2419 垂直軸風(fēng)力發(fā)電機(jī)的設(shè)計(jì),垂直,風(fēng)力發(fā)電機(jī),設(shè)計(jì) 8Self-Excitation and Harmonics in Wind Power GenerationE. Muljadi ， C. P. ButterfieldNational Renewable Energy Laboratory, Golden, Colorado 80401H. RomanowitzOak Creek Energy Systems Inc.,Mojave, California 93501R. YingerSouthern California Edison,Rosemead, California 91770Traditional wind turbines are commonly equipped with induction generators because they are inexpensive, rugged, and require very little maintenance. Unfortunately, induction generators require reactive power from the grid to operate，capacitor compensation is often used. Because the level of required reactive power varies with the output power, the capacitor compensation must be adjusted as the output power varies. The interactions among the wind turbine, the power network, and the capacitor compensation are important aspects of wind generation that may result in self-excitation and higher harmonic content in the output current. This paper examines the factors that control these phenomena and gives some guidelines on how they can be controlled or eliminated.1．Introduction Many of today’s operating wind turbines have fixed speed induction generators that are very reliable, rugged, and low cost. During normal operation, an induction machine requires reactive power from the grid at all times. The most commonly used reactive power compensation is capacitor compensation. It is static, low cost. Different sizes of capacitors are generally needed for different levels of generation.Although reactive power compensation can be beneficial to the overall operation of wind turbines, we should be sure the compensation is the proper size and provides proper control. Two important aspects of capacitor compensation, self-excitation and harmonics ,are the subjects of this paper.2．Power System Network Description A diagram representing this system is shown in Fig(1). The power system components analyzed include the following:? An infinite bus and a long line connecting the wind turbine to the substation? A transformer at the pad mount? Capacitors connected in the low voltage side of the transformer? An induction generator9For the self-excitation, we focus on the turbine and the capacitor compensation only the right half of Fig. For harmonic analysis, we consider the entire network shown in Fig.3. Self-Excitation3.1 The Nature of Self-Excitation in an Induction Generator. Self-excitation is a result of the interactions among the induction generator, capacitor compensation, electrical load, and magnetic saturation. This section investigates the self-excitation process in an off-grid induction generator, knowing the limits and the boundaries of self-excitation operation will help us to either utilize or to avoid self-excitation.Fixed capacitors are the most commonly used method of reactive power compensation in a fixed-speed wind turbine. An induction generator alone cannot generate its own reactive power; it requires reactive power from the grid to operate normally, and the grid dictates the voltage and frequency of the induction generator.One potential problem arising from self-excitation is the safety aspect. Because the generator is still generating voltage, it may compromise the safety of the personnel inspecting or repairing the line or generator. Another potential problem is that the generator’s operating voltage and frequency may vary. Thus, if sensitive equipment is connected to the generator during self-excitation, that equipment may be damaged by over/under voltage and over/ under frequency operation. In spite of the disadvantages of operating the induction generator in self-excitation, some people use this mode for dynamic braking to help control the rotor speed during an emergency such as a grid loss 10condition. With the proper choice of capacitance and resistor load, self-excitation can be used to maintain the wind turbine at a safe operating speed during grid loss and mechanical brake malfunctions。3.2 Steady-State Representation. The steady-state analysis is important to understand the conditions required to sustain or to diminish self-excitation. As explained above, self-excitation can be a good thing or a bad thing, depending on how we encounter the situation. Figure 2 shows an equivalent circuit of a capacitor compensated induction generator. As mentioned above, self-excitation operation requires that the balance of both real and reactive power must be maintained. Equation （1）gives the total admittance of the system shown in Fig(2):+ + =0 （1）SY'M'Rwhere= effective admittance representing the stator winding, the capacitor, SYand the load seen by node M= effective admittance representing the magnetizing branch as seen by 'Mnode M,referred to the stator side= effective admittance representing the rotor winding as seen by node 'RM, referred to the stator sideEquation 1 can be expanded into the equations for imaginary and real parts as shown in Eqs.2and3:（2）Fig. 2 Per phase equivalent circuit of an induction generator under self-excitation mode11Fig.3 A typical magnetization characteristic= stator winding resistanceSR= stator winding leakage inductanceL= rotor winding resistance'= rotor winding leakage inductance'R= stator winding resistance'MS = operating slip= operating frequency?= load resistance connected to the terminalsLC = capacitor compensation=阻抗SR12One important aspect of self-excitation is the magnetizing characteristic of the induction generator. Figure 3 shows the relationship between the flux linkage and the magnetizing inductance for a typical generator; an increase in the flux linkage beyond a certain level reduces the effective magnetizing inductance . This graph can 'MLbe derived from the experimentally determined no-load characteristic of the induction generator. The voltage at the terminals of the induction generator presented in Fig . （5） shows the impact of changes in the capacitance and load resistance. As shown in Fig. （5）, the load resistance does not affect 13the terminal voltage, especially at the higher rpm （higher frequency）, but the capacitance has a significant impact on the voltage profile at the generator terminals. A larger capacitance yields less voltage variation with rotor speed, while a smaller capacitance yields m ore voltage variation with rotor speed. As shown in Fig. 6, for a given capacitance, changing the effective value of the load resistance can modulate the torque-speed characteristic.These concepts of self-excitation can be exploited to provide dynamic braking for a wind turbine mentioned above to prevent the turbine from running away when it loses its connection to the grid; one simply needs to choose the correct values for capacitance （a high value） and load resistance to match the turbine power output. Appropriate operation over a range of wind speeds can be achieved by incorporating a variable resistance and adjusting it depending on wind speed.3.3 Dynamic Behavior. This section examines the transient behavior in self-excitation operation. We choose a value of 3.8 mF capacitance and a load resistance of 1.0 for this simulation. The constant driving torque is set to be ?4500 Nm. Note that the wind turbine aerodynamic characteristic and the turbine control system are not included in this simulation because we are more interested in the self-excitation process itself. Thus, we focus on the electrical side of the equations.Figure 7 shows time series of the rotor speed and the electrical output power. In this case, the induction generator starts from rest. The speed increases until it reaches its rated speed. It is initially 14connected to the grid and at t=3.1 seconds （s）, the grid is disconnected and the induction generator enters self-excitation mode. At t=6.375 s, the generator is reconnected to the grid, terminating the self-excitation. The rotor speed increases slightly during self-excitation, but, eventually, the generator torque matches the driving torque （4500 Nm）, and the rotor speed is stabilized. When the generator is reconnected to the grid without synchronization, there is a sudden brief transient in the torque as the generator resynchronizes with the grid. Once this occurs, the rotor speed settles at the same speed as before the grid disconnection.Figure 8 (a) plots per phase stator voltage. It shows that the stator voltage is originally the same as the voltage of the grid to which it is connected. During the self-excitation mode 3.1 s0,Q>0. (c) Phasor diagram for P>0,Q 0, Q0, Q>0 (the turbine generates both real and reactive power), then < and we may experience saturation.'MS