98 CHAPTER 6 UNIT VECTOR GENERATION FOR DETECTING VOLTAGE ANGLE 6.1 INTRODUCTION Process industries use wide range of variable speed motor drives, air conditioning plants, uninterrupted power supply systems and various power electronic converters to improve system efficiency and hence the productivity. These loads draw reactive power from the grid. Excess reactive power will result in poor voltage regulation and poor utilization of the power system, especially the distribution transformer for the plant. These constraints make it necessary to compensate the reactive power. Traditionally, passive elements like ac capacitor banks are used for reactive power compensation, but the effectiveness of these capacitors is limited. Moreover they have disadvantages such as drawing fixed amount of leading reactive power irrespective of the load requirements. For continuously varying load, which is the case in most of the process industries, these fixed capacitor banks fail to control the power factor effectively. Thyristor switched or mechanically switched capacitor banks are also used to improve this situation. However they too cannot maintain the power factor near unity when the load varies rapidly. Also, the life span of these passive elements is less due to load harmonics and current sinking, resulting in the need for regular maintenance. Due to these limitations of passive filters, various active filters have been used for reactive power compensation.
99 6.2 UNIT VECTOR GENERATION The three phase shunt active filter is a fully controlled three phase boost converter, connected to the grid through a three-phase series choke. This converter supplies the required reactive power to the load to maintain the grid side power factor at unity. A series choke separates the two voltage sources namely grid and inverter. The capacitor voltage is maintained at a constant value by closed loop control, which regulates the active power drawn from the grid and caters to the internal losses of the system. Synchronous d-q reference frame based control strategy is proposed to control this converter. This control strategy requires sensing of grid voltage and generation of unit vectors for orientation along the grid voltages. Figure 6.1 explains the generation of UVG. The sensed grid voltages are filtered using a first order digital low pass filter whose corner frequency is. In the present work, is chosen to be equal to the nominal grid frequency (50 Hz). So, after filtering, the percentage of the h th order harmonics of the sensed grid voltage is reduced by a factor of ( ) (with respect to the fundamental component). It is clear that the 5 th and higher order harmonics, which can normally be present in the line-to-line grid voltage, are reduced using this low pass filter. Higher frequency noise gets eliminated almost completely. Finally, dividing the filter output signals with their magnitude generates the required unit vectors. However, this low pass filter introduces a phase lag to the unit vector. For nominal grid frequency (50Hz), this phase lag can be easily compensated (Figure 6.2). Since, the grid frequency varies within a small range (±2.5 Hz), there is a negligible phase error in unit vector generation if constant phase compensation is done.
100 Figure 6.1 Block diagram of UVG 6.3 CONTROL STRATEGY The control scheme is presented in Figure 6.2. The three phase currents of the load and the converter are transformed into the synchronously rotating reference frame using Equations (6.1) and (6.2). Figure 6.2 Control scheme for UVG based SAPF
101 The Unit vectors required for the transformation are generated from grid voltages as described earlier. In other words the first step in the control scheme is orienting the converter and grid currents along the grid voltage. The load current will be a composite current containing the fundamental and harmonics. After orientation, the fundamental components of d-axis and q- axis currents are the active and reactive parts respectively of the fundamental load currents. For grid reactive power compensation, the fundamental q-axis load current is used as the reference of q-axis current controller of the converter. There is a PI controller to maintain the dc bus constant. The output of this controller generates the reference of d-axis current controller of the converter. 1 1 = 2 3 0 2 cos = sin 1 2 3 (6.1) 2 sin cos (6.2) and (6.4). The control laws along the d and q axis are given in Equations (6.3) = + + (6.3) = + (6.4) Here R and L are the resistance and inductance of the series choke; V d and V q are d and q axis voltage commands respectively and v g is the grid voltage. There are two PI current controllers to control the d-axis and q-axis currents of the converter. The outputs of these current controllers are added with feed forward terms based on Equations (6.3) and (6.4) to generate the d-
102 axis and q-axis voltage references for the converter. Finally, the d-q voltage references are transformed back to 3-phase stationary voltage references using the unit vectors. These reference signals are fed to the PWM modulator to generate the gate pulses for the converter. 6.4 ALGORITHM FOR UVG As discussed in the previous section, the position angle of voltage was determined by using PLL in the literatures discussed. But a new idea of getting the voltage position angle in terms of extracting unit vectors is proposed in this section. An algorithm for the same is developed and is as follows: Step 1: Step 2: Step 3: Step 4: Line voltages of grid is measured Convert the line voltage in abc coordinates to αβ coordinates V α and V β are passed through low pass filters to filter out the higher order harmonics Magnitude of instantaneous line voltage is determined using ( ) = + Step 5: The unit vectors of voltage is determined using = ( ) and = ( ) Step 6: The generated unit vectors are used for transforming the grid voltages from αβ coordinates to dq0 coordinates.
103 6.5 SIMULATION The whole system was simulated in MATLAB. As it has been the convention adopted in all the previous research works, for simulation purpose, a balanced and sinusoidal three-phase source and a nonlinear load were considered. Figure 6.3 MATLAB/SIMULINK diagram of SAPF using UVG
104 Figure 6.3 shows the simulation diagram of the SAPF using UVG. The inverter current is the anti-harmonic currents generated by the SAPF to compensate the harmonic components in the load current. The grid current is the sum of inverter current and load current. The Control board generates the command voltages for the SAPF from inputs of actual inverter current, load current and grid voltage. Based on the command voltage, switching states of SAPF S a, S b and S c are generated and accordingly SAPF generates the compensating current vectors to inject anti-harmonics at the PCC and hence the harmonic contents of the grid current is reduced. Figure 6.4 MATLAB/SIMULINK diagram of UVG Figure 6.4 explicitly indicates the simulation of the above algorithm using MATLAB simulink package. This UVG ensures generation of sine and cosine of the angle of the input voltage in its coordinates. This block also gets the magnitude of the input voltage. These angles and magnitude are used for the action of SAPF.
105 6.6 RESULT AND ANALYSIS The simulation result shown in Figures 6.5 clearly indicates that the grid current is sinusoidal for each phase and so it can be viewed that the harmonics are reduced. Figure 6.5 MATLAB/SIMULINK result of phase 'A' showing (a) Load current (b) source current after compensation and (c) compensation current injected by SAPF at PCC 6.7 CONCLUSION This chapter proposed an improved algorithm to generate unit vector from the sensed grid voltage for a reduced effect of harmonics and noise present in the feedback signal. This simplified algorithm was used in synchronous d-q reference frame method for the control of SAPF.
106 In this chapter, synchronous d-q reference frame based control strategy is presented for a two-level shunt active filter. The control law is derived for the compensation of reactive power drawn from grid. This chapter also presents a simple and efficient method of unit vector generation, which will minimize the effect of harmonics and noise present in the grid voltage feedback.