stability and accuracy analysis of power hardware-in-the

Extended Summary 本文は pp.902–912

Stability and Accuracy Analysis of Power Hardware-in-the-loopSimulation of Inductor Coupled Systems

Miao Hong Student Member (Osaka University)

Yushi Miura Member (Osaka University)

Toshifumi Ise Member (Osaka University)

Yuki Sato Non-member (Osaka Gas CO., LTD)

Toshinari Momose Non-member (Osaka Gas CO., LTD)

Christian Dufour Non-member (Opal-RT Technologies Inc.)

Keywords: power hardware-in-the-loop simulation, inductor coupled systems, gas engine cogeneration system, matrix converter

Previous Hardware-in-the-loop (HIL) simulations developed inpower system are limited to the design of controller. Presently, HILsimulation is extended to test other power devices such as generator,power converter, etc. and it is so called power hardware-in-the-loop(PHIL) simulation. This paper focuses on the stability issue of in-ductor coupled PHIL simulation shown as Fig. 1. Analysis resultsshow that:

( 1 ) To keep the stability of the inductor coupled PHIL simula-tion, the real inductor (L2) must be larger than the simulatedinductor (L1).

( 2 ) The combined relationship of the time delay and impe-dence in the PHIL simulation also affecys the stability area

Fig. 1. Simple example of a PHIL simulation of induc-tor coupled system

Fig. 2. a PHIL simulation of inductor coupled system

of PHIL simulation.In order to verify above conclusions, experiment as Fig. 2 is car-

ried out and results are shown in Fig. 3, where Ksmax means the max-imum value of the K in Fig. 2 which can insure the stability.

In order to improve the stability of PHIL simulation in Fig. 2, amethod is proposed: the inductor in the simulated part decreasedfrom 6 mH to 4 mH and the real inductor increased from 4 mH to6 mH. Analysis results show that this method not only improves sta-bility but also improves accuracy of PHIL simulation.

To verify the proposed method to improve stability, a PHIL sim-ulation of a gas engine cogeneration system with a matrix converter(shown as Fig. 4) is developed. The PHIL simulation achieves sta-ble with the proposed method and results are verified by off-linesimulation of original GECS system.

Fig. 3. Relationship of L2/L1 and the value of Ksmax ob-tained by experiment

Fig. 4. Original PHIL simulation of a GECS with a MC

– 8–

Paper

Stability and Accuracy Analysis of Power Hardware-in-the-loopSimulation of Inductor Coupled Systems

Miao Hong∗ Student Member

Yushi Miura∗ Member

Toshifumi Ise∗ Member

Yuki Sato∗∗ Non-member

Toshinari Momose∗∗ Non-member

Christian Dufour∗∗∗ Non-member

This paper focuses on the stability issue of power hardware-in-the-loop (PHIL) simulation of inductor coupled sys-tems. Main factors which influence the stability of this type system are analyzed and verified through experiments. Amethod to resolve the instability problem of the PHIL simulation without decreasing the simulation accuracy is alsoproposed. Moreover, a PHIL simulation of a gas engine cogeneration system with a matrix converter is introduced andthe application of proposed method to improve stability is demonstrated.

Keywords: power hardware-in-the-loop simulation, inductor coupled systems, gas engine cogeneration system, matrix converter

1. Introduction

Due to the great progress of computer technology,hardware-in-the-loop (HIL) simulation is widely used inpower system fields (1) (2). In comparison to conventional off-line simulation, HIL simulation provides advantages such asmore reliability, lower cost, design efficiency, etc. Neverthe-less, most HIL simulations in power system are limited tothe design of controllers. Hardware under test (HUT) in thistype HIL simulation is controller and it is so called controllerhardware-in-the-loop (CHIL) simulation. In CHIL simula-tion, signals which are exchanged between the simulator andHUT are low power level (+/−10 v, mA) and can be trans-ferred easily by A/D and D/A converters. Presently, the con-cept of HIL simulation is extended to test power componentsother than controllers, for example, generator, power con-verter, etc. In these cases, transferred signals are high powerlevel (kV, kA) and HUTs absorb/sink power, which demandsthat real power be exchanged between the simulation part ofHIL system and actual HUTs. Therefore, proper power in-terfaces are necessary. This is so called power HIL (PHIL)simulation. Fig. 1 illustrates different configurations of CHILand PHIL simulation. Obviously, PHIL simulation bringsnew challenges and extends the application of HIL simula-tion. However, there are two obstacles which severely limitits development: calculation accuracy and stability issue.

Calculation accuracy is the primary consideration for all

∗ Division of Electric, Electronic and Information Engineering, GraduateSchool of Engineering, Osaka University2-1, Yamada-oka, Suita 565-0871

∗∗ Energy Technology Labaratories, Osaka Gas CO., LTD6-19-9, Torishima-ku, Osaka 554-0051

∗∗∗ Opal-RT Technologies Inc.1751 rue Richardson, Suite 2525, Montreal (Quebec) Canada, H3K1G6

Fig. 1. Configurations of controller HIL and Power HILsimulation

HIL simulation, otherwise, the simulation results may losemeaning. According to Ref. (3), the accuracy of PHIL sim-ulation is severely affected by the time delay which mainlyarises from the computation time of the simulation and thetime caused by A/D, D/A converters. However, practicaltime step size achieved in PHIL simulation rarely goes be-neath 50 μs even with GHz-speed processor because of rea-sons such as I/O delay, communication latencies and solvingmethods (2). The large time step size does not only cause in-accuracy of results but also may cause the PHIL simulationfailure. For example, if the power devices under test havea sampling frequency of 20 kHz, any step size longer than50 μs will make the PHIL simulation a futile effort.

The other obstacle which constricts the development ofPHIL simulation is the problem of closed-loop instability.Even the investigated real system is stable, the PHIL sim-ulation for it may lose stability due to the inevitable issuessuch as time delay, harmonic injection, limited bandwidth,etc. The instability problem must be treated seriously, other-wise, it may cause critical damage to the HUT.

There are some trials and analyses on the PHIL simula-

c© 2010 The Institute of Electrical Engineers of Japan. 902

Stability and Accuracy of Power Hardware-in-the-loop Simulation

Fig. 2. Configuration of the proposed GECS with a ma-trix converter

tion (4)–(6). In Ref. (4), an implementation of a PHIL simula-tion is described. However, there is no analysis about thestability. Papers (5) and (6) both mention that the instabilityof PHIL simulation is caused by the sampling frequency ofthe power interface. The conclusion only addresses the inter-face performances while neglects the fact that PHIL simula-tion is a closed-loop system. In Ref. (7), different interfacealgorithms for PHIL simulation are proposed and compared.It indicates that the interface algorithm has serious influenceon the accuracy and stability. Nevertheless, authors simplymention that the stability of PHIL simulation depends on themagnitude of the open loop transfer function and providesno detail analysis. Furthermore, the analysis uses very sim-ple model, in which the simulation part is represented by aresistor and the real hardware consisted of a resistor and aninductor. The model is relatively simple and results may beinsufficient for PHIL simulation which has more complicateconstruction.

In this research, a PHIL simulation is developed to inves-tigate the application of a matrix converter (MC) in a gas en-gine cogeneration system (GECS) shown as Fig. 2. Differentto general MC, this MC transfers three-phase electricity tosingle-phase directly. In the PHIL simulation, a gas engineand a generator are represented by their time-domain realtime models and simulated by a digital simulator. The realMC, including its filter and controller, is the HUT. Since bothsimulation part and real part have inductor, this type PHILsimulation is an inductor coupled system. In fact, this typesystem is the most common system in power system. Forexample, 1) an AC electric drive system consisting of ACmotor, an inverter, transformer and 2) a distribution systemconsisting of power converter, transformer and transmissionline, etc., are both inductor coupled systems. The time delayof this PHIL simulation is as short as 15 μs, which can insurea high accuracy according to Ref. (3). This paper focuses onthe stability issue of the PHIL simulation and a method toimprove stability without deteriorating simulation accuracyis proposed and verified.

Because the GECS shown as Fig. 2 is relatively compli-cated, the stability issue of the inductor coupled PHIL simu-lation is firstly analyzed using a simple R, L, C circuit. Sta-bility conditions and stable area of a PHIL simulation areanalyzed and verified by experiment in section 2. Section 3proposes a solution to the instability problem without deteri-orating its accuracy. Section 4 describes the PHIL simulationof a GECS with a MC and its results are verified by off-linesimulation. Conclusions are presented in the final section.

Fig. 3. Simple example of a PHIL simulation of induc-tor coupled system

2. Stability Analysis of the Power Hardware-in-the-loop Simulation

2.1 Configuration of the Power Hardware-in-the-loopSimulation To investigate the stability problem, a simplePHIL simulation of inductor coupled system shown in Fig. 3is considered as an example. The original circuit consists ofR, L and C. In the PHIL simulation built for the original cir-cuit, the voltage source Vs and the source resistor R1, induc-tor L1 are simulated by a real time digital simulator, while theHUT is a linear load consisting of a resistor R2, an inductorL2 and a capacitor C2. Signal of output voltage V1 is trans-ferred to a power amplifier through a D/A converter. Thepower amplifier receives the voltage signal and reproducesit as a physical voltage, V2. Then, the voltage V2, workingas a controlled voltage source, is supplied to the real loadas power source. On the other hand, the actual current I2 ofthe real impedance is measured and fed back to the simula-tion part as a controlled current source (I1) through an A/Dconverter. This type interface algorithm is called ideal trans-former model (ITM) which is widely used in PHIL simula-tion due to its high accuracy (7).

It is obviously that under an ideal situation, voltage V2

should equal to V1 and I1 equal to I2. However, this idealsituation can not be realized due to the non-ideal of inter-face. Assuming that all signals are transferred ideally exceptthe introduced time delay in the PHIL simulation, followingequations can be obtained:

V2 = V1e−Td1 s · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (1)

I1 = I2e−Td2 s · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (2)

Td1 is the delay time of the forward loop which mainlyintroduced by numerical calculation time of simulation, D/Aconverter, time delay of power amplifier. Td2 is the time delayof feedback loops and is mainly introduced by A/D converter.Then, the block diagram of the PHIL can be drawn as Fig. 4,where Z1(s) and Z2(s) are impedances of simulation part andreal part and can be expressed by following Eqs. (3) and (4).

Z1(s) = R1 + sL1 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (3)

Z2(s) = R2 + sL2 +1

sC2· · · · · · · · · · · · · · · · · · · · · · · · · (4)

The open loop transfer function Go(s) of the PHIL simula-tion can be presented by Eq. (5):

電学論 D，130 巻 7 号，2010 年 903

Fig. 4. Block diagram of PHIL simulation

G0(s) =Z1(s)Z2(s)

e−Td s · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (5)

where Td = Td1 + Td2 and it is the whole time delay inthe PHIL simulation. Typically, if there were no time delay,Eq. (5) can be presented by Eq. (6).

G0(s) =Z1(s)Z2(s)

· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (6)

2.2 Stability Analysis of the PHIL SimulationCharacteristic equation of the system in Fig. 4 can be de-

scribed as Eq. (7).

1 +Z1(s)Z2(s)

e−Td s = 0 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (7)

To simplify the analysis, e−Td s is represented by first orderPade approximation:

e−Td s ≈ 1 − Td s/21 + Td s/2

=−s + as + a

a > 0 · · · · · · · · · · · · · (8)

where, a is a constant defined by the time delay Td. It shouldbe noted that a larger Td corresponds to a smaller value of a(a = 2/Td) and vice versa. Substituting Eqs. (3), (4) and (8)to (7), Eq. (9) can be obtained:

(L2 − L1)C2s3 + (R2 − R1 + aL1 + aL2)C2s2

+ (1 + a(R1 + R2)C2)s + a = 0 · · · · · · · · · · · · · · · · · · (9)

Applying Routh rule to Eq. (9), Eqs. (10), (11) and (12)must be satisfied to keep the system stable:

L2 > L1 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (10)

a >R1 − R2

(L1 + L2)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (11)

a2(R1 + R2)(L1 + L2)C2

+ a(2L1 + R22C2 − R2

1C2) + (R2 − R1) > 0 · · · · · · · (12)

From Eqs. (10), (11) and (12), following statements can beconcluded:

( 1 ) To keep the stability of the inductor coupled PHILsimulation, the real inductor must be larger than thesimulated inductor.

( 2 ) The constant a, which is determined by the time de-lay Td, also has effect on the simulation stability. Ac-cording to Eqs. (11) and (12), a smaller time delay,which means a larger value of a, benefits to the PHILstability. On the contrary, a larger time delay will im-poses more critical request on the impedance value.Detail relationship of the time delay and the value ofimpedance which can maintain PHIL simulation sta-bility can be calculated from Eqs. (11) and (12).

Fig. 5. a PHIL simulation of inductor coupled system

2.3 PHIL Simulation to Verify the Analysis of the Sta-bility2.3.1 An Inductor Coupled PHIL Simulation SystemTo verify conclusions in the previous section, a PHIL sim-

ulation illustrated in Fig. 5 is carried out. As shown in Fig. 5,the PHIL simulation is a closed-loop system. In order to ap-ply root locus method to analyze the stability of this PHILsimulation system and to analyze the stability of a PHIL sim-ulation by using a quantitative method, a gain, K, is intro-duced intentionally in the feedback current loop for the fol-lowing reasons. (1) By introducing the K, it is possible toevaluate the stable area for the PHIL simulation by using theconcept of gain margin. The value Ksmax is also introducedto indicate the maximum value of K by which stability canbe achieved in a PHIL. The Ksmax should be greater than “1”for successful PHIL simulation, because the results with K= 1 is meaningful as a PHIL simulation. Moreover, the dif-ference between Ksmax and 1 (Ksmax − 1) gives gain margin.The larger gain margin means higher stable ability and morereliable simulation results. (2) When a PHIL simulation iscarried out, the K must not be set as “1” from the beginning.It should be increased from “0” to “1” step by step with cau-tious to avoid unanticipated instability which may destroy thehardware of the system.

In this PHIL simulation system, an integrated real time(RT) simulation platform, RT-LAB, is adopted to carryout calculation. RT-LAB simulator works with MAT-LAB/simulink, using ultra-fast processors, the best avail-able inter communication technology and FPGA-based I/Os.This simulator achieves real-time performance by distribut-ing models to across multi-processor targets.

Table 1 shows the main structure of RT-LAB simulator.CPUs and FPGA can provide fast calculation speed. TheOpal-RT OP5110 family of I/O cards is used. Opal-RTOP5110 FPGA based I/O cards feature 100 nanosecond dig-ital in and digital out, 2 microsecond A/D converter and 1microsecond D/A converter. Both the fast FPGA based I/Oaccess and A/D, D/A converter contribute to fast calculationspeed, which can decrease the time delay of the PHIL simu-lation. Actually, the time delay achieved in this PHIL simu-lation is only 15 μs.

Values of impedances are summarized in Table 2. In thisPHIL simulation, since the time delay is as short as 15 μs, theconstant a is as high as about 1.33×105. Therefore, Eqs. (11)and (12) are both satisfied. However, because the simulatedinductor is 6 mH and the real inductor is 4 mH, which meansEq. (10) is not satisfied, the system is unstable. In fact, this

904 IEEJ Trans. IA, Vol.130, No.7, 2010


Table 1. Structure of OPAL RT simulator

Table 2. Impedance values

Fig. 6. Block diagram of the closed-loop PHIL simula-tion

PHIL simulation loses stability when the value of the K islarger than 0.67.2.3.2 Fundamental Cause for Instability If there

were no time delay in the PHIL simulation, the open looptransfer function of the PHIL simulation of Fig. 5 includingthe introduced K can be presented as:

G0(s) =Z1(s)Z2(s)

= K6s2 + 3700s

4s2 + 10000s + 108. · · · · · · · · ·(13)

Considering the time delay, which is mainly caused bycomputation time and A/D, D/A converter, the open looptransfer function can be written as Eq. (14):

G0(s) =Z1(s)Z2(s)

e−Td s = K6s2 + 3700s

4s2 + 10000s + 108e−Td s

· · · · · · · · · · · · · · · · · · · (14)

where Td = Td1 + Td2 = 15 μs and it mainly includes timestep of the calculation of the simulator (12 μs), A/D and D/Aconverter shown in Table 1.

The block diagram of PHIL simulation in Fig. 5 is drawnas Fig. 6, where K is the value of gain in the current feedbackloop. Fig. 7 is root locus figure for this closed-loop systemif the system has no time delay (Td = 0). Fig. 8 is root lo-cus figure when the time delay of this system is 15 μs. Fig. 7shows that the closed loop system should always be stable ifthere were no time delay, no matter what the value of the Kis. However, Fig. 8 clearly indicates that, when time delayis considered, the system changes from stable state to unsta-ble state with the increasing value of K. Fig. 8 also showsthe maximum value of K which can keep the system stable,named as Ksmax, is 0.67. Because only when K equals to1means the measured current is fully fed back to the simula-tion part and a complete PHIL simulation is realized, the sys-tem of Fig. 5 is unstable. Obviously, the fundamental causefor the instability is the time delay, even it is as short as 15 μs.

Fig. 7. Root locus figure of the closed-loop PHIL simu-lation without time delay

Fig. 8. Root locus figure of the closed-loop PHIL simu-lation with time delay

2.3.3 Analysis of Stable Area The characteristicequation of the system in Fig. 6 is:

1 + KZ1(s)Z2(s)

e−Td s = 0 · · · · · · · · · · · · · · · · · · · · · · · · · · · (15)

(L2 − KL1)C2s3 + (R2 − kR1 + aKL1 + aL2)C2s2

+ (1 + a(KR1 + R2)C2)s + a = 0 · · · · · · · · · · · · · · · (16)

Considering the high value of a(1.33 × 105), together withvalues of R, C in Table 2, the PHIL system in Fig. 5 can main-tain stability under the following condition:

L2 > KL1 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(17)

Eq. (17) also means that the maximum value of the feed-back gain (Ksmax) which can maintain the stability of thePHIL simulation in Fig. 5 is determined by following equa-tion:

Ksmax = L2/L1 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(18)

If Ksmax is equal or greater than 1, the PHIL simulation isstable. The value (Ksmax−1) shows the gain margin and PHILwith a larger gain margin shows higher stable ability. To ver-ify Eqs. (17) and (18), experiments which had same configu-ration as Fig. 5 were carried out. Values of impedances usedin the experiment are summarized in Table 3 and results ofexperiments are shown in Fig. 9 and Fig. 10.

Fig. 9 shows the comparison of Ksmax calculated fromEq. (18) and Ksmax obtained by experiment. The below areaof the line means a stable area for the PHIL simulation andthe upper area means an unstable area. Fig. 10 shows the re-lationship of the measured Ksmax and the ratio of L2/L1 in thatexperiment. From Fig. 9 and Fig. 10, two main conclusionscan be achieved:

電学論 D，130 巻 7 号，2010 年 905

Table 3. Parameters for stability experiment

Fig. 9. Comparison of values of the Ksmax calculatedfrom Eq. (18) and obtained by experiment, respectively

Fig. 10. Relationship of L2/L1 and the value of Ksmax ob-tained by experiment

( 1 ) Under the condition of a constant simulated induc-tor, a larger real inductor means a larger stable area forthe PHIL simulation.

( 2 ) In the PHIL simulation of Fig. 5, the maximumfeedback gain in the current loop which can maintainthe PHIL stability approximates to the ratio of L2/L1,as shown in Fig. 10.

( 3 ) The good match of the analysis results and the ex-perimental results also verify that the application of1st order Pade approximation in Eq. (8) is enough forthe stability analysis.

3. Proposed Solution to PHIL Simulation Insta-bility

3.1 Modification of the PHIL SimulationAccording to conclusions in the previous section, the

PHIL simulation in Fig. 5 is intrinsically instable because ofL1 > L2. Ref. (7) also points out the interface algorithmused in this PHIL simulation, ITM, exhibits high accuracybut low stability. In order to improve stability, the PHILsimulation system of Fig. 5 has to be modified. One pro-posed method is to change the interface algorithm. How-ever, other interface algorithms, such as transmission linemodel (TLM), partial circuit duplication (PCD) method anddamping impedance method (DIM), only theoretically pro-vide high stability while are difficult to be implemented.

Fig. 11. Modified PHIL simulation

Fig. 12. Equivalent circuit of PHIL simulation

Furthermore, these interfacing algorithms exhibit lower ac-curacy than ITM (7).

To improve the stability without deteriorating the accuracyof the PHIL simulation, we proposed a method which can beimplemented easily in practice: the inductor in the simulatedpart decreased from 6 mH to 4 mH and the real inductor in-creased from 4 mH to 6 mH. The total inductor of the PHILsimulation is still 10 mH while the ratio of L2/L1 increases to1.5, therefore, stable operation with K = 1 can be expected.The modified PHIL simulation is shown in Fig. 11. Otherparameters of the system are same as that in Fig. 5.3.2 Verification of the Modification Obviously, the

modified PHIL simulation should have same behaviors as theoriginal one. Otherwise, the proposed method is unaccept-able.

According to Thevenin’s theory, all the part of the PHILsimulation system before real R2, L2 and C2 can be repre-sented by an equivalent voltage source Ves and an equivalentinternal impedance Zes. Therefore, Fig. 3 can be simplified asFig. 12. The voltage source Ves and the internal impedanceZes are expressed by following Eqs. (19) and (20). Eq. (21)presents the total impedance of whole PHIL simulation.

Ves = Vse−Td1 s · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(19)

Zes = Z1e−Td s · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(20)

Zs = Z1e−Td s + Z2 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(21)

where, Vs is the simulated voltage source; Z1 is the simu-lated impedance, R1 + sL1. It should be noted that Ves andZes behalf integrated characteristics of Vs, Z1, A/D, D/A con-verter and power amplifier. Eq. (19) indicates that the pro-posed method has no effect on Ves. However, Eq. (21) showsthat total impedance of the whole PHIL simulation, Zs, maybe affected by the proposed method.

Bode diagrams of Zs of the original and modified systemsare both shown in Fig. 13. Assuming the interested frequencyregion is 0 to 1000 Hz, Fig. 13 shows that performance of Zs

of original and modified PHIL simulation are same in this



Fig. 13. Bode diagram of Zs of the original and modifiedPHIL simulation (the time delay is 15 μs)

Fig. 14. Block diagram of PHIL simulation includingTFP

bandwidth region. Therefore, the PHIL simulation of Fig. 11has same performance as the one shown in Fig. 5.

It should be noticed that if the time delay increases, char-acteristics of Zs may change greatly due to the proposed sta-bility method according to Eq. (21)

It also should be pointed out that according to previousconclusions of section 2, modifications of the PHIL simula-tion of Fig. 5 which decrease L1 less than 4 mH and increaseL2 lager than 6 mH also can improve the stability. Never-theless, these modifications have more serious effects on Zs

according to Eq. (21) and then performances of original PHILsimulation may be seriously changed.3.3 Accuracy Analysis of the Proposed Solution to In-

stability Problem The other issue which should be con-cerned about is how the modification affects the accuracy ofthe PHIL simulation. Error of PHIL simulation is mainlycaused by the non-ideal PHIL interface, which is called in-terface transfer function perturbation (TFP) and noise intro-duced in the real system, which is called noise perturbation(NP) (3).3.3.1 Interface Transfer Function Perturbation (TFP)Assuming that all the signals are transferred ideally and the

error of the PHIL simulation shown in Fig. 3 is only causedby the time delay, Fig. 4 can be drawn as Fig. 14, in whichthe dashed line means introduced errors by TFP. It is obviousthat without the dashed line, factually, Fig. 14 is the blockdiagram of the original R, L, C circuit in Fig. 3.

It is assumed that V1 is the interested signal. Definiting V1

as original value and V1−T FP as the value with TFP, a reason-able approach to evaluating the accuracy can be defined byfollowing equation:

Ev1−T FP =

∣∣∣∣∣

V1−T FP − V1

V1

∣∣∣∣∣· · · · · · · · · · · · · · · · · · · · · · ·(22)

Subsituting impedance parameters of PHIL simulation to

Fig. 15. Ev1−T FP versus time delay for original and mod-ified PHIL simulation

Fig. 16. TFP errors versus frequency for original andmodified PHIL simulation

Eq. (22), Ev1−T FP can be presented as follwing:

Ev1−T FP =

∣∣∣∣∣∣

Z1(s)/Z2(s)(1 − e−Td s)1 + Z1(s)/Z2(s)e−Td s

∣∣∣∣∣∣

· · · · · · · · · · · · · ·(23)

Ev1−T FP indicates the difference of V1 between the PHILsimulation and the original real circuit of R, L, C (shown asFig. 3). Eq. (23) shows that the amplitude of the error also in-cludes the error caused by phase difference between V1−T FP

and V1.TFP errors of original PHIL simulationn of Fig. 5 and mod-

ified PHIL simulation of Fig. 11 can be calculated respec-tively by Eq. (23). It is obviously the value of Ev1−T FP variesagainst both the frequency and the time delay Td. With-out loss of generality, it is assumed interested frequency is300 Hz and Fig. 15 is the TFP error versuses the time delay.On the other hand, assuming time delay of the PHIL sim-ulation is 15 μs, the TFP error versuses frequency is shownFig. 16. It is clearly that Ev1−T FP increase dramatically withthe increasing of time delay for certain frequency. At thesame time, TFP error also increases with the increasing offrequency when the time delay is a constant.

It can be concluded from Fig. 15 and Fig. 16 that the pro-posed modification to stabilize the PHIL simulation can alsodecrease the simulation error caused by TFP.3.3.2 Noise Perturbation (NP) Supposing that all

signals in the PHIL simulation of Fig. 3 transferr ideally ex-cept that there is a sensor noise when the real current I2 ismeasured, block diagram of Fig. 4 can be drawn as Fig. 17.Treating the sensor noise as white noise ε and assuming V1

is interested siganl, PHIL simulation error can be evaluatd byfollowing eqution:

Ev1−NP =

∣∣∣∣∣

V1−NP − V1

V1

∣∣∣∣∣· · · · · · · · · · · · · · · · · · · · · · · · ·(24)

電学論 D，130 巻 7 号，2010 年 907

Fig. 17. Block diagram of PHIL simulation includingNP

Fig. 18. Value of∣∣∣∣

Z1(s)1+Z1(s)/Z2(s)

∣∣∣∣ versus frequency

V1 is the value without NP and V1−NP is the value with NP.Then, Ev1 can be written as:

Ev1−NP = |ε|∣∣∣∣∣

Z1(s)1 + Z1(s)/Z2(s)

∣∣∣∣∣· · · · · · · · · · · · · · · · · · ·(25)

Fig. 18 shows the value of∣∣∣∣

Z1(s)1+Z1(s)/Z2(s)

∣∣∣∣ against frequency.

Disconnected line means original system of Fig. 5 and solidline means modified system of Fig. 11.

Fig. 18 shows that the proposed modification of PHIL sim-ulation can decrease the simulation error caused by NP in thefrequecy region of 0–800 Hz, while slightly deterioate accu-racy when frequency is larger than 800 Hz. Considering thesmall magnitude of ε, this deterioation can be neglected.

From above analysis, it can be concluded that the proposedmodification to improve stability of PHIL simulation can alsoimprove its accuracy.

4. A PHIL Simulation of a Gas Engine Cogener-ation System with a Matrix Converter

4.1 Configuration of the PHIL Simulation of GECSThis PHIL is developed to investigate a gas engine cogen-

eration systenm (GECS) with a matrix converter (MC) asshown in Fig. 19 (8). In order to investigate how the torquepulsation of gas engine (GE) affects the operation of MC andhow the proposed modulation (9) of the MC affects the opera-tion of the GE and the permanent magnet synchronous gen-erator (PMSG) before the real building of the GECS with theMC, a PHIL simulation is proposed due to the difficulty tocarry out the experiment with a real gas engine. In this PHILsimulation, the HUT is the MC including its controller andfilter.

Fig. 20 is the original configuration of the PHIL simulationbuilt for the GECS to test the MC. The models of GECS andPMSG are described in the reference paper (10).

In this PHIL, time-domain numerical models of GE and thePMSG are simulated based on MATLAB/simulink/ SimPow-

Fig. 19. Configuration of the proposed GECS with amatrix converter

Fig. 20. Original PHIL simulation of a GECS with aMC

Table 4. Parameters of the gas engine

erSystem, compiled by the host computer and then down-loaded to the Opal-RT simulator (11).

The signal of the PMSG output voltage is transferred to apower amplifier via a D/A converter which is installed on theRT simulator. The power amplifier receives the voltage sig-nal and regenerates it as physical voltage which is used as thepower source of the proposed MC. Currents of the MC on thethree phase side are measured and fed back to the simulatorvia an A/D converter.

Parameters of the GE, PMSG and power amplifier used inthis research are shown in Tables 4, 5 and 6.

Fig. 21 is the control block diagram of the MC. Detail de-scription of it can be found in ref (9). As shown in Fig. 19, theMC in this GECS transfers three-pahase electricity (307 Hz)to single-phase (60 Hz) directly. Since the proposed MC con-figuration does not have any energy storage component, thepower pulsation that has twice the frequency of the singlephase utility appeared directly on the three phase side. There-fore, a novel method is proposed to treat this power pulsa-tion in Ref. (8). This method realizes that the instantaneousthree phase power is synchronously modulated with the sin-gle phase pulsation. Detail parameters of the MC are shown



Table 5. Parameters of the permanent magnet syn-chronous generator

Table 6. Rated values of the power amplifier

Fig. 21. Control block diagram of the matrix converter

in Table 7. Because the sampling time for control of the MCis 100 μs, the time step size of the PHIL simulation should beless than it.

The MC is a non-linear HUT in this PHIL simulation.However, in this GECS, the MC adopts a power factor mod-ulation on the three phase side (8) and the power factor on thethree phase side of MC is kept constant 1, which means thatinput voltages (vus, vvs, vws) and input currents (ius, ivs, iws) ofMC has same phase angle. Then, the MC,including its outputfilter and Rload , can be ideally treated as an equivelent resistorat the standpoint on the MC three phase side. As a result, thewhole HUT, which includes MC, its input filter, output filterand Rload, can be ideally treated as a linear impedence load.Therefore, previous conclusions in section 2 and section 3can be applied to this PHIL simulation.

Tables 5 and 7 show that the internal inductor of PMSGis 6 mH while the inductor of MC input filter is 4 mH. Sincethe inducor of simulation is larger than the real inductor, thePHIL simulation is unstable. In fact, the value of Ksmax canbe achieved is only 0.67, which equals to L2/L1.

To achieve stable operation of the PHIL simulation, a mod-ification, that the simulated inductor decreases to 4 mH andthe filter inductor increases to 6 mH, is made. The modifiedPHIL simulation is shown in Fig. 22. With this modification,a stable PHIL simulation under the condition that K = 1, isachieved and the time delay is 15 μs. The validity of chang-ing the ciucuit as shown in Fig. 22 is discussed in section 3.2and 3.3.4.2 Results of the Modification PHIL Simulation and

Verification of Results In order to verify results of themodified PHIL simulation, off-line simulation of the original

Table 7. Parameters of MC

Fig. 22. Modified PHIL simulation of a GECS with a MC

電学論 D，130 巻 7 号，2010 年 909

(a) output voltage of power amplifier (vau)

(b) output current of power amplifier iu (Gain = 0)

Fig. 23. PHIL simulation results when the feedbackgain K equals to 0

(a) output voltage of power amplifier (vau)

(b) output current of power amplifier iu

(c) matrix converter output voltage (vout)

(d) matrix converter output power

Fig. 24. Results of the modified PHIL simulation ofGECS

system, shown in Fig. 19, is also carried out based on MAT-LAB/simulink and SimPowerSystems. It should be notedthat in the off-line simulation, the inductor of the generatoris still 6 mH while the inductor of the input filter of the MCis still 4 mH. Results of modified PHIL simulation of Fig. 22and off-line simulation of Fig. 19 are shown in Figs. 23, 24,and 25 respectively.

(a) output voltage of generator (vtu)

(b) output current of generator iu

(c) matrix converter output voltage (vout)

(d) matrix converter output power

Fig. 25. Results of the off-line numerical simulation ofthe original GECS

Figs. 23 are results obtained by modified PHIL simulationwhen the K equals to 0, which means the open loop conditionof the PHIL simulation. Fig. 23(a) shows the output voltageof the power amplifier (Vau) and Fig. 23(b) is the waveformof the current iu, respectively. Fig. 23(a) indicates that with-out feedback current, which assumes the modulation of MChad no feedback influence to PMSG voltage, the voltage hasa perfect sinusoidal waveform. Because GE has torque pulsa-tion, the speed of GE-PMSG unit also has pulsation. Hence,the value of voltage also changes slightly. Fig. 23(b) showsthat the MC input current is distorted. It is caused by themodulation of the three phase power of MC which is syn-chronous with single phase power pulsation.

Figs. 24(a), (b), (c) and (d) are results obtained by modifiedPHIL simulation when K equals to 1. Waveforms from topare output voltage of the power amplifier (Vau), output cur-rent of the power amplifier (iu), output voltage of the singlephase (Vout) and output power of the MC on the single phase,respectively.

Figs. 24(a) shows that when the feed back gain K equals“1”, the output voltage of the power amplifier, which is al-most equivalent to the generator output voltage except thevoltage drop of the 2 mH inductor moved to the hardware partin Fig. 22, is distorted. The distortion means that modulation



of MC three phase power has substantial feedback influenceon the output voltage of generator. This influence is causedby the voltage drop when the current flows through the inter-nal impendence of the generator. Comparing Figs. 23(b) and24(b), it can be concluded the output current of the poweramplifier, which ideally is the output current of the PMSG,has little relationship with the value of feedback current andis merely affected by the MC modulation. Figs. 24(c) indi-cates that waveforms of the output voltage of MC (60 Hz)are sinusoidal with distortions. Because the load of the MCis a pure resistor Rload, the current has similar waveform tovoltage. Therefore, waveforms of output power of the MC,shown in Fig. 24(d) also have obvious distortions. However,even under adverse conditions that GE torque has pulsationand input voltage is fluctuated, the stable operation of MCis achieved. As a result, the proposed application of MC inGECS is demonstrated through the proposed PHIL simula-tion.

Fig. 25 shows the offline simulation results of GECS inFig. 19. From (a) to (d), they are generator output voltage,generator output current, output voltage of the MC and theoutput power of the MC.

Comparing Fig. 24 to Fig. 25, results are similar and bothcan well indicate characteristics of the application of MCin GECS. The difference between Figs. 24(a) and 25(a) isdue to the inductor voltage across the 2 mH inductor movedto the hardware part in Fig. 22. The difference betweenFigs. 24(c) and 25(c) is due to the controller of matrix con-verter which needs some improvement to compensate voltagedrop of semiconductor devices and etc.

The good match of modified PHIL simulation (shown inFig. 22) and results by the off-line simulation of original sys-tem (shown in Fig. 19) indicates that the proposed method tostabilize the PHIL simulation is acceptable.

5. Conclusions

This study focuses on the stability issue of PHIL simula-tion of inductor coupled systems. Following conclusions areachieved:

( 1 ) Time delay introduced by numerical calculation ofsimulation, A/D and D/A conversion, etc, is the fundamentalcause for the instability happened in the closed-loop systemof PHIL simulation. Even the originally investigated systemis in stable, the PHIL simulation developed for it may losestability due to the time delay.

( 2 ) In a PHIL simulation of inductor coupled system, thestable area is defined by the ratio of the real inductor and sim-ulated inductor (L2/L1). It only can achieve stability underthe condition that L2/L1 is greater than 1. Moreover, com-bined relationship of values of impedance and the time delayalso affects the stability.

( 3 ) A method to improve stability, which can be imple-mented easily in practice, is proposed. Furthermore, thismodification can also improve the accuracy of the PHIL sim-ulation.

( 4 ) A high fidelity PHIL simulation with a non linearHUT, which is a MC of a GECS, is described in this pa-per. Through this PHIL simulation, the proposed method tostabilize the PHIL simulation of inductor coupled system isdemonstrated and results are verified by off-line simulation

results.Since inductor coupled systems are the most common sys-

tems in power system, these conclusions can be widely ap-plied and then are benefit to the development of PHIL simu-lation of power systems.

AcknowledgmentThis research was partly supported by a grant for Osaka

University GCOE program, “Center for Electronics DevicesInnovation”, from the Ministry of Education, Culture, Sports,Science and Technology of Japan.

(Manuscript received Oct. 16, 2009,revised Feb. 9, 2010)

References

( 1 ) P. Forsyth, T. Maguire, and R. Kuffel: “Real time digital simulation of controland protection system design”, 35th Annual IEEE Power Electronics Special-ist Conference 2004, PESC, Vol.1. pp.329–335 (2004)

( 2 ) S. Abourida, J. Belanger, and C. Dufour: “High Fidelity Hardware-in-the-loop Simulation of Motor Drives with RT-LAB and JMAG”, Industrial Elec-tronics, 2006 IEEE International Symposium on Vol.3, No.9-13, pp.2462–2466 (2006-7)

( 3 ) W. Ren, M. Steurer, and S. Woodruff: “Accuracy Evaluation in Power Hard-ware-in-the-Loop (PHIL) simulation”, Proc. the 2007 Summer ComputerSimulation Conference, pp.489–493 (2007)

( 4 ) X. Wu, S. Lentijo, A. Deshmuk, A. Monti, and F. Ponci: “Design and imple-mentation of a power-hardware-in-the–loop interface: a nonlinear load casestudy”, Twentieth Annual IEEE Applied Power Electronics Conference andExposition, 2005, Vol.2 (2006-3)

( 5 ) W. Zhu, S. Pekarek, J. Jastkevich, O. Wasynczuk, and D. Delisle: “A Model-in-the-loop interface to Emulate Source dynamics in a Zonal DC DistributionSystem”, IEEE Trans. Power Electronics (2005-3)

( 6 ) S. Ayasun, R. Fischl, S. Vallieu, J. Braun, and D. Cadirh: “Modeling and sta-bility analysis of a simulation-stimulation interface for hardware-in-the-loopapplication”, Available: http://www.science direct.com

( 7 ) W. Ren, M. Steurer, and T.L. Baldwin: “Improve the Stability and the Ac-curacy of power Hardware-in-the Loop Simulation by selecting AppropriateInterface Algorithms”, IEEE Trans. on Industry Applications, Vol.44, No.4,pp.1286–1294 (2008-7/8)

( 8 ) Y. Miura, S. Kokubo, D. Maekawa, and T. Ise: “Efficiency Improvement ofa Gas Engine Cogeneration System by Power Factor Control with an IGBTRectifier”, Proc. the Power Conversion Conference Nagoya, 2007 (PCC’07),pp.534–541 (2007-4)

( 9 ) Y. Miura, S. Kokubo, D. Maekawa, S. Horie, T. Ise, T. Momose, and Y.Sato: “Power Modulation control of a Three Phase to Single Phase MatrixConverter for a Gas Engine Cogeneration System”, 39th IEEE Annual PowerElectronics Specialist Conference Greece, 2008 (PESC’08), pp.2704–2710(2008-6)

(10) H. Miao, S. Horie, Y. Miura, T. Ise, T. Momose, Y. Sato, T. Momose, and C.Dufour: “Power Hardware-in-the-loop Simulation of a Gas Engine Cogener-ation System for Developing Power Converter Systems”, to be published inIEE of Japan Transactions on Industry Applications, Vol.130, No.5 (2010)

(11) Reference for RT-LAB, www.opal-RT.com

Miao Hong (Student Member) received the B.Eng. degree in Electri-cal Engineering from Hefei Techonology University,China and the M.Eng degree in Power System Engi-neering from Sichuan University, China in 1992 and1995, respectively. Since 1995, she is a lecturer in theDepartment of Electrical Engineering, Sichuan Uni-versity, China. Currently, she is persuing Ph.D. fromOsaka University, Japan. Her research interests in-cluding distributed generation systems, power elec-tronic, etc.

電学論 D，130 巻 7 号，2010 年 911

Yushi Miura (Member) received doctor degree in Electrical and Elec-tronic Engineering from Tokyo Institute of Technol-ogy in 1995. From 1995 to 2004, he joined JapanAtomic Energy Research Institute as a researcherand developed power supplies and superconductingcoils for nuclear fusion reactors. Since 2004, he hasbeen an associate professor of the Division of Electri-cal, Electronic and Information Engineering of OsakaUniversity. His areas of research involve applicationsof power electronics and superconducting technol-

ogy. Currently he is in control of distributed generations and energy storagein the power system.

Toshifumi Ise (Member) was born in 1957. He received the Bachelor,Master, and Dr. of Engineering degrees inelectricalengineering from Osaka University, Osaka, in 1980,1982 and 1990, respectively. Currently, he is a Pro-fessor with the Division of Electrical, Electronic andInformation Engineering, Graduate school of Engi-neering, Osaka University, where he has been since1990. From 1986 to 1990, he was with the Nara Na-tional College of Technology, Nara, Japan. His re-search interests are in the areas of power electronics

and applied superconductivity including superconducting magnetic energystorages (SMES) and new distribution systems. Dr. Ise is the president ofthe Japan Institute of Power Electronics.

Yuki Sato (Non-member) was born in 1977. He received the Bache-lor and Master of Engineering degrees in mechanicalengineering from Tokyo University, Tokyo, Japan in1999 and 2001 respectively. From 2001, he joinedat the Energy Technology Laboratories of Osaka GasCo., Ltd.

Toshinari Momose (Non-member) was born in 1969. He received theB.E. and M.E. degree in from Osaka University, Os-aka, Japan in 1992 and 1994 respectively. From 1994to 2003, he joined at the Gas Appliance DevelopmentDepartment of Osaka Gas Co., Ltd. and from 2003 hejoined at the Energy Technology Laboratories of it.He received a Dr. degree in from Osaka University in2005.

Christian Dufour (Non-member) is a Simulation Software Special-ist at Opal-RT Technologies, Montreal, Canada. In2000, he received his Ph.D. degree from Laval Uni-versity, Quebec, Canada. Before joining Opal-RT, heworked on the development of Hydro-Quebec real-time simulators as well as the MathWorks’ SimPow-erSystems blockset. His current research interestsare mainly focused on numerical techniques relatedto real-time simulation of power systems and motordrives in RT-LAB, the real-time simulation platform

of Opal-RT.


stability and accuracy analysis of power hardware-in-the

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