Research on main circuit parameter coupling relationship of single-phase shunt active power filter

ZHANG Zi-qi, TIAN Ming-xing, SUN Li-jun, GAO Yun-bo

(1. School of Automation and Electrical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China；2. Rail Transit Electrical Automation Engineering Laboratory of Gansu Province,Lanzhou Jiaotong University, Lanzhou 730070, China)

Abstract： There is a certain coupling relationship among the main circuit parameters of a single-phase shunt active power filter (SAPF), which has a great influence on the reasonable selection of various parameter values. By analyzing the calculation methods of the inductance of alternating current (AC) side and the voltage and capacitance values of direct current (DC) side in the existing single/three-phase SAPF main circuit, a specific single-phase SAPF circuit parameter analytical expression was obtained. Aiming at the coupling relationship among the variables in the resulting expression, the model was optimized and analyzed in MATLAB, and a complete set of parameters design scheme was obtained, which ensure the comprehensive optimization target of the post-harmonic content below 2% is compensated under a specific load. The simulation and experimental procedures verify the correctness of the selected parameters.

Key words： shut active power filter (SAPF); coupling relationship; parameter design scheme

0 Introduction

In recent years, single-phase nonlinear power electronic equipment has been widely used in large industrial power stations such as electrified railways and electric arc furnaces, and the pollution of power grid has become more and more serious. Single-phase shut active power filter (SAPF) can effectively suppress the harmonics of the power grid and compensate for reactive power. Therefore, it is widely concerned.

At present, the research on SAPF is mainly focused on the topological structure, detection methods and control strategies of three-phase SAPF devices. A new structure of SAPF compensation circuit, new ideas different from other detection algorithms and various optimized control strategies have been proposed[1-4]. However, the reasonable selection of the key parameters of the SAPF main circuit is also an indispensable part in the entire compensation system. Proper parameter selection helps to achieve a more ideal compensation effect.

With respect to the problem of SAPF main circuit parameter selection, relevant scholars have done a lot of research, but mainly focus on the theoretical analysis of the selection of a specific parameter and the analytical formula for its convenient calculation. Peng et al. qualitatively analyzed the single or three-phase SAPF main circuit parameters, and the calculation method of relevant parameters was analyzed from the working principle of SAPF circuit[5-8], but the specific parameter calculation formula was not accurately given.

Aiming at the harmonic characteristics of the load current in the three-phase SAPF circuit, Tian et al. studied the selection of alternating current (AC) side inductance when the trigger angle of the full-controlled rectifier bridge was changed, and gave the analytical formula for calculating the inductance rating[9], but it lacked a detailed derivation of the inductance value of the single-phase circuit. For the capacitance and voltage fluctuation relationship of single-phase SAPF direct current (DC) side, Zhang et al. gave the calculation formula of capacitance value under certain compensation capacity and capacitor voltage fluctuation amplitude[10]. However, the influence of other parameters of the main circuit on the selection of the capacitance value was not considered.

For the unified calculation of the main circuit parameters and the coupling relationship problem, although some scholars have carried out related research, the current results are not perfect, and there is no systematic parameter selection method and design scheme of single-phase SAPF main circuit. Quan et al. comprehensively analyzed the selection principle of each parameter of the main circuit and quantitatively research the mutual influence between the capacitor and inductor. The obtained result has certain reference value[11-14], but the parameters applicable to the single-phase SAPF circuit, optimization scheme, parameter selection method that satisfies different load characteristics are still not given. For the coupling relationship between the AC side inductance and the DC side voltage parameters, Shen et al. have made detailed arguments and have certain practical significance[15]. However, the change of the load trigger angle was not considered, and the coupling problem between the DC side capacitor and other parameters was not analyzed.

In response to the deficiencies in the above literatures, this paper starts from the coupling relationship among the main circuit parameters and analyzes the existing calculation methods. Based on the harmonic characteristics of the specific load, the analytical expressions of the AC side inductance, DC side capacitance and voltage value of the single-phase SAPF circuit are obtained. Besides, the coupling relationship between variables is analyzed in detail, and a method for comprehensive optimization of multiple parameters is obtained. Finally, the correctness and practicality of the method are verified by simulation and experiments.

1 Analytical expression of single-phase SAPF main circuit parameters

Fig.1 shows the circuit structure of a single-phase SAPF compensation system, whereusis the supply voltage,isis the supply current,ipis the compensation current,iLis the load current,udcis the instantaneous value of the DC-side capacitor voltage of SAPF,udis the instantaneous value of the DC side capacitor voltage of the load rectifier bridge.

The analysis shows that under the condition of neglecting the influence of line impedance, the voltage constraint equation that matches the real-time tracking ability of single-phase SAPF is

(1)

Fig.1 Circuit structure diagram of single phase SAPF compensation system

It can be seen that there is a certain coupling relationship between the inductanceLand the DC-side voltageudc. In order to facilitate the study of the coupling relationship, unnecessary calculation steps are omitted, and the derivation result in Ref.[9] is directly quoted here

(2)

whereUsis the power supply voltage, andIpmΣis the sum of the amplitudes of each harmonic of the compensation current. For a single-phase fully-controlled bridge with resistive and inductive load circuits, ignoring its commutation process and current ripple, Fourier decomposition of the load current can be obtained as

(3)

whereαis the trigger angle and its phase-shift range is 0°-90°. Assume that the highest number of harmonics that SAPF can compensate isN=2N′-1, whereN′=1,2,3,…. The inductanceLhas a smooth effect on the load current. If the value ofLis large, the load currentidis continuous and the waveform is approximately a straight line. The value ofidis equal to the average valueIdof the DC output to the load[6].

Let SAPF compensate the harmonics and reactive power of the load at the same time, then the compensated supply current is the fundamental active component of the load current. Therefore, the expressions of the compensated supply current and the actual compensation current can be obtained as

(4)

(5)

Continue to deriveIpmΣexpressions with the method in Ref.[9] and it can be obtained as

(6)

WhenN′ is large, the effect of sinαon the entire result can be ignored. The approximate expression of Eq.(6) can be obtained by

(7)

Substituting Eq.(7) into Eq.(2), the AC side inductance of the single-phase SAPF can be obtained as

(8)

(9)

(10)

(11)

(12)

(13)

according to the result obtained by Eq.(13) and the basic formula for calculating capacitance energy, the energy expression of the capacitor charging or discharging process in one fluctuation cycle is obtained by

(14)

Therefore, the capacitance expression that matches the minimum capacity design requirement is

(15)

By analyzing the above formula, it is known that the selection of the capacitanceCshould consider the change of three parameters at the same time, namely the voltageUdcof DC side, voltage fluctuation rateδand load characteristicRd. Among them, the parameters determined by the load characteristics may change under the actual operating conditions, and the rated value is generally taken as the design standard in the design process. Therefore, the selection of DC side capacitanceCis mainly affected byUdcandδ.

Fig.2 Curve diagram of trigger angle α and

In summary, the analytical expressions for the inductance and capacitance parameters of the single-phase SAPF main circuit are summarized as

(16)

2 Coupling relationship analysis of main circuit parameters

There is a certain coupling relationship among the AC-side inductance, DC-side voltage and capacitance of the single-phase SAPF main circuit. The determination of any one of these parameters has a direct impact on other parameters. This paper starts with the DC side voltageUdcand the voltage fluctuation rateδ, analyzes the selection of the specific circuit parameters based on the actual change of the trigger angleαof the load side rectifier bridge.

First, according to the analysis of Eq.(16), the selection ofLandCare all related toUdc. Therefore, in the actual calculation, it is necessary to preliminarily determineUdcvalue. The minimum value ofUdcshould be greater than the peak value of the phase voltage of the AC power supply. Otherwise it may happen that the compensation current does not change as required. On the basis of it, the larger the value ofUdc, the faster the tracking speed, but the too high voltage will lead to higher voltage withstand requirements for the switching device. Therefore, combined with practical engineering experience, the margin of 1.2～1.5 is taken on the basis of the phase voltage peak[18]. Finally, based on the pulse-width modulation (PWM) voltage modulation ratioM≤0.75, a reasonable DC side voltage is obtained by

(17)

In order to verify the rationality of this formula, this paper selects the minimum value within its value range, that is, the voltage approximate valueUdc=500 V under 1.2 times of margin as the preliminary determination of the DC side reference voltage.

Because SAPF needs to be compensated in real time according to the changes in load, the design of parameters should take into account the compensation requirements under all operating conditions for a particular load type. In this paper, the application of a fully-controlled bridge with resistive and inductive load circuits is taken as an example to analyze the compensation effect when the trigger angleαchanges in the 0°-90° range and theαvalue is disturbed. At the same time, the voltage fluctuation rateδas an important factor affecting the DC-side voltage and capacitance also needs to be considered.

Substituting Eq.(3) into Eq.(8), the calculating formula of inductanceLcan be derived as

(18)

As shown in Fig.3, withαandδas independent variables, a three-dimensional parameter model ofLandCis established in MATLAB according to Eq.(18).

Fig.3 Three-dimensional parameter model of changes in L, C

The basic parameters of the simulation are as follows: the rated phase voltage of the power supplyUs=220 V, the DC side voltage of SAPFUdc=500 V, resistanceRd=4 Ω, switching frequencyfsmax=6 000 Hz, current ripplehmax=7 A, maximum number of harmonics compensatedN=49 times, and inductance capacitance value expanded is 10 times.

It can be seen from Fig.3 that eachαandδcorresponds to an uniqueLandC. The simulation of the above 4 parameters in the specific circuit shows that the corresponding compensation effect under this parameter is the best. Ref.[9,16] used the ratings ofLandCto match the compensation range as the final selection result, it can match the load range and reduce the size and cost of the device to a certain extent. However, with the increase of the load trigger angle, the harmonic characteristics of nonlinear power electronic devices become more and more obvious. At this time, the compensation device can easily inject a large number of high-frequency harmonics into the entire system. Simulation results show that its total harmonic distortion (THD) cannot match the requirements. So, it is necessary to re-select the parameters in combination with the actual characteristics of the load to ensure that the compensated harmonic content is less than 2% of the comprehensive optimization target.

In fact, after the DC side voltageUdcis determined, it can be seen from the analysis result of the capacitance value calculation expression of Eq.(16) that the voltage fluctuation rateδdetermines the final value of the capacitanceC. Because the capacitance value of SAPF is limited by its voltage peak, the range ofδvalue is stable within 0%-5%. Theoretically, the larger the capacitance is, the more stable the DC side voltage will be. However, actual application should also consider the cost of the device itself, whether it is easy to install and other issues. At the same time, if the value ofδis too large, it will increase the voltage fluctuation of DC side, which will cause some damage to the capacitor itself and reduce its service life. So we need to take a compromise on the parameters. In this paper, the voltage fluctuation rateδ=0.025 is selected as the final value based on the final compensation effect and the current tracking speed.

The second step is the determination of inductance parameters. This paper starts from the load characteristics of the compensation circuit, and based on the idea of the top-k query algorithm, performs statistical analysis on the data of Fig.3, eliminates some bad points, filters the data that matches the requirements. Finally, theLvalue of inductance parameters with the highest frequency on the AC side when the trigger angle changes is obtained asL=0.625 2 mH. Substituting it into Eq.(18),

(19)

The trigger angleα=25.84° is obtained. In order to fully verify the reasonability of the selection of the above-mentioned inductanceLvalue, Fig.3 is adjusted to obtain the correspondence between the trigger angle and theLvalue, as shown in Fig.4. The inductance value at the registration point matches the change range of the trigger angle, and it is the highest point drop and the lowestLvalue in the entire range.

Fig.4 Determination of L value

Table 1 Comparison of parameters before and after coupling

Combining the parameters before and after the coupling in Table 1 to verify the compensation results. For the case that the change of the trigger angle results in the increase of the harmonic distortion after compensation, this paper analyzes the compensation of two sets of parameters when the triggering angle is disturbed, and gives the THD atα=60°, as shown in Fig.5.

Fig.5 shows that considering the characteristics of load harmonics, the coupling processing of the main circuit parameters can be better applied to the circuit where the trigger angle changes. The tracking response speed of the compensation current and the harmonic distortion rate after compensation are all obviously improved, which illustrates the rationality of the method used in this paper.

Fig.5 Supply current waveform and THD before and after coupling

3 Examples and results

3.1 Materials

In order to verify the correctness of the above analysis method, parameters in Ref.[10] are cited: the rated phase voltage of the power supplyUs=220 V, the DC side voltage of SAPFUdc=510 V, the resistanceRd=4 Ω, the maximum value of the SAPF compensation currentIp=50 A, the trigger angle of the thyristorα=0°. The highest harmonicN=49 is to be filtered out. The value ofLandCcan be calculated from Eq.(15) as

(20)

The parameters calculated in Ref.[10] are:L=0.6 mH,C=4 839 μF. Using the above two sets of parameters for simulation analysis, the compensated power supply current waveform is shown in Fig.6.

Fig.6 Power supply current waveforms under two sets of parameters

From the Fig.6, it can be seen that after inputing compensation device at 0.12 s, the current tracking effect under the selected parameters of this paper is better, while the transient current transition process under the parameters of Ref.[10] is longer and the amplitude changes greatly. This is because that the response speed of active power filter (APF) can be better controlled and adjusted in time by choosing reasonableLandCparameters under the condition of consistent transient control methods, thus effectively reducing the transition time.

Fig.7 shows the steady-state current change ofis, in which the trigger angle changes from 30° to 60° at 0.2 s. It can be seen that the current tracking is timely and the transition process is small, which achieves the intended purpose. The specific compensation effect (α=30°) is shown in Figs.8 and 9.

Fig.7 Load current, compensation current and compensated supply current waveforms

Fig.8 Supply current THD before and after compensation

Fig.9 DC side voltage Udc waveform

It can be seen that the current THD in the power grid before compensation is 34.74%, and it drops to 1.23% after inputing compensation. It shows that the parameters selected in this paper match the requirements, which has a good harmonic compensation effect and achieves a comprehensive optimization target with less than 2% harmonic content after compensation. At the same time, after inputing compensation at 0.06 s, the DC side voltage can be well controlled in the vicinity of the preset value, and the voltage fluctuation rate is controlled within the range ofδ=0.025. Based on this, the rationality verification of the primary DC side voltage valueUdcis performed. Derivation of the range ofUdcvalues according to Eq.(9) can be expressed as

Udc≤LK2hmaxfsmax.

(21)

Substituting the specific data into the DC side voltage, it can obtain thatUdc≤518.32 V. Therefore, the initial value of this paperUdc=500 V matches this limit. It also shows that the above steps are reasonable.

3.2 Methods

The single-phase SAPF equivalent circuit model is used to derive the coupling formula, the simulation model is built by MATLAB software, and the relevant parameters are programmed and calculated.

3.3 Experimental results

In order to fully verify the validity and practicality of the derivation theory and simulation results, an actual circuit is built for verification. The experimental circuit is shown in Fig.10. The load parameter values used are the same as those in Ref.[10].

This circuit control system used digital signal processor (DSP) chip TMS320F28335, and realized SAPF compensation by unipolar hysteresis control algorithm. The model of the insulated gate bipolar translator (IGBT) chip in the module is PS21865, the output rated current is 8 A, 150% overload capacity, and the power supply input AC voltage is 170-250 V, which was made by Shanghai Jiashang Company, and the switching frequency is set to 6 K in this system. The sensor TV19G/LV25-P made by LEM company have been used respectively for sensing the voltage and QBC10PS3.3 and LTS25-NP for sensing the currents.

Fig.10 Experimental circuit structure

Taking into account the limitations of the experimental environment, the compensation capacity is reduced by the step-down transformer to complete the verification of the entire circuit. Finally, use the FLUKE 345 power quality clamp meter to collect the compensated power supply current, and whenα=60°, the current waveforms before and after compensation and the screenshots of THD values are shown in Fig.11.

Fig.12 is the experimental result of Ref.[10]. It can be seen that the compensated power supply current THD=2.89%. Comparing the experimental results of THD=1.9%, the main circuit parameters designed in this paper can match the harmonic compensation requirements of the single-phase SAPF compensation system, and the effect is better.

Fig.11 Compensation effect screenshot

Fig.12 Harmonic content and THD of grid current after compensation

4 Conclusions

1) Through the research on the calculation method of the existing main circuit parameters, the analytical expressions of all the necessary parameters of the single-phase SAPF circuit are deduced. The required formula not only matches the compensation requirements under all operating conditions for a specific load, but also has a simple form and a strong universality, which can be easily extended to multi-phase circuits.

2) According to the coupling relationship between the main circuit parameters, this paper starts from the actual working conditions, through the three-dimensional modeling of MATLAB and data optimization, a clear method of parameter selection is obtained, the research shows that this method can better match the THD requirements, simulation and the experimental results verify the correctness and feasibility.

3) This paper improves the deficiencies of existing theory for the single-phase SAPF circuit parameter calculation. The proposed parameter coupling scheme systematically realizes the parameter design requirements for the entire circuit and is convenient for industrial design. To some extent, it increases the practical price of single-phase SAPF.