3136 ieee transactions on power systems, vol. 32, no. 4, …ieee-ac.org/docs/samson.pdf · 3136...

3136 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 32, NO. 4, JULY 2017

Voltage Control Strategies for Solid Oxide Fuel CellEnergy System Connected to Complex Power Grids

Using Dynamic State Estimation and STATCOMShenglong Yu, Student Member, IEEE, Tyrone Fernando, Senior Member, IEEE,

Tat Kei Chau, Student Member, IEEE, and Herbert Ho-Ching Iu, Senior Member, IEEE

Abstract—In this paper, a novel Dynamic State Estimation–current feedback with STATCOM control scheme is proposedfor the mitigation of voltage fluctuation of Solid Oxide Fuel Cell(SOFC) power station connected to the complex power grids dur-ing electrical faults. The proposed control scheme is compared totwo existing control strategies and shows its superiority in alleviat-ing voltage flickers and deviations as well as protecting the internalmembranes of the fuel cells. Since SOFC internal dynamic statesare able to closely reflect the transience and dynamic behavior ofSOFC, using them in controller designs can generate better reg-ulations of the state-related internal voltage of SOFC than othermethods. STATCOM is also utilized in this study to mitigate thevoltage oscillations induced by unavoidable voltage fluctuationsduring electrical faults. The power system with proposed controlstrategy is proven to be stable through linear analysis. The acqui-sition of the useful internal dynamic states is realized using un-scented Kalman filter algorithm based state estimator. The successof incorporating estimated states into the development of controlstrategies is conducive to the designs and implementations of newcontrol schemes for power systems and also the applications ofinterdisciplinary control theories.

Index Terms—Dynamic state estimation, fluctuation mitigation,SOFC, STATCOM, voltage control.

I. INTRODUCTION

FUEL CELLS (FCS) are considered a type of cleanenergy source due to their zero emission and high fuel

efficiency. Although finding more affordable catalysts andeconomical methodologies to produce huge quantities ofhydrogen still challenge researchers and manufacturers, theefforts of exploiting and perfecting fuel cell energy systemshave never ceased. Fuel cells have an extremely wide spectrumof domestic and industrial applications. Fig. 1 summarizes fuelcell applications[1], [2]. It can be clearly seen that low tem-perature Proton Exchange Membrane FC (PEMFC) and hightemperature Solid Oxide FC (SOFC) have the widest variety ofapplications. Recent research work has focused on SOFC andPEMFC mathematical modeling, dynamic state estimation and

Manuscript received April 27, 2016; revised July 28, 2016 and September 6,2016; accepted October 1, 2016. Date of publication October 4, 2016; date ofcurrent version June 16, 2017. Paper no. TPWRS-00655-2016.

The authors are with the School of Electrical, Electronic and Computer Engi-neering, University of Western Australia, Crawley, WA 6009, Australia (e-mail:[email protected]; [email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPWRS.2016.2615075

Fig. 1. Fuel cell applications.

control strategy developments. In [3], an application-orientedmathematical model of SOFC has been developed and verifiedin MATLAB SIMULINK, as well as with physical electriccircuits, and has been widely adopted in research papersthereafter. The study of dynamic behavior and internal states ofSOFC have been performed in [4], where SOFC power plant isconnected to a complex power grid and a decentralized dynamicstate estimator is designed and implemented to obtain theotherwise unaccessible dynamic states. Similarly, researchersof [5] have devised an adaptive state estimation methodologyto track the internal dynamic states of PEMFC.

On the control front, in [6] a simplified sliding mode controlscheme is proposed to maintain the internal gas pressures inPEMFC to dwell in a safe region so as to protect the preciousmembrane, and in [7] a novel quasi-2D tubular anode-supportedSOFC modeling approach is proposed for real-time controlimplementations. Optimal charging rate control strategy of plug-in electric vehicles (PEVs) is proposed in [8] to reduce the stressof power systems caused by poorly allocated multiple simulta-neous charging terminals. In [9], the authors proposed a controlscheme using the output DC current of the SOFC or the currentmagnitude of the AC load to modulate the hydrogen-flow rateof the SOFC connected to a multi-type power generation sys-tem. In [3], a constant fuel utilization control strategy has beenproposed and implemented to an infinite-bus connected SOFCin order to make best use of the fuel. An analysis of a grid-connected fuel cell during faulty situations is performed in [10],where different faults are implemented and analyzed. In [11],an SOFC-ultracapacitor hybrid system is investigated, wherethe fuel starvation problem is prevented by regulating the fuelcell currents. Nevertheless, there has been no reported work on

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YU et al.: VOLTAGE CONTROL STRATEGIES FOR SOLID OXIDE FUEL CELL ENERGY SYSTEM CONNECTED TO COMPLEX POWER GRIDS 3137

stability enhancement of SOFC power plant connected to com-plex power systems. With the growing popularity of SOFCpower plants and the tendency of using SOFC as stationarypower supply systems, it is necessary to investigate the dynamicbehavior of SOFC connected to power networks with realis-tic configurations and speculations. Furthermore, the existingstability enhancement strategies mainly make use of the DCcurrent of SOFC or fuel utilization rate. However, the protec-tion of membranes and voltage stability enhancement strategieshave not been investigated.

In this study, an SOFC power plant is connected to an IEEEstandard complex power system and its dynamical behavior dur-ing electrical faults is studied and presented. In order to mitigatethe voltage fluctuation and deviation and the damage that may becaused to the internal structure of fuel cells during faults, threecontrol methods are proposed and presented. The newly pro-posed DSE-current dual feedback strategy demonstrates bettercontrol performances than existing ones with less voltage os-cillations, a more favorable voltage level, and a faster settlingtime. The proposed DSE-current dual feedback scheme is alsocapable of regulating the pressures of reactant gases inside theSOFC channels, which produces a better protection for the inter-nal membranes of SOFC units. STATCOM is also incorporatedso as to further improve the voltage regulation performances.The control strategy for SOFC is to regulate the DC voltageoutput voltage in order to control the AC bus voltage, to whichit connects. Moreover, a STATCOM is provided to further miti-gate the fluctuations in AC bus voltage during electrical faults.SOFC control strategy and STATCOM are linked in a comple-mentary fashion to stabilize and maintain the AC bus voltageduring electrical faults. The proposed combined DSE-currentdual feedback and STATCOM control strategy issues the bestcontrol results among all control schemes. The dynamic stateestimator is designed using unscented Kalman filter algorithm[4]. The proposed control strategies theoretically achieve the re-alization of using electrical signals and power electronic devicesto regulate chemical energy systems. Linear analysis shows thatthe power system with proposed control strategy retains overallsystem stability.

STATCOM is a shunt device of Flexible AC TransmissionSystems (FACTS) family that uses electronic devices to con-trol power flow and improve transient stability on power grids.STATCOM is capable of regulating bus voltages by providingor absorbing reactive power to or from bus-bars [12]. In the fieldof power system analysis and stability enhancement, this devicehas been reported to be used to alleviate fluctuations in powersystems and thus improve power quality and stability in recentpublished academic papers [13], [14]. The former examines theapplication of STATCOM and battery energy storage to en-hance the transient stability of large-scale multi-machine powersystems, while the latter proposes an adaptive power oscillationdamping (POD) controller for STATCOM equipped with energystorage in order to increase the damping effect at frequencies ofinterests. The utilization of STATCOM in this paper is aimed tofurther enhance the stability of SOFC terminal voltage.

The rest of the paper is organized as follows. In Section II,the mathematical model of electrochemical and thermochemicalaspects of SOFC is concisely presented, which is followed by its

Fig. 2. Single solid oxide fuel cell schematic.

mathematical connection to a complex power system. Differentcontrol strategies are proposed in subsections of Section III,all of which are then implemented in the case study with theirsimulation results compared and discussed. The paper concludesin Section IV.

II. SOFC MATHEMATICAL MODEL

AND SYSTEM CONFIGURATION

A. Stand-Alone SOFC Mathematical ModelSOFC uses an oxide ion-conducting ceramic material as the

electrolyte. The most effective electrolytes are built on zirco-nia with a small percentage of yttria and the former materialbecomes an O2− conductor above 800 ◦C. The state-of-the-artSOFCs operate between 800 ◦C and 1100 ◦C. Internal reform-ing happens in SOFC, where the entry fuel (CH4) is ‘reformed’into hydrogen, which transfers to anode and participates in thechemical reaction. Mixed gas containing hydrogen and carbonmonoxide after the reforming process exits SOFC as part ofthe anode exhaust. High operating temperatures make preciousmetal electro-catalysts unnecessary in SOFC. For more detailsabout internal reforming of SOFC and additional information inregard to its electrochemical aspect, see [1]. The schematic of anSOFC unit is shown in Fig. 2, and its mathematical derivationsare briefly presented in Appendix A. Important dynamical equa-tions of an SOFC are shown as follows. With SOFC states beingxfc = [P ch

H2, P ch

H2 O , P chO2

, ηedl, T, Tast, Tannair , Tfuel, T

astair ]T , the state

space equations of SOFC can be formed with dynamic equa-tions (26), (27), (28), (38), (40), (41), (42), (43) and (44). Thisstate space equation is shown as follows,

xfc =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

P chH2

P chH2 O

P chO2

ηedl

T

Tast

T annair

Tfuel

T astair

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

− J RT2FVa

+2M v

a RT (P inH 2

−P chH 2

)Va Pa

− J RT4FVc

+2M v

c RT (P inO 2

−P chO 2

)Vc Pc

− J RT4FVc

+2M v

c RT (P inO 2

−P chO 2

)Vc Pc

1C eq

(J − ηedl

R act+R conc

)

Q rad+Qastouterconv −Q astinner

conv −Qairastflow

m astCastQ ann

convm ann

air CairQ fuel

convm fuelCfuelQ astinner

convm airCair

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

. (1)


Fig. 3. SOFC power plant connected to IEEE standard 39-bus test systemwith estimation and control schemes.

This state space equation set will be reformatted later to suit theimplementation of state estimation.

B. System Configuration

Fig. 3 illustrates the configuration of the test power systemin question. The upper half of the figure is a simplified SOFC–PEMFC hybrid system. The rationale behind this design is thatdirectly burning the highly concentrated hydrogen that comesout of the anode of SOFC has been considered a great waste ofenergy due to the high cost of acquiring purified hydrogen. Inthe hybrid system, hydrogen existing in SOFC anode exhaustis filtered and purified, which is then fed to the anode inlet ofPEMFC through a series of further reactions, as shown in Fig. 3.This establishment has been proven to able to minimize heat andexergy losses. For more information about the SOFC–PEMFChybrid system, see [1] and [15]. In this study, the inclusion ofPEMFC in the yellow region in Fig. 3 is to reduce fuel wastes,which only provides power for local customers and does notshare any power consumption from the main grid. A widelyused validated PEMFC model can be found in [16].

The output DC voltage of SOFC power station passes a DC-DC boost converter and a DC-AC inverter and connects to bus40 through a transformer. Bus 40 is then connected to bus 19of the IEEE standard 3-area, 10-generator, 39-bus hybrid powersystem, which is shown in the lower half of Fig. 3, whoseconfiguration is adopted from[17] where detailed mathematicalmodeling procedures are presented. The detailed mathematicalmodel of SOFC and its derivation can be found in [3]. Assum-ing individual fuel cells can be lumped together to form a fuelcell stack and ignoring manufacturing dissimilarities and agingeffects, the total fuel cells output voltage Vfc is linearly propor-tional to the output voltage of a single fuel cell Vcell [3], [10],

[18]. With given connections, SOFC’s mathematical model isre-addressed as follows. The dynamic state vector of SOFCis xfc = [P ch

H2, P ch

H2 O , P chO2

, ηedl, T, Tast, Tannair , Tfuel, T

astair ]T , input

vector from the power system is ufc = [V40 , θ40 , I40 , γ40 ]T ,where V40∠θ40 and I40∠γ40 are the voltage of bus 40 and thecurrent injected to bus 40, and the output is yfc = Vfc. The ter-minal voltage and current are affected not only by the intrinsiccharacteristics of SOFC power plant, but also by the dynamicalbehavior of the complex power system to which SOFC is con-nected. Considering the dynamical equations, the general formof SOFC can be written as [4],

xfc = ffc(xfc, ufc),

0 = gfc(xfc, ufc),

yfc = hfc(xfc, ufc), (2)

where ffc(·) and hfc(·) are the fuel cell state and output func-tions derived from Section II and gfc(·) represents the algebraicequations derived based on KVL that describe the connectionof the SOFC power plant to the bus bar. The 10 synchronousgenerators are in three separate areas, and in each area one gen-erator has a type I, IEEE ST1A AVR with PSS excitation systemand all other generators are equipped with excitation systems oftype II, IEEE DC1A AVR without PSS. Speed-governing sys-tems of the 10 generators are categorized into two main types:(i) mechanical-hydraulic and (ii) electro-hydraulic with/withoutsteam feedback. Hydro and steam turbines are also consideredin the generation units. All the implemented steam turbines aretandem-compound, double or single reheat type. For generatorand speed-governing equations, see reference [17]. The dynamicbehavior of synchronous generators connected to SOFC powerplant is studied in [4]. For the purpose of this study, this aspectis omitted. All the equations can be expressed mathematicallyin the following compact form [4],

˙xi = fi(xi , ui),

0 = gi(xi , ui),

yi = hi(xi , ui), (3)

for i ∈ {1, . . . , 10}, where state vector xi consists of dynamicstates of each generator, ui is the input vector, yi is the outputvector, fi(·) and hi(·) are state and output functions derivedfrom the mathematical models of each generator and gi(·) isa set of algebraic equations that relate each generator stator tothe bus voltage. The above equation compact form, togetherwith the following power balance equation describes the wholepower system [17],

PLl + jQLl + VlIlej (θl −γl ) −

40∑r=1

vlvrYlr ej (θl −θr −φl r ) = 0,

(4)

where Ylr∠φlr is the admittance of the transmission line con-necting bus l and r, PLl and QLl are active power and reactivepower consumed by the loads connected to busbar l at time t.The above discussion and the compact format facilitate the im-plementation of the UKF in order to acquire the internal dynamicstates. The detailed explanation, implementation and procedures


of using UKF filtering algorithm to obtain the internal dynamicstates of SOFC has been reported in [4]. While other possiblemethods can also be utilized to acquire the internal dynamicstates of SOFC, in this study, we make use of UKF algorithm tofulfill the task as it has been proven to be capable of providingaccurate state estimates in [4], [19].

III. SOFC CONTROL STRATEGIES AND SIMULATION RESULTS

In this section, four control strategies are presented for themitigation of the voltage fluctuations and deviations during elec-trical faults and the newly proposed DSE-based control togetherwith STATCOM demonstrates the best flicker mitigation perfor-mance and fuel cell membrane protection. The motives behindthe design of the control strategies are briefly presented as fol-lows. In order to regulate the terminal voltage to settle to a lowervalue, we need to consider the components that contribute to thesteady state voltage generated by a unit of the fuel cell. Basedon equation (32), one can easily obtain the equation below,

Vcell = Enst − ηact + ηconc − ηohm

= E0 +RT

4F ln

((P ch

H2)2P ch

O2

(P chH2 O )2

)− ηact − ηohm

−RT

4F ln

((P ch

H2)2(P eff

H2 O )2P chO2

(P effH2

)2(P chH2 O )2P eff

O2

)

= E0 − ηact − ηohm +RT

4F ln

((P eff

H2)2P eff

O2

(P chH2 O )2

), (5)

where standard potential Eo is a constant determined by theintrinsic characteristics of the fuel cells, and both activation andohmic polarization voltage losses are functions of both temper-ature and current. According to equations (29), (30), (31), alleffective partial pressures of gases are related to their partialpressures in the channels P ch

H2, P ch

O2, P ch

H2 O and the current den-sity J . According to (26), (27) and (28), partial pressures inthe channels are determined by the inlet gas molar flow ratesand gas pressures at anode and cathode. It now follows thatcontrolling the output voltage of a fuel cell (Vcell) is equivalentto controlling the input molar flow rate, electrical current, andinput pressures of anode and cathode.

A. Constant Fuel Utilization Control

Fuel utilization ratio RF U is defined as[2], [3],

RF U =Mv

consumedfuel

Mvinletfuel

, (6)

where Mvinletfuel denotes the molar follow rate of the inlet fuel.

Hence, for hydrogen fuel cells, the fuel utilization factor inequation (6) can be rewritten as,

RH2 =Mv

consumedH2

MvtotH2

=Ifc

2FMvtotH2

. (7)

Therefore, the molar flow rate of hydrogen at anode is calculatedas,

MvH2

=Ifc

2FRH2

. (8)

Fig. 4. Schematic representation of constant fuel utilization control.

Fig. 5. Schematic representation of current feedback control.

Figure 4 illustrates the operating principle of this control strat-egy. The constant fuel utilization control is performed by adap-tively controlling the inlet fuel flow rate to maintain a constantfuel utilization ratio. A 62% fuel utilization factor is adoptedin this study[1], the rest of which goes to the PEMFC systemfor reuse. When the electrical fault occurs, the current fluctuatesand thus the inlet flow rate of hydrogen at anode changes ac-cordingly. More details about this control method can be foundin [3]. This control scheme poses such shortcoming that as onlythe fuel utilization ratio is taken into consideration, the SOFCoutput voltage may still experience oscillations, and that theinternal partial pressures may change significantly so that themembrane may be damaged.

B. Current Feedback Control

Current change during faults can partially reflect the demandof entry fuel and oxidant, and thus we propose a current feedbackcontrol strategy to regulate the input molar flow rate of hydrogenand oxygen by minimizing the difference between the fuel cellcurrent Ifc and its nominal value Ifc.

Fig. 5 demonstrates the schematic of this control method,based on which the differential equations describing the inputmolar flow rate of hydrogen and oxygen are derived as follows,

dMvH2

dt=

1Ti1

(MvH2

(1 + Kp1(Ifc − Ifc)) − MvH2

),

dMvc

dt=

1Ti2

(Mvc (1 + Kp2(Ifc − Ifc)) − Mv

c ) , (9)

where Kp and Ti are gain and time constant, respectively andMv denotes nominal molar flow rate of specified gas speciesduring initial steady state. The anode entry gas molar flow rateMv

a is obtained as,

Mva = Mv

H2+ Mv

H2 O . (10)

It can be noticed that during initial steady state, dMvH2

/dt anddMv

c /dt in (9) and (9) equal zero and Ifc = Ifc, which renderMv

H2= Mv

H2and Mv

O2= Mv

O2. This control scheme has such

limitation that using electrical current as feedback signal may


Fig. 6. Schematic representation of estimated gas pressures and current feed-back control.

not be an adequate method to control the terms in equation (5)that relate to internal and effective partial pressures.

C. DSE–Current Dual Feedback Control

Internal partial pressures of gases in SOFC can reflect theperformances of the fuel cell more precisely than merely ob-serving the fuel usage ratio or current. For the purpose of thisstudy, dynamical changes of internal partial pressures are usedto construct the control signals that regulate the entry molarflow rates of hydrogen and air. The acquisition of the internaldynamic states is realized in a decentralized manner with theutilization of unscented Kalman filter algorithm and phasor mea-surement units. Estimated internal gas partial pressures P ch

H2and

P chO2

, together with their nominal values during normal workingcondition are used to construct the control signal [6]. As bothinternal partial pressures and electrical current play importantroles in regulating the output voltage of SOFC, current feedbackis also used to control the pressures of anode and cathode inletgases. Fig. 6 shows the schematic of this control strategy. Thefollowing differential equations are used to obtain their inletmolar flow rates,

dMvH2

dt=

1Ti3

(Mv

H2(1 + Kp3(Pch

H2− P ch

H2)) − Mv

H2

),

dMvc

dt=

1Ti4

(Mv

c (1 + Kp4(PchO2

− P chO2

)) − Mvc

), (11)

where Pch denotes nominal partial pressure of the specified gasduring normal operation condition. Equation (10) for calculatingmolar flow rate of gases at anode still holds. A set of propor-tional controllers are also incorporated to control the input gaspressures at anode and cathode with the following equations,

Pa = Pa (1 + Kp5(Ifc − Ifc)) , (12)

Pc = Pc (1 + Kp6(Ifc − Ifc)) . (13)

Maintaining the internal partial pressures of reactant gases hasprofound significance in not only alleviating the fluctuations ofthe output voltage and diminishing the voltage gap before andafter fault, but also in protecting the precious membranes of fuelcells [6].

Fig. 7. (a) STATCOM schematic (b) VSC equivalent circuit.

Fig. 8. (a) STATCOM DC-bus controller (b) STATCOM AC-bus controller.

D. STATCOM Control

With the aforementioned dual feedback controller, there maystill be a number of unavoidable voltage fluctuations and voltagedrops during electrical faults and thus STATCOM is used inthis study to resolve this issue. The mathematical model ofSTATCOM in [20] is adopted in this study and briefly discussedas follows. The following power balance equation can be derivedfor the DC and AC parts of STATCOM,

P statac = P stat

dc + P statloss. (14)

The configuration of STATCOM model, as shown in Fig. 7consists of a two-level voltage source converter (VSC), whichis physically built with a two-level converter using an arrayof PMW-driven self-commutating power electronic switches. Itcan be modeled as a load tap changing (LTC) transformer withits primary side connected to a small-rating capacitor bank andthe secondary winding connected to the AC terminal through aseries impedance [21]. As shown in Fig. 7(b), the model alsoincludes a conductance Gstat

sw to account for switching losses onthe DC side and an equivalent shunt susceptance Bstat

eq on the ACside, capable of providing and absorbing reactive power. Giventhe schematics for STATCOM and the VSC inside it, it has be-come clear that modulation index mstat

a and phase angle αstat aretwo crucial parameters that control the behavior of STATCOM,whose acquisition can be found in the block diagram in Fig. 8.From the block diagram, it is clear that controlling phase angleαstat is equivalent to controlling susceptance Bstat

eq . The outputmstat

a and αstat become the input of STATCOM to perform thevoltage regulation, as shown in Fig. 7(a).

Fig. 8 shows the control blocks inside the STATCOM em-ployed in this study, subscripts ‘ref’, ‘max’, ‘min’, ‘gen’,‘reg’ denote the reference value, maximum value, minimumvalue, generated value and regulated value of specific variables,respectively, superscript ‘init’ denotes the initial value of equiv-alent susceptance, K and T ′ with different subscripts representgains and time constants, and s is the Laplace variable. The


block ‘algebraic relations’ refer to (16). Generally speaking, theDC side generates the phase angle αstat by minimizing the dif-ference of DC voltage V stat

dc and its reference value, while themodulation index mstat

a is generated at the AC end with the gapof bus voltage Vk and Vkr e f

being zeroed (k = 40 in this partic-ular study). For more details about the STATCOM model andcontroller, refer to [20]. The STATCOM control block diagramcan be translated into the following differential equations [20]and [22],

d

dt

⎡⎢⎢⎣

Bstateq

Qstatreg

V statreg

m′a

⎤⎥⎥⎦ =

⎡⎢⎢⎣

T ′−1dc

(Kdc(V stat

dcref− V stat

dc ) − Bstateq

)T ′

ac−1 (Kac(Vk ref − Vk ) − Qstat

reg

)Kq (Qstat

reg − Qstatgen)

Kv (V statreg − V stat

gen )

⎤⎥⎥⎦ .

(15)

As the STATCOM power losses come from both seriesimpedance Zstat

s and switching loss conductance Gstatsw , with

equation (14) being valid, the following equations hold,

P statac + m′

aVkV statdc

(Gstat

s cos (θk − αstat) + Bstats sin (θk − αstat)

)

− V 2k Gstat

s = 0,

Qstatac + m′

aVkV statdc

(Gstat

s sin (θk − αstat) − Bstats cos (θk − αstat)

)

+ V 2k Bstat

s = 0,

P statdc + m′

aVkV statdc

(Gstat

s cos (αstat − θk ) + Bstats sin (αstat − θk )

)

−m′a(Gstat

s + Gstatsw )(V stat

dc )2 = 0,

Qstatdc + m′

aVkV statdc

(Gstat

s sin(αstat − θk ) − Bstats cos (αstat − θk )

)

+m′a(Bstat

s + Bstateq )(V stat

dc )2 = 0,

(16)

where the conductance Gstats and susceptance Bstat

s are obtainedby Gstat

s + jBstats = 1/Zstat

s . Differential-algebraic (15) and (16)are utilized for transient stability investigation in this study.STATCOM is used here to mitigate the residual voltage oscilla-tions and regulate the voltage value by providing or absorbingproper amounts of reactive power to or from the bus bar. In thisstudy, STATCOM is utilized with the proposed DSE-currentfeedback control scheme to alleviate the voltage oscillationsand deviations during electrical faults.

E. Simulation Results

The simulation is conducted in MATLAB 2014b coding en-vironment on a desktop computer with Intel Core i7-4790,3.6 GHz CPU, 64-bit Windows7 operating system. The entirepower system is simulated with MATLAB codes and simula-tion results are observed, acquired and analyzed using MAT-LAB built-in algebraic-differential-equation solvers in contin-uous time. The test system configuration is shown in Fig. 3.The simulation lasts for 20 seconds and the system is in steadystate in the beginning. When t = 1.2 s, an electrical fault occursand the transmission line between bus 19 and bus 20 is discon-nected. Bus 19 is connected to bus 40, to which SOFC powerstation is connected, and thus any sudden change that occurs

Fig. 9. Active power injected to bus 40 during the simulation.

TABLE IMAJOR PARAMETERS

(1) Constant fuel utilization rate controlRF U 10

(2) Current feedback controlTi 1 0.001 Ti 2 0.001 Kp 1 0.0358 Kp 2 0.0358

(3) DSE-current feedback controlTi 3 0.01 Ti 4 0.01 Kp 3 0.01 Kp 4 0.05Kp 5 0.04 Kp 6 0.035

(4) ∗STATCOM (used with DSE-current feedback control)T ′

d c 0.05 T ′a c 0.75 Kd c 40 Ka c 10

Kv 10 Kq 0.01

∗STATCOM parameters are adopted and modified from [20].

Fig. 10. Partial pressure of hydrogen in anode channel.

on bus 19 will affect the performances of SOFC. The choice oftransmission line is aimed at best demonstrating the proposedcontrol strategies during faults. The fault remains for the restof the simulation. The aforementioned estimation and controlschemes are implemented.

Fig. 9 shows the power variations during the simulation underno control situation. This figure is only to verify that less poweris required during the fault and is within the capacity of SOFCpower station. Table I demonstrates the parameters used in thethree proposed control strategies. The rest of the parameters arethermodynamic constants and coefficients that can be found in[3], [23].

Figures 10 and 11 demonstrate the variations in hydrogen andoxygen partial pressures for the proposed constant fuel utiliza-tion (CFU) feedback (FB) control, current feedback control andcombined DSE-current dual FB control. With their zoomed-incurves, one can observe their transience with different controlstrategies when the fault happens. As mentioned before, theDSE-current FB control strategy is aimed to maintain a small


Fig. 11. Partial pressure of oxygen in cathode channel.

Fig. 12. Fuel cell current.

Fig. 13. Current injected to bus 40.

fluctuation in the internal partial pressures of hydrogen andoxygen and the figures have shown significantly better results inthis aspect than other control schemes. To this end, the proposedDSE-current dual feedback control can provide the best protec-tion for the membrane. We can also notice that the current FBcontrol has issued the largest disturbance in the internal partialpressures, which may lead to damages of the physical structureinside fuel cells. Moreover, the CFU-FB control does not in-fluence the partial pressure of oxygen but it is able to regulatethe hydrogen partial pressure to a reasonable value. Figs. 12and 13 show the regulations of fuel cell current and the currentinjected into bus 40 for the three control schemes and the newlyproposed DES-current feedback control with STATCOM.

With the relationship between the electric double layer (EDL)voltage loss and the fuel cell current, Fig. 14 shows the EDLvoltage drop for 4 control strategies. It can be noticed that cur-rent FB control has issued the lowest voltage drop in this type ofpolarization. Fig. 15 demonstrates the resultant terminal voltageof different controllers and it is obvious that the DSE-currentdual FB controller produces the best result than other fuel cellinput regulation control methods with a closest voltage level tothe bus voltage under normal circumstances and fewest oscil-

Fig. 14. Electric double layer voltage.

Fig. 15. Voltage of bus 40.

Fig. 16. (a) Generated reacitve power. (b) DC side voltage. (c) Modulationindex. (d) Phase angle.

lations. However, the utilization of STATCOM issues an evenmore favorable voltage regulation result where STATCOM iscapable of bringing the voltage during faulty operating condi-tion almost to its regular level and alleviating the fluctuations inthe DSE-current dual feedback control strategy.

On the STATCOM front, Fig. 16(a)∼(d) show the generatedreactive Qstat

gen, capacitor voltage V statdc , the modulation index mstat

a

and the phase angle φ during the simulation. Together with thevoltage variations and the control schematics, one can tell whenthe terminal voltage starts deviating, the modulation index andDC side voltage start changing, which lead to the variations ingenerated reactive power and the phase angle. Overall speaking,STATCOM manages to provide or absorb reactive power to orfrom the bus bar to try maintaining the bus voltage and DC sidevoltage at their nominal values.

It is noteworthy that the combined control strategy proposedin this study makes use of local current and voltage measure-ments to generate estimated internal dynamic states and alsoprovide feedback signals. That is to say, the proposed method


operates in a decentralized manner, which makes the novelcontrol strategy able to regulate SOFC power plants in anyreasonable power network connections within the power capac-ity. The execution times for no-control, constant-fuel-utilizationcontrol, current-FB control and DSE-current dual FB controlare respectively approximately 5.14 s, 5.18, 6.22 s and 11.3 s.These execution times may vary with different setting in MAT-LAB solvers, computer configurations and sampling times forUKF-based dynamic state estimator. The last factor has beenreported in detail in [4].

F. Stability Assessment for Controller-Incorporated System

In order to assess the stability of the overall power system withcontrol strategies, linear analysis is required. Due to the com-plexity of the power system in question, linearization processis only briefly discussed as follows. The overall STATCOM-integrated IEEE standard 39-bus, 10-generator power systemcan be written in the following compact form [17],

d

dtX = F (X,U),

0 = G(X,U), (17)

X =

⎡⎣

xgen

xctrl

xstat

⎤⎦ , U =

⎡⎣

ugen

uctrl

ustat

⎤⎦ , (18)

where F (·) and G(·) are respectively the state differential andalgebraic functions of the system model, X is the system dy-namic state vector consisting of generator state vector xgen (in-cluding fuel cell state vector), control dynamic vector xctrl, andSTATCOM state vector xstat and U is the system input vector,comprised of generator input vector ugen, control input vectoructrl and STATCOM input vector ustat. The following equationsdemonstrate the elements in state and input vectors for the afore-mentioned STATCOM-integrated power system,

xgen = [xgen1, xgen2

, . . . , xgen1 0, xfc]T , (19)

xstat = [Bstateq , Qstat

reg , V statreg ,m′

a ]T , (20)

and xctrl can be obtained based on different control strategiesmentioned above. Detailed description of generator states xgen

can be found in [17]. The following equations illustrate thestructure of the input vector,

ugen = [ugen1, ugen2

, · · · , ugen1 0, ufc]T , (21)

ustat = [V statref , V stat

dc ref]T , (22)

and again uctrl varies according to different control strategiesand is constituted by the reference values, for instance, Ifc.Reference [24] provides detailed description of generator inputvector ugen. As for the fuel cell input vector,

ufc = [MvH2

,Mvc ,Pa ,Pc ]T . (23)

See [17] and [24] for specifics.For small-signal stability analysis of the state space model,

the following linearized system equation can be obtained,

ΔX = AΔX + BΔU, (24)

Fig. 17. System eigenvalue plot with DSE-current-FB-STATCOM method.

where A and B are coefficients of the linearized system. Fordetailed steps and derivations of linearizing nonlinear powersystems, refer to [24].

After arduous mathematical procedures, a 152 × 152 systemmatrix A is obtained for the SOFC-connected power systemwith DSE-current-FB-STATCOM control method, equippedwith control parameters shown in Table I. The system eigen-value plot on the complex plane is shown in Fig. 17, where wecan easily see that all the eigenvalues are on the open left halfplane, hence system stability proven. Note that only a sub-partof the complex plane is shown for easy observation, and thereare no positive-real-part eigenvalues found in this simulationstudy.

IV. CONCLUSION

In this paper, a dynamic state estimates-current dual feedbackcontrol strategy is proposed to mitigate the voltage oscillationsand deviations during electrical faults, which uses electrical con-trol signals to perform chemical control. The DSE-current dualfeedback control has demonstrated its superiority in controllingthe output voltage during electrical faults as well as its capabilityof protecting the fuel cell membranes by maintaining the inter-nal partial pressures of reactant gases. This method, however,may still not be adequate to best alleviate the fluctuations inAC bus voltages that inherently exist during faults. Therefore, apower electronics device STATCOM is implemented to furtherreduce the voltage oscillations and deviations, which togetherwith the DSE-current feedback controller has proven to be ableto generate the best AC bus voltage regulation result. The overallpower system with proposed control strategy retains its stabil-ity, which is proven through system linear analysis. Future workmay involve further investigations of the universality of suchelectrical-chemical control methodologies by applying them todifferent types of power sources and energy systems.

APPENDIX ADERIVATION OF SOFC STATE EQUATIONS

The equations relating to stand-alone SOFC presented inSection II are briefly derived as follows. Assuming ideal gasesparticipate in the chemical reaction, the following equation canexpress the Nernst potential in an SOFC unit [2],

Enst = E0 +RT

4F ln

((P ch

H2)2P ch

O2

(P chH2 O )2

), (25)


where E0 is the internal potential under standard temperatureand pressure conditions [3], R and F are the ideal gas constantand Faraday’s constant respectively, T is the operating tempera-ture and P ch

H2, P ch

O2, P ch

H2 O denote the partial pressure of gases inthe channels. Note that temperature T has a significant impacton fuel cell operations. Its acquisition will be discussed laterin this section. Using Maxwell-Stefan diffusion equation with aseries of mathematical manipulations [23], the differential equa-tions of partial pressures in channels P ch

H2, P ch

H2 O and P chO2

, areshown as follows [25],

dP chH2

dt= − JRT

2FVa+

2Mva RT (P in

H2− P ch

H2)

VaPa, (26)

dP chH2 O

dt=

JRT

2FVa+

2Mva RT (P in

H2 O − P chH2 O )

VaPa, (27)

dP chO2

dt= − JRT

4FVc+

2Mvc RT (P in

O2− P ch

O2)

VcPc, (28)

where J is the current density flowing through an SOFC unit, Va

and Vc denote the volumes of anode and cathode channels, re-spectively and Mv

a and Mvc denote the molar flow rates at anode

and cathode. Then the reversible potential Enst can be acquiredbased on (25). The effective partial pressures of hydrogen andwater vapor at the actual reaction site can be calculated as [3],[4],

P effH2

= P chH2

+dP ch

H2

dxDar = P ch

H2− JRTDar

2FDH2 ,H2 O, (29)

P effH2 O = P ch

H2 O +dP ch

H2 O

dxDar = P ch

H2 O +JRTDar

2FDH2 O,H2

, (30)

P effO2

= P chO2

exp

(RTJDcr

4FP chc DO2 ,N2

)

+ P chc

(1 − exp

(RTJDcr

4FP chc DO2 ,N2

)), (31)

where Dar and Dcr are the distances from anode and cathodesurface to the reaction site respectively.

Due to several types of irreversible voltage losses insideSOFC, the actual voltage of fuel cell becomes lower than theNernst potential [2]. The following equation describes the out-put voltage of an SOFC unit (Vcell),

Vcell = Enst − ηact − ηohm − ηconc, (32)

where ηact, ηohm and ηconc denote voltage drops of activationpolarization, ohmic polarization and concentration polarizationrespectively, the first two of which are functions of both currentdensity and SOFC operating temperature, while the voltage dropfrom concentration polarization is a function of partial pressuresof gases in the channels P ch

H2, P ch

H2 O , P chO2

and at the reaction siteP eff

H2, P eff

H2 O , P effO2

. Butler-Volmer equation is used to express theactivation polarization as follows,

J = J0

(exp

(βne

Fηact

RT

)− exp

(−(1 − β)ne

Fηact

RT

)),

(33)

where J0 is the exchange current density, ne is the number ofelectrons and β is ion transfer coefficient. Under high-activationpolarization, Tafel equation can be derived for the calculation ofactivation polarization voltage loss, which is shown as follows,

ηact =RT

neβF ln(J) − RT

neβF ln(J0). (34)

It can be seen that activation polarization voltage is a functionof fuel cell internal temperature and can be rewritten in thefollowing form,

ηact = ηact0 + ηact1, (35)

where ηact0 is a function of internal temperature, while ηact1

depends on both temperature and current density. Voltage dropdue to ohmic polarization can be simply expressed with

ηohm = JReq, (36)

where Req is the equivalent ionic resistance of fuel cell, a func-tion of the operating temperature. Concentration polarizationhappens at both cathode and anode, and can be expressed usingfollowing equations,

ηconc = ηanconc + ηca

conc

= −RT

2F ln

(P ch

H2 O

P chH2

· P effH2

P effH2 O

)− RT

4F ln

(P eff

O2

P chO2

),

=RT

4F ln

⎛⎝(

P chH2

P effH2

· P effH2 O

P chH2 O

)2

·(

P chO2

P effO2

)⎞⎠ . (37)

With the simplified model of Electrical Double Layer (EDL)charging effect, the following equation holds[1], [3],

dηedl

dt=

1Ceq

(J − ηedl

Ract + Rconc

), (38)

where Ract and Rconc are the equivalent resistances of activationand concentration polarizations. Then the expression of fuel celloutput voltage can be modified as [3],

Vcell = Enst − ηedl − ηact0 − ηohm. (39)

With (34)–(37), the output voltage of a fuel cell unit in equation(39) is obtainable given the operating temperature of SOFC.

Radiation, convection and mass flow are the three main waysheat transfer occurs in an SOFC unit. For detailed explanationand derivations of equations, see [2], [3], [23]. Temperature-related differential equations are listed as follows,

dT

dt=

Qgen − Qout

Ccellmcell, (40)

dTast

dt=

Qrad + Qastouterconv − Qastinner

conv − Qairastflow

mastCast, (41)

dT annair

dt=

Qannconv

mannair Cair

, (42)

dTfuel

dt=

Qfuelconv

mfuelCfuel, (43)

dT astair

dt=

Qastinnerconv

mairCair, (44)


where Q with subscripts ‘gen’, ‘out’, ‘rad’, ‘conv’ and ‘flow’stand for generated, output, radiative, convective and flowingheat, superscripts ‘ann’ represents annulus, and C and m de-note the heat capacity and mass of specified gas or componentof SOFC. For more explanations and derivations of thermody-namic aspects of SOFC, see [1], [3] and [4].

REFERENCES

[1] J. Larminie, A. Dicks, and M. S. McDonald, Fuel Cell Systems Explained,vol. 2. New York, NY, USA: Wiley, 2003.

[2] A. J. Appleby, Fuel Cell Handbook, 7th ed. EG&G Tech. ServicesInc., U.S. Dept. Energy Office Fossil Energy, Washington, DC, USA,Nov. 2004.

[3] C. Wang and H. M. Nehrir, “A physically based dynamic model for solidoxide fuel cells,” IEEE Trans. Energy Convers., vol. 22, no. 4, pp. 887–897,Dec. 2007.

[4] S. Yu, T. Fernando, and H. H.-C. Iu, “Dynamic behavior study and stateestimator design for solid oxide fuel cells in hybrid power systems,” IEEETrans. Power Syst., to be published.

[5] R. Vepa, “Adaptive state estimation of a PEM fuel cell,” IEEE Trans.Energy Convers., vol. 27, no. 2, pp. 457–467, Jun. 2012.

[6] G. Park and Z. Gajic, “A simple sliding mode controller of a fifth-ordernonlinear PEM fuel cell model,” IEEE Trans. Energy Convers., vol. 29,no. 1, pp. 65–71, Mar. 2014.

[7] F. Gao, M. G. Simoes, B. Blunier, and A. Miraoui, “Development of aquasi 2-D modeling of tubular solid-oxide fuel cell for real-time control,”IEEE Trans. Energy Convers., vol. 29, no. 1, pp. 9–19, Mar. 2014.

[8] Y. Xu, “Optimal distributed charging rate control of plug-in electric vehi-cles for demand management,” IEEE Trans. Power Syst., vol. 30, no. 3,pp. 1536–1545, May 2015.

[9] L. Wang and D.-J. Lee, “Load-tracking performance of an autonomousSOFC-based hybrid power generation/energy storage system,” IEEETrans. Energy Convers., vol. 25, no. 1, pp. 128–139, Mar. 2010.

[10] E. M. Stewart, R. Tumilty, J. Fletcher, A. Lutz, G. Ault, and J. McDonald,“Analysis of a distributed grid-connected fuel cell during fault conditions,”IEEE Trans. Power Syst., vol. 25, no. 1, pp. 497–505, Feb. 2010.

[11] T. Allag and T. Das, “Robust control of solid oxide fuel cell ultracapac-itor hybrid system,” IEEE Trans. Control Syst. Technol., vol. 20, no. 1,pp. 1–10, Feb. 2012.

[12] N. G. Hingorani and L. Gyugyi, Understanding FACTS. Piscataway, NJ,USA: IEEE Press, 2000.

[13] A. Kanchanaharuthai, V. Chankong, and K. A. Loparo, “Transient sta-bility and voltage regulation in multimachine power systems vis-a-visSTATCOM and battery energy storage,” IEEE Trans. Power Syst., vol. 30,no. 5, pp. 2404–2416, Sep. 2015.

[14] M. Beza and M. Bongiorno, “An adaptive power oscillation dampingcontroller by STATCOM with energy storage,” IEEE Trans. Power Syst.,vol. 30, no. 1, pp. 484–493, Jan. 2015.

[15] A. Rabbani and M. Rokni, “Modeling and analysis of transport pro-cesses and efficiency of combined SOFC and PEMFC systems,” Energies,vol. 7, no. 9, pp. 5502–5522, 2014.

[16] C. Wang, M. H. Nehrir, and S. R. Shaw, “Dynamic models and modelvalidation for PEM fuel cells using electrical circuits,” IEEE Trans. EnergyConvers., vol. 20, no. 2, pp. 442–451, Jul. 2005.

[17] T. Fernando, K. Emami, S. Yu, H. H.-C. Iu, and K. P. Wong, “Anovel quasi-decentralized functional observer approach to LFC of in-terconnected power systems,” IEEE Trans. Power Syst., vol. 31, no. 4,pp. 3139–3151, Jul. 2016.

[18] C. Wang, M. Nehrir, and H. Gao, “Control of PEM fuel cell dis-tributed generation systems,” IEEE Trans. Energy Convers., vol. 21, no. 2,pp. 586–595, Jun. 2006.

[19] A. K. Singh and B. C. Pal, “Decentralized dynamic state estimation inpower systems using unscented transformation,” IEEE Trans. Power Syst.,vol. 29, no. 2, pp. 794–804, Mar. 2014.

[20] L. M. Castro, E. Acha, and C. R. Fuerte-Esquivel, “A novel STATCOMmodel for dynamic power system simulations,” IEEE Trans. Power Syst.,vol. 28, no. 3, pp. 3145–3154, Aug. 2013.

[21] C. A. Canizares, “Power flow and transient stability models of FACTScontrollers for voltage and angle stability studies,” in Proc. IEEE PowerEng. Soc. Winter Meeting, 2000, vol. 2, pp. 1447–1454.

[22] E. Acha and B. Kazemtabrizi, “A new STATCOM model for power flowsusing the Newton–Raphson method,” IEEE Trans. Power Syst., vol. 28,no. 3, pp. 2455–2465, Aug. 2013.

[23] M. Planck, Treatise on Thermodynamics. North Chelmsford, MA, USA:Courier Corp., 2013.

[24] P. W. Sauer, Power System Dynamics and Stability. Englewood Cliffs, NJ,USA: Prentice Hall, 1998.

[25] G. N. Hatsopoulos and J. H. Keenan, Principles of General Thermody-namics, vol. 398. New York, NY, USA: Wiley, 1965.

Shenglong Yu (S’15) received the Bachelor’s de-gree (Hons.) in measurement and control technologyand instrumentation from China University of Geo-sciences, Beijing, China, in 2011 and the Master’sdegree in electrical and electronic engineering withDistinction from the University of Western Australia,Crawley, WA, Australia, in 2014, where he is cur-rently working toward the Ph.D. degree. His researchinterests are in renewable energy integration, powersystem analysis and control, smart grids, microgirds,load and renewable power forecasting, and dynamic

state estimation algorithms.

Tyrone Fernando (M’95–SM’05) received theB.Eng. (Hons.) degree and the Doctor of Philosophydegree from the University of Melbourne, Parkville,VIC, Australia, in 1990 and 1996, respectively. In1996, he joined the School of Electrical Electronicand Computer Engineering, University of WesternAustralia, where he is currently a Professor. His re-search interests include power systems, renewableenergy, functional observers, state estimation, andbiomedical engineering.

Dr. Fernando has served as an Associate Editorfor the IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE

and also as a Guest Editor for the Journal of Optimal Control Applications andMethods. He is currently an Associate Editor for the IEEE TRANSACTIONS ON

CIRCUITS AND SYSTEMS–II and IEEE ACCESS.

Tat Kei Chau (S’16) received the B.Eng. (Hons.)degree in electronic and communication engineer-ing with first-class honors from the City Univer-sity of Hong Kong, Hong Kong, in 2010, and theMaster’s degree in electrical and electronic engineer-ing with Distinction from the University of WesternAustralia, Crawley, WA, Australia, in 2014, where heis currently working toward the Ph.D. degree. His re-search interests are in power electronics, power sys-tem analysis and control, microgrids, smart grids,renewable energy integration, load and power gener-

ation forecasting, and dynamic state estimation.

Herbert Ho-Ching Iu (S’98–M’00–SM’06) re-ceived the B.Eng. (Hons.) degree in electrical andelectronic engineering from the University of HongKong, Hong Kong, in 1997. He received the Ph.D.degree from the Hong Kong Polytechnic University,Hong Kong, in 2000. In 2002, he joined the Schoolof Electrical, Electronic and Computer Engineering,University of Western Australia where he is currentlya Professor. His research interests include power elec-tronics, renewable energy, nonlinear dynamics, cur-rent sensing techniques, and memristive systems.

Dr. Iu currently serves as a Guest Editor for the IEEE TRANSACTIONS ON

INDUSTRIAL ELECTRONICS, leading Guest Editor in Chief of the IEEE TRANSAC-TIONS ON EMERGING AND SELECTED TOPICS IN CIRCUIT AND SYSTEMS SpecialIssue on “Complex Networks for Modern Smart Grid Applications” and severalother journals including IET Power Electronics.

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