Hybrid compensation method for traction power quality compensators in electrified railway power supply system

0 Introduction

AC traction loads impose a lot of problems related to the power quality (PQ) due to the nonlinear nature of these kinds of loads and also being single-phase, such as significant amount of negative sequence current (NSC), low power factor (PF), harmonic injection, reactive power consumption, etc.[1].These problems inflict undesirable effects on power grid and cause additional power losses of feeder lines, decreasing the output capability of traction transformers, malfunction of protection relays, and incorrect operation of transmission line control systems [2].Over the last few years, extensive studies have been carried out to enhance the PQ indices of the electrified railway power supply system.The issue of low PF has been solved by adopting four-quadrant pulse-width modulation (PWM) converters in the latest generation of electric locomotives [3].Various approaches are proposed in literatures to compensate NSC.For instance, the phase-shift technique is presented in [4].The compensation of NSC by means of specially balanced transformers e.g.Scott, Woodbridge, impedance-matching balance, and LeBlanc have been investigated in [5].In order to compensate the reactive power, static synchronous compensator (STATCOM) [6] and static VAR compensator (SVC) [7] have been utilized.It should be noted that the SVC and STATCOM are also able to compensate the NSC but not at the same time.In [8], a new model was analyzed to eliminate harmonic currents.A comprehensive review of PQ compensation methods in AC traction power supply systems is investigated in [9].The described methods are not capable of compensating all PQ problems simultaneously and therefore, a comprehensive compensator named railway power conditioner (RPC) [10] and its derivatives such as active power quality compensator (APQC) [11] and half-bridge RPC (HBRPC) [12] was introduced to improve all PQ indices at the supply grid side.A comparative study of these compensators including evaluation of size and cost has been investigated in [13].

In addition to the PQ problems, the main issue of the RPC and the other railway active compensators is their high kVA rating, which results in high manufacturing and investment cost.Thus, some research efforts have been currently put on power rating reduction of compensators, which can be classified as I) hybrid approaches, II) synthesizing passive elements and active devices, III) applying multi-purpose balanced transformer (MPBT), and IV) Modular Multilevel Converter (MMC).Hybrid approaches utilize an auxiliary device together with the main compensator in order to decrease the power rating of the main compensator while minimizing the initial costs.To reduce the compensation capacity of active power compensator, chen et al.adopted magnetic SVC (MSVC) along with RPC named electrical magnetic hybrid compensation system (EMHCS) [14] and with hybrid power quality compensator (HPQC) in co-phase railway power supply system called hybrid electrical magnetic power quality compensator (HEMPQC) [15].A combination of APQC with delta configuration of threephase SVC in electrified railway system is proposed in [16], which compensates NSC and reduces the rating of APQC.Since SVC is known as a low-cost dynamic compensator, it has been used as a secondary device in many studies [17].In [2], a reducing method is proposed based on thyristor switched capacitor (TSC) in order to keep the power rating under the optimal value in different traction load conditions.As previously mentioned, the use of passive elements is another method so as to moderate the kVA rating of primary compensator.A passive power filter (PPF) composed of three LC branches is applied by Sijia Hu et al.to absorb low-order harmonics and reactive power [18].That is to say, passive filters are massive and have slow response and might cause harmonic resonance due to their parameter variation.Many other works have done in this field with the aim of reducing the operating DC-link voltage of RPC and improving the performance of the compensator [19-24].Another way to alleviate compensation capacity is to connect the converters directly to MPBT’s secondary winding.In this scheme, the traction transformer and the step-down transformers are removed and MPBT is adopted instead of them [12], [20], [25-26].MPBT is not a commonly used equipment and moreover, it has complicated structure, therefore it is not economical and also its manufacturing cost is high.Another approach for enhancing the voltage and current ratings of single-module RPC is to use RPC in a modular manner.Recently, MMCs have been introduced as a modern solution in the power electronics industry.Modular multilevel RPC scheme composed of back to back full bridge power submodules in parallel is proposed in [27].In this method, the power is distributed equally between the submodules.By connecting of identical converters in series or parallel, the compensation will be achieved at any desired capacity.In addition, as the number of submodules increases, the switching frequency will decrease, as well as lower harmonic content will be produced due to the greater number of output voltage levels.This approach substantially increases the converter controller complexity, overall size and manufacturing costs.

Remainders of the paper are as follows: the structure of the proposed scheme and its performance characteristics is discussed in section 1.The PQ compensation principles in traction power supply systems are presented in section 2.The control strategies for SVC, RPC and APQC and implementation process are expounded in section 3.A comprehensive economic analysis is performed on a real sample in section 4.In section 5, the simulation verification is carried out using Matlab/Simulink software.Finally, section 6 draws the conclusion.

1 Configuration of the proposed scheme

The configuration of the proposed structure is depicted in Fig.1(a).RPC and APQC as the main compensators are shown in Fig.1(b) and Fig.1(c), respectively.The public grid is considered as a three-phase source which is divided into the two single-phase voltage sources that are connected to the two feeder sections via three-phase V/V traction transformer.The turn’s ratio of the V/V traction transformer is KV.

The RPC compensator is composed of two single-phase converters which are connected back to back by means of a common dc capacitor.Actually, this capacitor is used for dc-link voltage stabilization.These two converters can be controlled as two current sources to shift a certain amount of active power from one section to the other section, Hence, the active powers of two feeder sections will become the same.The RPC can also suppress harmonic currents and compensate reactive power and NSC simultaneously.It should be noted that the power generated by RPC converters are different from each others, while in practice, the capacity of converters must be equal and therefore, the converter with higher capacity determines the capacity of each converter.This issue will impose additional costs on the system.

APQC is composed of six power switches and a DC capacitor.Like RPC, the capacitor provides a stable dclink voltage.The APQC is only used for active power transferring and active harmonic currents suppression.It should be noted that the power switch with greater rating in APQC determines the nominal rating of all power switches.Since, the branch currents of APQC are unequal and the APQC is an integrated device and thus, its switches can’t be different from each other.

In this paper, a combinational scheme of traction arm connected single-phase SVC together with RPC and APQC devices is proposed.In order to reduce the initial investment cost of the system and also to decrease the power rating of converters, the SVC is used to compensate reactive power.The SVC is formed by Thyristor Controlled Reactor (TCR) and the third and fifth-order filters.The combination of SVC with RPC is named hybrid RPC (HRPC) and with APQC is called hybrid APQC (HAPQC) in this article.Since SVC is a low-cost dynamic compensator, it would be better to compensate the reactive power by using the SVC.As a result, the power rating of the main compensator and the initial investment cost of the compensation system will considerably reduce.

2 Principle of power quality compensation

First of all, it is worth mentioning that all PQ compensation steps are the same for both systems in Fig.1.The right and left feeder sections in Fig.1 are specified as phase a and phase b, respectively.The similar phases on the primary side of the V/V traction transformer are specified as phases A and B, respectively.Assume that the three-phase voltages of the main network are

In equation (1), V is the fundamental voltage Root Means Square (RMS) value of the public grid side.At the beginning, in order to acquire an exact relationship for PQ compensation, it is assumed that the load currents are purely sinusoidal and finally, it can be generalized for the case of harmonic currents.The fundamental currents of both feeder sections are in phase with V˙AC and V˙BC, respectively and can be expressed as

Fig.1 Different compensation schemes

Where, ILaf and ILbf represent the fundamental load current RMS values in phases a and b, respectively.Three-phase currents of the public grid side are

The phasor diagram of the system before compensation is depicted in Fig.2.As can be seen, the three-phase currents are unbalanced.Phase A current lags corresponding phase voltage by 30 ° and phase B current leads corresponding phase voltage by 30 °.In this condition, the three-phase currents include significant negative sequence component.

Fig.2 Phasor diagram before compensation

At the first step, in order to balance the currents of two feeder sections, half of the current difference of two section currents should be shifted from the heavily loaded section to the lightly loaded section using the main compensators as illustrated in Fig.3.As this figure shows, the main compensators should shift from phase a to phase b (assume that the load of phase a is greater than phase b).The currents of phases A and B are

Fig.3 Phasor diagram after power balancing of two feeder sections

In this condition, the current values of phase A and phase B are equal but, phase C current is not yet equal.Phase A current lags corresponding phase voltage by 30 °and phase B current leads corresponding phase voltage by 30 ° and phase C is in phase with corresponding phase voltage.

In the next step, in order to make three-phase network currents balanced, a certain amount of reactive power should be added to phase A and phase B to make the phase angle of the currents in phase with the corresponding phase voltages.As can be seen in Fig.4, the essential reactive power that should be compensated (see from public grid side) is

Fig.4 Phasor diagram after power balancing and reactive power compensation

After compensating the reactive power, the three-phase currents of the main network will be balanced.The RMS values of three-phase currents are

The corresponding phase currents on the secondary side are

In (7), ω refers to the angular frequency of the source voltages.The total compensation currents containing active and reactive currents at the fundamental frequency are

Where, ILafr and ILbfr are fundamental reactive current RMS values of the load in phases a and b, respectively.In the both relations of equation (8), the first term of current is real and should be compensated by the main compensator and the second term of current is imaginary and should be compensated by SVC.According to the Fig.1, the compensation current references of the main compensators in phases a and b are

The hysteresis current control method is applied to a switching algorithm to ensure fast response of the compensation system.The compensation current references of the converters on the low voltage side of the step-down transformer with the turn’s ratio of KS are

3 Control strategy of hybrid scheme

A collaborative control strategy is applied for coordination between SVCs and main compensator.When the SVC is out of service or it does not operate for any reason, the signal detecting system of main compensator responds instantaneously.The reference current of main compensator is the desired current minus the load current and the SVC current, so the reactive power will be supplied by main compensator.When the SVC switches on or returns to the traction power supply, the reactive power supplied by main compensator will reduce until the transient time is up and whole system reaches to the steady state and since then, the reactive power will be completely compensated by SVC.

3.1 Implementation of main controller

Presume that the load currents of two feeder sections are written according to the fundamental and the harmonic components as below

Where, ILah and ILbh are the hth-order harmonic current RMS values in phases a and b, respectively, φah and φbh are the phase angles of the hth-order harmonic current in phases a and b, respectively.In order to extract the active load current RMS value (ILaf), the load current of phase a (iLa) should be multiplied with Then

There is a dc component in equation (12) which can be extracted after passing the product through a low-pass filter.Similary, the term of can be derived after passing the product through a low-pass filter.The sum of two dc components is

With multiplying IP by the amplitudes of iaf and ibf will be obtained as given in equation (7).The desired currents of phases a and b can be achieved by multiplying the amplitudes of iaf and ibf with the voltage synchronous signals.According to equation (9), the current references of the converters will be obtained as shown in Fig.5.As can be seen in this figure, a dc-link voltage controller is also used so that the main compensators track the compensation current references correctly, so as to keep the dc-link voltage stable.The converters should charge the dc-link capacitor when the voltage UDC is less than the reference value Uref.On the other hand, the dc-link capacitor should be discharged when the voltage UDC is more than the reference value Uref.This can be achieved by adding a PI controller.The output of PI controller is multiplied with the synchronous voltage signals so that the currents could be in phase with the corresponding voltages of phases a and b.The complete controllers for HRPC and HAPQC are shown in Fig.5(a) and Fig.5(b).

After generating the reference current signals, the main purpose is to force the main compensator to follow these signals.To achieve this, the hysteresis control method has been used to ensure fast response.The status of the power switches are changed whenever the actual current goes beyond a given boundary.Assume that the output current of single-phase converter is less than the reference current, therefore, the power switches T1, T4 are turned on and T2, T3 are turned off.If the output current is more than the reference current, hence, the status of power switches is reversed.

3.2 Implementation of SVC controller

The control of the SVC is performed by current control in the TCR through the control of firing angle.The amplitude of the fundamental reactor current can be expressed as a function of the delay angle α as follows

In equation (14), VPCC is the amplitude of the applied voltages (Vac, Vbc) and LTCR is the inductance of TCR.

According to equation (8), the current reference RMS values of the SVC can be obtained from

In equation (15), the negative symbol means it is a capacitive current.The current references of the TCR can be obtained as shown in Fig.6.

Fig.5 Block diagram of controllers

Fig.6 Block diagram of SVC controller

4 Economical analysis

Assume that the model of locomotives used in traction systems are SS6B [28].Total harmonic distortion (THD) of load current is 23.4% and PF is 0.82 and apparent power is 10MVA.Presume the locomotive is only in phase a, then the active, reactive and harmonic powers of load are as follow

The compensation powers of phases a and b are, regardless of the type of compensator

Where, Pra and Prb are active compensation powers of phases a and b, respectively.Qra and Qrb are reactive compensation powers of phases a and b.Prha and Prhb are harmonic compensation powers of phases a and b.

The compensation capacity of each phase is

Sa and Sb are compensation capacity of phases a and b, respectively.In practice, the feeder section that consumes more power determines the overall capacity of the main compensator because the two converters of RPC or six power switches of APQC must be identical, then

Assume 70% harmonic currents would be eliminated by passive filters.The new compensation capacity of the main compensators and SVCs are

The initial cost of SVC is about 1/8 of RPC and 1/6 of APQC.Assume the initial cost of RPC is x/MVA and the initial cost of APQC is (3/4) /MVAx.The cost of RPC is 17.88x and the cost of APQC is 13.41x.The cost of proposed scheme is 9.58x for HRPC and 7.93x for HAPQC.The initial cost of HRPC is approximately 53% comparing with RPC and the initial cost of HAPQC is about 59% comparing with APQC.

A complete comparison of the various compensation devices with respect to the price and compensation performance is given in Table 1 that shows the performance advantage of the hybrid scheme.

Table 1 Comparison of various compensation devices

Device NSC Compensation Reactive power compensation Harmonic suppressing Initial Investment cost SVC yes yes no Low RPC yes yes yes High APQC yes yes yes High HRPC yes yes yes Middle HAPQC yes yes yes Middle

5 Simulation results

To ensure the validity of the proposed structure and the compensation strategy, a simulation is carried out using Matlab/Simulink software.The parameters of system are shown in Table 2.The locomotive model can be considered as a resistive-inductive load in parallel with an uncontrollable rectifier to take harmonic currents into account.The main compensators switch on at 0.1 s and the SVCs switch on at 0.4 s.In this section, two different cases are discussed for a detailed analysis.

Table 2 Parameters of the system

Parameter value Network line voltage 220 kV Resistance of the section impedance 0.2 Ω Inductance of the section impedance 0.5 mH Traction transformer turn’s ratio (Kv) 220:27.5 Step-down transformer turn’s ratio (KS) 27.5:1 La and Lb 0.5 mH DC-link capacitors of RPC and APQC 80000 μF

5.1 Both feeder sections have the same loads

In this case, the loads of two feeder sections supposed to be equal.The apparent powers of traction loads are 7 MVA with a THD of 8% and unity power factor.Three-phase network currents, NSC and PSC of the network, the apparent powers of the RPC converters, the branch currents of APQC and reactive powers of the RPC converters are depicted in Fig.7.As can be seen in Fig.7, after compensators turning, the three-phase network currents become symmetrical and NSC reduces by 0%.After SVC turning, it is observed that the reactive power of the RPC becomes zero and the branch currents of APQC reduce.Therefore, the reactive power which should have been provided by main compensator, it will be compensated by SVC.In this particular condition means the loads of two feeder sections are equal that seldom occurs, the RPC and APQC suppress only the harmonic currents and therefore the apparent power of RPC and the branch currents of APQC are almost zero.By using the SVC, it causes to reduce the power rating of main compensators.

Fig.7 Simulation results for case 1

5.2 The loads of two feeder sections are not the same

In this case, the load of phase b remains as before and the load of phase a will change.The apparent power of phase a is 4.5 MVA with a THD of 14% and a power factor of 0.87.Three-phase network currents, NSC and PSC of the network, the apparent powers of the RPC converters, the branch currents of APQC and reactive powers of the RPC converters are depicted in Fig.8.In this condition, it needs to be mentioned that the main compensators are used to balance active powers of two adjacent feeder sections and suppress harmonic currents and the SVCs are used to compensate reactive power.In addition, as shown in Fig.8(e) and Fig.8(f), the apparent powers of two converters in RPC and the currents of APQC branches are the same after compensation.The simulation results before and after compensation with HRPC and HAPQC for two cases are shown in Table 3 which certify the performance maintenance of the traction power supply while reducing the initial investment costs.

Fig.8 Simulation results for case 2

Table 3 Simulation results before and after compensation

Simulation Results Case 1 Before compensation After compensation HRPC HAPQC APQC RPC THD (iA)% 7.13 2.07 2.94 2.97 2.2 THD (iB)% 7.27 2.56 2.90 2.81 2.71 THD (iC)% 4.66 3.13 3.18 3.16 3.4 PF (A) 0.77 0.99 1 0.99 1 PF (B) 0.93 1 1 1 1 PF (C) 0.98 0.99 0.99 0.99 1 Case 2 THD (iA)% 13.80 3.18 1.4 2.38 3.42 THD (iB)% 7.27 3.31 1.18 2.64 3.46 THD (iC)% 5.86 3.44 2.20 2.59 3.49 PF (A) 0.48 0.99 1 1 0.99 PF (B) 0.93 0.99 0.99 1 1 PF (C) 0.91 1 0.99 0.98 1

6 Conclusion

In this paper, a hybrid scheme was proposed.The hybrid configuration consists of SVC and a principal compensator.The main compensator was applied to balance the currents of two adjacent feeder sections and suppress harmonic currents.The SVC was used to compensate reactive power and suppress the third and fifth harmonic currents.The proposed technique reduced the power rating of the main compensator and the initial investment cost of compensation system.The principle of PQ compensation and the control strategies were studied and a new controller was suggested for SVC.Finally, the proposed configuration was simulated on a network in Matlab/Simulink software.The simulation results verified the effectiveness and correctness of the proposed structure and compensation strategy.

Declaration of Competing Interest

We have no conflict of interest to declare.