A YD Multifunction Balance Transformer-Based Power ... - IEEE Xplore

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 52, NO. 2, MARCH/APRIL 2016

A Y-D Multifunction Balance Transformer-Based Power Quality Control System for Single-Phase Power Supply System Sijia Hu, Student Member, IEEE, Yong Li, Senior Member, IEEE, Bin Xie, Mingfei Chen, Zhiwen Zhang, Longfu Luo, Member, IEEE, Yijia Cao, Senior Member, IEEE, Andreas Kubis, Student Member, IEEE, and Christian Rehtanz, Senior Member, IEEE Abstract—This paper proposes a Y-D multifunction balance transformer (YD-MFBT)-based power quality control system (MBT-PQCS) to deal with the power quality problems in the single-phase power system. The MBT-PQCS mainly consists of a YD-MFBT and a three-phase full-bridge converter (FBC). It fully explores the inherent negative sequence current (NSC) suppressing the ability of YD-MFBT, which makes the power flow transformed by FBC less than that of the conventional transformer-based compensating system. In addition, since the YD-MFBT exits three-phase output ports in relatively low-voltage level, FBC can directly connect with the main transformer via the output ports, without using the auxiliary step-down transformer. Therefore, the initial investment cost, installing difficulties and covering space of the whole compensating system, can be reduced significantly. In this paper, the current transforming relationship and the compensating principle of MBT-PQCS are presented, and the detection and control methods are given as well. Both the simulation and the experiment are used to verify the effectiveness of the proposed system. Index Terms—Active compensation, electrical railway, fullbridge converter (FBC), power quality, single-phase supply system.

I. I NTRODUCTION

W

ITH the increase of nonlinear single-phase loads (e.g., electrical trains and photovoltaic converters), due to the inherent unsymmetrical single-phase topology, a large number

Manuscript received July 31, 2015; revised November 11, 2015; accepted November 16, 2015. Date of publication November 23, 2015; date of current version March 17, 2016. Paper 2015-PSEC-0706.R1, presented at the 2015 International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles, Aachen, Germany, March 3–5, and approved for publication in the IEEE TRANSACTIONS ON I NDUSTRY A PPLICATIONS by the Power Systems Engineering Committee of the IEEE Industry Applications Society. This work was supported in part by the National Natural Science Foundation of China under Grant 51477046 and Grant 51377001 and in part by the International Science and Technology Cooperation Program of China under Grant 2015DFR70850. (Corresponding author: Yong Li.) S. Hu, Y. Li, B. Xie, Z. Zhang, L. Luo, and Y. Cao are with the College of Electrical and Information Engineering, Hunan University, Changsha 410082, China (e-mail: [email protected]; [email protected]; xiebin_1215@ 163.com; [email protected]; [email protected]; [email protected]). M. Chen is with the State Grid Loudi Electric Power Supply Company, Loudi 417000, China (e-mail: [email protected]). A. Kubis and C. Rehtanz are with the Institute of Energy Systems, Energy Efficiency and Energy Economics, TU Dortmund University, 44227 Dortmund, Germany (e-mail: [email protected]; [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/TIA.2015.2503389

of harmonic currents, reactive power, and negative sequence current (NSC) are injected into the utility, which seriously affect the safety of the grid, and arouse widespread attention of related industrial departments and engineers [1]–[5]. Considering the initial costs, the phase-rotation technique is commonly used in the three-phase grid to alleviate the unbalancing relevant problems. However, the method is always ineffective in un-robust power system. Additionally, it also lacks flexibility [6]. Because of the good ability of suppressing NSC, balance transformers are widely used in the case of three-phase to twophase power system, and the most successful application is the traction transformer used in the electrical railway power system [6]–[8]. However, its ability of suppressing NSC is strongly affected by the working condition of load, that is to say, the more imbalance of two-phase load, the worse the NSC suppressing performance of balance transformer. In addition, the balance transformer has no ability to suppress harmonics and reactive power from the nonlinear single-phase loads (e.g., the electrical railway locomotives and arc furnace loads). Thyristor-controlled/switched capacitors and reactors can also be used to compensate the NSC and the reactive power in a single-phase power system [9]. However, it is difficult to get a satisfactory performance in both technical and economic aspects [10]. In addition, it also has the risk of arousing grid resonance [11]. Considering the limited installation space in the practical case, the relatively low system integration level of SVC is also a problem in some places. To solve those problems, some IGBT- or IGCT-based active compensating systems are put forward in the last 20 years [10], [12]–[29], in which the static var generator (SVG) and the railway static power conditioner (RPC) are the representative ones in single-phase supply system. SVG is often installed at the three-phase high-voltage side of the main transformer, and the step-down transformer is needed as the interface between the grid and the converter [18]. Therefore, the initial costs, power losses, and installing difficulties are increased while the system’s integration level decreases consequently. Multilevel topology is another developing trend of SVG [22]–[26]. It has the potential to eliminate the need of step-down transformer in medium-voltage application cases (2.3−13.8 kV); however, in high-voltage condition (>13.8 kV), the reliability and the cost-efficiency level of the pure multilevel scheme are decreased. In addition, the control and protection

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HU et al.: Y-D MBT-PQCS FOR SINGLE-PHASE POWER SUPPLY SYSTEM

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Fig. 2. Secondary voltage phasor diagram of YD-MFBT.

Fig. 1. Topology of MBT-PQCS.

in that system is much complex than the one of the twolevel converter. Therefore, the step-down transformer is commonly used in these systems to enhance its safety and provide isolation [26]. Derived from the topology of the single-phase SVG, RPC is constructed by the single-phase back-to-back converter. By reallocating the active power flow of the two-phase loads, and compensating the reactive power or harmonics of each phase independently, RPC can deal with almost all the power quality problems in the electrical railway power system (e.g., NSC, reactive power, harmonics, and feeder voltage fluctuation) [5], [10], [14], [27]–[29]. However, similar to SVG, two large capacity single-phase multiwinding step-down transformers are needed as the isolation part of the converter. The large compensating capacity and high initial investment slowdown its large-scale industrial application. To the authors’ knowledge, RPC has been used in a few traction substations in China and Japan, since it was first proposed in 1993 [28]. To enhance the integration and reliability level, and decrease the initial cost of the system, a novel Y-D multifunction balance transformer (YD-MFBT) [30]-based power quality control system (MBT-PQCS) is proposed in this paper (for other two “winding compensating” topologies, please refer to [13] and [19]). As shown in Fig. 1, MBT-PQCS is mainly composed by a YD-MFBT, three-coupling reactors, and a full-bridge converter (FBC). Because the FBC connects with the main balance transformer in taps c, d, and e in low- or medium-voltage levels, the auxiliary transformer can be eliminated. Therefore, the initial investment can be decreased significantly. Moreover, considering that YD-MFBT is a balance transformer, the power regulated by FBC is less than that of the conventional transformer (e.g., Y/Δ or V/v transformer)-based system, so the

efficiency and reliability of the active part are higher than others [13], [19]. This paper is organized as follows. The topology and YD-MFBT’s wiring scheme are presented in Section II. Section III gives the compensating principle. The nonlinear passivity principle-based control system of MPB-PQCS is discussed in Section IV. Sections V and VI give the simulation and experimental results, respectively. Section VII gives the conclusion.

II. T OPOLOGY AND W IRING P RINCIPLE OF MPT-PQCS A. Topology and Wiring Principle Fig. 1 shows the proposed topology of MPT-PQCS. The main transformer, YD-MFBT, connects with the 110 kV (or 35 kV) high-voltage grid, which transfers the power from high-voltage grid to two single-phase loads. For FBC, it connects with taps d, c, and e through three L branches. The two-phase system can be supplied by YD-MFBT from the output ports ae and bd, respectively. From the voltage phasor diagram of YD-MFBT shown in Fig. 2, it can be seen that to make the two-phase output voltages perpendicular to each other, and the three-phase output voltages in taps d, c, and e balance, the turns’ number of the main transformer W2 , W3 , and W4 should satisfy (1), i.e.,

√ W3 = [(√3 + 1)W2 ]/2 . W4 = [( 3 − 1)W2 ]/2

(1)

Application of the geometry theorem in Fig. 2, the relation of the no-load voltages in secondary three-phase system—Vdc , Vec , and Vde —with the two-phase output voltages—Vae and Vbd —satisfy Vdc = Vec = Vde =

√ √ 3−1 3−1 √ Vae = √ Vbd . 6 6

(2)

It can be seen from (2) that the three-phase output voltage’s level in d, c, and e are about 0.2989 times than that of the two-phase output voltage. Therefore, the high-voltage system is converted to the low- or medium-voltage system by YD-MFBT, and the auxiliary transformer can be eliminated when the active system is connected in taps d, c, and e.

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TABLE I C HARACTERISTICS OF MPBT AND YD-MFBT

W3

a

b

A

W2

iA W1

W1

o iC

iB

B

W4 ia

W2

e

d

ib

c

W4 ic

W1

C Fig. 3. Equivalent circuit of MBT-PQCS when two-phase is no-load. *Two extend windings are fully coupled with specific leakage impedance.

In addition, to meet the decoupling and balancing condition of YD-MFBT, the equivalent impedances of each winding should satisfy ⎧ √ √ ⎪ 3−1 3+1 ⎪ ⎪ Zdc = Zad , Zab = Zad ⎪ ⎪ 2 2 ⎨ Zad = Zbe , Zdc = Zec (3) ⎪ √ ⎪ ⎪ ⎪ ⎪ ⎩ξ = 3 − 3 3 where Zmn is the equivalent impedance of winding mn (m, n = a, b, c, d, e); ξ is the ratio of some short-circuit impendences, which satisfies ξ=

√ √ √ 1+3 3 5− 3 3−3 3 Z + Z + ZSA23 SA12 SA13 4 4 √ √ 4 √ (1+ 3)ZSA12 + ZSA13 + (1− 3)ZSA23 + 2+2 3 ZSB12

(4)

is the short-circuit impendence between windings where ZSklm 1 , 2 , and 3 (1 = m), see Figs. 1 and 2] l and m [1, m = in phase-k (k = A, B, and C), which is converted to a basic winding with turns W . The comparison on the main characteristics of the proposed YD-MFBT and the commonly used multipurpose balance transformer (MPBT) are listed in Table I. It can be seen that the main indicators of the YD-MFBT, i.e., the impedance matching condition, the winding number, and the material utilization ratio, are much better than that of MPBT, which makes YD-MFBT easier for manufacture and less investment costs. That is to say, the proposed system has higher cost-efficiency.

III. C OMPENSATING P RINCIPLE A. Current Transforming Relationship When three-phase load in taps d, c, and e equals to 0, the relationship between the primary currents with the two-phase load currents is [30] √ ⎤ ⎡√ ⎡ ⎤ 3√ +3 3√ −3 IA 1 ⎣ −2 3 −2 3 ⎦ Iα = S1 Iα ⎣ IB ⎦ = (5) √ Iβ Iβ 6K √ IC 3−3 3+3 where K = W1 /W2 .

In addition, referring to Fig. 3, when the two-phase loads equal to 0, based on the Kirchhoff’s law, we can obtain that ⎧ Iad + Ia = Idc ⎪ ⎪ ⎨ Idc + Ib = Ice (6) Ice + Ic = Ieb ⎪ ⎪ ⎩ Ieb = Iba = Iad Iad Zad + Idc Zdc + Ice Zce + Ieb Zeb + Iba Zba = 0.

(7)

Ignoring the exciting currents, the ampere-turns balance equations can be obtained as follows: ⎧ ⎪ ⎨ IA W1 + Iad W2 + Idc W4 = 0 IB W1 + Iba W3 = 0 . (8) ⎪ ⎩ IC W1 + Ice W4 + Ieb W2 = 0 Combining (1)–(3) and (6)–(8), the relationship between the primary three-phase currents and the secondary three-phase currents can be obtained as ⎡ ⎤⎡ ⎤ ⎡ ⎤ ⎡ ⎤ √ −1 1 0 Ia Ia IA 3 − 1 ⎣ 1 0 −1 ⎦ ⎣ Ib ⎦ = S2 ⎣ Ib ⎦ . (9) ⎣ IB ⎦ = 6K IC Ic Ic 0 −1 1 From (5) and (9), and considering the superposition principle, the primary currents can be expressed as ⎡ ⎤ ⎡ ⎤ IA Ia ⎣ IB ⎦ = S 1 Iα + S 2 ⎣ Ib ⎦ . (10) Iβ IC Ic B. Compensating Method If the two-phase load currents Iα and Iβ can be separated into two symmetric active part Iplα and Iplβ , and two “harmonic + reactive” parts Ilα and Ilβ (see Fig. 4), then, (10) can be modified to (11), i.e., ⎡ ⎤ ⎡ ⎤ Ia IA I I ⎣ IB ⎦ = S1 plα + S1 lα + S2 ⎣ Ib ⎦ . (11) Iplβ Ilβ IC Ic It can be seen from Fig. 4 that Iplα = Iplβ equals to 0.5(a+b) (note: a and b is the active part of Iα and Iβ , respectively). Let Iplα = IL ∠0◦ (12) Iplβ = jIplα = IL ∠90◦


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Fig. 5. Detection algorithm of MBT-PQCS.

where iαlp and iβlp are the fundamental active parts of iα and iβ , respectively; iαlq and iβlq are the fundamental reactive parts ∞ ∞ of iα and iβ , respectively; iαk and iβk are the harmonic k=2

Fig. 4. Phasor diagram of Iplα , Iplβ ; Ilα , Ilβ .

and substituting (12) into (5), the primary three-phase currents can be calculated as ⎡ ∗⎤ ⎡ ⎤ √ IA ∠ − 15◦ 6 ⎣ I∗B ⎦ = IL ⎣ ∠ − 135◦ ⎦ . (13) 3K ∗ IC ∠75◦ It can be seen from (13) and Fig. 2 that I∗A , I∗B , and I∗C inducted by Iplα and Iplβ are balanced with unit power factor. Therefore, in (11), if the compensating currents Ia , Ib , and Ic satisfy ⎡ ⎤ Ia Ilα ⎣ ⎦ S 2 Ib + S 1 = 0. (14) Ilβ Ic Then, IA , IB , and IC will only remain the fundamental positive sequence components I∗A , I∗B , and I∗C , i.e., (13). From (14), Ia , Ib , and Ic can be calculated by ⎡ ⎤ ⎡ √ ⎤ Ia √3 + 2 √ 1 Ilα Ilα ⎣ Ib ⎦ = ⎣ − 3 − 1 ⎦ = S . (15) √3 + 1 Ilβ Ilβ Ic −1 − 3−2 In addition, the winding current’s distribution is shown in (A.1) of the Appendix, which is useful for transformer design. IV. C ONTROL S YSTEM A. Detection Algorithm Fig. 5 shows the detection algorithm of MBT-PQCS. First, based on Fourier’s method, the two-phase load currents can be expressed as (suppose that sin(ωt) and cos(ωt) are in phase with vα and vβ , respectively) ⎧ ∞ ⎪ ⎪ iα (t) = Iαlp sin(ωt) + Iαlq cos(ωt) + iαk ⎪ ⎪

k=2 ⎪ ⎨ iαlp iαlq (16) ∞ ⎪ ⎪ i (t) = I cos(ωt) − I sin(ωt) + i ⎪ β βlp βlq βk ⎪

k=2 ⎪ ⎩ iβlp

iβlq

k=2

one of iα and iβ , respectively. Based on the compensating principle shown in Fig. 4, first, we should obtain (a + b)/2. Consider that ⎧ i sin(ωt) ⎪ ⎪ α ∞ ⎪ ⎪ Iαlq Iαlp ⎪ Iαlp ⎪ ⎪ cos(2ωt) + sin(2ωt) + = − iαk sin(ωt) ⎪ 2 ⎪ 2 2 ⎪ ⎪ k=2 ⎪

⎪ ⎨ harmonic components (k≥2)

iβ cos(ωt) ⎪ ⎪ ⎪ ∞ ⎪ ⎪ Iβlq Iβlp Iβlp ⎪ ⎪ cos(2ωt) − sin(2ωt) + = + iβk cos(ωt) ⎪ 2 ⎪ 2 2 ⎪ ⎪ k=2 ⎪ ⎪

⎩ harmonic components (k≥2)

(17) Filtering out the harmonic components in iα sin(ωt) and iβ cos(ωt) via LPF, the average amplitude of iαp and iβp , G (corresponds (a + b)/2 in Fig. 4), can be obtained (see Fig. 5) G=

1 (Iαlp + Iβlp ) . 2

(18)

The desired currents of phase- α and phase- β iplα and iplβ can be obtained by multiple G into the synchronous signals sin(ωt) and cos(ωt), i.e., ⎧ 1 ⎪ ⎨ iplα = G sin(ωt) = (Iαlp + Iβlp ) sin(ωt) 2 . (19) ⎪ ⎩ iplβ = G cos(ωt) = 1 (Iαlp + Iβlp ) cos(ωt) 2 Separating iplα and iplβ from iα and iβ , the compensating reference currents of phase- α and phase- β can be obtained as ⎧ 1 ⎪ ⎨ ilα (t) = iα (t) − (Iαlp + Iβlp ) sin(ωt) 2 . (20) ⎪ ⎩ ilβ (t) = iβ (t) − 1 (Iαlp + Iβlp ) cos(ωt) 2 Reference to (15), the reference currents i∗a , i∗b , and i∗c of FBC can be calculated by ⎡ ∗⎤ ia ⎣ i*b ⎦ = S ilα . (21) ilβ i*c

.

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Therefore, the Euler–Lagrange parameters of FBC can be obtained as ⎧ EM = 0.5LC˙ d2 (t) + 0.5LC˙ q2 (t) ⎪ ⎪ ⎪ ⎪ ⎨ EJ = 0.5rC˙ d2 (t) + 0.5rC˙ q2 (t) (25) EP = 0 ⎪ ⎪ ˙ ˙ ⎪ D = −ωLCq (t), Dq = ωLCd (t) ⎪ ⎩ d Γd = 1, Γq = 1 where EM , EJ , and EP represent the magnetic energy function, dispatch function, and electric potential function, respectively; Dd and Dq are the disturbances in d and q-axes, respectively; Γd and Γq are the constants. The Lagrange energy function fL can also be obtained as

Fig. 6. Equivalent circuit of FBC.

B. Control System To get a satisfactory compensating performance in both the fundamental and the harmonic frequency, here, the nonlinear passivity control principle [31] is adopted to design the controller of FBC. First, the no-load Y-form voltages in taps d, c, and e va , vb , and vc (see Fig. 6) can be calculated as ⎡ ⎤⎡ ⎤ ⎤ 1 0 −1 edc va ⎣ vb ⎦ = 1 ⎣ 0 −1 1 ⎦ ⎣ ece ⎦ 3 vc eed −1 1 0 ⎡ ⎤⎡ ⎤ √ 1 −1 0 vA 3−1⎣ 0 1 −1 ⎦ ⎣ vB ⎦ = 6Kx vC −1 0 1

⎡

(22)

T

where edc , ece , and eed are the no-load voltages of windings dc, ce, and ed (-form); vA , vB , and vC are YD-MFBT’s primary phase voltages; Kx = W1 /(W2 + W4 ). Equation (22) indicates that the system’s synchronization signal (e.g., ωt from PLL) can be obtained by the sensors installed at the primary side of the main transformer, without adding the extra voltage sensors in taps d, c, and e. Ignoring the leakage inductances of the main transformer [in fact, it is rather smaller than L (see Fig. 1)], the mathematical model of FBC in rotation dq frame can be obtained as [32] ⎧ did ⎪ ⎨L + ωLiq + rid = vcd − vd dt ⎪ ⎩ L diq − ωLi + ri = v − v d q cq q dt

id = C˙ d (t) . iq = C˙ q (t)

where vck is the control variable in k-axis, k = d, q. Substituting (25) and (26) into (27), the differential equation of the converter can be calculated as LC¨d + rC˙ d + vd = vcd − ωLC˙ q . (28) LC¨q + rC˙ q + vq = vcq + ωLC˙ d Ignoring the disturbance (or coupling) parts ωLid and ωLiq (because they represent the system’s inner circulating energy), multiplying id and iq in both sides of (28), and integrating it from 0 to t, we can get ⎤ ⎡ 1 ˙ 2 (t) − C˙ 2 (0) L C d d 2 ⎣ ⎦ 1 2 ˙ (t) − C˙ 2 (0) L C q q 2

system‘s stored energy

⎤ ⎡ t ⎤ 2 ˙ ˙ ⎢ 0 (vcd − vd )Cd dt ⎥ ⎢ r 0 Cd dt ⎥ ⎥−⎢ ⎥. =⎢ ⎦ ⎣ t ⎦ ⎣ t 2 ˙ ˙ (vcq − vq )Cq dt r Cq dt ⎡

t

0

input energy

(23)

where vd , vq and id , iq are the variables of va , vb , vc and ia , ib , ic in d- and q-axes, respectively; vcd and vcq are the d, q components of vca , vcb , vcc (see Fig. 6); r is the inner resistance of L. Based on the passivity control principle, to get the Euler– Lagrange model of FBC, id and iq should be defined as the derivative of the “circulating chargers” Cd and Cq , i.e.,

1 ˙2 1 LCd (t) + LC˙ q2 (t) (26) 2 2 whereas the Euler–Lagrange equation is [31] ∂f d ∂fL ∂J ˙ L ˙ Ck , Ck Ck , C˙ k + Ck − dt ∂ C˙ k ∂Ck ∂ C˙ k (27) = Γk vck + Dk f L = EM − E P =

(24)

0

(29)

dissipated energy

The physical meaning of (29) is that the energy stored in the system is less than the one injected from the outside, because some energy is dissipated by the resistance. Hence, the compensating system is passivity, and then the nonlinear passivity controller can be designed for the proposed system. For the consideration of convenience, we rewrite (23) as the matrix form Lx˙ − Gx + Rx = v where

L 0 0 −ωL r 0 , G= , R= , 0 L ωL 0 0 r v − vd i v = cd , x= d . vcq − vq iq L=

(30)


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On the other hand, an adjoint system of the reference state variable x∗ (x∗ = [i∗d i∗q ]T ) can also be constructed as Lx˙ ∗ − Gx∗ + Rx∗ = v.

(31)

Combining (30) and (31), we get LΔx˙ − GΔx + RΔx = 0

(32)

∗

where Δx = x − x . Because the control object of the compensating system is to make x track x∗ , a Lyapunov energy function Es , which describes the convergence of Δx in (32), can be constructed as: 1 T Δx LΔx. (33) 2 It can be calculated from (32) and (33) that dEs /dt = −ΔxT RΔx < 0. Based on the Lyapunov stability theorem [33], it can be deduced that Δx will converge to 0 in a relatively long time, because the damping element r in original system is so small. To get a faster converge speed of Δx in dc and harmonic frequency, a virtual damping matrix Re can be added in (31) (note: the projections of the fundamental positive current vector in d and q-axes are the dc components, whereas the vectors in other frequency and sequence correspond the harmonic one), i.e., Es =

Lx˙ ∗ − Gx∗ + Rx∗ − Re Δx = v where

Re =

σ 0 ; 0 σ

σ > 0.

Fig. 7. Comprehensive control system of MBT-PQCS.

TABLE II PARAMETERS OF S IMULATION S YSTEM

(34)

(35)

It can be obtained from (30) and (34) that LΔx˙ − GΔx + (R + Re )Δx = 0.

(36)

The derivative of Es here is E˙ s = ΔxT LΔx˙ = −ΔxT (R + Re )Δx.

(37)

By comparing (37) with (33), it can be observed that E˙ s ≤ −2(r + σ)L−1 Es < 0.

(38)

Based on Lyapunov’s theory, it can be concluded that Δx in (36) will exponentially converge to 0 with a satisfactory speed if a proper σ is adopted. From (34), the modulation signals of the converter in dq frame can be calculated as ∗ vcd = L didtd + ωLiq ∗ + rid ∗ + vd − σ (id − id ∗ ) . (39) di ∗ vcq = L dtq − ωLid ∗ + riq ∗ + vq − σ (iq − iq ∗ ) A PI controller is adopted to control dc-link voltage; its output signal io is added in i∗d (see Fig. 7), which can dynamically compensate the losses of the converter and make vdc stable [32]. In addition, if the reactive power demand of the grid is considered, a reactive power control loop can also be added in i∗q (see the dotted line box in Fig. 7), though it is not the main discussion topic of this paper. The comprehensive control system of MBT-PQCS is shown in Fig. 7 (note: P(ωt), P−1 (ωt), and fs are the Park’s, invert Park’s transformation, and sample frequency, respectively).

V. S IMULATION R ESULTS To verify the effectiveness of the proposed system, a simulation model about the system shown in Fig. 1 has been established by MATLAB/Simulink. The main parameters are listed in Table II. Fig. 8 shows the dynamic response of the MBT-PQCS experiencing three typical working scenarios (the load’s waveforms are adopted from the measured locomotives’ currents of a real traction substation), and the corresponded main power quality indexes are listed in Table III. It can be seen from Fig. 8 and Table III that when MBTPQCS starts operation, the unbalanced and distorted primary three-phase currents are tend to be the balanced sinusoidal waveforms in the PF ≈ 1. The dc-link voltage is controlled around 17.3 kV in steady state and shows the overshoot about 1.156% (about 200 V) in the condition of load changes. In

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Fig. 8. Dynamic response of MBT-PQCS. TABLE III M AIN P OWER Q UALITY I NDEXES OF THE S IMULATION R ESULTS∗

TABLE IV PARAMETERS OF E XPERIMENTAL S YSTEM

*T1 : 0.05–0.2 s, T2 : 0.2–0.4 s, T3 : 0.4–0.6 s; εI and εu are the primary three phase current and voltage unbalance ratio (εI = I− /I+ , εu = U− /U+ ), respectively.

addition, the simulation results also indicate that the compensating system has a good dynamic performance, because the waveforms return to steady state from one working condition to another is in about 1–2 main grid periods. VI. E XPERIMENTAL R ESULTS A 5-kVA laboratory platform has been built to validate the proposed system. The load in phase- α and β is 0.65 and 0.3 kW (nonlinear load), respectively. The control algorithm mentioned in Fig. 7 is carried out in DSP (TMS320F28335) for digital implementation (the carrier frequency is 12.8 kHz). HIOKI3198 power quality analyzer is used for data acquisition (note:

to make the waveforms more convenient to be observed, some data are saved in MATLAB workspace). The basic parameters of the experimental system are listed in Table IV. The experimental results are shown in Fig. 9 and Table V. It can be seen from Fig. 9(a), (b), and (d) that when the MBTPQCS starts operation, the primary currents of YD-FMBT are changed from unbalanced and distorted three-phase waveforms to the sinusoidal ones (note: because some harmonic currents from other adjacent nonlinear loads are flowing into the primary side in our experimental period, the current shows light distortion after compensation). The dc-link voltage fluctuates around its reference value 185 V within about 1 V, as


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VII. C ONCLUSION This paper has proposed a YD-MFBT-based power quality control system for the single-phase power system. The compensating principle was investigated in detail. In addition, the corresponding detection and control method are given in this paper as well. Both the simulation and experimental results verify the effectiveness of the proposed system. In the premise of getting good compensating performance, the MBT-PQCS does not need the large capacity step-down transformer as the interface between FBC and the main transformer. The system integration level is significantly enhanced, and the initial costs, covering space, and installing difficulties are greatly decreased. Additionally, considering the excellent property of the main transformer, MBT-PQCS is a power quality control system with high cost-efficiency. A PPENDIX The winding current’s distribution of MBT-PQCS can be expressed as follows: √ ⎧ √ 2( 3−1) ⎪ √3+3 Iplα + √ I I − Ilα − 3 √23+1 Ilβ = − ⎪ ad ⎪ 3( 3+1) 3( 3+1) plβ ( ) ⎪ ⎪ √ √ √ ⎪ 3+3 3+3 12−6 3 ⎪ ⎪ Idc = − 3 √3+1 Iplα − 3 √3+1 Iplβ + 3 √3+1 Ilα ⎪ ⎪ (√ ) (√ ) ( √) ⎪ ⎨ 3+3 3+3 12−6 Ice = − 3 √3+1 Iplα − 3 √3+1 Iplβ + 3 √3+13 Ilβ . ( ) ( ) ( ) ⎪ √ ⎪ √ ⎪ 2( 3−1) ⎪ ⎪ √ √3+3 √2 ⎪ ⎪ Ieb = 3( 3+1) Iplα − 3( 3+1) Iplβ − 3( 3+1) Ilα − Ilβ ⎪ ⎪ √ √ ⎪ 2( 3−1) 2( 3−1) ⎪ ⎩ Iba = 3 √3+1 Iplα + 3 √3+1 Iplβ − 3 √23+1 Ilβ ( ) ( ) ( ) (A.1) R EFERENCES

Fig. 9. Experimental waveforms of MBT-PQCS. (a) Currents’ waveforms before and after the operation of MBT-PQCS. (b) Primary three phase phasors before and after compensation (I4 is disturbance). (c) DC-link voltage. (d) Spectrum of IA before and after compensation. TABLE V M AIN P OWER Q UALITY I NDEXES OF THE E XPERIMENTAL R ESULTS

shown in Fig. 9(c). The power quality indexes before and after MBT-PQCS starts operation are listed in Table V. It is clear that the proposed system represents an effective compensating performance on power factor correction, NSC, and harmonic suppression.

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Sijia Hu (S’14) was born in Hunan, China, in 1987. He received the B.Sc. and Ph.D. degrees in electrical engineering (and automation) from Hunan University of Science and Technology, Xiangtan, China, and Hunan University, Changsha, China, in 2010 and 2015, respectively. He is currently an Assistant Professor of Electrical Engineering with Hunan University. His research interests include power flow control and power quality analysis and control of electric railway power systems, high-power converters, and FACTS technologies.

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. In 2009, he became a Research Associate with the Institute of Energy Systems, Energy Efficiency, and Energy Economics (ie3 ), TU Dortmund University, Dortmund, Germany, where he received the second Ph. D. degree in June 2012. He then became 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 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.

Bin Xie was born in Hunan, China, in 1990. He received the B.Sc. degree in electrical engineering from Shaoyang University, Hunan, China, in 2013. Since 2015, he has been working toward the Ph.D. degree 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.

Mingfei Chen was born in Hunan, China, in 1989. He received the B.Sc. and M.Sc. degrees in electrical engineering from Hunan University of Science and Technology, Xiangtan, China, and Hunan University, Changsha, China, in 2012 and 2014, respectively. He is currently with the State Grid Loudi Electric Power Supply Company, Loudi, China. His research interests include power quality analysis and control of electric railway power systems, and power system protection.

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 technologies of ac/dc energy transforms, theory and applications of newtype electric apparatus, harmonic suppression for electric railways, power electronics applications, and computer control.


Longfu Luo (M’09) was born in Hunan, China, in 1962. He received the B.Sc., M.Sc., and Ph.D. degrees in electrical engineering 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. Currently, he is a Full Professor of Electrical Engineering with the College of Electrical and Information Engineering, Hunan University. His 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. degree in computer science and the Ph.D. degree in electrical engineering 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 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, Hangzhou, China. He was appointed as Deputy Dean of the College of Electrical Engineering, Zhejiang University, in 2005. Currently, he is 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.

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Andreas Kubis (S’11) was born in Germany in 1985. He received the B.Eng. degree in electrical engineering from the University of Applied Sciences, Dortmund, Germany, and the M.Sc. degree in electrical engineering from the University of Kassel, Kassel, Germany, in 2009 and 2011, respectively. Since 2011, he has been with the Institute of Energy Systems, Energy Efficiency and Energy Economics, TU Dortmund University, Dortmund, Germany. His research interests include power system stability, monitoring, and control. Mr. Kubis is member of the German National Committee of CIGRE.

Christian Rehtanz (M’96–SM’06) was born in Germany in 1968. He received the Diploma and Ph.D. degrees in electrical engineering from TU Dortmund University, Dortmund, Germany, in 1994 and 1997, respectively. In 2003, he received the venia legendi in electrical power systems from the Swiss Federal Institute of Technology, Zurich, Switzerland. In 2000, he joined ABB Corporate Research, Baden, 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, Beijing, China, in 2005. Since 2007, he has been the Head of the Institute of Energy Systems, Energy Efficiency and Energy Economics (ie3 ), TU Dortmund University. In addition, he has been a Scientific Advisor of ef.Ruhr GmbH, Dortmund, Germany, 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 has authored more than 150 scientific publications, three books, and 17 patents and patent applications. His research interests include electrical power systems and power economics, technologies for network enhancement and congestion relief such as stability assessment, wide-area monitoring, protection, and coordinated network-control, and integration and control of distributed generation and storage. Dr. Rehtanz was a recipient of the MIT World Top 100 Young Innovators Award 2003.