A Novel Co-Phase Power Supply System for Electrified Railway Based on V Type Connection Traction Transformer

Abstract

Power quality and neutral section are two technical problems that hinder the development of electrified railway to high-speed and heavy railway. The co-phase power supply technology is one of the best ways to solve these two technical problems. At present, a V type connection traction transformer is widely used in a power frequency single-phase AC traction power supply system, especially in high-speed railway. In this paper, a new type of co-phase power supply system for electrified railway based on V type connection traction transformer is proposed. One single-phase winding in the V type connection traction transformer is used as main power supply channel, and three ports are used as compensation ports. Neutral section is no longer set with traction substation, and the train is continuously powered through. The independent single-phase Static Var Generators (SVGs) are used to compensate the three-phase imbalance caused by single-phase traction load. When necessary, the power factor can be improved at the same time. The principle, structure, control strategy, and capacity configuration of the technical scheme are analyzed in this paper, and the effectiveness of the scheme is verified by using the measured data of electrified railway. The advantage of this scheme lies in the universal applicability of the V type connection traction transformer, and the flexibility of the SVG device.

1. Introduction

As the backbone of modern comprehensive transportation system and one of the main modes of transportation, railway plays an important role in the process of social and economic development in China [1,2]. According to the railway statistics bulletin of 2019 issued by the State Railway Administration of China, by the end of 2019, business mileage has reached 139,000 km, and the railway electrification rate reached 71.9% [3].

With the development of electrified railways, power quality has always been a research hotspot, because of the characteristics of the traction power supply system [4]. A power frequency single phase AC system is widely used in China’s electrified railways. The structure diagram of existing electrified railways is shown in Figure 1. As a single-phase power load essentially, traction load will cause power quality problems including mainly negative sequence in three-phase power system [5,6,7]. In order to reduce the influence of traction load on the three-phase unbalance at the Point of Common Coupling (PCC) of power system, the scheme of supplying power by sections in traction network and each section using three-phase power system in turn is usually adopted. The neutral section is set between two adjacent power supply sections [8,9,10]. However, it brings about a series of problems, such as the reduction of train speed, loss of traction force, frequent action of phase passing device, short service life, and low reliability, which seriously affect the safe and stable operation of the train. It shows that the neutral section is the weakest link in the AC traction power supply system of electric railway, and greatly restricts the traction power supply system Railway Development [11,12].

With widespread use of AC-DC-AC electric locomotives using Pulse Width Modulation (PWM) technology, compared to the traditional AC-DC electric locomotives, the harmonic problem has been greatly improved, and the power factor is close to 1, which has overcome the shortcomings of traditional AC-DC electric locomotives [13,14,15,16,17,18]. However, at the same time, because of the huge increase in traction power of AC-DC-AC electric locomotives, the high-power single-phase traction load will cause more three-phase unbalance problems in the power system. Therefore, negative sequence will become the focus of power quality research of electrified railways.

In view of how to effectively solve the power quality problems including mainly negative sequence and neutral section, a lot of research work has been carried out, and different solutions have been put forward. The scheme to solve the negative sequence and electrical phase separation in Germany is adopting special railway power generation, transmission, and distribution system and setting a three-phase/single AC-DC-AC converter in the traction substation. At the same time, the neutral section is cancelled [19]. In Japan, Scott traction transformer and Railway Static Power Conditioner (RPC) are used in Shinkansen to compensate three-phase unbalance and voltage fluctuation so as to reduce the influence of traction load on three-phase power system [20,21,22]. It can solve the problem of power quality, and automatic passing neutral section technology is used to solve the problems caused by neutral section. Bilateral power supply technology is adopted in Russia to cancel neutral section between traction substations [19]. However, the traction power supply system is parallel with the power system transmission lines, and maybe there is current power in the traction power supply system, which needs to be restrained.

The idea of a co-phase power supply system to eliminate the neutral section and solve power quality problem is first proposed in [23]. The co-phase power supply refers to the power supply mode that a traction substation or multiple traction substations of a railway line supply the whole traction network with the same phase (line) voltage in the same three-phase power grid. If two adjacent traction substations adopt bilateral power supply, the co-phase power supply network formed by multiple traction substations on the line is called through co-phase power supply, referred to as through power supply [24,25].

Since the concept of co-phase power supply system was proposed, there have been some related studies on topological structure, compensation technology, and control strategy about co-phase power supply system. The co-phase power supply scheme based on three-phase-two-phase balanced connection traction transformer and Power Flow Controller (PFC) is proposed in [26]. Furthermore, more co-phase power supply schemes are proposed in [19,27,28]. Moreover, the schemes proposed in [19,26] have been applied in the Meishan traction substation of Chengdu Kunming railway, Shayu traction substation of Central South Passage of Shanxi Province, and Wenzhou City railway S1 line. The practice results show that the co-phase power supply technology can effectively solve the power quality problem with negative sequence as the main factor and cancel the neutral section at the traction substation.

In order to effectively reduce the PFC device capacity, a co-phase power supply scheme based on Hybrid Power Quality Conditioner (HPQC) was proposed in [29]. By using relatively inexpensive passive components to provide a part of reactive power, the active device capacity can be reduced. In order to obtain satisfactory compensation effects, the HPQC system often needs to consider more complex factors in design. A scheme to reduce the device capacity of RPC by using a C-type filter is proposed in [30], the C-type filter can compensate for a part of reactive power of the traction load while filtering out harmonics. Therefore, the device capacity of RPC can be reduced to a certain extent. In addition, based on the Modular Multilevel Converter (MMC) technology, the co-phase power supply schemes by using three-phase/single-phase AC-DC-AC converter is introduced in [31,32,33]. The outstanding advantage of these design schemes is that they can realize the balanced transformation between a three-phase system and single-phase system without generating power quality problems. However, it should be noted that in these schemes, all the power of the traction load will be transmitted through the power electronic converter, so the required device capacity will be equivalent to the capacity of a traditional traction transformer [34].

In recent years, Static Var Generator (SVG) has been widely used in various transmission and distribution systems due to its outstanding performance in compensating reactive power, etc. [35]. Compared with the traditional Static Var Compensator (SVC), SVG has the characteristics of faster dynamic response and lower harmonic content [36,37,38].

In view of this, a co-phase power supply scheme based on SVG for V type connection traction transformer which is widely used in high-speed railway is proposed in this paper. The feature of the scheme is that the traction load and compensation equipment share the same transformer, which can realize the comprehensive compensation of negative sequence and reactive power, effectively solve the problem of power quality, and cancel the neutral section at traction substation. Furthermore, the capacity of compensation equipment is minimized.

2. System Structure

Based on V type connection traction transformer and SVG, a novel co-phase power supply system for electrified railway is proposed in this paper. By means of unequal side V type connection traction transformer and setting single-phase SVG on multiple ports of the secondary side, the negative sequence and reactive power comprehensive compensation is carried out for three-phase unbalance and power factor, so that the power quality can meet the standard. For traction load, neutral section at the outlet of traction substation can be cancelled to realize co-phase power supply. The scheme of system is shown in Figure 2.

In Figure 2, the system mainly includes the Traction Compensation Transformer (TCT), the Comprehensive Compensation Equipment (CCE), and the Measurement and Control System (MCS). TCT is composed of unequal side V type connection traction transformer. The primary side terminal of TCT is connected with three-phase power system. The secondary side port ab of TCT is traction port, and port ac, b’c, and ad are compensation ports.

CCE is composed of three single-phase SVGs, which are connected with compensation ports, respectively. MCS includes the Voltage Transformer (VT), the Current Transformer (CT), and the Controller Device (CD), and the signal output terminal of CD is connected with the control terminal of CCE.

Traction port ab of TCT is connected to traction network with VT and CT. If the power supply mode of traction network is direct power supply mode or direct power supply mode with return line, as shown in Figure 2a, terminal a of traction port ab is connected with traction network, terminal b is connected with rail.

If the traction network power supply mode is AT power supply mode, as shown in Figure 2b, terminal a of traction port ab of TCT is connected with traction network, and terminal b is connected with negative feeder.

3. Comprehensive Compensation Principle

The system takes the negative sequence limits of three-phase high-voltage bus and power factor as the compensation target. By controlling the reactive power generated by CCE, the reactive power and negative sequence generated by single-phase traction load are comprehensively compensated, so that the compensated power factor and negative sequence meet the requirements of the compensation target. CCE only changes the reactive power flow and does not change the active power flow.

3.1. Comprehensive Compensation Principle

According to reference [39], any traction port or compensation port $\lambda$ on the secondary side of the traction transformer, the positive and negative sequence currents ${\dot{I}}_{\lambda }^{+}$ and ${\dot{I}}_{\lambda }^{-}$ generated on the primary side can be expressed as

$$\left\{\begin{array}{l}{\dot{I}}_{\lambda }^{+}=\frac{1}{\sqrt{3}}{k}_{\lambda }{I}_{\lambda }{e}^{-j{\varphi }_{\lambda }}\\ {\dot{I}}_{\lambda }^{-}=\frac{1}{\sqrt{3}}{k}_{\lambda }{I}_{\lambda }{e}^{-j\left(2{\psi }_{\lambda }+{\varphi }_{\lambda }\right)}\end{array}\right.,$$

(1)

where $I_{\lambda }$ is the effective value of the port current; ${\psi }_{\lambda }$ is the angle at which ${\dot{U}}_{\lambda }$ lags ${\dot{U}}_A$; ${\varphi }_{\lambda }$ is the power factor angle; $k_{\lambda }=U_{\lambda }/\sqrt{3}{U}_A$. $U_{\lambda }$ is the effective value of the port voltage ${\dot{U}}_{\lambda }$.

The traction load current and power factor angle of TCT secondary traction port are set as ${\dot{I}}_L$ and ${\varphi }_L$, respectively. Taking the traction load in traction condition as an example, the comprehensive compensation principle of CCE is analyzed as follows.

When CCE performs comprehensive compensation, its positive and negative sequence phasor diagram is shown in Figure 3.

In Figure 3, ${\dot{U}}_A$, ${\dot{U}}_B$, and ${\dot{U}}_C$ are the A, B, C three-phase voltage of the three-phase high-voltage bus, and ${\dot{U}}_1$, ${\dot{U}}_2$, and ${\dot{U}}_3$ are the compensation port voltage of TCT secondary side SVG1, SVG2, and SVG3, respectively, and ${\dot{U}}_L$ is the traction port voltage of the TCT secondary side. The corresponding negative sequence voltage are ${\dot{U}}_A^{-}$, ${\dot{U}}_B^{-}$, ${\dot{U}}_C^{-}$, ${\dot{U}}_1^{-}$, ${\dot{U}}_2^{-}$, ${\dot{U}}_3^{-}$, and ${\dot{U}}_L^{-}$. According to the topology of CCE, the relation diagram of positive sequence phasor and negative sequence phasor can be determined. Furthermore, the reactive currents generated by SVG1, SVG2, and SVG3 are ${\dot{I}}_1$, ${\dot{I}}_2$, and ${\dot{I}}_3$, respectively, where ${\dot{I}}_1$ is inductive current and ${\dot{I}}_2$ and ${\dot{I}}_3$ are capacitive current. The corresponding negative sequence currents are ${\dot{I}}_1^{-}$, ${\dot{I}}_2^{-}$, and ${\dot{I}}_3^{-}$, respectively. The resultant negative sequence current ${\dot{I}}^{’}{}_L^{-}$ can be used to offset the negative sequence current ${\dot{I}}_L^{-}$ generated by the traction load. When the negative sequence is fully compensated, Equation (2) is correct:

$${\dot{I}}_L^{-}+{\dot{I}}^{’}{}_L^{-}={\dot{I}}_L^{-}+{\dot{I}}_1^{-}+{\dot{I}}_2^{-}+{\dot{I}}_3^{-}=0.$$

(2)

3.2. Comprehensive Compensation Model

According to the above analysis, it can be seen that CCE compensates the negative sequence and reactive power compensation simultaneously. Generally, the check point of negative sequence and power factor is Point of Common Coupling (PCC), so the negative sequence and reactive power generated by traction load at PCC are compensation object. In case of CCE compensation, the active power of traction load remains unchanged at PCC, then reactive power $Q_{CSS}$ and power factor $\cos {\varphi }_L^{\prime }$ after compensation can be expressed as follows:

$$Q_{CSS}=S_L\sin {\varphi }_L+{\displaystyle \sum }_{k=1}^n{S}_k\sin {\varphi }_K=(1-K_C)S_L\sin {\varphi }_L,$$

(3)

$$\cos {\varphi }_L^{\prime }=\frac{S_L\cos {\varphi }_L}{\sqrt{{\left(S_L\cos {\varphi }_L\right)}^2+{\left(Q_{\mathrm{CSS}}\right)}^2}},$$

(4)

where $S_L$ and ${\varphi }_L$ are the total apparent power and power factor angle of traction load. $S_k$ and ${\varphi }_k$ are the reactive power and power factor angle of SVG, respectively. n is the number of compensation ports, so n = 3 for Figure 2. $K_C$ is the reactive power compensation degree.

According to Equation (3), $K_C$ can be expressed as

$$K_C=-\frac{{{\displaystyle \sum }}_{k=1}^n{S}_k\sin {\varphi }_k}{S_L\sin {\varphi }_L}.$$

(5)

After using CCE to compensate, the negative sequence power at PCC is

$${\dot{S}}^{-}=S_L{e}^{j{\theta }_L}+{{\displaystyle \sum }}_{k=1}^n{S}_k{e}^{j{\theta }_k}=\left(1-K_N\right)S_L{e}^{j{\theta }_L},$$

(6)

where ${\theta }_L=2{\psi }_L+{\varphi }_L$, ${\psi }_L$, and ${\varphi }_L$ are angle of ${\dot{U}}_L$ lagging behind ${\dot{U}}_A$ and traction load power factor angle; ${\theta }_k=2{\psi }_k+{\varphi }_k$, ${\psi }_k$, and ${\varphi }_k$ are angle of compensating port k voltage lagging behind ${\dot{U}}_A$ and power factor angle of SVG, respectively; $K_N$ is the negative sequence compensation degree.

According to Equation (6), $K_N$ can be expressed as

$$K_N=-\frac{{{\displaystyle \sum }}_{k=1}^n{S}_k{e}^{j{\theta }_k}}{S_L{e}^{j{\theta }_L}}.$$

(7)

According to Equations (5) and (7), the comprehensive compensation effects of reactive power and negative sequence can be determined respectively by $K_C$ and $K_N$. $K_C$ and $K_N$ are real numbers, and the range is $K_C$, $K_N\in \left[0,1\right]$.

Equation (7) is expanded according to the real part and the imaginary part, respectively, and constitutes the simultaneous equations together with Equation (5). The comprehensive compensation model shown as Equation (8):

$$\left\{\begin{array}{c}{K}_C{S}_L\sin {\varphi }_L=-{{\displaystyle \sum }}_{k=1}^n{S}_{k}sin{\varphi }_k\\ K_N{S}_L\cos {\theta }_L=-{{\displaystyle \sum }}_{k=1}^n{S}_{k}cos{\theta }_k\\ K_N{S}_L\sin {\theta }_L=-{{\displaystyle \sum }}_{k=1}^n{S}_{k}sin{\theta }_k\end{array}\right..$$

(8)

The reactive power generated by SVG1, SVG2, and SVG3 are $S_1$, $S_2$, and $S_3$, respectively, and according to Section 3.1, ${\varphi }_1=\pi /2$, ${\varphi }_2=-\pi /2$, and ${\varphi }_3=-\pi /2$, the comprehensive compensation model can be obtained as follows according to Equation (8):

$$\left\{\begin{array}{l}{K}_C{S}_L\sin {\varphi }_L=-S_1+S_2+S_3\\ K_N{S}_L\cos (2{\psi }_L+{\varphi }_L)=S_1\sin 2{\psi }_1-S_2\sin 2{\psi }_2-S_3\sin 2{\psi }_3\\ K_N{S}_L\sin (2{\psi }_L+{\varphi }_L)=-S_1\cos 2{\psi }_1+S_2\cos 2{\psi }_2+S_3\cos 2{\psi }_3\end{array}\right.,$$

(9)

where ${\psi }_L=-\pi /6$, ${\psi }_1=-5\pi /6$, ${\psi }_2=-\pi /2$, and ${\psi }_3=-\pi /6$.

$S_1$, $S_2$, and $S_3$ can be solved by Equation (9):

$$\left\{\begin{array}{l}{S}_1=\frac{1}{\sqrt{3}}{K}_N{S}_L\cos {\varphi }_L+\frac{1}{3}\left(K_N-K_C\right)S_L\sin {\varphi }_L\\ S_2=\frac{1}{\sqrt{3}}{K}_N{S}_L\cos {\varphi }_L-\frac{1}{3}\left(K_N-K_C\right)S_L\sin {\varphi }_L\\ S_3=\frac{1}{3}\left(2K_N+K_C\right)S_L\sin {\varphi }_L\end{array}\right.,$$

(10)

where $S_k>0 \left(k=1, 2\right)$ means that SVG1 and SVG2 output inductive and capacitive reactive power, respectively; otherwise, SVG1 and SVG2 output capacitive and inductive reactive power, respectively; SVG3 always output capacitive reactive power.

If Equation (10) is divided by $U_L$, the reactive current generated by SVG1, SVG2, and SVG3 are shown in Equation (11):

$$\left\{\begin{array}{l}{I}_1=\frac{k_M}{\sqrt{3}{k}_L}\left[K_N{I}_L\cos {\varphi }_L+\frac{1}{\sqrt{3}}\left(K_N-K_C\right)I_L\sin {\varphi }_L\right]\\ I_2=\frac{k_M}{\sqrt{3}{k}_L}\left[K_N{I}_L\cos {\varphi }_L-\frac{1}{\sqrt{3}}\left(K_N-K_C\right)I_L\sin {\varphi }_L\right]\\ I_3=\frac{k_M}{3k_L}\left(2K_N+K_C\right)I_L\sin {\varphi }_L\end{array}\right.,$$

(11)

where $k_L=\sqrt{3}{U}_A/U_L$, $k_M=\sqrt{3}{U}_A/U_k\begin{array}{c} \end{array}\left(k=1,\begin{array}{c} \end{array}2,\begin{array}{c} \end{array}3\right)$, and satisfies $U_1=U_2=U_3$.

4. Comprehensive Compensation Control Strategy

As shown in Figure 4, set the instantaneous value of voltage on primary side of TCT as $U_A\left(t\right)=\sqrt{2}{U}_A\sin (\omega t)$. With ${\dot{U}}_A$ as the reference, the port voltage of traction port ${\dot{U}}_L$ and load current ${\dot{I}}_L$ are shown as follows:

$$U_L\left(t\right)=\sqrt{2}{U}_L\sin (\omega t-{\psi }_L)=\sqrt{2}{U}_L\sin (\omega t+\frac{\pi }{6}),$$

(12)

$$I_L\left(t\right)=I_{L1}\left(t\right)+I_{Lh}\left(t\right)=\sqrt{2}{I}_{L1}\sin (\omega t+\frac{\pi }{6}-{\varphi }_{L1})+I_{Lh}\left(t\right),$$

(13)

where $I_{L1}\left(t\right)$ is the fundamental current; $I_{Lh}\left(t\right)$ is the harmonic current; $I_{L1}$ is the effective value of the fundamental current; $\omega$ is the angular frequency; and ${\varphi }_{L1}$ is the fundamental power factor angle. The fundamental component $I_{L1}$ of load current can be further decomposed into instantaneous active component $I_{L1p}$ and instantaneous reactive component $I_{L1q}$:

$$I_{L1}\left(t\right)=\sqrt{2}{I}_{L1p}\sin (\omega t+\frac{\pi }{6})-j\sqrt{2}{I}_{L1q}\cos (\omega t+\frac{\pi }{6}),$$

(14)

where $I_{L1p}=I_{L1}\cos {\varphi }_L$, $I_{L1q}=I_{L1}\sin {\varphi }_L$.

By introducing Equation (14) into Equation (13) and multiplying both sides of the equation by $\sin (\omega t+\frac{\pi }{6})$ and $\cos (\omega t+\frac{\pi }{6})$, Equations (15) and (16) can be obtained:

$$I_L\left(t\right)\sin (\omega t+\frac{\pi }{6})=\left[\frac{\sqrt{2}}{2}{I}_{L1p}-\frac{\sqrt{2}}{2}{I}_{L1p}\cos (2\omega t+\frac{\pi }{3})-\frac{\sqrt{2}}{2}{I}_{L1q}\sin (2\omega t+\frac{\pi }{3})\right]+I_{Lh}\left(t\right)\sin (\omega t+\frac{\pi }{6}),$$

(15)

$$I_L\left(t\right)\cos (\omega t+\frac{\pi }{6})=\left[-\frac{\sqrt{2}}{2}{I}_{L1q}+\frac{\sqrt{2}}{2}{I}_{L1q}\cos (2\omega t+\frac{\pi }{3})+\frac{\sqrt{2}}{2}{I}_{L1p}\sin (2\omega t+\frac{\pi }{3})\right]+I_{Lh}\left(t\right)\cos (\omega t+\frac{\pi }{6}).$$

(16)

DC components $\frac{\sqrt{2}}{2}{I}_{L1p}$ and $-\frac{\sqrt{2}}{2}{I}_{L1q}$ can be separated from Equations (15) and (16), and then $I_{L1p}$ and $I_{L1q}$ can be obtained.

4.1. System Control Strategy

When CCE operates, ${\dot{U}}_1$, ${\dot{U}}_2$, and ${\dot{U}}_3$ are, respectively, locked by phase-locked loop (PLL) to generate synchronous signals $\sin (\omega t-\frac{\pi }{6})$, $\sin (\omega t-\frac{\pi }{2})$, and $\sin (\omega t+\frac{\pi }{6})$. Under the traction condition of traction load, SVG1 outputs inductive reactive power, SVG2 and SVG3 output capacitive reactive power. Therefore, the synchronous signals of compensation current of SVG1, SVG2, and SVG3 are, respectively, $-\cos (\omega t-\frac{\pi }{6})$, $\cos (\omega t-\frac{\pi }{2})$, and $\cos (\omega t+\frac{\pi }{6})$. According to Equation (11), the expected values of compensation current of SVG1, SVG2, and SVG3, $I_1^{*}$, $I_2^{*}$, and $I_3^{*}$ are

$$\left\{\begin{array}{l}{I}_1^{*}=-\frac{\sqrt{2}{k}_M}{\sqrt{3}{k}_L}\left[K_N{I}_{L1p}+\frac{1}{\sqrt{3}}\left(K_N-K_C\right)I_{L1q}\right]\cos (\omega t-\frac{\pi }{6})\\ I_2^{*}=\frac{\sqrt{2}{k}_M}{\sqrt{3}{k}_L}\left[K_N{I}_{L1p}-\frac{1}{\sqrt{3}}\left(K_N-K_C\right)I_{L1q}\right]\cos (\mathsf{\omega }\mathrm{t}-\frac{\pi }{2})\\ I_3^{*}=\frac{\sqrt{2}{k}_M}{3k_L}\left[\left(2K_N+K_C\right)I_{L1q}\right]\cos (\omega t+\frac{\pi }{6})\end{array}\right..$$

(17)

According to Equation (17), the block diagram of the expected value detection of compensation currents of the CCE is shown in Figure 5.

The expected compensation currents $I_1^{*}$, $I_2^{*}$, and $I_3^{*}$ are compared with the actual currents value $I_1$, $I_2$, and $I_3$ on the compensation port. After PI adjustment, the PWM control signal driving SVG is generated by carrier modulation technology. Therefore, the CCE can be controlled to send out the corresponding expected compensation currents. The control block diagram of CCE is shown in Figure 6.

4.2. Determination Method and Steps of K_C and K_N

In the integrated compensation control strategy, the key to achieve the compensation goal is to confirm the appropriate reactive power compensation degree $K_C$ and negative sequence compensation degree $K_N$.

The relationship between the $K_C$ and power factors can be obtained by solving Equations (3) and (4) simultaneously:

$$K_C=1-\sqrt{\frac{{(\tan {\varphi }_L^{’})}^2}{{(\tan {\varphi }_L)}^2}}=1-\sqrt{\frac{{(\cos {\varphi }_L^{\prime })}^{-2}-1}{{(\cos {\varphi }_L)}^{-2}-1}},$$

(18)

where $\cos {\varphi }_L$ and $\cos {\varphi }_L^{\prime }$ are power factors before and after compensation.

The following relationship between the limit of three-phase voltage unbalance degree at PCC ${\epsilon }_{U2}$ and the allowable negative sequence power at PCC $S_{\epsilon }$ is

$$S_{\epsilon }={\epsilon }_{U2}\cdot S_d,$$

(19)

where $S_d$ is the short circuit capacity at PCC.

If the residual negative sequence power caused by traction load at PCC after compensation is ${\dot{S}}^{-}$, its magnitude shall meet $\left|{\dot{S}}^{-}\right|\le S_{\epsilon }$. The relationship between $K_N$ and expected value of three-phase voltage unbalance degree ${\epsilon }_{U2}^{*}$ can be obtained by solving Equations (6) and (19), as shown in Equation (20):

$$K_N=\frac{S_L-{\epsilon }_{U2}^{*}\cdot S_d}{S_L}.$$

(20)

At present, AC/DC/AC electric locomotive and AC/DC electric locomotive are widely used in electrified railway. According to load characteristics, the methods for determining the values of $K_C$ and $K_N$ can be summarized as follows, the specific steps are

(1)

When the negative sequence power $S_L^{-}$ generated by the traction load is greater than the allowable negative sequence power $S_{\epsilon }$ at PCC, and the power factor $\cos {\varphi }_L$ is less than the target power factor value $\cos {\varphi }^{*}$, the negative sequence and reactive power are compensated by CCE at the same time. Based on the expected target, the value of $K_C$ and $K_N$ can be determined according to Equations (18) and (20). Then, according to Equation (10), the $S_1$, $S_2$, and $S_3$ are obtained. Under the traction condition of traction load, $S_1$ is inductive or capacitive reactive ($S_1>0$ or $S_1<0$), $S_2$ is capacitive or inductive reactive ($S_2>0$ or $S_2<0$), and $S_3$ is capacitive reactive;

(2)

When $S_L^{-}$ is greater than $S_{\epsilon }$, and $\cos {\varphi }_L$ is greater than or equal to $\cos {\varphi }^{*}$. Only the negative sequence power is compensated by CCE, and the power factor is not changed before and after compensation. Therefore, $K_C$ can be determined by $K_C=0$, and based on the expected target after compensation, the value of $K_N$ can be determined according to Equation (20). Then according to Equation (10), the $S_1$, $S_2$, and $S_3$ are obtained. Under the traction condition of traction load, $S_1$ is inductive reactive, $S_2$ and $S_3$ are capacitive reactive;

(3)

When $S_L^{-}$ is less than or equal to $S_{\epsilon }$, and $\cos {\varphi }_L$ is less than $\cos {\varphi }^{*}$. Only the reactive sequence power is compensated by CCE. Therefore, $K_N$ can be determined by $K_N=0$, and based on the expected target after compensation, the value of $K_C$ can be determined according to Equation (18). Then, according to Equation (10), the $S_1$, $S_2$, and $S_3$ are obtained. Under the traction condition of traction load, $S_1$, $S_2$, and $S_3$ are all capacitive reactive;

(4)

When $S_L^{-}$ is less than or equal to $S_{\epsilon }$, and $\cos {\varphi }_L$ is greater than or equal to $\cos {\varphi }^{*}$. The negative sequence and reactive power generated by the traction load can meet the compensation target, no additional compensation is required. Therefore, $K_N$ and $K_C$ can be determined by $K_N=0$ and $K_C=0$. CCE operates in standby.

In summary, the schematic diagram of the process of determining the values of $K_C$ and $K_N$ is shown in Figure 7.

5. Effectiveness Verification

5.1. Analysis and Verification of Comprehensive Compensation Scheme Based on Actual Case

Take the actual data of an electrified railway traction load as an example for illustration. The traction transformer is single-phase wiring, and its primary side is connected to the A and B phases of the 110 kV power system. The primary and secondary side transformation ratio is 110/27.5. By using the power quality test device, the amplitude and phase angle of the voltage and current of the primary and secondary sides of the traction transformer are recorded. The measurement period is 24 h. After processing the data, the diagram of 24-h load curve of the traction load is shown in Figure 8.

After further statistical analysis of the load data, it shows that the 95% probability value of the three-phase voltage unbalance degree of the traction substation is 1.2%, and the maximum is 3.6%. The maximum value has exceeded 2.6%, the limit of the three-phase voltage unbalance degree standard [40]. In addition, the daily average power factor of the traction substation is 0.79, which is lower than the economic power factor of 0.9 required by the power system. Therefore, it is necessary to set up an appropriate compensation scheme for comprehensive treatment of the negative sequence and reactive power in the traction substation. The diagram of 24-h three-phase voltage unbalance degree curve of the traction substation is shown in Figure 9.

The design target of the compensation scheme proposed in this paper is that after compensation, the maximum value of the three-phase voltage unbalance degree of the traction substation will be reduced to a value less than the limit, for example, 2.5%, the 95% probability value will be further reduced to a value less than the limit, for example, 1%, and the daily average power factor is increased to 0.9.

In order to reduce the capacity of the compensation device as much as possible, for the condition where the three-phase voltage unbalance degree caused by the traction load is greater than 1.2%, the first negative sequence allowable amount $S_{\epsilon 1}$ will implemented as the assessment reference value, $S_{\epsilon 1}$ = 12.5 MVA. According to Equation (19), it can be known that the corresponding three-phase voltage unbalance degree target is 2.5%. If $S_L^{-}$ is greater than $S_{\epsilon 1}$, the expected value of the three-phase voltage unbalance degree after compensation is set to 2.5%. Otherwise, $S_L^{-}$ meets the requirements of $S_{\epsilon 1}$, so that the CCE is standby. However, for the condition where the three-phase voltage unbalance degree is less than or equal to 1.2%, the allowable second negative sequence $S_{\epsilon 2}$ will implemented as the assessment reference value, $S_{\epsilon 2}$ = 5 MVA. Moreover, the corresponding three-phase voltage unbalance degree target is 1.0%. If $S_L^{-}$ is greater than $S_{\epsilon 2}$, the expected value of the three-phase voltage unbalance degree after compensation is set to 1.0%. Otherwise, $S_L^{-}$ meets the requirements of $S_{\epsilon 2}$ and similarly there is also no need to compensate for the negative sequence power.

Based on the selection of the above limits, by using the determination method and steps of $K_C$ and $K_N$ given in Section 4.2, the values of $K_C$ and $K_N$ corresponding to the load at each moment of the traction substation can be calculated. As shown in Figure 10.

According to the calculation results of $K_C$ and $K_N$ in Figure 10, it can be further calculated by Equation (10) that the maximum reactive power compensation amount required by SVG1, SVG2, and SVG3 are 2.66 MVA, 2.66 MVA, and 3.55 MVA, respectively. Therefore, combined with actual engineering applications, a comprehensive compensation design scheme for the traction substation can be determined. The device capacity of SVG1, SVG2, and SVG3 can be selected respectively as 3 MVA, 3 MVA, and 5 MVA. Furthermore, the capacity of each device above is the actual value of required to meet the compensation target.

Based on the above compensation design scheme, after implementing the comprehensive compensation of negative sequence and reactive power for the traction substation, the diagram of 24-h device output power of the CCE is shown in Figure 11.

The diagram of 24-h three-phase voltage unbalance degree curve and power factor curve of the traction substation before and after compensation are shown in Figure 12 and Figure 13, respectively.

In Figure 14, the statistical result after compensation shows that the 95% probability value of the three-phase voltage unbalance degree of the traction substation has reduced from 1.2% to 1.0%, and the maximum also has reduced from 3.6% to 2.5%. At the same time, the daily average power factor of the traction substation has increased from 0.79 to 0.91, achieving compensation design target.

5.2. Analysis and Verification of Comprehensive Compensation Control Strategy

To verify the effectiveness of the comprehensive compensation control strategy, a simulation model is established with MATLAB/SIMULINK, as shown in Figure 15. In the simulation model, the short-circuit capacity of the power system is set to 500 MVA; on the primary-side of TCT, the power system voltage is 110 kV; on the secondary side of TCT, the voltage of traction port is 27.5 kV. Furthermore, the constant power source is used for simulating the traction load.

The compensation is only needed when the negative sequence power or reactive power does not meet the requirements of the compensation target. Therefore, based on the actual traction load data within 24 h given in Section 5.1, three typical cases are selected for simulation verification in this section. Among of them, case 1 will conduct simulation analysis for the condition when negative sequence power and reactive power need to be compensated simultaneously; and case 2 will conduct simulation analysis for the condition when only the negative sequence power need to be compensated; finally, case 3 will conduct simulation analysis for the condition when only the reactive power need to be compensated.

• Case 1:

In case 1, take the traction load data at 21.574 h as an example, at this time traction the load power is 18.2 MVA, three-phase voltage unbalance degree ${\epsilon }_{U2}^{L1}$ at the PCC is 3.6%, and power factor $\cos {\varphi }_{L1}$ is 0.8. Because ${\epsilon }_{U2}^{L1}$ exceeds the limit of 2.5%, and $\cos {\varphi }_{L1}$ is also lower than the limit of economic power factor 0.9. Therefore, according to the comprehensive compensation strategy, comprehensive compensation for negative sequence and reactive power is required. Set the compensation target of three-phase voltage unbalance degree at PCC as ${\epsilon }_{U2}^{*}=2.5\%$, and power factor compensation target as $\cos {\varphi }^{*}=0.9$, so that $K_N=0.31$, $K_C=0.35$.

CCE was put into operation at 0.3 s. The simulation results are shown in Figure 16. It can be seen that after CCE operates, the three-phase voltage unbalance degree at the PCC is rapidly reduced from 3.6% to 2.5%. At the same time, the power factor also increased rapidly from 0.8 to 0.9. The compensation target of CCE is realized for negative sequence and reactive power.

Table 1. Statistical results of typical values before and after comprehensive compensation.

Parameters	Three-Phase Voltage		Three-Phase Voltage Unbalance Degree	Power Factor
	Positive Sequence	Negative Sequence
Before compensation	61.89 kV	2.23 kV	3.6%	0.8
After compensation	62.28 kV	1.56 kV	2.5%	0.9

shows the results of case 1 before and after comprehensive compensation.

• Case 2:

In case 2, take the traction load data at 21.563 h as an example, at this time traction load power is 14.3 MVA, three-phase voltage unbalance degree ${\epsilon }_{U2}^{L2}$ at the PCC is 2.9%, and power factor $\cos {\varphi }_{L2}$ is 0.9. Because ${\epsilon }_{U2}^{L2}$ exceeds the limit of 2.5%, $\cos {\varphi }_{L2}$ still meets the requirement of economic power factor. Therefore, according to the comprehensive compensation control strategy, only the negative sequence power needs to be compensated. Set the compensation target of three-phase voltage unbalance degree at PCC as ${\epsilon }_{U2}^{*}=2.5\%$, and power factor compensation target as $\cos {\varphi }^{*}=0.9$, so that $K_N=0.31$, $K_C=0$.

CCE was put into operation at 0.3 s. The simulation results are shown in Figure 17. It can be seen that after CCE operates, the three-phase voltage unbalance degree at the PCC is rapidly reduced from 2.9% to 2.5%. At the same time, because of the CCE does not inject additional reactive power into the system and the reactive power at PCC will not change, the power factor can always be stabilized at 0.9. The compensation target of CCE is realized for negative sequence power.

Table 2. Statistical results of typical values before and after negative sequence power compensation.

Parameters	Three-Phase Voltage		Three-Phase Voltage Unbalance Degree	Power Factor
	Positive Sequence	Negative Sequence
Before compensation	62.48 kV	1.80 kV	2.9%	0.9
After compensation	62.48 kV	1.56 kV	2.5%	0.9

shows the results of case 2 before and after negative sequence power compensation.

• Case 3:

In the case 3, take the measured load data of the traction substation at 21.634 h as an example, at this time traction load power is 4.0 MVA, three-phase voltage unbalance degree ${\epsilon }_{U2}^{L3}$ at the PCC is 0.8%, and power factor $\cos {\varphi }_{L3}$ is 0.9. The other simulation parameters are the same as above. Because ${\epsilon }_{U2}^{L3}$ meets the 1.0% limit, $\cos {\varphi }_{L3}$ is lower than the limit of economic power factor 0.9. Therefore, according to the comprehensive compensation control strategy, only the reactive power needs to be compensated. Set the compensation target of three-phase voltage unbalance degree at PCC as ${\epsilon }_{U2}^{*}=0.8\%$, and power factor compensation target as $\cos {\varphi }^{*}=0.9$, so that $K_N=0$, $K_C=0.35$.

CCE was put into operation at 0.3 s. The simulation results are shown in Figure 18. It can be seen that after CCE operates, the power factor at the PCC is rapidly increased from 0.8 to 0.9. At the same time, the three-phase voltage unbalance degree is always maintained at a low level of 0.8%, and no further compensation for negative sequence power is required. The compensation target of CCE is realized for reactive power.

Table 3. Statistical results of typical values before and after reactive power compensation.

Parameters	Three-Phase Voltage		Three-Phase Voltage Unbalance Degree	Power Factor
	Positive Sequence	Negative Sequence
Before compensation	63.15 kV	0.50 kV	0.8%	0.8
After compensation	63.26 kV	0.51 kV	0.8%	0.9

shows the results of case 3 before and after reactive power compensation.

In summary, through the above three simulation experiment results based on measured load data, the effectiveness of the comprehensive compensation control strategy proposed in this paper is fully verified. The system responds quickly and the compensation effect is better.

6. Conclusions

In this paper, a novel co-phase power supply system for electrified railway based on V type connection traction transformer was proposed to cancel neutral section at the outlet of traction substation, and compensate for the negative sequence and reactive power. It is beneficial to reduce the adverse effects caused by the train passing the neutral section and improve the safety of train operation. Moreover, it can also effectively solve the power quality problem mainly caused by the negative sequence power generated by the electrified railway.

The Traction Compensation Transformer (TCT) presented in the scheme has both traction port and compensation port, and the windings of the traction port and compensation port can be shared. It has obvious advantages such as high functional integration, effectively reducing equipment footprint and transformer manufacturing difficulty. Furthermore, the traction port of the TCT is essentially a single-phase transformer with a high capacity utilization rate, which can effectively reduce the installation capacity of the equipment.

The scheme proposed in this paper is suitable for the comprehensive treatment of negative sequence and reactive power of various AC-DC and AC-DC-AC electric locomotives, and the working conditions of the CCE are reversible. When the traction load is working under the regenerative braking conditions, it can still feed power that meets the standard to the power system.