A New Integrated Hybrid Power Quality Control System ... - IEEE Xplore

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 62, NO. 10, OCTOBER 2015

A New Integrated Hybrid Power Quality Control System for Electrical Railway Sijia Hu, Student Member, IEEE, Zhiwen Zhang, Yuehui Chen, Guandong Zhou, Yong Li, Senior Member, IEEE, Longfu Luo, Member, IEEE, Yijia Cao, Senior Member, IEEE, Bin Xie, Xiaoting Chen, Bin Wu, Fellow, IEEE, and Christian Rehtanz, Senior Member, IEEE

Abstract—This paper presents an integrated hybrid railway power quality control system (HRPQC) to deal with the power quality problems in the electrical railway supply system. The prominent advantage of HRPQC is that, in the premise of adopting a hybrid compensating scheme for better performance, it can integrate the active system with the main transformer without other expensive low-frequency high-power auxiliary transformers. HRPQC’s mathematical model, control idea, and transforming relationship in harmonic frequency are ﬁrst presented. Second, the harmonic-suppressing mechanism and the resonance characteristics are analyzed in detail. Finally, simulation and experimental results verify the effectiveness of the proposed compensating system. Index Terms—Auxiliary transfomerless, electrical railway, harmonics and reactive power, hybrid compensation, unbalanced current.

I. I NTRODUCTION

A

S the development of Chinese railway construction, some new generation ac–dc–ac locomotives are applied in highspeed railway networks (about 10%–13% of the total railroad mileage [1]). On the other hand, due to historical reasons, conventional locomotives still act as the main role of the active-

Manuscript received November 14, 2014; revised January 24, 2015 and February 26, 2015; accepted March 10, 2015. Date of publication April 6, 2015; date of current version September 9, 2015. This work was supported in part by the National Natural Science Foundation of China under Grant 51477046 and Grant 51377001, in part by the National Science and Technology Support Program of China under Grant 2013BAA01B01, in part by the Hunan Province Innovation Foundation for Postgraduate under Grant CX2014B131, in part by the Key Project of Hunan Provincial Natural Science Foundation of China under Grant 12JJ2034, in part by the Science and Technology Program of the China State Grid Corporation under Grant 5216A014007V, and in part by the Scientific and Technological Research for Hunan Province Strategic and New Industries under Grant 2014GK1037. (Corresponding author: Zhiwen Zhang.) S. Hu, Z. Zhang, Y. Li, L. Luo, Y. Cao, B. Xie, and X. Chen are with the College of Electrical and Information Engineering, Hunan University, Changsha 410082, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; yjcao@ hnu.edu.cn; [email protected]; [email protected]). Y. Chen is with the State Grid Hunan Electric Power Company, Changsha 410007, China (e-mail: [email protected]). G. Zhou is with the Science and Technology Department of Environmental Protection, State Grid Human Electric Power Company, Changsha 410199, China. C. Rehtanz is with the Institute of Energy Systems, Energy Efficiency and Energy Economics, TU Dortmund, 44227 Dortmund, Germany (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2015.2420614

duty trains (about 85% of the total railroad mileage [1]). For cost efficiency consideration, they are particularly commonly used in the freight-lines of the vast resource-rich regions. A large number of harmonics, reactive power, and negative sequence currents inject into the utility, which seriously affects the power quality and stability of the grid and arouses widespread attention of related departments and engineers [1]–[3]. Due to the good performance of suppressing negative and zero sequence components, balance traction transformers are widely used in many countries’ electrical railway power systems (ERPSs) [4], [5]. However, it has no ability of compensating harmonics and reactive power. To overcome this problem, the authors presented the multipurpose balance transformer (MPBT) in [6]. Because MPBT has an interface for passive power filter (PPF) in its secondary winding, both harmonics and reactive power can be compensated in the premise of retaining the inherent advantages of a conventional balance traction transformer. However, in industrial applications, the authors found that the harmonic filtering performances in phases A, B, and C are not the same and show a big difference when the load changes [7]. Moreover, its resonance mechanism is unclear when PPF is connected. Unfortunately, there is still no effective method to analyze them, so it needs further study. Various IGBT or IGCT-based active compensating systems have been put forward in the last 20 years [8]–[20]. Among them, railway static power conditioner (RPC) [16]–[19] and active power quality compensator (APQC) [20] are the representative models. They can successfully deal with the main power quality problems in ERPS. However, RPC requires two large-capacity single-phase multiwinding step-down transformers, while a complex high-power Scott transformer is also needed for APQC as the interface of its converter. All of these bulky low-frequency auxiliary transformers are the major unfavorable factor in reducing the costs and improving the system’s integration [8]. To overcome these problems, an integrated hybrid railway power quality control system (HRPQC) is proposed in this paper. As shown in Fig. 1, HRPQC is composed of an MPBT, three LC branches, and a three-phase full-bridge converter (FBC). The LC branches of HRPQC are designed based on the magnetic potential balance principle (MPBP) in harmonic frequency [6], [21], [22], so we also called it MPBP-based integrated HRPQC. This paper is organized as follows. The topology and characteristics of HRPQC are discussed in Section II. In Section III,

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HU et al.: NEW INTEGRATED HYBRID POWER QUALITY CONTROL SYSTEM FOR ELECTRICAL RAILWAY

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3) Take full use of MPBT’s inherent ability of suppressing negative sequence currents. The 95% probability value of the negative sequence voltage rate (NSVR) at the high voltage side can be reduced significantly (note: whether the 95% probability value of NSVR is less than 2% in the point of common coupling is the negative sequence component’s assessment index of Chinese national standard). It is found that adoption of a balance traction transformer can get a satisfactory performance of suppressing negative sequence components in practical applications [23]. III. H ARMONIC M ATHEMATICAL M ODEL AND T RANSFORMING C HARACTERISTICS OF HRPQC A. Basic Current Transforming Relationship of HRPQC

Fig. 1. Topology of HRPQC.

HRPQC’s harmonic mathematical model and transforming relationship are presented. Based on the harmonic transforming relationship, both the harmonic filtering mechanism and the resonance characteristics of HRPQC are discussed in Section IV in detail. Section V gives the control system. The simulation and experimental results are given in Section VI. Finally, the conclusion is given in Section VII. II. TOPOLOGY OF HRPQC As shown in Fig. 1, a three-phase 110-kV (or 220 kV) highvoltage grid is stepped down into the two-phase voltage at the rank of 27.5 kV by MPBT. Another three-phase voltage in taps U, V, and W can be adjusted to an appropriate value matched with FBC by changing the turns’ ratio in taps U and W. For FBC, the outgoing lines connect with U, V, and W taps via three LC branches. Multiple or single filtering branch scheme can be used for HRPQC [23]. The advantages of HRPQC are mainly exhibited in the following aspects. 1) Since the turns’ ratios Na2 /Na1 and Nc2 /Nc1 of windings UV and VW can be adjusted in the designing process of MPBT, FBC can connect with the main transformer without auxiliary transformers. Therefore, it significantly simplifies the system’s structure and makes it easier for system integration. 2) MPBP is adopted in the designing process of PPF for better harmonic blocking performance [6], [21]–[23]. PPF is mainly adopted to absorb low-order harmonics and reactive power, while the influences of load fluctuation and system resonance can be effectively attenuated by FBC to further improve the harmonic filtering performance of PPF. That is to say that the hybrid compensating scheme can improve the system’s reliability and harmonic filtering performance and reduce the power rating of the converter [24]–[30].

Referring to Fig. 1, the number of turns and the impedances of MPBT are defined as follows: ⎧ ⎧ ⎪ ⎪ N ZA = ZB = ZC = ZI = N = N = N A B C I ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ N = N = N = N b c II ⎨ a ⎨Zb = λZa = λZc = λZII Na = Na1 + Na2 Za = Za1 + Za2 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ N = N + N Zc = Zc1 + Zc2 ⎪ ⎪ c c1 c2 ⎪ ⎪ ⎪ ⎪ ⎩N = N = 0.366N ⎩Z = Z = xZ b1 b2 II a2 c2 II (1) where Nk and Zk are the turns’ number and the impedance of winding k, respectively (k = A, B, and C; a, b, and c; a1 and a2 ; and c1 and c2 ). To satisfy the balancing condition, λ = 2.732, and x = 1.577y (note: y = Na2 /Na = Nc2 /Nc ) [6]. By selecting an appropriate value of y in the designing process of MPBT, the voltages in tapes U, V, and W can be adjusted. By using the Kirchhoff’s law and the ampere-turns balancing equations of MPBT in Fig. 1, the basic current transforming relationship of HRPQC can be calculated as follows [8]: ⎡ ⎤

IA ⎣IB ⎦ = B1 Iα + B2 IU (2) Iβ IW IC where IA , IB , and IC are the primary currents, Iα and Iβ are the two phase load currents, IU and IW are the currents absorbed from taps U and W √ √ ⎤ ⎡ 1− 3 1+ 3 √ ⎢ d ⎥ d2 1 ⎥ 3NII ⎢ ⎢ B1 = −2 −2 ⎥ ⎢ ⎥ 6N ⎦ I ⎣ d3√ √ m1 1+ 3 1− 3 ⎡ ⎤ 2 1 xNII ⎣−1 √ 1 ⎦. B2 = (3 + 3)NI −1 −2

m2

From (2), we can obtain the following conclusions: 1) The sum of the column elements of B1 and B2 is 0; there are no zero sequence currents in MPBT’s primary side. 2) Although the impact of the filtering branches is not taken into account, (2) is still the necessary condition

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where ZIh and ZIIh are the harmonic impedances of ZI and ZII , respectively; N is the turns’ number of a virtual winding (N > 0); and the physical meaning of all of the “K-coefficients” in (4) is the turns’ ratio between the virtual winding with each winding of MPBT. From Figs. 1 and 2 and according to the multiwinding transformer theory [31], the ampere-turns balancing equations and the voltage equations can be obtained in (5) and (6) ⎧ ⎪ ⎨IAh /K1 + Ia1h /K2 + Ia2h /K3 = 0 (5) IBh /K1 + Ibh /K5 + (Iαh + Iβh )/K4 = 0 ⎪ ⎩ ICh /K1 + Ic1h /K2 + Ic2h /K3 = 0 ⎧ K1 VAsh − K2 Va1h = K1 IAh Z1h − K2 Ia1h Z2h ⎪ ⎪ ⎪ ⎨K V 1 Ash − K3 Va2h = K1 IAh Z1h − K3 Ia2h Z3h (6) ⎪ K 1 VCsh − K2 Vc1h = K1 ICh Z1h − K2 Ic1h Z2h ⎪ ⎪ ⎩ K1 VCsh − K3 Vc2h = K1 ICh Z1h − K3 Ic2h Z3h

Fig. 2. Harmonic equivalent circuit of HRPQC.

of HRPQC, regardless of whether the filtering system is connected in taps U, V, and W. 3) It can be seen from (2) that IA , IB , and IC can be affected by changing IU and IW . That is to say that, by appropriate control of FBC, the primary three-phase currents of MPBT can be regulated. It is the essential reason of why the proposed system can be combined with FBC. B. Modeling of HRPQC in Harmonic Frequency When FBC is equivalent to three controlled voltage sources, by using Y → Δ transformation in Fig. 1, the harmonic equivalent circuit of HRPQC can be converted into Fig. 2 (note: the subscript “h” represents the harmonic component of the variables). To suppress the harmonics in IA , IB , and IC , the control target of FBC is to make ⎧ ⎪ ⎨Vahp = τ IAh (3) Vbhp = τ IBh τ > 0 ⎪ ⎩ Vchp = τ ICh , where Vahp , Vbhp , and Vchp are the equivalent voltage sources of FBC in the “Δ-axis” (see Fig. 2); IAh , IBh , and ICh are the harmonic currents in the MPBT’s primary side; and τ is a constant greater than 0. For discussion convenience, according to Figs. 1 and 2, the following variables are defined as ⎧ ⎧ ⎪ K1 = N/NI ⎪ ⎪ ⎪ ⎪ ⎪K2 = N/ [(1 − y)NII ] ⎪Z1h = ZIh ⎪ ⎪ ⎨ ⎨Z = (1 − x)Z 2h IIh K3 = N/(yNII ) ⎪ ⎪ √ Z = xZ 3h IIh ⎪ ⎪ ⎪ ⎪ K4 = N/ ( 3 − 1)NII /2 ⎪ ⎩ ⎪ ⎪ Z4h = λZIIh ⎩K = N/N 5 II (4)

where Va1h , Va2h and Vc1h , Vc2h are the voltages of MPBT’s secondary winding in phases A and C, respectively. Ignoring the zero sequence components in the MPBT’s primary side, we can obtain the following voltage and current equations: ⎧ Va2h = ZF h IaΔh + Vahp ⎪ ⎪ ⎪ ⎪ ⎪ V c2h = ZF h IcΔh + Vchp ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ZF h (IaΔh + IbΔh + IcΔh ) = 0 Vahp + Vbhp + Vchp = 0 ⎪ ⎪ ⎪Z2h Ia1h + Z2h Ic1h + Z4h Ibh − Ec1h ⎪ ⎪ ⎪ ⎪ ⎪ −Ebh − Ea1h = ZF h IbΔh + Ubhp ⎪ ⎪ ⎩ Ea1h + Ec1h + Ebh + Ea2h + Ec2h = 0 ⎧ ⎪ Ia1h − Ia2h = IaΔh − IbΔh ⎪ ⎪ ⎪ ⎪ ⎪ I ⎨ c1h − Ic2h = IcΔh − IbΔh Ibh − Ia1h = Iβh ⎪ ⎪ ⎪ Ibh − Ic1h = Iαh ⎪ ⎪ ⎪ ⎩I + I + I = 0 Ah Bh Ch

(7)

where IaΔh , IbΔh , and IcΔh are the harmonic currents in the Δ-filtering loop; ZF h is the harmonic impedance of PPF; and Ea1h , Ea2h , Ec1h , Ec2h , and Ebh are the induced electromotive forces of windings aU, UV, bW, WV, and ab, respectively. To offset the main harmonic magnetic flux in the iron-core of MPBT, ZF h should satisfy (8) in the design process of PPF [23] K2 (8) ZF h + Z3h = 0, h = 3, 5, 7. 1+ K3 The aforementioned (3)–(8) construct the mathematical model of HRPQC in harmonic frequency. Based on this model, we will give the transforming relationships between harmonic sources Iαh , Iβh ; VAsh , VBsh , and VCsh with primary harmonic currents IAh , IBh , and ICh in the following two cases. Case 1: Let VAsh = VBsh = VCsh = 0; the harmonic currents’ transforming relationship, where the characteristic of the filtering system is taken into account, can be obtained by (3)–(8)


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TABLE I PARAMETERS OF A MPBT ∗

and is shown in (9) at the bottom of the page. In (9), Z1∗ h , Z2∗ h , Zαh , and Zβh are the “characteristic impedances” of HRPQC, which are decided by the leakage reactance of MPBT and ZF h of PPF (see (A.1) in the Appendix); Δ = 3K32 τ 2 + 2K3 (2Z1∗ h − Z2∗ h )τ + (Z21∗ h − Z22∗ h ). Case 2: Let Iαh = Iβh = 0; similarly, the relationship of IAh , IBh , and ICh with the grid-side’s background harmonic voltages VAsh , VBsh , and VCsh can be obtained, and it is shown in (10) at the bottom of the page. It can be seen from (9) and (10) that the primary three-phase harmonic currents are coupled with the harmonic sources, which are highly associated with Δ1 ∼ Δ6 and Δ in Tp and Ts . Furthermore, it can be observed that Δ1 ∼ Δ6 and Δ are the functions of τ , which indicates that IAh , IBh , and ICh can be controlled by changing the value of τ . More specifications will be discussed in Section IV. IV. F ILTERING C HARACTERISTICS OF HRPQC A. Harmonic’s Filtering Characteristics It can be seen from (9) that IAh , IBh , and ICh not only depend on Iαh and Iβh but are also associated with Δ1 /Δ, Δ2 /Δ, and Δ3 /Δ strongly. In order to analyze the harmonicsuppressing ability of HRPQC, according to (9) and B1 in (2), the “harmonic filtering factor (HFF)” is first defined in ⎧ ⎪ γ1 = [1 − (|Δ1 |/|Δ|) / (m1 |d1 |)] × 100% ⎪ ⎪ ⎪ ⎨γ2 = [1 − (|Δ2 |/|Δ|) / (m1 |d2 |)] × 100% (11) (|Δ3 |/|Δ|) / (m1 |d3 |)]× 100% γ3 = [1 − ⎪ ⎪ ⎪ ⎪ ⎩γcom = 1 − (|Δ1 |+|Δ2 |+|Δ3 |)/|Δ| × 100%. m1 (|d1 |+|d2 |+|d3 |)

Remark 1: Because both the amplitude and phase angle of Iαh and Iβh are random variables in real working condition [1],

Fig. 3. Curves of γ1 (τ ), γ2 (τ ), γ3 (τ ), and γcom (τ ).

the “comprehensive HFF” γcom is introduced in (11) to evaluate the harmonic filtering performance in phases A, B, and C. The following discussions will take the third harmonic as an example, and the conclusions are also applicable to other loworder harmonics such as fifth, seventh, and so on. 1) Relationship Between HFFs With τ : Substituting (A.1) and (8) into (9) and combining the parameters of a real MPBT (see Table I), the relationship of γ1 , γ2 , γ3 , and γcom versus τ can be obtained from (11) and is shown in Fig. 3.

⎤ K3 (2Zβh − Zαh )τ + Z1∗ h Zβh − Z2∗ h Zαh

⎥ ⎥ Δ2 ⎥ (Zαh + Zβh )(Z2∗ h − Z1∗ h − K3 τ ) ⎥ ⎥

⎦ Δ3 K3 (2Zαh − Zβh )τ + Z1∗ h Zαh − Z2∗ h Zβh

⎡ K3 (2Zαh − Zβh )τ + Z1∗ h Zαh − Z2∗ h Zβh ⎡ ⎤

⎢ IAh ⎢ Δ1 1 ⎢ ⎣IBh ⎦ = (Zαh + Zβh )(Z2∗ h − Z1∗ h − K3 τ ) ⎢ Δ⎢ ICh ⎣ K3 (2Zβh − Zαh )τ + Z1∗ h Zβh − Z2∗ h Zαh

I Iαh = Tp αh Iβh Iβh

⎡ 3K τ + Z1∗ h + Z2∗ h 3

⎢ ⎡ ⎤ Δ6 ⎢ IAh ⎢ ∗ ⎣IBh ⎦ = K3 ⎢ −2K3 τ − Z1 h Δ ⎢ ⎢ ICh ⎣ −K3 τ − Z2∗ h

(9)

K3 τ + Z2∗ h −K3 τ − Z2∗ h

Δ5

0

Ts

0

⎤

⎥⎡ ⎤ ⎥ VAsh −2K3τ − Z1∗ h ⎥ ⎥ ⎣VBsh ⎦ ⎥ ⎥ VCsh 2K3 τ + Z1∗ h ⎦

Δ4

(10)

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Fig. 4. Curves of γcom (y) in the condition of different τ . Fig. 5. Curves of γcom (τ ) when ZI and ZII are not constants.

It can be seen from Fig. 3 that, when τ = 0, excepting γ2 is relatively large, both γ1 and γ3 are less than 50%, leading to γcom being only about 60% (the measured data in practical case are 57.3% [7]). Moreover, the phenomenon that the harmonic filtering ratios in phases A, B, and C are not the same in the “MPBT+PPF” operating model [23] can also be explained by the unequal value of γ1 , γ2 , and γ3 in the condition of τ = 0. However, when τ > 0, the harmonic filtering ratio increases significantly (e.g., τ > 35 → γcom > 80%); moreover, γ1 , γ2 , γ3 , and γcom tend to have the same value. It implies that the harmonic filtering capability of the proposed system can be greatly improved by appropriately increasing the value of τ . Remark 2: When τ 100, γcom will not increase too much (Fig. 3), but the power rating (or dc-link voltage) of FBC should be significantly increased [33]; a tradeoff between harmonic filtering performance with costs is to select τ ∈ (35, 100). 2) Relationship Between HFF With y: As mentioned in Section II, the turns’ ratio y in taps U, V, and W can be adjusted, which is a prominent advantage of HRPQC. However, whether the changes of y will affect the filtering performance of HRPQC is still unknown. Therefore, it is worth in-depth analysis. The relationship between γcom with y in the condition of different τ is shown in Fig. 4, which is obtained by substituting (A.1) and (8) to (11), making τ a fixed value and y ∈ (0, 1). From Fig. 4, it can be seen that, in the condition of τ = 0, more than 56% harmonics are eliminated when y > 0.4. However, when y is designed relatively small (e.g., y ∈ (0.1, 0.2)), the system shows poor harmonic filtering performance (γcom < 40%). However, the situation becomes better when τ is designed larger than 0. It can be seen from Fig. 4 that the slope of the red line (τ = 80) is rather smaller than that of the black one (τ = 0), γcom is always larger than 80%, and HRPQC shows good harmonic filtering performance. The aforementioned discussions indicate that HRPQC can get an ability of insensitive to the variation of y by appropriately adjusting τ . That is to say that it has a big influence on the harmonic filtering performance in the “MPBT+PPF” model when the turns’ ratio of windings UV and VW changes; however, this problem can be overcome by controlling τ . 3) Relationship Between HFF With MPBT’s Leakage Impedance and System’s Short-Circuit Capacity (i.e., Sd ): Consider that Sd and ZII are not always constant when the system operating mode or the environment changes. Their influences are discussed as follows.

Fig. 6. Frequency characteristics of ξ1 , ξ2 , and ξ3 .

It can be seen from the curves that correspond to ZIIr = 0.9ZII and ZIIr = 1.1ZII shown in Fig. 5 that the small variation of ZII (±10%) almost has no influence on the harmonic filtering performance of HRPQC. On the other hand, consider that the Sd of a traction substation always changes from 500 to 1500 MVA, which means MPBT’s primary equivalent impedance ZIeq ∈ (1.27ZI, 1.8ZI ) (ZI is given in Table I). From Fig. 5, it is shown that the variation of ZIeq has a great influence on the filtering performance when τ is designed to be 0, while when τ > 25, its impact is attenuated. B. Resonance Characteristics of HRPQC 1) Parallel Resonance Characteristics: From (9), the parallel resonance of HRPQC is determined by the frequency characteristics of Δ1 /Δ, Δ2 /Δ, and Δ3 /Δ in matrix Tp . Here, three variables are first defined as follows: ξ1 = |Δ1 /Δ|, ξ2 = |Δ2 /Δ|, and ξ3 = |Δ3 /Δ|. The frequency characteristics of ξ1 , ξ2 , and ξ3 are shown in Fig. 6 (the parameters of MPBT and PPF used in Figs. 6–9 are listed in Tables I and II, respectively). It can be observed from Fig. 6 that, when τ = 0, ξ1 , ξ2 , and ξ3 have some resonance points in the low-frequency band. However, all of these points disappear when τ is designed to be 80. It indicates that the parallel resonance of HRPQC can be suppressed effectively by adjusting τ . Moreover, the LC parameters of PPF usually deviate from its design value in practical cases, which may affect the harmonic filtering performance and the safety of the compensating system [32].


Fig. 7. Frequency characteristics of ξ1 , ξ2 , and ξ3 when the parameters of PPF deviate its design value of −4.2%.

Fig. 8. Frequency characteristics of ξ4 , ξ5 , and ξ6 .

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Fig. 10. Control system of HRPQC.

2) Series Resonance Characteristic: Equation (10) reveals the transforming relationship between the primary harmonic currents and the background grid harmonic voltages. Therefore, the series resonance characteristic of HRPQC is determined by the frequency characteristics of Δ4 /Δ, Δ5 /Δ, and Δ6 /Δ in matrix Ts . Here, three variables are defined as follows: ξ4 = |Δ4 /Δ|, ξ5 = |Δ5 /Δ|, and ξ6 = |Δ6 /Δ|. Like the discussions on parallel resonance, the frequency characteristics of ξ4 , ξ5 , and ξ6 with normal parameters and deviated parameters of PPF are shown in Figs. 8 and 9, respectively. It can be observed that, by adjusting τ , the series resonance points are damped effectively. V. C ONTROL S YSTEM OF HRPQC

Fig. 9. Frequency characteristics of ξ4 , ξ5 , and ξ6 when the parameters of PPF deviate its design value of −4.2%. TABLE II PARAMETERS OF PPF (y = 0.4676)∗

Fig. 10 shows the control system of HRPQC. Based on the instantaneous power theory [33], the primary fundamental positive and negative sequence currents iA(+1) , iB(+1) , iC(+1) and iA(−1) , iB(−1) , iC(−1) can be obtained by using the positive and negative sequence Park’s transformation (i.e., P(ωt) and P(−ωt)), the low-pass filters, and the inversed positive and negative sequence Park’s transformation. Separating them from iA , iB , and iC , we can get the primary harmonic currents iAh , iBh , and iCh . Considering “Δ → Y ” transforming relationship and (3), the modulation signals of FBC vUhp , vV hp , and vW hp can be obtained, as shown in (12). Moreover, the dc-link voltage of FBC can be regulated by PI controller via compensating a small amount of active power from the grid [29], [33] ⎡ ⎤ ⎤ ⎡ ⎤ ⎡ ⎤⎡ 1 −1 0 iAh vUhp iAh ⎣ vV hp ⎦= τ ⎣−1 0 1 ⎦⎣iBh ⎦= TΔ→Y ⎣iBh ⎦ . (12) 3 vW hp iCh 0 1 −1 iCh

VI. S IMULATION AND E XPERIMENT When all of the LC parameters deviate from their design value of −4.2% (note: the error band of PPF(−5%, +5%)), the frequency characteristic curves of ξ1 , ξ2 , and ξ3 are shown in Fig. 7. It can be seen that the resonance in seventh harmonic frequency can be easily excited in the condition of τ = 0. While when τ = 80, all of the resonance points disappear, which implies that the parallel resonance caused by PPF’s parametric variation can be suppressed effectively by HRPQC.

A. Simulation Results The simulation model associated with the system shown in Fig. 1 has been established. The relevant parameters are listed in Tables I–IV. 1) Veriﬁcation of the Harmonic Mathematical Model of HRPQC (Sd = ∞): Fig. 11(a) shows the waveforms of the two-phase loads and the primary currents when the filtering

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TABLE III PARAMETERS OF PPF (y = 0.1)

TABLE V H ARMONIC F ILTERING R ATIO∗

TABLE IV PARAMETERS OF FBC AND L OADS∗

Fig. 11. Current waveforms of HRPQC. (a) Waveforms of load currents and primary three-phase currents without filtering branches (Sα∗ = 1.0 pu, and Sβ ∗ = 1.0 pu). (b) Primary three-phase currents when y = 0.1 [t < 0.06 s : PPF; t > 0.06 s : PPF+FBC (τ = 80)]. (c) Primary three-phase currents when y = 0.4676 [t < 0.06 s : PPF; t > 0.06 s : PPF+FBC (τ = 80)].

branch is absent. It can be seen from Fig. 11(b) and (c) that, no matter if y = 0.1 (Fig. 11(b), t < 0.06 s) or y = 0.4676 (Fig. 11(c), t < 0.06 s), the primary harmonic currents are suppressed to a certain extent, but the filtering performance in the condition of y = 0.4676 is better than that of y = 0.1. Additionally, the comprehensive harmonic filtering ratios in both simulation and calculation cases are almost the same (Table V), which validates the HRPQC’s harmonic model. Moreover, the harmonic filtering performances are enhanced obviously when FBC starts operation (see Fig. 11(b) and (c), t > 0.06 s). It can also be seen from Table V that the simulation and calculation values of γcom are almost the same, which further verifies the effectiveness of HRPQC and the correctness of its harmonic model. 2) Resonance-Suppressing Performance of HRPQC (y = 0.4676): Fig. 12 shows the resonance-suppressing performance of HRPQC, where Fig. 12(a) and (b) shows the parallel resonance damping performance, and Fig. 12(c) and (d)

Fig. 12. Waveforms of HRPQC in the resonance condition. (a) Waveforms in the parallel resonance case. (b) Current spectrum in the parallel resonance case. (c) Waveforms in the series resonance case. (d) Current spectrum in the series resonance case.

corresponds to the series one. The trigged conditions of those two kinds of resonances are listed in Table VI. In the absence of FBC, the compensating system is composed of MPBT and PPF. It can be seen from Fig. 12(b) and (d) that


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TABLE VI PARAMETERS IN R ESONANCE C ASES∗

Fig. 14. Experimental wiring diagram of HRPQC. Fig. 13. Comprehensive compensating performance of HRPQC.

TABLE VIII S PECIFICATIONS OF S ENSORS AND D RIVE U NIT

TABLE VII W ORKING C ONDITION OF F IG . 13 AT D IFFERENT T IME P ERIODS

unbalanced voltage ratio Uunb % is less than 2% in the whole compensating period. The national standards are satisfied [34]. B. Experimental Results the system is resonated at the seventh harmonic frequency, which is consistent with the theoretical analysis stated in Section IV-B (the PPF’s deviation shown in Table VI is almost the same with −4.2% shown in Figs. 7 and 9). On the other hand, when the FBC starts operation, the primary currents tend to be sinusoidal waveforms (Fig. 12(a): t > 0.04 s; and Fig. 12(c): t > 0.2 s); both the parallel and series resonances are damped effectively. These results verify the resonancesuppressing ability of the HRPQC system. 3) Comprehensive Compensating Performance of HRPQC (y = 0.4676, Sd = 950 MVA): Fig. 13 shows the comprehensive compensating performance of HRPQC, in which the load currents, the primary three-phase currents, the dc-link voltage, and the power factor (PF) are given from top to bottom. The working conditions of Fig. 13 are listed in Table VII. It can be seen from the first to the third subfigures in Fig. 13 that the primary three-phase currents tend to be the sinusoidal waveforms in steady state, and the dc-link voltage fluctuates within 5% of its reference value 1.2 kV as well. Moreover, from the fourth and fifth subfigures in Fig. 13, the PF in the MPBT’s grid side increases significantly (PF > 0.93) when HRPQC starts operation, and the primary three-phase

A physical platform of about 5 kVA has been built in the laboratory to validate the proposed system. Fig. 14 shows the experimental wiring diagram of HRPQC. Four diode-controlled “L − R” loads with the apparent power of SL0 = 645 VA are adopted to simulate the locomotives. Primary three-phase currents, voltages, and dc-link voltage are detected as the input signals of TMS320F2812 DSP. It can be seen from Fig. 14 and Table VIII that, before the voltages and currents input A/dc inside the DSP, two stages have to be passed: the first stage is the ac or dc sensors, and the second one is the conditioning circuit in the control panel; it can convert the A (or V)-level signals output from the sensors to the 0∼3.3-mV-level ones which DSP can identify. The detection and control algorithms mentioned in Fig. 10 are carried out in DSP for digital implementation. Six PWM signals derived from DSP are amplified by the drive unit to control the FBC, and we set the carrier frequency fcr = 12.8 kHz. An IPM-based converter with the level of 600 V/200 A is selected as FBC. A HIOKI-3196 power quality analyzer is used for data acquisition. Excepting the parameters shown in Fig. 14, the other parameters of the experimental system are listed in Table IX. The experimental results are shown in Fig. 15.

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TABLE IX PARAMETERS OF E XPERIMENTAL S YSTEM∗

within about a main period (20 ms). The system represents good dynamic performance. VII. C ONCLUSION HRPQC fully explores the potentials of MPBT, PPF, and FBC, which makes the system obtain a good harmonics and reactive power compensating performance in ERPS. Additionally, it successfully integrates the active system with the main transformer and decreases the initial costs, covering space, and installing difficulties. Moreover, the probability of resonance is decreased significantly. Hence, HRPQC is an electrical railway power quality control system with high cost efficiency. However, the function of flexibly control of reactive power should be further improved in the future study. A PPENDIX C HARACTERISTIC I MPEDANCES OF HRPQC ⎧ K 2 (K +K ) 5 ⎪ Z1∗ h = K1 Z1h + 2KK31K Z2h + 3 K12K2 5 Z ⎪ 3h ⎪ ⎪ K32 K3 K5 (K2 +K3 ) ⎪ K3 K5 ⎪ + K1 Z4h + + K1 ZF h ⎪ K1 K2 ⎪ ⎪ ⎪ ⎪ K K K K3 3 5 3 ⎪Z2∗ h = K 2Z Z + Z + Z + 1 + 2h 3h 4h F h ⎪ K2 K2 ⎪ 1 ⎨ K3 Zαh = K4 (K4 + 2K5 )Z2h + K3 K5 Z3h + K5 Z4h ⎪ ⎪ ⎪ K3 ⎪ 1 + Z + K 5 F h ⎪ K2 ⎪ ⎪ ⎪ ⎪ K3 K3 ⎪ ⎪ ⎪Zβh = K4 (K4 +2K5)Z2h+ K2 (K4 +K5)Z3h +K5 Z4h ⎪ ⎪ ⎩ . + (K + K ) 1 + K3 Z 4

5

K2

Fh

(A.1) R EFERENCES

Fig. 15. Experimental results of HRPQC. (a) Dynamic waveforms of primary currents when HRPQC starts operation (Sα = SL0 , and Sβ = SL0 ). (b) Dynamic waveforms of the primary currents and the dc-link voltage when the load in phase β increases. (c) Dynamic waveforms of the primary currents and the dc-link voltage when the load in phase α decreases.

It can be seen from Fig. 15(a) that, in the absence of HRPQC, the primary three-phase currents of MPBT are distorted seriously (THDI−av = 17.8%, and PF = 0.84). When HRPQC starts operation, however, iA , iB , and iC tend to be the sinusoidal waveforms (THDI−av = 4.2%, and PF = 0.97). Although the PPF is only designed in third harmonic frequency (Table VIII), including Fig. 15(b) and (c) (THDI−av = 4.71%, and PF > 0.94), the average three-phase total current harmonic filtering ratio of Fig. 15(a) and (c) is still close to 75.3%. Moreover, it can be seen from Fig. 15(b) and (c), in the condition that load changes, iA , iB , iC , and vdc return to the steady state

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Sijia Hu (S’14) was born in Hunan, China, in 1987. He received the B.Sc. degree in electrical engineering and automation from the College of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, China, in 2010. He has been working toward the Ph.D. degree in electrical engineering in the College of Electrical and Information Engineering, Hunan University, Changsha, China, since 2012. His research interests include power flow control and power quality analysis and control of electrical railway power systems, high-power converters, and FACTS technologies. Zhiwen Zhang received the B.Sc. and M.Sc. degrees in electrical engineering and the Ph.D. degree in control theory and control engineering from Hunan University, Changsha, China. He was a Visiting Scholar at Tsinghua University, Beijing, China, and a Visiting Professor at Ryerson University, Toronto, ON, Canada. He is currently a Full Professor with the College of Electrical and Information Engineering, Hunan University. His research interests include power quality analysis and control of electric railway power systems, theory and new technology of ac/dc energy transform, theory and application of new-type electric apparatus, harmonic suppression for electric railways, power electronics applications, and computer control.

Yuehui Chen was born in Hunan, China, in 1965. He received the Ph.D. degree from Huazhong University of Science and Technology, Wuhan, China in 2012. He is currently a Deputy Chief Engineer with the State Grid Hunan Electric Power Company, Changsha, China. His research interests include power system planning, management of power grid, and power quality analysis and control.

Guandong Zhou was born in Hunan, China, in 1965. He received the M.Sc. degree in electrical engineering from Hunan University, Changsha, China, in 1991. He is currently a Director of the Science and Technology Department of Environmental Protection, State Grid Hunan Electric Power Company, Changsha. His research interests include power system stability analysis and control, grid security and economic operation, and power quality analysis and control. Yong Li (S’09–M’12–SM’14) was born in Henan, China, in 1982. He received the B.Sc. and Ph.D. degrees from the College of Electrical and Information Engineering, Hunan University, Changsha, China, in 2004 and 2011, respectively, and the Ph.D. degree from the Institute of Energy Systems, Energy Efficiency, and Energy Economics (ie3 ), TU Dortmund, Dortmund, Germany, in 2012. In 2009, he became a Research Associate with the Institute of Energy Systems, Energy Efficiency, and Energy Economics (ie3 ), TU Dortmund. He was then a Research Fellow with The University of Queensland, Brisbane, Australia. Since 2014, he has been a Full Professor of electrical engineering with Hunan University. His current research interests include power system stability analysis and control, ac/dc energy conversion systems and equipment, analysis and control of power quality, and HVDC and FACTS technologies. Dr. Li is a member of the Association for Electrical, Electronic and Information Technologies (VDE) in Germany.

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Longfu Luo (M’09) was born in Hunan, China, in 1962. He received the B.Sc., M.Sc., and Ph.D. degrees from the College of Electrical and Information Engineering, Hunan University, Changsha, China, in 1983, 1991, and 2001, respectively. From 2001 to 2002, he was a Senior Visiting Scholar at the University of Regina, Regina, SK, Canada. He is currently a Full Professor of electrical engineering with the College of Electrical and Information Engineering, Hunan University. His current research interests include the design and optimization of modern electrical equipment, the development of new converter transformers, and the study of corresponding new HVDC theories.

Yijia Cao (M’98–SM’13) was born in Hunan, China, in 1969. He received the B.Sc. degree in mathematics from Xi’an Jiaotong University, Xi’an, China, in 1988 and the M.Sc. and Ph.D. degrees from Huazhong University of Science and Technology (HUST), Wuhan, China, in 1991 and 1994, respectively. From September 1994 to April 2000, he was a Visiting Research Fellow and Research Fellow at Loughborough University, Loughborough, U.K.; Liverpool University, Liverpool, U.K.; and the University of the West of England, Bristol, U.K. From 2000 to 2001, he was a Full Professor with HUST, and from 2001 to 2008, he was a Full Professor with Zhejiang University, Zhejiang, China. He was appointed as a Deputy Dean of the College of Electrical Engineering, Zhejiang University, in 2005. He is currently a Full Professor and the Vice President of Hunan University, Changsha, China. His research interests include power system stability control and the application of intelligent systems in power systems.

Bin Xie was born in Hunan, China, in 1990. He received the B.Sc. degree in electrical engineering from Shaoyang University, Shaoyang, China, in 2013. He is currently working toward the Ph.D. degree in electrical engineering in the College of Electrical and Information Engineering, Hunan University, Changsha, China. His research interests include power quality analysis and control of electric railway power systems.

Xiaoting Chen was born in Hunan, China, in 1990. She received the B.Sc. degree in automation and control from Changsha University of Science and Technology, Changsha, China, in 2013. She is currently working toward the Master’s degree in electrical engineering in the College of Electrical and Information Engineering, Hunan University, Changsha, China. Her research interests include power quality analysis and control of electric railway power systems.

Bin Wu (S’89–M’92–SM’99–F’08) received the Ph.D. degree in electrical and computer engineering from the University of Toronto, Toronto, ON, Canada, in 1993. After being with Rockwell Automation, Canada, as a Senior Engineer, he joined Ryerson University, Toronto, ON, Canada, where he is currently a Professor and the NSERC/Rockwell Industrial Research Chair in Power Electronics and Electric Drives. He has published more than 280 technical papers, is the author/coauthor of two Wiley-IEEE Press books, and holds more than 20 issued/pending patents in the area of power conversion, advanced controls, adjustable-speed drives, and renewable energy systems. Dr. Wu received the Gold Medal of the Governor General of Canada, the Premiers Research Excellence Award, the Ryerson Distinguished Scholar Award, the Ryerson Research Chair Award, and the NSERC Synergy Award for Innovation. He is a Fellow of the Engineering Institute of Canada and the Canadian Academy of Engineering

Christian Rehtanz (M’96–SM’06) was born in Germany in 1968. He received the Diploma and Ph.D. degrees from TU Dortmund, Dortmund, Germany, in 1994 and 1997, respectively, and the Venia Legendi in electrical power systems from the Swiss Federal Institute of Technology, Zurich, Switzerland, in 2003. In 2000, he joined ABB Corporate Research, Switzerland. He became the Head of Technology for the global ABB business area of power systems in 2003 and the Director of ABB Corporate Research in China in 2005. Since 2007, he has been the Head of the Institute of Energy Systems, Energy Efficiency and Energy Economics (ie3 ), TU Dortmund. In addition, he has been a Scientific Advisor of ef.Ruhr GmbH, a joint research company of the three universities of Bochum, Dortmund, and Duisburg-Essen (University Alliance Metropolis Ruhr), since 2007. He is an Adjunct Professor with Hunan University, Changsha, China. He is the author of more than 150 scientific publications, three books, and 17 patents and patent applications. His research interests include electrical power systems and power economics, including technologies for network enhancement and congestion relief such as stability assessment, wide-area monitoring, protection, and coordinated network control as well as integration and control of distributed generation and storages. Dr. Rehtanz received the MIT World Top 100 Young Innovators Award in 2003.