At present, with the development of power electronics technology, a large number of nonlinear loads have been added to the power system, such as various thyristor controlled rectifiers, inverters, arc furnaces, UPS uninterruptible power supplies, etc., which have brought serious harmonic pollution to the power system and a significant reduction in power factor, resulting in increased reactive power demand and grid voltage fluctuations, and deterioration of various power operation indicators. The serious pollution problem of harmonics on loads and power supply systems has attracted special attention from relevant experts [1,4]. High-order harmonic currents cause additional losses in motors and transformers, bring noise interference to communication lines and industrial automatic detection and control systems, and cause refusal or malfunction of overcurrent, undervoltage, distance and frequency protection relays in substations, causing protection devices to fail or unstable.

Although traditional reactive power compensation and passive LC filters have obvious effects in absorbing high-order harmonics, they have the following problems [6]:

(1) The power supply impedance seriously affects the filtering characteristics;

(2) As the harmonics on the power supply side increase, the filter may be overloaded;

(3) When many LC filter circuits are set up in the same system, it is difficult to achieve a balance of high-order harmonics;

(4) The passive LC filter circuit will have a parallel resonance problem with the system due to changes in the system impedance parameters, causing the harmonic current on the power supply side to double at a certain frequency.

Based on the theoretical analysis of the principle of active reactive power and harmonic compensation in power systems, this paper mainly discusses the structure and working principle of a power active filter compensator main circuit and a double closed-loop control system with nonlinear control using the relevant analysis results. A variable structure nonlinear current tracking control idea is given, and the control scheme is extended to a three-phase system. The simulation study is carried out using PCPICE software. The simulation results confirm the correctness and feasibility of the system and control method.

2 Principle of reactive power and harmonic compensation

Assuming that the power supply voltage is a sine wave, its expression is


If the current drawn by the nonlinear load from the AC power supply is a periodic non-sinusoidal waveform, it can be expressed by Fourier analysis as


The first term in formula (1) is the fundamental active current component, denoted as ip, the second term is the fundamental reactive current ir, the third term is the DC component, and the fourth term is the sum of the higher harmonic components of the load current il, denoted as ih. The average power calculation for one cycle gives the active power:


After integrating this equation, except for the first term, all other terms are zero, so


Among the many sinusoidal components contained in the periodic distorted current, only the components ip, io and ir with the same frequency and phase as the power supply voltage are related to active power. They generate base frequency reactive power, and ih is the fundamental reason for the generation of distorted power.

According to equations (1) to (3), consider introducing an appropriate compensation current between the power supply and the load:

ic=-(ir+ih-io) (4)

Then the output current of the compensated power supply is: is="il"+ic=ip

, that is, ic=ip-il (5)

Since ip is a pure sinusoidal active current with the same frequency and phase as the power supply voltage, no matter what kind of distortion occurs in the load current, as long as equation (4) is satisfied, the current provided by the power supply to the outside can be a sinusoidal waveform with the same frequency and the power factor is equal to 1. Since the integral results of the last three terms in equation (2) are all zero, in an ideal case, the active compensator that provides the compensation current does not consume active power, but only provides reactive power to the grid to balance the reactive power consumption of the load. In other words, the power supplied by the power supply to the outside is exactly equal to the load power.

3 System composition and variable structure nonlinear control

The single-phase active reactive power and harmonic compensation and control system based on the above principle is shown in Figure 1. The main circuit adopts a half-bridge PWM converter. The control system is functionally divided into four units, namely, DC side voltage closed-loop control, reference current formation, current closed-loop control and gate switch control signal generation. The latter two parts are completed by a nonlinear controller with loop relay characteristics. The nonlinear controller has two functions and can be realized by an operational comparator and peripheral resistors through parameter design. The reactive power and harmonic compensation main circuit of the system, as the nonlinear control object of the system, works in a switch switching mode. The complementary on-off action of the two power switches corresponds to two linear sub-circuit topological structures. Therefore, the system actually has a variable structure control object [3,2]. Specifically, the two different sub-circuit topologies correspond to different variation rules of the compensation current IC. For example, in the corresponding structure when the switch tube M1 is turned on and M2 is turned off, IC can be controlled to decrease because the terminal voltage of the input filter inductor LS on the AC side satisfies lsdic/dt<0 (because the main circuit is a step-up PWM converter, which is guaranteed by a higher voltage on the DC side). On the contrary, in the corresponding structure when the switch tube M2 is turned on and M1 is turned off, IC can be controlled to increase because the terminal voltage of the inductor LS satisfies lsdic/dt>0. We know that the key to the reactive power and harmonic compensation of the system is the control effect of the compensation current IC, and the controllability of IC is achieved through the variable structure switching of the above two circuit topologies. The nonlinear controller with hysteresis relay characteristics proposed in this paper is designed based on the variable structure control idea of ​​the compensation current [5,7]. Corresponding to the two topological structures of the control object, the controller has two output logic states. By properly selecting the feedback polarity of the compensation current and designing the loop width of the nonlinear controller, the tracking deviation of the compensation current ic from its given signal i*c can be limited to a very small loop width. The current closed-loop control implements effective control for nonlinear objects through the nonlinear control method of the loop relay. In essence, it uses the maximum principle [3] to make the time-optimal control component (the driving signal of m1 and m2) a piecewise constant function of time t, and only the jump between the two constant values ​​occurs at the switching time. The two gate switch signals are converted back and forth between their two edge values, achieving the purpose of time-optimal fast control.

Figure 1. Active reactive power and harmonic compensator system simulation circuit model


The working process of the whole system is as follows: the comparison error signal between the DC voltage feedback signal vd and its given value v*d is obtained by the pi regulator to obtain the amplitude given i*p of the active current of the power supply, which is multiplied by the detection signal of es to obtain the instantaneous active reference current i*p. The voltage transformer ensures that i*p and es are in the same frequency and phase. The required reactive compensation current given signal i*c is generated by the subtraction operation of formula (5), and finally the variable structure control and switch drive of the controlled object are achieved through the nonlinear controller with loop relay characteristics, so that the main circuit of the compensator undergoes structural transformation according to the given control law i*c, and the current tracking of the compensation current ic to i*c is realized. The automatic adjustment function of the DC voltage control unit ensures that the size of i*p just meets the requirement of balancing the power output power and the load power in the steady state of the system (ignoring the device loss of the compensator itself), and there is no need to detect and calculate the reactive current component of the load in real time, and the DC side voltage vd is basically constant.
4 System Simulation Research

 Figure 1 shows a dual closed-loop control system for active reactive power and harmonic compensation. The pi regulator and multiplier involved are all conventional control links. Many literatures have detailed introductions on the selection of control parameters. As for the design of nonlinear controller, based on the above variable structure current tracking control idea, it is not difficult to design an operational comparator with loop relay characteristics by electronic technology. It should be pointed out here that experience tells us that many parameter design methods can only provide guidance and reference for the system to be realized, and the specific system parameters still need to be adjusted and determined through experiments. The pspice simulation software package provides an important means for the author's circuit parameter experimental selection and adjustment, especially for the design of power electronic systems. The software package has very rich and flexible analysis methods, human-machine interface and component library, which can simulate almost any parameter changes and parasitic parameters on the system waveform and response characteristics, greatly reducing the time and investment spent on completing the experimental debugging of the strong power system. Due to space limitations, this paper only focuses on the pspice circuit simulation study on the influence of parameter changes of the AC side reactor of the converter on the system performance, aiming to show the effectiveness of the simulation method and the proposed active compensation system.

For the active filter compensator with variable structure current tracking control, the minimum value of the AC side filter reactor is mainly determined by the harmonic requirements caused by the switch, and the filter reactor should limit this harmonic current within the specified range. On the other hand, under the condition of a given DC side voltage, the speed at which the output current of the active compensator follows the command changes determines the maximum value of the reactor. If the selected reactor parameter is too low, the pulsation amplitude of the switching harmonics of the active compensator output current will increase; if this parameter is too high, the active compensator output current cannot be guaranteed to have a faster following characteristic due to the excessive current inertia, making the compensation effect worse. A compromise should be considered in actual debugging. This system initially selected parameters according to the conventional design method, and then adjusted through pspice circuit simulation. The final selected parameters are shown in Figure 1, and its main simulation waveforms are shown in Figure 2. As shown in Figure 2(a), the current waveform of the power supply after compensation is very close to a sine wave, and is in phase with the power supply voltage, and the power factor is approximately 1; Figure 2(c) shows the nonlinear load current waveform; the compensation current command signal in the current control link and the current tracking waveform under variable structure control are shown in Figure 2(b). It can be seen that when the compensation current command changes rapidly, the current following performance is relatively ideal. Figure 2(d) shows the effect of the initial large filter reactance value ( , other parameters remain unchanged) on the current waveform. It can be seen that the reduction of the filter reactance parameters has significantly improved the current following characteristics and thus the power supply current waveform.

Figure 2 Simulation waveform of single-phase system


The same control scheme can be used for the three-phase active compensation system. Of course, since the AC power supply and nonlinear load are both three-phase, the compensation main circuit needs to use a three-phase bridge PWM converter. The multiplier and loop hysteresis comparator required by the corresponding control part also need to be expanded from one to three, but the PI regulator still uses one for three-phase control sharing. Figure 3 shows the simulation waveform of the three-phase active compensation system.

Figure 3 Simulation waveform of three-phase system


5 Conclusion

Compared with the previous similar systems, the active reactive power and harmonic compensator and control method proposed in this paper has the following main features:

(1) It can realize reactive power and high-order harmonic compensation at the same time under any load conditions, and there is no need to detect and calculate the reactive current component of the load in real time;

(2) According to the switch working mode and nonlinear mathematical model of the main circuit of the system, its current control link adopts variable structure nonlinear current tracking control mode, which has the characteristics of fast dynamic response;

(3) The voltage and current double closed-loop control is simple and easy.

Regarding the design of active dynamic compensation and nonlinear controller of power system, it can be considered to use the state space average method to model the PWM converter in Figure 1, so as to further study the static and dynamic performance of the system and provide a basis for the quantitative selection of system parameters.