A Fast Series Active Filter using Sliding Mode Cont rol to Correct and Regulate Unbalance Voltage in Three-Phase System

Problem statement: A Sliding Mode Controller (SMC) with fast reference voltage generation to correct and regulate unbalance voltag e in three-phase system was proposed. Approach: The compensation algorithm was not based on three-s ymmetrical component decomposition so the controller can yield a fast re ponse that was essential in such a critical real t ime control work. The reference voltages were fed to th e SMC, which was a robust closed loop controller. Results: The proposed algorithm and control scheme of series active filter could correct and regulate unbalance voltage in three-phase system under arbit rary fault conditions of the utility supply. Conclusion: A design example and its simulation results proved the concept and validated the proposed algorithm.


INTRODUCTION
Power quality in ac three-phase system could be analyzed by IEEE std. 1159-1995, for example; voltage unbalance, voltage sags, voltage swells, partial or total loss of one or more phases. Voltage unbalance can occur due to an incomplete transposition of transmission lines, unbalanced loads, open delta transformer connection, disconnected three-phase capacitor bank and the proliferation of nonlinear and large single-phase loads [1] . Voltage unbalance worsens the operation of AC electric machines. The negative sequence component in voltage unbalance causes large transient current that leads to reduction of the net torque, increase in losses and temperature rise [2] . These poor power qualities can degrade or damage the electrical equipment connected to the system. The method to improve the power qualities can be done by using a three-phase series active filter, which can correct the unbalance voltage and regulate to the desired level.
At present, a number of algorithms and principles are proposed in the literature [3][4][5][6][7] . By the way, most of them are open loop control by using the decomposition of the three symmetrical components.
This study proposed a compensation algorithm using a Series Active Filter (SAF) associated with the sliding mode controller to correct and regulate the unbalance voltage in three-phase system. The principle of proposed voltage correction is not based on threesymmetrical component decomposition so the controller can yield a fast response that is essential in such a critical real time control work. Three SMCs are employed to shape the actual load voltage according to the reference voltage. SMC is a robust closed loop controller, which basically performs better than the conventional open-loop feed forward technique. The SAF employed for the compensation is composed of a three-phase PWM voltage source inverter injecting compensation voltages through three separate 1-φ transformers. The output of the inverter is connected to a second order filter to eliminate high frequency caused by the switching action of the inverter. The secondary winding of each transformer is connected in series with each phase of the power supply as shown in Fig. 1. Under fault condition, the voltage in each phase of Fig. 2 is unbalance. The instantaneous voltage of phase A with amplitude V a and phase angle φ can be written as shown in Eq. 1: This voltage can be derived by Eq. 2: where, v ab and v ca represent the instantaneous line-toline voltages shown in Fig. 2.
The amplitude, V a , can be calculated from data in a short time window using two samples of the signal v a (t) as shown in Eq. 3 [6] : Where: v a(k+1) and v a(k) = The phase-A voltage at instant t (k+1) and t (k) Respectively T s = Sampling period equal to t (k+1) -t (k) The reference voltages for the SMCs are calculated as given in Eq. 4 and 5: Where: V rated = Rated amplitude of load voltage  The variable structure control law of SMC is given by: Where: ρ = Sliding gain sgn(· ) = The signum or the sign function The switching function s(t) is defined by: where, e is tracking error = load phase voltage-v ref

PWM gating signal generation:
The gating signals of the inverter are generated by comparing the control command, u(t) in Eq. 7 with a triangular waveform whose frequency is kept constant at 6 kHz as shown in Fig. 4.   Fig. 1, the power circuit of the series active filter consists of a three-phase PWM voltage source inverter, three separate 1-φ transformers and a second order passive filter. The circuit design for the implementation can be found in [7] , hence it is not included here.

Voltage correction and regulation flowchart:
The procedure to correct and regulate the unbalance voltage is shown in a flowchart (Fig. 5).
Design example: In order to prove and validate the concept of the proposed algorithm, a design example is done in accordance as the procedure illustrate above. The design parameters are shown in Table 1.

RESULTS AND DISCUSSION
The proposed algorithm has been verified by simulation. The results are given into 5 categories in accordance as the arbitrary imposed supply conditions, as shown in Fig. 6-10. In each case, the compensator begins to operate at 40 m sec.
In order to quantify the degree of unbalance in the voltages, an unbalance factor must be defined. The unbalance factor, UF is the ratio between the sum of zero sequence and negative sequence voltages v 0 +v 2 and the positive sequence voltage v 1 : The poor quality power supply was imposed to the load in arbitrary cases, which possible occurs in real situation. The above results show good performance of the filter in dealing with all cases of the poor power supply, which were quantified by two factorss; MF and UF. The filter could bring the load phase voltages to their normal condition after the compensating voltages were injected into the system within 2 msec. As can be seen in the UF and MF curves, they were eventually brought to the normal value at 0 and 1 respectively.

CONCLUSION
In this study, a sliding mode controller with fast reference voltage generation to correct and regulate unbalance voltage in three-phase system is presented and analyzed. The algorithm avoids the computational burden from three-symmetrical component decomposition. It was successfully implemented with the sliding mode controller. The simulation results show a very good performance of the proposed algorithm and control scheme under arbitrary fault conditions of the utility supply.