123 CHAPTER 5 ACTIVE AND REACTIVE POWER CONTROL OF DOUBLY FED INDUCTION GENERATOR WITH BACK TO BACK CONVERTER USING DIRECT POWER CONTROL 5.1 INTRODUCTION Wind energy generation has attracted much interest during the last few years. Large wind farms have been planned and installed in various locations around the world. Many of these wind farms are based on the Doubly Fed Induction Generator (DFIG) technology with converter ratings around 30 percent of the generator ratings. DFIG have more advantages over synchronous and induction generators when used in wind farms, such as robustness, reliability, low price, variable speed operation, active and reactive power control, relatively high efficiency, and lower converter cost. DPC technique based on grid voltage orientation has been proposed in this chapter. The DPC gets the same control performances as vector control, but has better robustness and simple structure. This DPC approaches the Instantaneous Reactive Power (IRP) p-q theory, which is based on the Clarke transform of voltages and currents in three-phase systems into α and β orthogonal coordinates. In this proposed control, DPC is used to control both active power and reactive power under steady state condition. Simulation is accomplished using MATLAB/Simulink software. The simulations are verified with laboratory hardware setup.
124 5.2 OPERATION OF DFIG A three-phase wound-rotor induction machine can be setup as a doubly-fed induction motor. In this case, the machine operates like asynchronous motor whose synchronous speed can be varied by adjusting the frequency of the ac currents fed into the rotor windings. The same woundrotor induction machine setup can also serve as a doubly-fed induction generator. In this case, mechanical power at the machine shaft is converted into electrical power supplied to the ac power network via both the stator and rotor windings. Furthermore, the machine operates like a synchronous generator whose synchronous speed (speed at which the generator shaft must rotate to generate power at the AC power network frequency) can be varied by adjusting the frequency of the AC currents fed into the rotor windings. In a conventional three-phase synchronous generator, when an external source of mechanical power (prime mover) makes the rotor of the generator rotate, the static magnetic field created by the DC current fed into the generator rotor winding rotates at the same speed as the rotor. As a result, a continually changing magnetic flux passes through the stator windings as the rotor magnetic field rotates, inducing an alternating voltage across the stator windings. Mechanical power applied to the generator shaft by the prime mover is thus converted to electrical power that is available at the stator windings. In conventional (singly-fed) induction generators, the relationship between the frequency of the ac voltages induced across the stator windings of the generator and the rotor speed is expressed using the Equation (5.1). - Frequency of the ac voltages induced across the stator windings
125 Speed of rotor in rps Number of poles in the DFIG per phase From the above Equation (5.1), it is very clear that, when the speed of the generator rotor is equal to the generator synchronous speed, the frequency of the AC voltages induced across the stator windings of the generator is equal to the frequency of the ac power network. The same operating principles apply in a doubly-fed induction generator as in a conventional (singly-fed) induction generator. The only difference is that the magnetic field created in the rotor is not static (not static means, it is created using three-phase AC current instead of DC current), but rather rotates at a speed proportional to the frequency of the AC currents fed into the generator rotor windings. This means that the rotating magnetic field passing through the generator stator windings not only rotates due to the rotation of the generator rotor, but also due to the rotational effect produced by the AC currents fed into the generator rotor windings. Therefore, in a DFIG both the rotation speed of the rotor and the frequency of the AC currents fed into the rotor windings determine the speed of the rotating magnetic field passing through the stator windings, and thus, the frequency of the alternating voltage is induced across the stator windings. Taking into account the principles of operation of doubly-fed induction generators, it can thus be determined that, when the magnetic field at the rotor rotates in the same direction as the generator rotor, the rotor speed and the speed of the rotor magnetic field add up. The frequency of the voltages induced across the stator windings of the generator can thus be calculated using the Equation (5.2).
126 - Frequency of rotor current fed into the rotor of DFIG Conversely, when the magnetic field at the rotor rotates in the direction opposite to that of the generator rotor, the rotor speed and the speed of the rotor magnetic field are subtracted from each other. The frequency of the voltages induced across the stator windings of the generator can thus be calculated using the Equation (5.3). 5.2.1 DFIG Generate Fixed Frequency Voltages In other words, the frequency of the AC voltages produced at the stator of a DFIG is proportional to the speed of the rotating magnetic field at the stator. The speed of the stator rotating magnetic field itself depends on the rotor speed (resulting from the mechanical power at the rotor shaft) and the frequency of the AC currents fed into the machine rotor. When a DFIG is used to produce power at the AC power network voltage and frequency, any deviation of the generator rotor speed from the synchronous speed is compensated by adjusting the frequency of the AC currents fed into the generator rotor windings so that the frequency of the voltage produced at the stator remains equal to the AC power network frequency. In other words, the frequency is adjusted so that the speed of the rotating magnetic field passing through the stator windings remains constant. Consequently, to maintain the voltage produced at the stator equal to the AC power network voltage, a specific magnetic flux value must be maintained in the machine.
127 This can be achieved by applying a voltage to the generator rotor windings that is proportional to the frequency of the voltages applied to the rotor windings (it maintains the V/f ratio constant and ensures a constant magnetic flux value in the machine). The value of the V/f ratio is generally set; so that the reactive power at the stator is equal to zero. This is similar to the common practice used with conventional (singly-fed) synchronous generators where the exciter current is adjusted so as to zero the reactive power at the stator. 5.2.2 Advantages of Using DFIG for Wind Power Applications Using a DFIG instead of an asynchronous offers the generator in wind turbines following advantages: 1. Operation at variable rotor speed while the amplitude and frequency of the generated voltages remain constant. 2. Optimization of the amount of power generated as a function of the wind available up to the nominal output power of the wind turbine generator. 3. Virtual elimination of sudden variations in the rotor torque and generator output power. 4. Generation of electrical power at lower wind speeds. 5. Control of the power factor. On the other hand, the DFIG requires complex power conversion circuitry which the asynchronous generator does not need. Also, the slip rings on the wound-rotor induction machine used to implement the DFIG require periodic maintenance while no such rings are required on the rotor of the
128 squirrel-cage induction machine used to implement the asynchronous generator. Use of synchronous generator in wind turbines offers the same advantages as when a DFIG is used. Both types of generator require two AC/DC converters. However, the two AC/DC converters in DFIG are significantly smaller than those in synchronous generators of comparable output power. This is because the AC/DC converters in DFIG convey only about 30% of the nominal generator output power while the AC/DC converters in synchronous generators convey 100% of the nominal generator output power. 5.2.3 DFIG for Variable Speed Application DFIG s come into play for wind power conversion, as they allow the generator output voltage and frequency to be maintained at constant values. This is achieved by feeding ac currents of variable frequency and amplitude into the generator rotor windings. Iwanski & Koczara (2008) addressed, by adjusting the amplitude and frequency of the AC currents fed into the generator rotor windings, it is possible to keep the amplitude and frequency of the voltages (at stator) produced by the generator constant, despite variations in the wind turbine rotor speed caused by fluctuations in wind speed By doing so, this also allows operation without sudden torque variations at the wind turbine rotor, thereby decreasing the stress imposed on the mechanical components of the wind turbine and smoothing variations in the amount of electrical power produced by the generator. Using the same means, it is also possible to adjust the amount of reactive power exchanged between the generator and the AC power network. This allows the power factor of the system to be controlled. Finally, a doubly-fed induction
129 generator in variable-speed wind turbines allows electrical power generation at lower wind speeds than with fixed-speed wind turbines using an asynchronous generator. 5.3 DFIG MODEL The DFIG has two sets of three-phase windings that display self and mutual inductances. Mutual inductances change as the machine turns and the angle between stator and rotor circuits varies with time, which ultimately leads to a time-varying mathematical model of the machine. This angle dependency in DFIG s model and the associated complexities can be surmounted by making a transformation from three-phase magnitudes to twoaxis magnitudes (Clark s transformation) and transforming the magnitudes into direct and quadrature components referred to a synchronously rotating reference frame (Park s transformation). The DFIG model in the synchronous reference frame can be expressed as Equations (5.4) to (5.12), where the model corresponds to the angular speed of the rotating reference frame.
130 ( ) 5.3.1 Mathematical Representation of DFIG Ganti et al (2012) addressed the mathematical model, which is similar to the squirrel cage induction machine; the only difference is that the rotor voltage is non-zero in DFIG. In order to simulate the Wind Energy Conversion System a proven method is needed to represent the characteristics of DFIG. The rest of this section is devoted to the mathematical equations that describe a DFIG. The voltage equations to represent a 3-phase induction machine can be expressed by, [ ] [ ][ ] [ ] [ ] [ ][ ] [ ] [ ] [ ] Where ν, r, i, and ψ respectively refer to the voltage, resistance, current, and flux linkage of the phase windings. The subscripts a, b, and c refer to their phase component. The subscripts r and s refer to the stator and rotor windings. The term ρ represents the derivative (d/dt). The flux linkages shown in Figure 5.1 for a linear magnetically coupled circuit are expressed as Equation (5.17) to (5.20).
131 Figure 5.1 Equivalent circuit of induction machine in d-q reference frame Where and are rotor and stator voltages and are rotor and stator fluxes, are rotor and stator resistance & inductance. = Mutual inductance are Rotor & Synchronous angular speed In rotating reference frame the machine model is,
132 The mechanical part of the model is, The active and reactive powers inputs from the network can be calculated as, [ ]
133 [ ] 5.4 BASIC CONFIGURATION Figure 5.2 shows the basic configuration of DFIG. Based on the operation such as sub synchronous, synchronous and super synchronous speed of the DFIG, the power flow is from rotor to grid or grid to rotor. The total power supplied to grid is sum of the power from stator and rotor power. Figure 5.2 Basic configuration of DFIG wind turbine DFIG supplied the power to grid from its stator when P s > 0. Rotor received the power from grid when r< s, it means that P r < 0. Rotor also supplied power to grid when P r > s, it means that P r > 0. Here r, s, P r, P s are rotor speed, stator speed, power from rotor and power from stator respectively. Hence by operating the DFIG in sub synchronous, synchronous and super synchronous modes and the outputs in terms of rotor powers are Pr < 0, Pr = 0 and Pr > 0 respectively. 5.5 CONTROL METHODS Different control methods are popular in the industry, such as scalar method (V/f), vector control, direct and indirect field oriented control,
134 rotor and stator flux control, adaptive flux observer, stator flux orientation and field weakening control. All the said methods are complex, for reducing the complexity to choose the direct power control scheme to control the machine. The DFIG control level performs the control of the rotor side and the grid-side back-to-back converters. A vector control approach is adopted for the rotor controller, while two cross coupled controllers adjust the speed and power of the system. The goals of such controllers are to track the optimum operation point, limit the power in the case of high wind speeds, and control the reactive power exchanged between the wind turbine generator and the grid. The control of the grid-side converter keeps a constant DC-link voltage while injecting the active power to the grid. Internal current loops in both converters are typically using proportional integral (PI) controllers. DTC and DPC schemes have been presented as alternative methods which directly control machine flux and torque via the selection of suitable voltage vectors. It has been shown that DPC is a more efficient approach compared to modified DTC. However, the DPC method also depends on the estimation of machine parameters and it requires a protection mechanism to avoid over current during a fault in the system. In induction wind generators, unbalanced three phase stator voltages cause a number of problems, including overheating and stress on the mechanical components from torque pulsations. Therefore, beyond a certain amount of imbalance (6%), induction wind generators are switched out of the network. In DFIG control of rotor currents allows for adjustable speed operation and reactive power control. In addition, it is possible to control the rotor currents to correct the problems caused by unbalanced stator voltages. This research presents a new controller design for a doubly-fed induction generator that provides adjustable speed and reactive power control while greatly reducing torque pulsations.
135 5.5.1 Rotor Side Converter The RSC supplies the voltage to the rotor windings of the DFIG. The purpose of the rotor-side converter is to control the rotor currents such that the rotor flux position is optimally oriented with respect to the stator flux in order that the desired torque is developed has been studied by Jiabing Hu et al (2011). The rotor-side converter uses a torque controller to regulate the wind turbine output power and the voltage (or reactive power) measured at the machine stator terminals. The power is controlled in order to follow a pre-defined turbine power-speed characteristic to track the maximum power point. The actual electrical output power from the generator terminals, added to the total power losses (mechanical and electrical) is compared with the reference power obtained from the wind turbine characteristic. Usually, a Proportional-Integral (PI) regulator is used at the outer control loop to reduce the power error (or rotor speed error) to zero. The output of this regulator is the reference rotor current i rqref that must be injected in the rotor winding by rotor-side converter. This q-axis component controls the electromagnetic torque Te. The actual i rq component of rotor current is compared with i rqref and the error is reduced to zero by a current PI regulator at the inner control loop. Figure 5.3 shows the rotor side converter control scheme. The output of this current controller is the voltage v rq generated by the rotor-side converter. With another similarly regulated i rd and v rd component the required 3-phase voltages applied to the rotor winding are obtained.
136 Figure 5.3 Rotor side converter control scheme 5.5.2 Control of Real and Reactive Power Using the RSC The grid side converter is used to partly control the flow of real and reactive power from the turbine system to the grid. The grid-side converter feeds the grid through a set of interfacing inductors. The grid-side converter (a voltage source inverter) can generate a balanced set of threephase voltages at the supply frequency and that the voltage (E) can have a controllable magnitude and phase. Load angle control is used to illustrate the basics of real and reactive power control, though in practise, a more sophisticated control is used which provides superior transient response. Essentially, load angle control uses the angle ( ) between the voltage generated by the grid-side converter (E) and the grid voltage (V). The steady-
137 state equations relate to the real and reactive power flow from the grid-side converter to the grid are shown in Equation (5.35) and (5.36). Showing that P can be controlled using load angle δ l, and Q can be controlled using the magnitude of E. The combination of control and power electronics enables the grid-side converter to produce the necessary voltage magnitude (E) and load angle (δ l), in order to meet a required P s and Q s demand set by the main system controller. The controller should be able to synchronise the grid frequency and phase, in order to connect and supply power. At any instance, the power exported by the GSC is determined by the state of the DC- link voltage. The grid-side converter controller monitors the DC- link voltage. If the DC- link voltage rises, the grid-side converter can export more real power by increasing the load angle in order that the DC- link voltage moves back towards it nominal value. If more power is being exported by the GSC than is currently being generated by the RSC, the DC link voltage will fall below its nominal value has been dealt by Jiabing Hu et al (2013). The grid-side controller will then reduce the exported real power to allow the DC link voltage to recover to its nominal value. In this sense, the DC link voltage indicates power flow balance between the generated energy and the exported energy in the rotor side. If the input and output power to the DC link capacitor do not match, then the DC link voltage will change. The quality of the energy supplied to the network must meet basic requirements and it will be set by the grid code in force at the PCC.
138 The grid code specifies many performance indicators of the quality of the energy supplied by the grid-side converter, along with other important issues such as fault level. The relevant grid code(s) in operation must be determined prior to tendering for work on the turbine power electronics and control. The grid code has important implications on the control system of the turbine. If the generator-side controller continues to generate power, the DC link capacitance will be over charged. Therefore, a grid fault will require the generator to stop generating energy, which then means that there is no longer a restraining torque to control the blade speed. In a wind turbine, a loss of supply will cause an over speed condition, as the blade system will accelerate due to the aerodynamic torque produced by the blades. Shorting resistors, or a crowbar circuit, is often switched across the rotor circuit of the generator in order that the energy generated by the blade system can be absorbed and the high speed condition controlled to a safe and manageable level. In addition, there are often aerodynamic (pitch control) and mechanical braking mechanisms included in wind turbines as an additional over-speed safety measure. 5.5.3 Grid Side Converter Different control strategies are used to perform the control of the grid side converter. They all are focused on the same topics, the control of the DC-link voltage, active and reactive power delivered to the grid, grid synchronization and to ensure high quality of the injected power.they can be classified depending on the reference frame used in the control structure. In this research, the focus is on the synchronous and stationary reference frame control strategies. In both cases, the control strategy contains two cascaded loops. Figure 5.4 shows the grid side converter control scheme.
139 The inner loops control the grid currents and the outer loops control the DC-link voltage and the reactive power. The current loops are responsible for the power quality, thus harmonic compensation can be added to the action of the current controllers to improve it. The outer loops regulate the power flow of the system by controlling the active and reactive power delivered to the grid. The total current delivered into the grid is the sum of the currents from stator side and grid side. Since the negative-sequence current of the DFIG stator is eliminated with the effective control of GSC has been described by Jun Yao et al (2008). Figure 5.4 Grid side converter control scheme 5.5.4 Direct Power Control The DPC inherits most of its theoretical background from the DTC. DPC also exploits the geometrical relationship between stator and rotor fluxes and the fact that the rotor flux can be fully controlled through the RSC.
140 This distinction change in the control approach has a significant impact on the robustness and simplicity of the DPC strategy, whose main features include: 1) Independence from machine parameters 2) Reduced number of electrical magnitudes to be measured and 3) No need for reference frame transformations 5.5.5 P Q Controller Operation Once the voltage is induced in the stator, it is compared with the grid voltage at the other side of the coupling reactance and the stator current is calculated. Starting from the value of the stator voltages and currents, the actual active P and reactive Q powers interchanged with the grid are calculated. These powers are compared with their respective references, P* and Q*, so that a regulator can correct the error in the next calculation to be performed on the voltages needed to be induced in the stator. Once the machine is connected to the grid, the system may be operated in two different modes in order to set the commands for the active and reactive powers. Manual mode setting of P and Q references is one method and the other one is the activation of the maximum power point tracking operating mode. The second case, the quaintest essential is to operate the generator with zero reactive power reference. 5.6 SIMULATION RESULT Simulations of the proposed control strategy for a DFIG based wind power generation system were carried out, using MATLAB/Simulink. Discrete models were used with a simulation time step of 1.5s. The DFIG is rated at 1.3 kw. Choose the DC link capacitor as 1200µF, 600V. The nominal
141 converter DC- link voltage was set at 300V. The grid side converter has to maintain a constant DC-link voltage, and it is controlled by a method similar to the DC voltage controller in a PWM voltage source rectifier. During simulations, a sampling frequency of 10 khz was used for the proposed control strategy. A high-frequency ac filter is connected to the stator side to absorb the switching harmonics generated by the two converters. Figure 5.5 Simulink diagram of back to back converter with DFIG Figure 5.5 shows the SIMULINK modelling of back to back converter with DFIG. The filter is a single-tuned one with inductance and resistance connected in parallel instead of series, which results in a wide band filter having impedance at high frequencies limited by the resistance. In a practical system, voltages and currents are sampled at the beginning of each sampling period. The required rotor control voltage for the sampling period is
142 then calculated and passed to the SVM (Support Vector Machine) module. Impossible to avoid, there is a time delay between the instant sampling and SVM modulator s receiving the required rotor control voltage and updating its register values. Figure 5.6 Grid side converter phase volt and current for a sub synchronous speed (135 rad/s) Rotor voltage calculation of the proposed DPC strategy is relatively simple, and the time delay should be adroit small. In spite of that, the calculated output rotor voltage is delayed by 4 ms (one sampling period) to closely represent a practical DPC control system. During the simulation, the grid side converter is enabled first, so that the converter DC-link voltage is regulated. The generator is then excited by rotor-side converter with the rotor rotating at a fixed speed till the stator voltage matches with the network voltage, such that the DFIG system is switched into grid-connected operation.
143 Figure 5.7 Grid side converter phase volt and current for synchronous speed (157 rad/s) Figure 5.8 Grid side converter phase volt and current for super synchronous speed (179 rad/s)
144 Figure 5.9 Rotor side converter phase voltage and current for sub synchronous speed (135 rad/sec) The Figures 5.6 to 5.8 shows the grid side converter phase volt and current for a sub synchronous, synchronous and super synchronous speed. respectively. Figure 5.10 Rotor side converter phase voltage and current for synchronous speed (157 rad/sec)
145 Figure 5.11 Rotor side converter phase voltage and current for super synchronous speed (179 rad/sec) The Figures 5.9 to 5.11 shows the rotor side converter phase volt and current for a sub synchronous, synchronous and super synchronous speed respectively. The Figure 5.12 to 5.14 shows the stator phase volt and current for a sub synchronous, synchronous and super synchronous speed respectively. Figure 5.12 Stator phase volt and current for sub synchronous speed (135 rad/sec)
146 Figure 5.13 Stator phase volt and current for synchronous speed (157 rad/sec) Figure 5.14 Stator phase volt and current for super synchronous speed (179 rad/sec) Figure 5.15 to 5.17 shows the constant reactive power for a sub synchronous, synchronous and super synchronous speed respectively.
147 Figure 5.15 Constant reactive power with variable active power for sub synchronous speed (135 rad/sec) Figure 5.16 Constant reactive power with variable active power for synchronous speed (157 rad/sec)
148 Figure 5.17 Constant reactive power with variable active power for super synchronous speed (179 rad/sec) 5.7 DESCRIPTION OF THE EXPERIMENTAL WORK-BENCH As it can be seen in the picture shown in Figure 5.18, the bench is composed of two controlled electrical drives: one is the wind turbine emulator (DC motor) and the other is the electric generator (DFIG), coupled on the same shaft. The wind turbine emulator (WTE) consists of a DC motor driven by a Siemens AC/ DC converter that can be easily configurable. Figure 5.19 shows a proposed grid connected DFIG with all supporting components like GSC, RSC, measuring units (Power quality analyser) and FPGA - controller. The specific components used in the presented proposed grid connected DFIG are: A 1.3 kw, 220 V, 1500 rpm, DC shunt machine. It is mechanically coupled to the generator to transmit the desired torque.
149 Figure 5.18 DFIG and DC motor coupled on the same shaft Figure.5.19 Experimental test rig of DFIG An AC/DC Siemens converter for DC drives. It supplies the suitable voltage or current to the DC machine in order to achieve the specified torque reference. A 1.3 kw, 1410 rpm, 4 poles, 415 V wound rotor asynchronous machine an AC/DC, 1200 V, 25 A three-phase controlled IGBT converter. When working below the synchronous speed, it rectifies the
150 voltage or currents from the grid to feed the DC bus from which the generator converter will feed the wind generator rotor. Above that speed, it will control the DC bus voltage delivering power to the grid. At all times, the control system of this converter regulates the reactive power exchanged with the grid to which the generator s rotor is connected. A DC/AC 1200 V, 25 A, three-phase controlled IGBT s converter feeds the DFIG s rotor with AC obtaining the energy from the DC bus. The control system calculates how the rotor phases must be fed so that the generator s stator delivers the maximum electric power associated to different wind conditions to the grid. The control system also regulates the reactive power exchanged with the grid through the generator s stator by means of this converter. A FPGA - Spartan 6 based control system composed development board has been used as controller. This hardware allows for the simultaneous controlling of the IGBT firing signals in the DC/AC generator side converter and those of the AC/DC grid side converter. The interface included with this system allows for the real-time tracking of the change of any variable in the entire generation system. A Hall Effect sensors box for adapting voltage and current measurements to the FPGA input channels. 5.7.1 System Operation The described system is designed to be operated in the following manner 1. The DC machine coupled with DFIG act as wind turbine emulator and is initiated using a specific wind reference. The wind turbine emulator control system (Siemens control) reads the turbine speed from the generator control system (FPGA).
151 2. When the generator control system detects the minimum speed at which the DFIG must be started, both the grid converter and the generator converter are started in order to prepare the system for connection to the grid. 3. Once the DFIG stator generates three voltages equal to those of the grid to which it will be connected, the grid connection switch is closed. 4. When the generator stator is connected to the grid, the generator control system can operates the specified active and reactive power (zero). 5. At the same time, the grid converter control system maintains the DC bus voltage equivalent to the reference value. 6. From this point, the system works automatically and the only parameter that can be modified is the DC machine current or torque reference. 7. At any turbine speed, the DFIG will deliver the maximum active power established by a reference table, including the higher speed values at which the pitch angle must be changed. The generator control system operates to maintain zero reactive power interchanged with the grid. 8. According to the grid converter control system, it is important to remember that when the wind turbine operates below the synchronous speed, this converter (GSC) acts as a rectifier, allowing the energy to flow from the grid to the rotor. But when the turbine speed increases above the synchronous value, it works as an inverter, delivering power from the rotor to the grid. Moreover, this converter also collaborates in the global reactive power control.
152 5.7.2 Hardware Results To demonstrate the operating possibilities of this system, we present the results of a specific test consisting of the production of an increment of the wind speed while operating the system on manual reference mode. The test results are presented in Figures 5.20 and 5.22. Figure 5.20 Stator voltage, stator current and rotor current for sub synchronous speed as 135 rad/sec The intention of this test is that the wind increases carries an increment of the machine rotating speed which increases from 1288 rpm, under synchronous speed 1500 rpm, to a super-synchronous speed 1702 rpm.
153 Figure 5.21 Stator voltage, stator current and rotor current for synchronous speed as 157 rad/sec Figure 5.22 Stator voltage, stator current and rotor current for super synchronous speed as 179 rad/sec
154 Figure 5.20 and 5.22 shows the evolution of the voltage amplitude, the frequency, and the three phase currents injected into the grid, as well as the value of the active (P) and reactive (Q) power interchanged with the grid through the stator for different rotor frequencies, whose values follow at all times the constant references established for this test. Figure 5.23 shows the rotor side converter voltage, which is 350 volts line to line. Figure 5.23 Stator voltage, stator current and rotor side converter line voltage for super synchronous speed as 179 rad/sec 5.8 SUMMARY The operation of DFIG was reviewed and the mathematical model for real and reactive powers are derived from its equivalent circuit. The control circuit for GSC and RSC have been prepared by using direct power control scheme and implemented. The simulation of a 1.3 kw DFIG based GCWECS with PI controller is carried out using MATLAB/SIMULINK. The
155 steady state behaviour of system was analysed for synchronous (157 rad/sec), sub synchronous (135 rad/sec) and super synchronous speed (179 rad/sec). The reactive power supplied by DFIG for three modes of operations (synchronous, sub synchronous and super synchronous speeds) is zero, and has been justified by the simulation results. The hardware results also confirmed the simulation results.