [h]

5

10

15

node

0.8

0.85

0.9

0.95

1

(b) Voltage magnitudes (p.u.), 3 phases with control

Figure 3.2: Voltage magnitudes after OPF-BFS at all the buses for a sym-metrical single-phase (top) and a 3-phase (bottom) representation


5 10 15 20time [h]

5

10

15

node

-80

-60

-40

-20

0

(a) Reactive power generation (%), 1 phase

5 10 15 20time [h]

5

10

15

node

-80

-60

-40

-20

0

(b) Reactive power generation (%), 3 phases

Figure 3.3: Reactive power control in form of reactive power generation atall the buses for a symmetrical single-phase (top) and a 3-phase (bottom)representation


5 10 15 20time [h]

5

10

15

node

10

20

30

40

50

60

70

(a) PV curtailment (%), 1 phase

5 10 15 20time [h]

5

10

15

node

10

20

30

40

50

60

(b) PV curtailment (%), 3 phases

Figure 3.4: Active power control in form of PV curtailment at all the busesfor a symmetrical single-phase (top) and a 3-phase (bottom) representation


both currents and voltages are brought under acceptable thresholds usingactive measures.Fig. 3.2 - 3.4 show the voltage magnitude, APC and RPC profiles over allnodes and hours for the specified worst-case day. The figures cannot be inter-preted separately because of their cross-dependencies (i.e., control measuresinfluence voltage magnitudes and vice versa). Furthermore, in each figurethe 3-phase results obtained in this project are plotted together with the 1-phase reference following the algorithm of [1]. The resulting patterns showclear similarities for 1-phase and 3-phase, however with some non-negligibledifferences. These will be discussed in the following.

3.2.2 Discussion

During the problematic hours 9 - 18, voltages rise up to 1.04 p.u. (which isthe upper voltage constraint) both for 1-phase (according to [1]) and 3-phaseOPF-BFS computation. Highest voltages are experienced at PV nodes andnodes close to PV injection. The 3-phase OPF shows voltages dropping be-low 0.8 p.u. at certain nodes at night. This is an effect of the 3-times highertotal load applied in the 3-phase calculation. In order to better observe thecritical hours, every phase in the 3-phase system was loaded with the sameload as was the single phase in 1-phase calculation. At hours where PVinfeed is low, this leads to significantly higher voltage drops and thus a volt-age constraint relaxation has been performed in order to still get a feasibleresult. In real system operation, however, undervoltages of that degree arenot tolerable and this issue would need to be addressed.Apart from the lower voltage constraint, 1-phase computation and 3-phasecomputation yield similar but not equal results for the different nodes. Eventhe three phases amongst each other don’t show uniform results but usuallyslightly lower voltages on phase b-c than on phases a-b and c-a. The phasedifferences have to do with the line impedance matrix, which contains equalimpedances for phases a-b and c-a but different self- and mutual impedancesin relation with phase b-c (figure 3.5).Comparing 1-phase results to 3-phase results, it can be observed betweenhours 9 - 18 that the voltages lie around the same value, phases a-b andc-a being a bit higher than the 1-phase voltage and phase b-c a bit lower.The lower voltage on phase b-c stands in connection with some heavy PV-curtailment at node 19 mostly on phase b-c, which might reduce the voltageon that phase over the whole system.The most significant difference between the 1-phase and the 3-phase resultslies with node 12, where 1-phase computation gets to substantially lowervoltages than 3-phase. This is an effect of the higher degree of PV curtail-ment at node 12 with 1-phase OPF (Fig. 3.4 (a)).

Reactive Power Control is generated at all PV nodes, i.e. nodes 12, 16,


(a) line impedance matrices, 1-phase

(b) line impedance matrices, 3-phase

Figure 3.5: Line impedance matrices used in the 1-phase (left) and 3-phase(right) calculation. The two impedance matrices per system correspond totwo different line types.

18 and 19. During the hours experiencing overvoltages, RPC is mostly fullyexploited both for 1-phase and 3-phase OPF-BFS. This is due to the factthat RPC is economically preferred to APC, so that APC is only applied ifRPC is not sufficient to control the voltage. Fig. 3.3 and 3.4 nicely showthat RPC is used during the problematic hours 9 - 18 (3-phase) or 10 - 17(1-phase). APC is rolled out one hour later, when RPC is already fully ex-ploited but PV infeed still rises, and it is stopped again an hour before RPCbecause in that hour 18 (3-phase) or 17 (1-phase), RPC can make up for theovervoltages on its own. During the hours with little reactive power genera-tion, that is the “transition” hours, there is only RPC on phases a-b and c-aand none on phase b-c. Since voltages are also lower on phase b-c, it canbe assumed that this is an effect of phase interference and that, apparently,phase interference works mostly for the benefit of b-c. Comparing 1-phaseresults to 3-phase results, 1-phase OPF-BFS results in less RPC becausereactive power compensation starts later and ends earlier. This, however, issimply due to voltages being generally lower at hours 9 and 18 with 1-phasecomputation.

1-phase OPF-BFS resulted in excessive APC at node 12 during the after-noon hours while curtailing only a little percentage at nodes 16 and 18 andnone at all at node 19. With 3-phase OPF, these differences are levelledout a bit more: PV at nodes 12, 16, 18 and 19 are all curtailed to a rathersmall degree, and not in every phase uniformely. As has been observedpreviously, phase b-c shows a different pattern than the other two phases,resulting in slightly less curtailment at all nodes apart from node 19, wherethere is heavy curtailment in phase b-c, accounting for many of the phasedifferences observed hitherto. The fact that there is significantly more APCat node 12 in the 1-phase calculation than in the 3-phase system explainsthe lower voltages at node 12 observed for 1-phase before. As has also beenmentioned, APC generally takes place when RPC is fully exploited, and ispeaking at hours 13-14.


What seems to have no influence on the (over-)voltages is the BESS in-stalled at node 16. That is simply due to the fact that the battery has asmall capacity of only 2.7kWh and it reaches its maximal state of charge athour 8 already.

To make sure the differences in the results of 1-phase and 3-phase OPF-BFSdon’t base on algorithm disparities but on the different character of 1-phasesymmetrical components and 3-phase unbalanced systems, a test run withself-impedances in the impedance matrices only has been performed, just aswhat has been done for the BFS only in Fig. 2.4. The resulting patterns areplotted in Fig. 3.6. The results are completely identical.


5 10 15 20time [h]

5

10

15

node

0.94

0.96

0.98

1

1.02

(a) Voltage magnitudes (p.u.), 1-phase calculation according to [1]

5 10 15 20time [h]

5

10

15

node

0.94

0.96

0.98

1

1.02

(b) Voltage magnitudes (p.u.), 3-phase calculation without phase inter-ference

Figure 3.6: Voltage magnitudes at all the buses and hours, considering allthree phases but without mutual interference (no off-diagonal elements inthe impedance matrix), compared to the 1-phase reference of [1]

Chapter 4

Conclusion

This paper proposes a multi-period optimal power flow algorithm for unbal-anced distribution grids, using the backward-forward sweep technique. Itprovides an approach to efficiently use system controls in order to stabilizesystem operation and can thus be used in the operational planning of distri-bution networks. This in turn enables a more efficient use of infrastructurebecause operational control measures replace network reinforcement for con-gestion relaxation to a certain degree [7].The suggested algorithm has been applied to a Cigre benchmark system [6]and the most important results presented in the case study. The patternsand relationships of voltages, reactive power control and activer power cur-tailment over the whole system and a worst-case summer day are discussedand compared with the results obtained by a 1-phase symmetrical calcula-tion as has been proposed by [1]. It can be seen that the results show somenon-negligible differences due to phase-interference. Future work would needto take into consideration more constraints and elaborate on algorithm per-formance.

21

22 CHAPTER 4. CONCLUSION

Bibliography

[1] S. Karagiannopoulos, L. Roald, P. Aristidou, and G. Hug, “OperationalPlanning of Active Distribution Grids under Uncertainty,” 2017.

[2] J. H. Teng, “A direct approach for distribution system load flow solu-tions,” IEEE Transactions on Power Delivery, vol. 18, no. 3, pp. 882-887,2003.

[3] P. Kotsampopoulos, N. Hatziargyriou, B. Bletterie, and G. Lauss, “Re-view, analysis and recommendations on recent guidelines for the provi-sion of ancillary services by Distributed Generation,” Intelligent EnergySystems (IWIES), 2013 IEEE International Workshop on, pp. 185-190,2013.

[4] R. Tonkoski, L. A. C. Lopes, and T. H. M. El-Fouly, “Coordinated ac-tive power curtailment of grid connected PV inverters for overvoltageprevention,” IEEE Transactions on Sustainable Energy, vol. 2, no. 2, pp.139-147, 2011.

[5] G. Hug, “Power System Analysis,” lecture notes, ETH Zurich, 2016.

[6] K. Strunz, E. Abbasi, C. Abbey, C. Andrieau, F. Gao, T. Gaunt, A.Gole, N. Hatziargiou, and R. Iravani, “Benchmark Systems for NetworkIntegration of Renewable and Distributed Energy Resources,” CIGRE,Task Force C6.04, no. 273, pp. 4-6, 4 2014

[7] S. Karagiannopoulos, P. Aristidou, and G. Hug, “Hybrid approachfor planning and operating active distribution grids,” IET Generation,Transmission & Distribution, pp. 1-23, Feb 2017

23

stefanie aebip l power systems laboratory optimal … · 2017-10-31 · optimal power flow...

Documents