A Dual-Loop Control Strategy of Railway Static Power ... - IEEE Xplore

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 26, NO. 7, JULY 2011

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A Dual-Loop Control Strategy of Railway Static Power Regulator Under V/V Electric Traction System An Luo, Senior Member, IEEE, Fujun Ma, Chuanping Wu, Shi Qi Ding, Q.-C. Zhong, Senior Member, IEEE, and Zhi Kang Shuai

Abstract—For power quality in V/V traction system of the 350km/h high-speed railway, a kind of railway static power conditioner (RPC) is discussed, which is used to carry out the comprehensive compensation of negative sequence and harmonic currents in the traction substation. In order to improve the control effect and performance of RPC, a dual-loop control strategy is constructed for RPC. Taking into account the disturbance and variation of electrified railway environment, a recursive proportionalintegral control based on fuzzy algorithm is adopted to realize a fast and smooth tracking to the reference current. An energybalance control is proposed to suppress the fluctuation of dclink voltage and maintain the stability of RPC, which is an accurate and adaptive feedback control based on corresponding parameters. Finally, the correctness of the analysis proposed in this paper has been confirmed by the simulation and experiment results. Index Terms—Comprehensive compensation, recursive proportional-integral (PI) control, energy balance control, fuzzy rule, high-speed railway, negative sequence current (NSC).

I. INTRODUCTION ITH the development of Chinese electrified railway, power quality has been a major concern for power supply systems in ac electrified railway [1]. For Chinese high-speed railway, the speed will be more than 350 km/h in continuous operation. Because of the rapid development of the power electronic switching devices, the ac–dc–ac Pulse-Width Modulated (PWM) rectification and modulation are adopted by singlephase electrical trains, as a result, there is a large amount of negative sequence current (NSC) and harmonic current, which have a broad spectral range. Thus, these negative sequence and

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Manuscript received July 3, 2010; revised November 12, 2010; accepted December 20, 2010. Date of current version August 5, 2011. This work was supported by the Key Projects in the National Science & Technology Pillar Program during the Eleventh Five-Year Plan Period under Project 2009BAG12A09. Recommended for publication by Associate Editor P. Barbosa. A. Luo, F. Ma, C. Wu, and Z. K. Shuai are with the College of Electrical and Information Engineering, Hunan University, Changsha, Hunan 410082, China (e-mail: [email protected]). S. Q. Ding is with the Graduate School of Hunan University, Changsha, Hunan 410082, China, and also with HEFEI TONGGUAN GUOXUAN Copper Co. Ltd., Hefei, Anhui 230601, China. Q.-C. Zhong is with the Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2AZ, U.K., and also with Department of Electrical Engineering and Electronics, Liverpool University, Liverpool L69 3GJ, U. K. Digital Object Identifier 10.1109/TPEL.2010.2103383

harmonic currents become a direct threat to power grid as well as the safe operation of its own [2], [3]. To effectively reduce the impact of single-phase locomotive on power quality of the utility grid, electrified railway institutions commonly adopted phase sequence rotation, reasonable locomotive operation modes or balanced transformers [4], [5], and so on, which can weaken the effects of NSCs in electric railway. However, these methods have a lack of flexibility, which could not implement a dynamic adjustment for the power of traction substation. Therefore, many programs of installing high-voltage, large-capacity Static Var Compensator (SVC), Active Power Filter (APF), and Distribution STATic Synchronous COMpensator (DSTATCOM) were proposed to obtain a comprehensive compensation for NSCs and harmonic currents in electrified railway [6]–[9]. Japanese scholars proposed a notion of the electrified railway power regulator [railway static power conditioner (RPC)] in 1993; RPC based on the switching devices was connected between two secondary output phases of traction transformer, which had the ability to control the active power, reactive power, and harmonic currents of two traction power arms [10]. The research of RPC has focused on its topology, compensation principles, basic control methods, etc. The literatures [11] and [12] discussed about several novel power quality compensators, which adopted three-phase converter or multilevel structure to compensate NSC, reactive power, and harmonic currents. The literatures [13] and [14] elaborated on two optimized compensation strategies for RPC, which were priority to achieve reactive power or NSC compensation. Some detection methods [15]–[17] based on three phase to synchronous frame transformation or Fryze, Buchholz, Dpenbrock algorithm (FBD) theory were proposed to obtain the instruction signals.The literatures generally adopted a conventional proportional-integral (PI) control, PWM modulation, or hysteresis control [18]–[20] to realize current tracking. However, there were little literatures aiming at improving adaptability and control performance of RPC. In this paper, a dual-loop control strategy was proposed to enhance the control performance of RPC. This paper analyzed the principle of NSC compensation for V/V traction system in Section III. Then, a dual-loop control strategy was proposed for the realization of RPC in Section IV. In order to improve the tracking performance of inner current control, a recursive PI control based on fuzzy algorithm was adopted to realize a fast and smooth tracking to the reference current. The recursive control is used to eliminate the steady-state

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Fig. 2.

Vector diagram for negative sequence current compensation.

shown as follows:

Fig. 1.

Compensation topology of RPC.

error, while the fuzzy rules are adopted to adjust the control parameters enhancing dynamic performance and robustness of RPC. In particular, the stable control of dc-link voltage is the prerequisite for normal operation of RPC. Therefore, an improved energy balance control method is proposed in this paper based on the relationship of two sides’ active power balance of RPC, which could achieve an accurate, fast tracking to the reference voltage and inhibit the fluctuations of dc-link voltage. Finally, in Section V, simulations and experiments have been carried out, and the results have verified the theoretical analysis correctly. II. TOPOLOGY OF RPC The structure of railway static power regulator is shown in Fig. 1. Three-phase 220-kV high voltage is stepped down into two single-phase power supply voltages at the rank of 27.5 kV by V/V transformer. RPC is made of two back-to-back voltage source converters, and a common dc capacitor, which can provide a stable dc-link voltage. Two converters are connected to V/V traction transformer’s secondary power arms through the output reactance and step-down transformer. If it can adopt a reasonable control strategy to adjust output currents of two converters, it would achieve the purpose of transferring active power from one power supply arm to another, compensating NSCs and suppressing harmonic currents. As a result of the advantages of simplicity and high capacity utilization of V/V traction transformer, it has been widely used in Chinese traction power supply system. Therefore, the comprehensive compensation approach of NSC and harmonic currents for V/V traction power supply system deserves further research. In Fig. 1, the definition of the right side is α-phase power arm, while that of the left side is β-phase power arm. Assume that the fundamental current vector of α-phase power arm is Iα and the fundamental current vector of β-phase power arm is Iβ . According to the characteristics of V/V traction transformer, the three-phase currents of the high-voltage side are

⎧ Iα ⎪ ⎪ IA = ⎪ ⎪ K B ⎪ ⎪ ⎨ Iβ IB = (1) ⎪ KB ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ I C = −(I α + I β ) KB where KB is the ratio of V/V traction transformer, and setting the ◦ complex computing symbol a = ej 120 , the positive sequence current (PSC) and NSC calculation formulas are expressed as follows: ⎤ ⎡ √ + I π π 3 1 1 a a2 ⎣ A ⎦ I Iα ej 6 ej 2 π π IB = = I− Iβ 3 1 a2 a 3K e−j 6 e−j 2 IC − I η = + × 100% I

(2) (3)

where I+ and I− separately represent the PSC and NSC components of three-phase current, respectively, and η is the unbalance level of three-phase currents. According to (3), it indicates that when only one traction power arm has train, the unbalance level η is 100%, and when two traction power arms have the same train load, the unbalance level η is 50%; therefore, the traction supply system would have a large number of NSC without power compensation device. III. ANALYSIS OF COMPENSATION PRINCIPLE AND ACQUISITION OF REFERENCE INSTRUCTION SIGNALS FOR RPC A. Compensation Principle In order to analyze the compensation principle of NSC, we assume that the ratio of V/V traction transformer KB = 1. A four-quadrant PWM rectification is adopted for the train, and its power factor is close to 1. In Fig. 2, UA , UB , and UC are three-phase primary voltages of the traction transformer; Uα and Uβ are the secondary voltages, and the difference of their phase angle is π/3. Before RPC’s compensation, α-phase power arm has load current I α L and the β-phase power arm has load current I β L , and the active current amplitude of two power arms are Iα L and Iβ L , respectively. First, the compensation device transfers half of the difference of the active current of two traction power

LUO et al.: DUAL-LOOP CONTROL STRATEGY OF RAILWAY STATIC POWER REGULATOR

arms (namely, |Iα L − Iβ L | /2) from the light power supply arm to the heavy one. Then, the currents of two power arms are compensated into I α and I β , respectively. Their amplitudes are equal to (Iα L + Iβ L )/2 and the phase angle difference is π/3; therefore, the unbalance level was 50% at this time. On the basis of the transfer of active power, RPC once again compensates a certain quantity of capacitive reactive current I C α on the power arm α and a certain quantity of inductive reactive current I C β on the power arm β, which can make the current of α-phase power arm lead the corresponding voltage π/6 and the current of β-phase power arm lag behind the corresponding voltage π/6. At this point, the amplitudes of the reactive currents could be calculated as follows: IC α = IC β =

tan π/6(Iα L + Iβ L ) . 2

Fig. 3.

Simplified model of RPC.

Fig. 4.

Single-phase equivalent electrical model of RPC.

(4)

After compensation, the currents IA and IB are separately coincident with the currents Iα and Iβ of two power arms, respectively, as shown in Fig. 2, and their phase angle deference is 2π/3; then C phase current IC can be obtained as IC = −IA − IB . Now, the NSC in the primary side is zero and power factors of three-phase currents are all one; therefore, the compensation purpose has been achieved. For the V/V traction system under any load condition, the principle of transferring active power and compensating reactive power is the same. Therefore, RPC can effectively deal with NSCs in V/V electrified railway and can make the three-phase currents symmetrical. B. Detection of Negative Sequence and Harmonic Reference Signals According to the former analysis of the compensation principle, the NSC and harmonic reference signals of RPC can be obtained by using the instantaneous power detection method [21]. Assuming that the A phase grid voltage is eA (t) = sin wt, the traction supply voltages of two traction arms are eα (t) = sin(wt − π/6) and eβ (t) = sin(wt − π/2), respectively. Defining load currents of two power arms as iα L (t) and iβ L (t), the load currents can be expressed as the Fourier series representation as follows: ⎧ ∝

⎪ ⎪ Iα n sin(nwt + ϕα n ) ⎨ iα L = Iα p sin(wt) + Iα q cos(wt) + n =2

∝

⎪ ⎪ ⎩ iβ L = Iβ p sin(wt) + Iβ q cos(wt) + Iβ n sin(nwt + ϕβ n ) n =2

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(5) where Iα p and Iβ p are separately the fundamental active component of two load currents, respectively, Iα q and Iβ q are the fundamental reactive component of them respectively, and Iα n sin(nwt + ϕα n ) and Iβ n sin(nwt + ϕβ n ) are the nth harmonic component of them, respectively. According to the detection principle in Fig. 5, the load currents of two traction power arms are multiplied by the synchronous voltages, respectively, and then a sum Im , which can imply the power size of two traction power arms, can be obtained by adding up each other. The average value Im p of the fundamental active currents of two power arms can be gained

from the low-pass filter, and it implies to the average active power size of two traction power arms. Therefore, Im p =

1 (Iα p + Iβ p ). 2

(6)

According to the aforementioned analysis of compensation principle, the expected target currents of the two power arms are derived as follows: ⎧ π π π ⎨ iα (t) = Im p sin wt − + Im p tan cos wt − 6 6 6 ⎩ i (t) = I sin wt − π − I tan π cos wt − π . β mp mp 2 6 2 (7) As long as RPC can compensate a specified amount of current to make the currents of two traction power arms into iα (t) and iβ (t), it can realize the purpose of NSC and harmonic currents compensation. Therefore, the compensation reference signals can be calculated as follows: iα r (t) = iα (t) − iα L (t) (8) iβ r (t) = iβ (t) − iβ L (t). As output currents of RPC can fully track the given fundamental and harmonic currents, it would achieve the compensation for NSCs and harmonic currents, and greatly improve power quality of electrified railway. IV. DUAL-LOOP CONTROL STRATEGY OF RPC A. System Modeling and Overall Control Strategy In order to analyze the principles of active power transfer, and reactive and harmonic current compensations, we have established the simplified model of RPC, as shown in Fig. 3. In Fig. 3, uα and uβ are the equivalent voltages of two traction power arms, respectively, iC α and iC β are the output equivalent currents of RPC, respectively, RN is the equivalent loss resistance of two converters and capacitor, and Lα and Lβ are the

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Fig. 5.

Closed-loop control block diagram of comprehensive compensation system.

output equivalent reactance on ac sides of RPC, respectively. RPC is composed of two back-to-back converters connected by dc capacitor essentially, and we can independently control the two converters. One converter can be used for rectification absorbing active power ((Pα − Pβ )/2) to maintain dc-link voltage, while the other one is used for inversion releasing energy of dc-link capacitor to provide the train with active power. In this way, the converters can complete the transfer of active power, and they can output corresponding reactive power (Qα , Qβ ) and harmonic currents to achieve the compensation for NSCs and harmonic currents, respectively. In order to describe the principle of power transmission in detail, the single-phase equivalent model of RPC is established, as shown in Fig. 4, where, iC n denotes nth current flowing through L, uS n stands for nth voltage of traction power arms, and uN n is the output nth voltage of converter. Suppose that uS n = US n sin (nwt), uN n = UN n sin(nwt − θn ), θn is the phase difference between uS n and uN n , and w is the fundamental angular velocity; therefore, from equation LdiC n /dt = uS n − uN n , we can get iC n =

1 [UN n cos(nwt − θn ) − US n cos(nwt)]. nwL

(9)

Output fundamental power of the traction power arm can be expressed by T1 1 US 1 UN 1 sin θ1 ¯ P1 = (10) US 1 sin(wt)iC 1 dt = T1 0 2wL T1 US 1 UN 1 cos θ1 − US2 1 ¯1 = 1 Q US 1 cos(wt)iC 1 dt = T1 0 2wL (11) ¯ 1 are the output where T1 is the period of the grid, and P¯1 and Q active and reactive power of traction power arms, respectively. By observing (10), we can see that when 0◦ < θ1 < π, the converter is used for rectification, and the energy of power grid will flow into the dc-link capacitor, which will charge the dc-link capacitor, and when −π < θ1 < 0◦ , the converter is used for inversion, and the energy of dc-link capacitor will flow into the traction power arm. If we adopt control measures, it will achieve

a continuous and stable flow of active power. However, if two converters of RPC go into a nonnormal operation caused by the ambient interference or the voltage fluctuation, it may happen to continuously charge dc-link capacitor by rectification without timely releasing the energy of dc-link capacitor; therefore, a big rise will occur in dc-link voltage, and vice versa. The power pulsation such as the dc-link voltage fluctuation caused by the transferred energy and the variation of system parameters will be analyzed and formulated elaborately in Section IV-C. From (11), the converter can output a proper voltage to generate the expected reactive power without consuming active power. For the harmonics suppression, the total harmonic distortion (THD) of traction supply voltages is less than 2% according to national standards of power quality; therefore, the harmonic voltages uS n (n = 1) of traction power arms can be omitted. From (9), the harmonic current generated by the converter can be calculated as iC n = UN n cos(nwt − θn )/nwL. From the aforementioned analysis, we can see that if two converters can output a proper voltage, then the corresponding active, reactive, and harmonic currents can be obtained to achieve the transfer of active power, reactive power, and harmonics compensation. As is known to all, the output of the converter is a controlled voltage signal; in order to achieve the purposes of NSCs compensation and harmonic suppression, it should control the output of RPC as a controlled current source by the closed-loop control to realize real-time tracking to the instruction signal, and the closed-loop control block diagram of the system is shown in Fig. 5. In order to make two converters work normally, it is necessary to obtain a stable dc-link voltage. An improved energy-balance controller is proposed for two converters to keep dc-link voltage stable by absorbing or releasing fundamental active power. The implementation of RPC is up to the performance of tracking to the reference current; therefore, a recursive PI control based on fuzzy regulation is adopted to improve the dynamic and antidisturbance performance. The algorithm is a point-to-point regulation, which can effectively eliminate the steady-state error and inhibit vibration of the inner current control, and the PI parameters are optimized dynamically by fuzzy regulation to improve control performance and robustness of the system.


As shown in Fig. 5, the tracking error of dc-link voltage is processed by the improved energy-balance regulator so that a regulation signal ΔIout (k) of dc-link voltage can be obtained. The outer loop voltage regulation signals [ΔIout (k) sin(wt − 30◦ ), ΔIout (k) sin(wt − 90◦ )] for two converters can be obtained by multiplying their respective sync signals. As soon as they are superimposed with the reference instructions of NSCs and harmonics (iα r , iβ r ), the total current reference signals (i∗α r , i∗β r ) for two converters can be obtained. The errors of inner current control can be obtained from i∗α r and i∗β r by subtracting the output currents (iC α , iC β ) of two converters. Then, the recursive PI control based on fuzzy algorithm is adopted to output a proper control value according to the input errors. The PWM modulation is adopted by two converters to generate the corresponding output voltage on the basis of the control value so that the expected currents can be generated by two converters to transfer active power, compensate reactive, and harmonic currents. Therefore, RPC adopts the dual-loop control described earlier, and can achieve the compensation for NSCs and harmonics and maintain its own stable operation.

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TABLE I Δ KP PARAMETER ADJUSTMENT RULES

TABLE II Δ KI PARAMETER ADJUSTMENT RULES

B. Recursive PI Control Based on Fuzzy Rules for Current Control The control of NSC, harmonic compensation, and dc-link voltage fluctuation suppression, all have their own control objectives, but those objectives can be consolidated into current target of the converters by the control circuit. Therefore, the control quality of the current loop has an important influence on the implementation of the RPC function. The traditional PI control algorithm can realize zero-error tracking to the instruction signal, which is a dc signal or slowchanging variable. However, when the instruction signal is a fast-changing sinusoidal variable, the traditional PI control algorithm has limitations. Therefore, a recursive PI algorithm is adopted to execute point-to-point regulation in this paper [22], which is equivalent to N PI-controllers working in parallel and can effectively eliminate the steady-state error. The recursive algorithm can be expressed as follows: uc (k) = KP e(k) +

C

KI e(k − iN )C = k/N

(12)

i=0

where uc (k) and e(k) are the output value of PI controller and error-sampled value at k moment, respectively, N is the sampling number within a cycle, and KP and KI are proportional coefficient and integral coefficient, respectively. This algorithm is going to integrate the error at the same time in every cycle. To facilitate digital implementation, out(k) can be expressed as an incremental form as follows: out(k) = out(k − N ) + KP [e(k) − e(k − N )] + KI e(k) (13) where k − N stands for the k moment of last cycle. According to (13), it can be seen that recursive PI algorithm contains the cycle information of reference signal, making sure that output current can track reference signal with zero-error in steady state. However, its dynamical performance is slow and it always delays a

period of time to respond. Considering the variation of electrified railway, it is necessary to adopt an adjustment algorithm to enhance dynamic performance and robustness. In this paper, a fuzzy rule is adopted to dynamically adjust the control parameters [23], [24]. Assuming fuzzy sets E, EC, U1 , U2 of e, ec , ΔKP , ΔKI are {NB, NS, O, PS, PB}. The role of ΔKP is up to make the controller generate a controlling operation immediately and attenuate error quickly. Integral part ΔKI of the controller is mainly used to eliminate error and improve steady performance. According to the aforementioned analysis, the control rules of ΔKP and ΔKI can be derived as shown in Tables I and II. The steps of fuzzy reasoning algorithm are as follows. 1) Fuzzy E = λ1 E(k)

EC = λ2 EC (k) .

(14)

2) Fuzzy reasoning: According to E, EC fuzzy query table, it can find out U1 (k)and U2 (k). 3) Antiblur technology KP (k) = KP 0 + λ3 U1 (k) (15) KI (k) = KI 0 + λ4 U2 (k) where x stands for rounding x, λ1 and λ2 stand for the fuzzy factor, and λ3 and λ4 stand for antiblur factor. These values can be selected on the basis of the actual situation. C. DC-Link Voltage Control Based on Energy Balance In this paper, an energy-balance control based on exact feedback is proposed to maintain the stability of dc-link voltage. According to the energy-balance principle, the power and energy of RPC’s ac and dc sides are equal to each other, as shown in Fig. 3. The power pulsation such as the dc-link voltage fluctuation caused by the transfer of energy and the variation of

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system parameters will be formulated and analyzed elaborately. The following equation can be obtained according to the power balance of RPC: dudc diα diβ u2 = iα uα − Lα + iβ uβ − Lβ − dc udc C dt dt dt RN (16) The two traction power voltages are uα = E sin(wt − π/6) and uβ = E sin(wt − π/2). Assume that the two output currents of RPC are iC α = IC α sin(wt − (π/6) − ϕα ) and iC β = IC β sin(wt − (π/2) − ϕβ ). The dc-link voltage udc (t) can be expressed as the sum of its average value and ripple component, Ñ . Assuming that the current phase namely, udc (t) = Udc + u would not mutate suddenly, only if considering the fundamental component of currents, (16) can be expressed as follows: dUdc d˜ uN dUdc d˜ uN + Udc +u Ñ +u Ñ C Udc dt dt dt dt =

EIC α [cos ϕα − cos(2wt − (π/3) − ϕα )] 2 wLα IC2 α sin 2(wt − (π/6) − ϕα ) 2 Lα IC α (dIC α /dt)[1 − cos 2(wt − (π/6) − ϕα )] − 2 EIC β [cos ϕβ − cos(2wt − π − ϕβ )] + 2 −

wLβ IC2 β sin 2(wt − (π/2) − ϕβ ) 2 Lβ IC β (dIC β /dt) [1 − cos 2(wt − (π/2) − ϕβ )] − 2

=

1 dΔIα 1 E(Iα m + ΔIα ) cos ϕα − Lα (Iα m + ΔIα ) 2 2 dt 1 1 dΔIβ + E(Iβ m + ΔIβ ) cos ϕβ − Lβ (Iβ m + ΔIβ ) 2 2 dt −

(17)

As is known to us, the average value Udc of dc-link voltage is up to the active power variation. Therefore, the dc component of dc-link voltage, which does not contain ripples, can be separated from (17) by comparing the same frequency component on both sides, namely, dUdc 1 dIC α 1 = EIC α cos ϕα − Lα IC α CUdc dt 2 2 dt

(19)

According to the steady-state energy balance, the static component can be extracted from (19). Therefore, the equation can be obtained as follows: EIβ m cos ϕβ U∗ EIα m cos ϕα + − D =0 2 2 RN 2

(20)

where the expression of EIα m cos ϕα /2 or EIβ m cos ϕβ /2 denotes active power absorbed from the traction power arm by rectification or released to the traction power arm by inversion, 2 respectively. UD∗ /RN is the loss of RPC. Equation (20) illuminates that the energy absorbed from one traction power arm is nearly given to another power arm when the system is stable, 2 and RPC only absorbs a little power (UD∗ /RN ) to maintain its 2 ) can be omitted; own operation. The secondary offset (ΔUdc therefore, (19) can be simplified as follows: CUD∗

−

Ñ + u ˜2N U 2 + 2Udc u . − dc RN

(UD∗ + ΔUdc )2 . RN

1 dΔUdc dΔIα 1 = E cos ϕα ΔIα − Lα Iα m dt 2 2 dt 1 dΔIβ 1 + E cos ϕβ ΔIβ − Lβ Iβ m 2 2 dt 2UD∗ ΔUdc − . (21) RN

From the perspective of digital control, the discrete expression can be deduced from (21) with the control cycle TS CUD∗ =

[ΔUdc (k) − ΔUdc (k − 1)] 2UD∗ ΔUdc (k) + TS RN E cos ϕα ΔIα (k) Lα Iα m [ΔIα (k) − ΔIα (k − 1)] − 2 2TS +

E cos ϕβ ΔIβ (k) Lβ Iβ m [ΔIβ (k) − ΔIβ (k − 1)] − . 2 2TS (22)

Equation (22) can show the mutual constraint relation among dc-link voltage, the traction supply voltages, and the output U2 dIC β 1 1 − dc . (18) currents of RPC, and it can also reveal the presence of power + EIC β cos ϕβ − Lβ IC β 2 2 dt RN pulsation, such as the fluctuations of dc-link voltage. In orFundamental active currents, which are supplied by the two der to obtain the reference signal of dc-link voltage, the detraction power arms charge or discharge dc-link capacitor to sup- sired instruction signal is assumed as ΔIout (k). Consider the press the fluctuations of Udc . Assume that Udc = UD∗ + ΔUdc , responsibility of fluctuation suppression and that the power IC α = Iα m + ΔIα , and IC β = Iβ m + ΔIβ , in which UD∗ , Iα m , loss are up to two converters equally in the steady state, and Iβ m are the static value of dc-link voltage and two output namely, ΔI α (k) = ΔI β (k) = −ΔIout (k). Therefore, we can fundamental currents of RPC in steady state, respectively, while get ΔIout (k)from (22) as follows: ΔUdc , ΔIα , and ΔIβ are the offset of them. Udc , ICα , and ICβ ΔIout (k) = γ[ΔUdc (k) − ΔUdc (k − 1)] + λΔUdc (k) + ΔI(k) are linearly processed into the sum of static component and (23) offset, and substituting them into (18), the following can be where, γ = (CUD∗ /M ∗ TS ), λ = 2UD∗ /M ∗ RN , ΔI(k) = obtained: (−(Lα Iα m /2TS )ΔIα (k − 1) − (Lβ Iβ m /2TS )ΔIβ (k − 1))/ M, and M = −(1/2)[(E cos ϕα − (Lα Iα m /TS )) + dΔUdc C(UD∗ + ΔUdc ) − (L I (E cos ϕ β β β m /TS ))]. dt


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TABLE III PARAMETERS OF RPC FOR SIMULATION

√ In the steady state, there are |cos ϕα | = |cos ϕβ | = 3/2. According to the aforementioned analysis, the offset of current amplitudes would cause the variations of Udc . Therefore, it can be inversely deduced to the expected output offset of current amplitude, i.e., to say, the variations of dc-link average voltage can be suppressed by the corresponding offset of current amplitude, which is calculated exactly from this inverse reasoning of (23). The relationship is one-to-one causal relation, and the controller can automatically change control parameters according to the variation of corresponding parameters. In order to improve the dynamic response of dc-link voltage control, an improved energy-balance control is proposed for the voltage control, namely, ⎧ ⎪ ⎨ γ[ΔUdc (k) − ΔUdc (k − 1)] + λΔUdc (k) + ΔI(k), when |ΔUdc (k)| < ε ΔIout (k) = ⎪ ⎩ KΔUdc (k), when |ΔUdc (k)| > ε (24) where K is the proportional constant of voltage controller. As seen from (24), when the error is large and RPC has not yet entered the steady state, a proportional control is used to make voltage error decrease rapidly to the steady-state value. When the error is small, the energy-balance control is proposed to maintain stable dc-link voltage and inhibit the vibration of dc-link voltage. In this paper, a mean filter is presented to filter the secondary ripples of the dc-link voltage signal to avoid generating third harmonic in reference signals. Assuming sampling N points in each cycle, N/2 mean filter is adopted to filter the secondary ripples and is expressed as follows: N /2−1 1 x(k − m) = y(k − 1) y(k) = N/2 m =0

+

x(k) − x(k − N/2) . N/2

(25)

V. SIMULATION AND EXPERIMENT In order to prove the correctness of the detection method and analysis presented in this paper, simulations have been carried out. Simulation parameters of RPC are shown in Table III. Resistance and harmonic sources are used to replace the equivalent locomotive. The power of the load locomotive is generally 4.5 MW and its power factor is approximately 1, while the THD of current is 14.5%.

Fig. 6. Power arm currents and three-phase currents before and after comprehensive compensation. (a) Current waveforms of two supply arms before and after RPC’s compensation. (b) Three-phase current waveforms before and after RPC’s compensation.

A. Simulation Results Considering only α-phase power arm holding a load, we adopted the detection method and control strategy described in this paper. Switching on RPC at 0.1 s, the simulation results are shown in the following. As seen from Fig. 6, only α-phase power arm had current before compensation; therefore, only A and C phases had mutually reverse currents. After switching on RPC, a certain amount of active power was transferred from β-phase power arm to α-phase power arm for the train load. Then, RPC once again compensated a certain amount of reactive current and harmonics, respectively, to the corresponding power arms to suppress NSC and harmonics in accordance with the reference signals. After compensation, the amplitude of Iα was equal to the one of Iβ , and their phase angle difference was 2π/3. The original three-phase currents IA , IB , and IC were almost symmetrical; therefore, the unbalance degree of the three-phase currents dropped from original 100% to 3.1%, and the THD of α-phase power arm current reduced from 14.5% to 2.3%, respectively. In order to verify the performance of recursive PI control based on fuzzy algorithm, a resistive load considered as a disturbance was switched into α-phase power arm at 0.4 s, as shown in Fig. 7. The simulations would elaborate on two points of the dynamic response speed and compensation accuracy. The tracking error was kept the same before compensation. After

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Fig. 7. Waveforms with two different control methods. (a) Dynamic waveform of three-phase current with traditional PI control. (b) Dynamic waveform of three-phase current with fuzzy recursive PI control. (c) Current error of α-phase injection branch with traditional PI control. (d) Current error of α-phase injection branch with fuzzy recursive PI control. (e) Current spectrum of the steady-state error with traditional PI control. (f) Current spectrum of steady-state error with fuzzy recursive PI control. (g) Dynamic waveform of KP with fuzzy regulation. (h) Dynamic waveform of KI with fuzzy regulation.


TABLE IV HARMONIC AMPLITUDE OF STEADY ERROR

TABLE V PARAMETERS OF RPC FOR EXPERIMENT

switching on RPC, Fig. 7(a) and (c) showed that it took some time to make the error decay to zero when using a PI controller. However, in Fig. 7(b) and (d), a recursive algorithm was adopted to realize the point-to-point conditioning in real time, and fuzzy algorithm was used to adjust control parameters according to the error shown in Fig. 7(g) and (h). When the value of e was large, as shown in Fig. 5(e), KP rose rapidly to increase the control output and attenuate the error quickly, but KI decreased rapidly to attenuate its effect to prevent overshoot. As the error was gradually decreased, KP would decrease correspondingly to reduce the control output and avoid overshoot; however, KI would increase gradually to enhance its effect, and the steadystate error would be reduced. Finally, KP and KI could tend to be a stable value, as shown in Fig. 7(g) and (h). Therefore, output currents of RPC were fast tracking to the reference current, and the three-phase currents rose smoothly with a little vibration. Therefore, the fuzzy recursive algorithm could effectively improve the control effects and antidisturbance performance of RPC. A further comparison of the tracking accuracy of two control algorithms was carried out by analyzing error spectrums. Fig. 7(e) is the spectrum of the steady-state error with the PI control, while Fig. 7(f) is the spectrum with fuzzy recursive PI control. The amplitudes of fundamental, second, third, fifth component of the steady-state current error are shown in Table IV. As seen from Table IV, the system’s steady-state tracking accuracy has greatly improved with fuzzy recursive PI control algorithm. In Fig. 8, a simulation was executed to test the performance of improved energy-balance control for voltage loop. After stable operation of RPC, the reference voltage was changed suddenly from 2 to 2.2 kV at 0.5 s, therefore a simulation comparison was executed, as shown in Fig. 8. When using conventional PI control, Fig. 8(a) showed that the tracking error had experienced about 0.2-s vibration and attenuation process, and finally tended into the steady state. While adopting improved energy-balance control shown in Fig. 8(b) and (c), first, the voltage tracking error was big (ΔUdc > 50 V) and the proportional control was adopted. During the time from 0.5 to

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0.6 s, the β-phase output current was increasing to charge dc-link capacitor with more energy, while the α-phase output current including harmonic currents was decreasing to reduce energy release shown in Fig. 8(c) so that the dc-link voltage had to rise rapidly, as shown in Fig. 8(b). When the voltage tracking error was small (ΔUdc < 50 V) and an accurate feedback control based on energy balance was applied. During the time from 0.6 to 0.7 s, the β-phase output current gradually reduced, while the α-phase output current was increasing to enhance energy release shown in Fig. 8(c) so that the dc-link voltage rose slowly and finally the system maintained it all the time, as shown in Fig. 8(b). Compared with Fig. 8(a), the improved energy-balance control can realize a fast and smooth tracking to reference voltage signal; the mutual constraint relationship between dc-link voltages and currents can express the process of the power transmission and pulsation B. Experiment Results A V/V traction system at 220-V rank was build to simulate electrified railway traction system in the laboratory, and its structure is shown in Fig. 1. Two single-phase transformers with the ratio of 380:220 were used as the V/V traction transformer, and the ratio of two single-phase step-down transformers was 220:220. A 15-kW noncontrolled rectifier load was adopted to simulate the locomotive, and its THD was about 12.5%. Industrial computer as a host computer was used to complete the voltage and current acquisition and data calculation. TMS320F28335 was used as the main core of slave computer, which is made by TI company, which constituted a packaged module together with RPC’s two converters, and it would send PWM wave and drive the IGBT module. The V/V traction device and RPC’s controller are shown in Fig. 9, and the experiments results are shown in Fig. 10. RPC adopted the control strategy proposed in this paper, and the experiment results are shown in Fig. 9. Considering only α-power arm holding a load, it would illustrate the control performance of RPC. Before compensation, only A and C phases had mutually reverse currents, as shown in Fig. 10(a); therefore, the content of NSC was large. Comparing to traditional PI control shown in Fig. 10(b), we can find that the fuzzy recursive PI control can achieve a faster tracking to the reference current with a little vibration after switching on RPC, while it had a smooth dc-link voltage, as shown in Fig. 10(d). Energy exchange of RPC occurred in this dynamic process. During the first several cycles, the charging current iC β (the red line) was bigger than the discharging current iC α (the black line), as shown in Fig. 10(e), and the energy was flowing into dc-link capacitor from β power arm; therefore, the dc-link voltage ascended rapidly from 350 to 500 V, as shown in Fig. 10(d). When the voltage error was small, the energy-balance control was adopted. Then, two output currents of RPC tend to be equal to maintain stable dc-link voltage with a little vibration. Finally, the compensation system was going into the steady state. After compensation, the primary three-phase currents are nearly symmetrical, and the unbalance level and the THD of α power arm current are 5.5% and 4.3%,

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Fig. 8. Comparison of two kinds of control mode for outer loop. (a) Tracking error with conventional PI control. (b) Tracking error with the improved energy-balance control. (c) Output currents of RPC with the improved energy-balance control.

Fig. 9. Picture of integrated compensator. (a) V/V traction power supply system and locomotive load model. (b) RPC’s control panel and intelligence driver module.

respectively. By adopting the dual-loop control method proposed in this paper, the control performance and adaptability of RPC had effectively enhanced, and it can greatly improve power quality of electrified railway.

VI. CONCLUSION 1) This paper first analyzed the electrical characteristics of a V/V traction transformer in electrified railway and explored the compensation principle of RPC, and then the


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Fig. 10. Waveforms of experiment results. (a) Three-phase current waveform before compensation. (b) Dynamic waveform of three-phase current with traditional PI control. (c) Dynamic waveform of three-phase current with fuzzy recursive PI control. (d) Dynamic waveform of dc-link voltage. (e) Dynamic waveform of output currents of RPC.

method of generating the reference instruction signals was derived. 2) Second, a dual-loop control strategy was constructed for RPC in this paper. A fuzzy-algorithm-based recursive PI control was discussed to improve the control performance of RPC. A recursive control was employed to reduce the

error in steady state, and fuzzy rules were adopted to adjust parameters of controller online. Then, according to the relationship of the energy balance of the RPC’s two sides, an improved energy-balance control method was proposed, which can achieve a smooth track the reference voltage.

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3) Compared to functional singularity of other traditional compensation device, RPC can complete the transfer of active power, the compensation of reactive power and harmonics, and it can effectively ameliorate power quality of electrified railway. Finally, the simulation and experiment results have verified the correctness of the analysis in this paper. REFERENCES [1] X. Huang, L. Zhang, M. He, X. You, and Q. Zheng, “Power electronics used in Chinese electric locomotives,” in Proc. IEEE 6th Int. Conf. Power Electron. Motion Control, May, 2009, pp. 1196–1200. [2] T.-L. Lee and P.-T. Cheng, “Design of a new cooperative harmonic filtering strategy for distributed generation interface converters in an islanding network,” IEEE Trans. Power Electron., vol. 22, no. 5, pp. 1919–1927, Sep. 2007. [3] C.-C. Yeh and M. D. Manjrekar, “A reconfigurable uninterruptible power supply system for multiple power quality applications,” IEEE Trans. Power Electron., vol. 22, no. 4, pp. 1361–1372, Jul. 2007. [4] A. Bueno, J. M. Aller, J. Restrepo, and T. Habetler, “Harmonic and balance compensation using instantaneous active and reactive power control on electric railway systems,” in Proc. Appl. Power Electron. Conf. Expo., 2010, pp. 1139–1144. [5] Z. Zhang, B. Wu, J. Kang, and L. Luo, “A multi-purpose balanced transformer for railway traction applications,” IEEE Trans. Power Del., vol. 24, no. 2, pp. 711–718, Apr. 2009. [6] P.-C. Tan, P. C. Loh, and D. G. Holmes, “A robust multilevel hybrid compensation system for 25-kV electrified railway applications,” IEEE Trans. Power Electron., vol. 19, no. 4, pp. 1043–1052, Jul. 2004. [7] H. L. Ginn and G. Chen, “Flexible active compensator control for variable compensation objectives,” IEEE Trans. Power Electron., vol. 23, no. 6, pp. 2931–2941, Nov. 2008. [8] B. Singh, P. Jayaprakash, and D. P. Kothari, “AT-connected transformer and three-leg VSC based DSTATCOM for power quality improvement,” IEEE Trans. Power Electron., vol. 23, no. 6, pp. 2710–2718, Nov. 2008. [9] M. Jianzong, W. Mingli, and Y. Shaobing, “The application of SVC for the power quality control of electric railways,” in Proc. Int. Conf. Sustainable Power Gener. Supply, 2009, pp. 1–4. [10] Y. Mochinaga, Y. Hisamizu, M. Takeda, T. Miyashita, and K. Hasuike, “Static power conditioner using GTO converters for AC electric railway,” in Proc. Power Convers. Conf., 1993, pp. 641–646. [11] Z. Sun, X. Jiang, D. Zhu, and G. Zhang, “A novel active power quality compensator topology for electrified railway,” IEEE Trans. Power Electron., vol. 19, no. 4, pp. 1036–1042, Jul. 2004. [12] L. Zhou, Q. Fu, X. Li, and C. Liu, “A novel multilevel power quality compensator for electrified railway,” in Proc. 6th Int. Conf. Power Electron. Motion Control, 2009, pp. 1141–1147. [13] T. Uzuka, S. Ikedo, and K. Ueda, “A static voltage fluctuation compensator for AC electric railway,” in Proc. 35th Annu. Spec. Conf. Power Electron., 2004, vol. 3, pp. 1869–1873. [14] H. Morimoto, M. Ando, Y. Mochinaga, T. Kato, J. Yoshizawa, T. Gomi, T. Miyashita, S. Funahashi, M. Nishitoba, and S. Oozeki, “Development of railway static power conditioner used at substation for Shinkansen,” Power Conver. Conf., vol. 3, pp. 1108–1111, 2002. [15] V. M. Moreno, M. Liserre, A. Pigazo, and A. Dell’Aquila, “A comparative analysis of real-time algorithms for power signal decomposition in multiple synchronous reference frames,” IEEE Trans. Power Electron., vol. 22, no. 4, pp. 1280–1289, Jul. 2007. [16] V. M. Moreno and A. Pigazo, “Modified FBD method in active power filters to minimize the line current harmonics,” IEEE Trans. Power Del., vol. 22, no. 1, pp. 735–736, Jan. 2007. [17] M. Depenbrock, V. Staudt, and H. Wrede, “Concerning ‘Instantaneous power compensation in three-phase systems by using p-q-r theory’,” IEEE Trans. Power Electron., vol. 19, no. 4, pp. 1151–1152, Jul. 2004. [18] N. Prabhakar and M. K. Mishra, “Dynamic hysteresis current control to minimize switching for three-phase four-leg VSI Topology to compensate nonlinear load,” IEEE Trans. Power Electron., vol. 25, no. 8, pp. 1935– 1942, Aug. 2010. [19] M. Oettmeier, C. Heising, V. Staudt, and A. Steimel, “Dead-beat control algorithm for single-phase 50-kW AC railway grid representation,” IEEE Trans. Power Electron., vol. 25, no. 5, pp. 1184–1192, May. 2010.

[20] T. Jin and K. M. Smedley, “Operation of one-cycle controlled three-phase active power filter with unbalanced source and load,” IEEE Trans. Power Electron., vol. 21, no. 5, pp. 1403–1412, Sep. 2006. [21] H. Kim, F. Blaabjerg, and B. Bak-Jensen, “Spectral analysis of instantaneous powers in single-phase and three-phase systems with use of p-q-r theory,” IEEE Trans. Power Electron., vol. 17, no. 5, pp. 711–720, Sep. 2002. [22] A. Luo, C. Tang, Z. K. Shuai, W. Zhao, F. Rong, and K. Zhou, “A novel three-phase hybrid active power filter with a series resonance circuit tuned at the fundamental frequency,” IEEE Trans. Ind. Electron., vol. 56, no. 7, pp. 2431–2440, Jul. 2009. [23] M. F. Naguib and L. Lopes, “Harmonics reduction in current source converters using fuzzy logic,” IEEE Trans. Power Electron., vol. 25, no. 1, pp. 158–167, Jan. 2010. [24] Y.-S. Kung and M.-H. Tsai, “FPGA-based speed control IC for PMSM drive with adaptive fuzzy control,” IEEE Trans. Power Electron., vol. 22, no. 6, pp. 2476–2486, Nov. 2007.

An Luo (M’09–SM’09) was born in Chang Sha, China, on July 21, 1957. He received the B.S. and M.S. degrees from Hunan University, Changsha, Hunan, China, in 1982 and 1986, respectively, and the Ph.D. degree from Zhejiang University, Zhejiang, China, in 1993. From 1996 to 2002, he was a Professor with the Central South University, Changsha. Since 2003, he has been a Professor at the College of Electrical and Information Engineering, Hunan University. He is engaged in research on power conversion system, harmonics suppression, and reactive power compensation, electric power saving. He is the author or coauthor of more than 100 published journal and conference articles. Dr. Luo is a recipient of the 2006 National Scientific and Technological Award of China, the 2005 Scientific and Technological Award from the National Mechanical Industry Association of China, and the 2007 Scientific and Technological Award from the Hunan Province of China. He is currently the Associate Board Chairperson of Hunan Society of Electrical Engineering. He is also the Chief of Hunan Electric Science and Application Laboratory.

Fujun Ma was born in Hunan, China, in June, 1985. He received the B.S. and M.S. degrees from the College of Electrical and Information Engineering, Hunan University, Changsha, China, in 2008 and 2010, respectively. Since Sept. 2010, he has been a Ph.D. student in reading in the College of Electrical and Information Engineering, Hunan University. His research interests include power quality managing technique of electrified railway, electric power saving, reactive power compensation, and active power filters.

Chuanping Wu was born in Hunan, China, in March, 1984. He received the B.S. and M.S. degrees from the College of Electrical and Information engineering, Hunan University, Changsha, China, in 2007 and 2009, respectively. Since Sept. 2009, he has been a Ph.D. student in the College of Electrical and Information engineering, Hunan University. His research interests include power quality control technique for electric railway system, harmonics suppression and reactive power compensation.


Shi Qi Ding was born in July 1966. He received the B.S. and M.S. degrees in control engineering from Central South University, Hunan, China, in July 1989 and July 2002, respectively. He is currently working toward the Ph.D. degree at the Graduate School of Hunan University, Changsha, Hunan. His Ph.D. thesis focuses on control theory and control engineering. He is currently the General Manager of HEFEI TONGGUAN GUOXUAN Copper Co. Ltd. Hefei, Anhui, China. His research interests include the reactive power compensation and harmonic suppression. Dr. Ding was awarded the title of Senior Electrical Engineer and given special allowance of Anhui provincial government (Engineering Technology) in 2007.

Q.-C. Zhong (M’03–SM’04) was born in Sichuan, China, in 1970. He received the M.S. degree in electrical engineering from Hunan University, Hunan, China, in 1997, and the Ph.D. degree in control theory and engineering from Shanghai Jiao Tong University, Shanghai, China, in 1999. He started working in the area of control engineering after he graduated from Xiangtan Institute of Mechanical and Electrical Technology (now renamed as Hunan Institute of Engineering), in 1990. From 2000 to 2001, he was a Postdoctoral Researcher at Technion-Israel Institute of Technology, Israel. He is currently a Research Associate in the Department of Electrical and Electronic Engineering, Imperial College London, London, U.K. His current research interests include H-infinity control of time-delay systems, control in power electronics, process control, control in communication networks, and control using delay elements, such as input shaping technique and repetitive control.

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Zhi Kang Shuai was born in Shandong, China, on December 19, 1982. He received the B.S. and M.S. degrees from the College of Electrical and Information Engineering, Hunan University, Changsha, China, in 2005 and 2007, respectively. Since Sept. 2007, he has been a Ph.D. student in the College of Electrical and Information Engineering, Hunan University. His research interests include electric power saving, reactive power compensation, and active power filters.

A Dual-Loop Control Strategy of Railway Static Power ... - IEEE Xplore

A Dual-Loop Control Strategy of Railway Static Power ... - IEEE Xplore

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