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Self-Excitation and Harmonics in Wind Power Generation E. Muljadi ， C. P. Butterfield National Renewable Energy Laboratory, Golden, Colorado 80401 H. Romanowitz Oak Creek Energy Systems Inc.,Mojave, California 93501 R. Yinger Southern California Edison,Rosemead, California 91770 Traditional 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 generator For 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-Excitation 3.1 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 condition. 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） where = effective admittance representing the stator winding, the capacitor, and the load seen by node M = effective admittance representing the magnetizing branch as seen by node M,referred to the stator side = effective admittance representing the rotor winding as seen by node M, referred to the stator side Equation 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 mode Fig.3 A typical magnetization characteristic = stator winding resistance = stator winding leakage inductance = rotor winding resistance = rotor winding leakage inductance = stator winding resistance S = operating slip = operating frequency = load resistance connected to the terminals C = capacitor compensation =阻抗 One 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 be 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 the 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 as 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 connected 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. From Fig. 10, we can say that the circuit will resonate at different frequencies as the capacitor C is varied. Two harmonic components must exist to generate harmonics currents in the systems—a harmonic source (due to magnetic saturation as shown in Fig. 3) and a circuit that will resonate at certain levels of capacitance compensation. 4.3 Dynamic Simulation. Now consider how the harmonic sources are generated in the transformer. Most utility-size wind turbines are equipped with a pad-mount step-up transformer that connects them to the utility. When the transformer is saturated, the nonlinear characteristic of the magnetic circuit generates a nonsinusoidal current. Figure 11(a) shows the per-phase equivalent circuit of a transformer. The iron core loss of a transformer is usually represented as an equivalent resistance,, in parallel with the magnetizing reactance . In this study, the core loss is small enough to be neglected (i.e., the value of = represents an open circuit; thus, the equivalent resistance is not drawn in the equivalent circuit). The magnetizing flux linkage is proportional to the ratio of the voltage and the frequency: where = the magnetizing voltage = flux linkage = the base frequency = 磁化的電壓 The flux linkage of the transformer can be found from Eq.(7). The relationship between the flux linkage and the magnetizing inductance due to the magnetizing current is nonlinear. When the magnetizing current is low, the flux (and flux linkage) varies linearly with the magnetizing current, but eventually saturation is reached and the nonlinear characteristic starts; further increases in magnetizing current will produce smaller increases in the flux linkage. In the saturation region, the resulting output current will be nonsinusoidal , as shown in Fig. 12, due to the nonlinearity of the magnetizing inductance. Fig. 12 The output voltage and current of a transformer under light load condition There are two types of operation that can cause saturation. The first one occurs when the transformer operates at a higher voltage level. One example of this operation is when the transformer is lightly loaded. As a result, the magnetizing branch is exposed to a high voltage , producing a large magnetizing current in the magnetizing branch. The second type of operation that can result in high saturation is when the transformer is operated with a leading power factor (supplying reactive power to the grid Vs). The voltage across the magnetizing reactance (referred to the primary side) can be expressed as where =+ j= line impedance connecting the transformer to the voltage source VS = + j = primary winding impedance of the transformer == = resistance of the primary and secondary winding of the transformer == = leakage reactance of the primary and secondary winding of the transformer = voltage at the infinite bus = current flowing in the primary winding = reactance of the line = line resistance As an illustration, we can use the phasor diagrams shown in Figs. 11(b) and 11(c). For the case of simplicity in the phasor diagram illustrations, we can simplify the equivalent circuit shown in Fig. 11(a) as an ideal transformer with only its leakage reactance represented. In Fig. 11(a), the real power P and reactive power Q are considered to be flowing from the right to the left (positive values flow from the turbine to the grid). When P >0, Q<0 (the turbine generates real power but absorbs reactive power), then < , and we have normal operation. On the other hand, when P>0, Q>0 (the turbine generates both real and reactive power), then < and we may experience saturation. 22