Design of Polar-Fuzzy-Controller to Impair Current Harmonics in Power System

The aim of the paper is to design a new Fuzzy Logic Controller to control Three-phase Shunt Active Power Filter for achieving the upgraded operation of power system under nonlinearity. Methodology – The Polar fuzzy logic based Controller is implemented with only one input and one output. As it has less number of rules and membership function compared to conventional type of fuzzy logic controller. This Polar Fuzzy Logic Controller has given polar co-ordinate of dc link voltage as input. Findings –The simulation result show that the proposed method settle down dc link voltage better than Proportional Plus Integral controller and it reduces the Total Harmonic Distortion factor effectively. The estimated operation time of the system is reduced through Polar Fuzzy Logic Controller which is designed with two fuzzy rules. The stability and performance of the power systems are improved. Originality–A Polar co-ordinate based controller with minimum estimated operational time is developed, which is capable to meet requirements of IEEE standard-519. Keyword Keyword1, Active Power Filter, Estimated Time, Harmonics, Polar Fuzzy Logic Controller, Power System


II. FORMULATION OF REFERENCE SOURCE CURRENT
SAPF works on compensation principle. Either it has to supply a compensating current to the system or it has to draw a compensating current from the system to impair harmonics, reactive power balancing and to bring supply current in phase with supply voltage. Figure 1 shows working of SAPF as compensator. Applying Kirchhoff's law at Point of Common Coupling, Source current in terms of compensating current given by SAPF can be written as,

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(1) Source current is denoted by i t , load current is denoted as i t and i t is compensating current generated by SAPF. So, compensating current is written as (2) The productivity of the controller is on calculation of reference current. , (3) By controlling the dc link voltage i can be calculated. The Clarke transformation is used to achieve the results. In the Clarke Transformation, three-phase load voltages V , V , V and load currents I , I , I is used to generate active power pand reactive powerq according to following equations.  Fig. 2 (19). A Low Pass Filter is used to separate dc component from p and q . The total active power loss (switching and conduction loss) in the compensation process is referred asp . The reference currents i * , i * , i * is calculated using p * and q * from following equations. * * ( 7 ) * * * √ √ * * These currents are compared with actual source currents to generate gate pulses for the PWM VSI. In this model, Insulated Gate Bipolar Transistors (IGBT) is used as switching device for VSI. The pulses of gate which is given to the IGBTs are generated via current controller. The accuracy of the reference current depends on functioning of controller.

III. PROPOSED POLAR FUZZY LOGIC CONTROLLER
In the PFLC technique, fuzzy sets are represented by polar co-ordinates. The Real (x) and Imaginary (y) part of the cartesian co-ordinates can be represented into polar co-ordinates, magnitude (R) and angle θ as shown in Fig. 3. The execution of the PFLC essentially depends on angle θ. Fuzzy sets of PFLC can be illustrated in universe of circle therefore repeats shape in every360°. Conventional fuzzy logic techniques are based on two inputs, change in voltage v ∆v and derivative of change in voltage v but in PFLC only one input angle θ is given thus number of rules decreases instantly (20). Here, v and v are the real and imaginary part of the complex number which is converted into Polar co-ordinates, R and θ using following equations.
In PFLC angle θ is given as input. Two linguistic variables are formed MAX(θ) and MIN θ as shown in Fig. 4, where MAX(θ) + Min(θ)=1. Range of θ varies from -180° to +180°. The membership function value μ is determined by following equation.
(11) Where x is the fuzzy element. At sampling instant k, θ is given to the input Differential Sigmoidal membership function, corresponding value μ is mapped using equation number 11 into output Triangular membership function.
Output Membership function v is defined in two linguistic variables P (Positive) and N (Negative). When θ is -180° or +180°, the membership function value of MAX(θ) is minimum. Thus output v should be 'P'. When θ is -90° or +90°, both input membership function has same value so output v should not be changed. When θ is 0° MAX(θ) is maximum and MIN(θ) is minimum so outputv should be 'N'. Thus, only two rules are defined as follows.
(i) If θ is MAX(θ) then output v is P (ii) If θ is MIN(θ) then output v is N Centroid method is used to convert from fuzzy set to a crisp number. This crisp number which is output of the PFLC, is denoted as U as shown in Fig. 5. U is multiplied by R and final output p is developed, which is used to generate reference current for the proper functioning of SAPF. Thus, magnitude of the output depends on R and decision is taken by θ.

IV. MODELLING OF SHUNT ACTIVE POWER FILTER
The purpose of the VSI is to provide three phase sinusoidal voltage with required amplitude, frequency and phase difference. It has inductors on the supply side and dc-link capacitor on the other side as shown in Fig. 1. Dynamic model of PWM based VSI can be outlined by equation number (12) to (20).

V. ESTIMATION OF SYSTEM PARAMETERS
The SAPF consists of six IGBTs and capacitor on the DC side. The SAPF of power rating 45 KVA is designed for phase voltage of 230V and 50 Hz supply. Three phase diode rectifier is connected with three-phase supply which has non-linear characteristics. This rectifier is supplying 200A constant current to the load connected to it. Following equation is used to estimate capacitor voltage.
where I is the supply current of active filter, V is maximum value of DC link voltage of ripples, and , where f is the supply frequency. Filter impedance selection can be done using where I is current ripple, m is modulation index, a is overloading factor and f is switching frequency. The calculated system parameters for the simulation purpose are given in Table 1.

VI. SIMULATION RESULTS
Three-phase SAPF model is developed in Matlab/Simulink block and dc-link voltage has been controlled using PI controller and PFLC. The three-phase supply voltage is taken sinusoidal and balanced. The power system and SAPF are three-phase but the results are captured to show waveform for single phase because balanced non-linear load is taken for simulation. In the first case, the Total Harmonic Distortion (THD) factor is 20.65%, when the highly non-linear load is connected with the supply. Source current waveform deteriorates as shown in Fig. 7. This waveform shows the effect of non-linear load without SAPF in the system. The simulation result is shown in Fig. 9 when PFLC is connected to control SAPF in the system, it is depicted that the sinusoidal waveform received in two cycles. The Fig. 8 shows source current wave shapes when SAPF is connected and controlled with conventional PI.
In case of PI controller, the reduction in the level of odd harmonic factor(THD) is observed 4.7% and with PFLC the achieved the reduction to 4.41% of THD. The simulation results are compared by taking different values of capacitance (C) and inductance (L). By varying the parameters, the value of THD is varies 0.05%.
The value of kp and ki is taken 0.2 and 9.25 respectively to control the dc voltage with PI controller. DC link voltage settlement graph is shown in Fig. 6. It is clearly seen from the graph that DC link voltage achieves its steady state value earlier in case of PFLC.

VII.
CONCLUSION For more stable system Polar based three phase active filter is implemented. System stability depends on quick response of the controller when load disturbance occurs. Performance of the SAPF depends on entanglement and estimated operational time of the controller. In this paper, PFLC is designed with two membership functions to save the computational time. PFLC is better than traditional FLC because it has less number of fuzzy rules as compared to 49 fuzzy rules used in FLC.
The results of PFLC is compared with conventional PI controller. Simulation results shows that PFLC settles dc link voltage smoothly as compared to PI controller and reduces harmonics effectively and satisfies the permissible limit of 5% according to IEEE-519 standard.
In addition to that, the PFLC has been verified with different set of values of system parameters like filter inductance and filter capacitance. It is observed that the PFLC is enough robust to handle the various disturbances. Hence, polar fuzzy controller is good alternate to the conventional PI controller for reducing current harmonics.