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rugged, e generation curr guidelines 2 Power System Network Description bine can enter self-excitation operation. The voltage and fre- quency during off-grid operation are determined by the balance between the system’s reactive and real power. Downloaded 28 Mar 2008 to 211.82.100.20. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm We investigate a very simple power system network consisting of one 1.5 MW, fixed-speed wind turbine with an induction gen- erator connected to a line feeder via a transformer H208492 MVA, 3 phase, 60 Hz, 690 V/12 kVH20850. The low-speed shaft operates at 22.5 rpm, and the generator rotor speed is 1200 rpm at its syn- chronous speed. 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 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 oper- ating 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 H20849to dump the energy from the wind turbineH20850, self-excitation can be used to maintain the wind turbine at a safe operating speed during grid loss and me- chanical brake malfunctions. The equations governing the system can be simplified by look- ing at the impedance or admittance of the induction machine. To Contributed by the Solar Energy Division of THE AMERICAN SOCIETY OF MECHANI- CAL ENGINEERS for publication in the ASME JOURNAL OF SOLAR ENERGY ENGINEERING. Manuscript received: February 28, 2005; revised received: July 22, 2005. Associate Editor: Dale Berg. Journal of Solar Energy Engineering NOVEMBER 2005, Vol. 127 / 581Copyright ? 2005 by ASME 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 Self-Excitation Wind Power Traditional wind turbines they are inexpensive, tion generators requir is often used. Because the capacitor compensation among the wind turbine, tant aspects of wind content in the output ena and gives some H20851DOI: 10.1115/1.2047590 1 Introduction Many of today’s operating wind turbines have fixed speed in- duction generators that are very reliable, rugged, and low cost. During normal operation, an induction machine requires reactive power from the grid at all times. Thus, the general practice is to compensate reactive power locally at the wind turbine and at the point of common coupling where the wind farm interfaces with the outside world. The most commonly used reactive power com- pensation is capacitor compensation. It is static, low cost, and readily available in different sizes. Different sizes of capacitors are generally needed for different levels of generation. A bank of parallel capacitors is switched in and out to adjust the level of compensation. With proper compensation, the power factor of the wind turbine can be improved significantly, thus improving over- all efficiency and voltage regulation. On the other hand, insuffi- cient reactive power compensation can lead to voltage collapse and instability of the power system, especially in a weak grid environment. Although reactive power compensation can be beneficial to the overall operation of wind turbines, we should be sure the compen- sation is the proper size and provides proper control. Two impor- tant aspects of capacitor compensation, self-excitation H208511,2H20852 and harmonics H208513,4H20852, are the subjects of this paper. In Sec. 2, we describe the power system network; in Sec. 3, we discuss the self-excitation in a fixedspeed wind turbine; and in Sec. 4, we discuss harmonics. Finally, our conclusions are pre- sented in Sec. 5. and Harmonics in Generation are commonly equipped with induction generators because and require very little maintenance. Unfortunately, induc- reactive power from the grid to operate; capacitor compensation the level of required reactive power varies with the output power, must be adjusted as the output power varies. The interactions the power network, and the capacitor compensation are impor- that may result in self-excitation and higher harmonic ent. This paper examines the factors that control these phenom- on how they can be controlled or eliminated. H20852 Capacitors connected in the low voltage side of the trans- former An induction generator For the self-excitation, we focus on the turbine and the capaci- tor compensation only H20849the right half of Fig. 1H20850. For harmonic analysis, we consider the entire network shown in Fig. 1. 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 reac- tive power compensation in a fixed-speed wind turbine. An induc- tion 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. Although self-excitation does not occur during normal grid- connected operation, it can occur during off-grid operation. For example, if a wind turbine operating in normal mode becomes disconnected from the power line due to a sudden fault or distur- bance in the line feeder, the capacitors connected to the induction generator will provide reactive power compensation, and the tur- Downloaded 28 Mar 2008 to 211.82.100.20. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm operate in an isolated fashion, the total admittance of the induc- tion machine and the rest of the connected load must be zero. The voltage of the system is determined by the flux and frequency of the system. Thus, it is easier to start the analysis from a node at one end of the magnetizing branch. Note that the term “imped- ance” in this paper is the conventional impedance divided by the frequency. The term “admittance” in this paper corresponds to the actual admittance multiplied by the frequency. 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 H208491H20850 gives the total admittance of the system shown in Fig. 2: Y S + Y M H11032 + Y R H11032 =0, H208491H20850 where Y S H11005 effective admittance representing the stator winding, the capacitor, and the load seen by node M Y M H11032 H11005 effective admittance representing the magnetizing branch as seen by node M, referred to the stator side Y R H11032 H11005 effective admittance representing the rotor winding as seen by node M, referred to the stator side H20849Note: the superscript “ H11032” indicates that the values are referred to the stator side.H20850 Equation H208491H20850 can be expanded into the equations for imaginary and real parts as shown in Eqs. H208492H20850 and H208493H20850: R 1L /H9275 H20849R 1L /H9275H20850 2 + L 1L 2 + R R H11032/SH9275 H20849R R H11032/SH9275H20850 2 + L LR H11032 2 =0 H208492H20850 where Fig. 1 The physical diagram of the system under investigation Fig. 2 Per phase equivalent circuit of an induction generator under self-excitation mode 582 / Vol. 127, NOVEMBER 2005 1 L M H11032 + L 1L H20849R 1L /H9275H20850 2 + L 1L 2 + L LR H11032 H20849R R H11032/SH9275H20850 2 + L LR H11032 2 =0 H208493H20850 R 1L = R S + R L H20849H9275CR L H20850 2 +1 L 1L = L LS ? CR L H20849H9275CR L H20850 2 +1 R S H11005 stator winding resistance L LS H11005 stator winding leakage inductance R R H11032 H11005 rotor winding resistance L LR H11032 H11005 rotor winding leakage inductance L M H11032 H11005 stator winding resistance S H11005 operating slip H9275 H11005 operating frequency R L H11005 load resistance connected to the terminals C H11005 capacitor compensation R 1L and L 1L are the effective resistance and inductance, respectively, representing the stator winding and the load as seen by node M. One important aspect of self-excitation is the magnetizing char- acteristic of the induction generator. Figure 3 shows the relation- ship between the flux linkage and the magnetizing inductance for a typical generator; an increase in the flux linkage beyond a cer- tain level reduces the effective magnetizing inductance L M H11032 . This graph can be derived from the experimentally determined no-load characteristic of the induction generator. To solve the above equations, we can fix the capacitor H20849CH20850 and the resistive load H20849R L H20850 values and then find the operating points for different frequencies. From Eq. H208492H20850, we can find the operating slip at a particular frequency. Then, from Eq. H208493H20850, we can find the corresponding magnetizing inductance L M H11032 , and, from Fig. 3, the operating flux linkage at this frequency. The process is repeated for different frequencies. As a base line, we consider a capacitor with a capacitance of 3.8 mF H20849milli-faradH20850 connected to the generator to produce ap- proximately rated VAR H20849volt ampere reactiveH20850 compensation for full load generation H20849high windH20850. A load resistance of R L =1.0 H9024 is used as the base line load. The slip versus rotor speed presented in Fig. 4 shows that the slip is roughly constant throughout the speed range for a constant load resistance. The capacitance does not affect the operating slip for a constant load resistance, but a higher resistance H20849R L high=lower generated powerH20850 corresponds to a lower slip. The voltage at the terminals of the induction generator H20849pre- sented in Fig. 5H20850 shows the impact of changes in the capacitance Fig. 3 A typical magnetization characteristic Transactions of the ASME Downloaded 28 Mar 2008 to 211.82.100.20. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm and load resistance. As shown in Fig. 5, the load resistance does not affect the terminal voltage, especially at the higher rpm H20849higher frequencyH20850, 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 more 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 H20849as mentioned aboveH20850 to pre- vent the turbine from running away when it loses its connection to the grid; one simply needs to choose the correct values for capaci- tance H20849a high valueH20850 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 adjust- ing 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 H9024 for this simu- lation. The constant driving torque is set to be 4500 Nm. Note that the wind turbine aerodynamic characteristic and the turbine con- trol system are not included in this simulation because we are more interested in the self-excitation process itself. Thus, we fo- Fig. 4 Variation of slip for a typical self-excited induction generator Fig. 5 Terminal voltage versus rotor speed for different R L and C Journal of Solar Energy Engineering cus 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 H20849sH20850, the grid is discon- nected 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 driv- ing torque H208494500 NmH20850, 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 resyn- chronizes with the grid. Once this occurs, the rotor speed settles at the same speed as before the grid disconnection. Figure 8H20849aH20850 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 H208493.1 sH11021t H110216.375 sH20850, when the rotor speed increases as shown in Fig. 7, the voltage increases and the frequency is a bit higher than 60 Hz. The voltage and the frequency then return to the rated values when the induction generator is reconnected to the grid. Figure 8H20849bH20850 is an expansion of Fig. 8H20849aH20850 between t=3.0 s and t=3.5 s to better illustrate the change in the voltage that occurs during that transient. 4 Harmonic Analysis 4.1 Simplified Per Phase Higher Harmonics Representation. In order to model the harmonic behavior of the network, we replace the power network shown in Fig. 1 with the per phase equivalent circuit shown in Fig. 9H20849aH20850. In this circuit representation, a higher harmonic or multiple of 60 Hz is denoted Fig. 6 The generator torque vs. rotor speed for different R L and C Fig. 7 The generator output power and rotor speed vs. time NOVEMBER 2005, Vol. 127 / 583 4.1.2 Transformer. We consider a three-phase transformer with leakage reactance H20849X xf H20850 of 6 percent. Because the magnetiz- Downloaded 28 Mar 2008 to 211.82.100.20. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm by h, where h is the integer multiple of 60 Hz. Thus h=5 indicates the fifth harmonic H20849300 HzH20850. For wind turbine applications, the induction generator, transformer, and capacitors are three phase and connected in either Wye or Delta configuration, so the even harmonics and the third harmonic do not exist H208515,6H20852. That is, only h=5,7,11,13,17,..., etc. exist. 4.1.1 Infinite Bus and Line Feeder. The infinite bus and the line feeder connecting the wind turbine to the substation are rep- resented by a simple Thevenin representation of the larger power system network. Thus, we consider a simple RL line representa- tion. Fig. 8 The terminal voltage versus the time. ?a… Voltage during self-excitation. ?b… Voltage before and during self-excitation, and after reconnection. Fig. 9 The per phase equivalent circuit of the simplified model for harmonic analysis 584 / Vol. 127, NOVEMBER 2005 ing reactance of a large transformer is usually very large com- pared to the leakage reactance H20849X M H11032 H11015H11009→ open circuitH20850, only the leakage reactance is considered. Assuming the efficiency of the transformer is about 98 percent at full load, and the copper loss is equal to the core loss H20849a general assumption for an efficient, large transformerH20850, the copper loss and core loss are each approximately 1 percent or 0.01 per unit. With this assumption, we can compute the copper loss in per unit at full load current H20849I 1 FullH6018Load =1.0 per unitH20850, and we can determine the total winding resistance of the primary and secondary winding H20849about one percent in per unitH20850. 4.1.3 Capacitor Compensation. Switched capacitors represent the compensation of the wind turbine. The wind turbine we con- sider is equipped with an additional 1.9 MVAR reactive power compensation H208491.5 MVAR above the 400 kVAR supplied by the manufacturerH20850. The wind turbine is compensated at different levels of compensation depending on the level of generation. The ca- pacitor is represented by the capacitance C in series with the para- sitic resistance H20849R c H20850, representing the losses in the capacitor. This resistance is usually very small for a good quality capacitor. 4.1.4 Induction Generator. The induction generator H208491.5 MW,480 V,60 HzH20850 used for this wind turbine can be repre- sented as the per phase equivalent circuit shown Fig. 9H20849aH20850. The slip of an induction generator at any harmonic frequency h can be modeled as S h = hH9275 s ? H9275 r hH9275 s H208494H20850 where S h H11005 slip for hth harmonic h H11005 harmonic order H9275 s H11005 synchronous speed of the generator H9275 r H11005 rotor speed of the generator Thus for higher harmonics H20849fifth and higherH20850 the slip is close to 1 H20849S h =1H20850 and for practical purposes is assumed to be 1. 4.2 Steady State Analysis. Figure 9H20849bH20850 shows the simplified equivalent circuit of the interconnected system representing higher harmonics. Note that the magnetizing inductance of the transformers and the induction generator are assumed to be much larger than the leakages and are not included for high harmonic calculations. In this section, we describe the characteristics of the equivalent circuit shown in Fig. 9, examine the impact of varying the capacitor size on the harmonic admittance, and use the result of calculations to explain why harmonic contents of the line cur- rent change as the capacitance is varied. From the superposition theorem, we can analyze a circuit with only one source at a time while the other sources are turned off. For harmonics analysis, the fundamental frequency voltage source can be turned off. In this case, the fundamental frequency voltage source H20849infinite busH20850, V s , is short circuited. Wind farm operator experience shows us that harmonics occur when the transformer operates in the saturation region, that is, at higher flux levels as shown in Fig. 3. During the operation in this saturation region, the resulting current can be distorted into a sharply peaked sinusoidal current due to the larger magnetizing current imbedded in the primary current. This nonsinusoidal cur- rent can excite the network at resonant frequencies of the network. From the circuit diagram we can compute the impedance H20849at any capacitance and harmonic frequencyH20850 seen by the harmonic source, V h , with Eq. H208495H20850, where the sign “ H20648 ” represents the words “in parallel with:” Transactions of the ASME Downloaded 28 Mar 2008 to 211.82.100.20. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm ZH20849C,hH20850 = H20849Z line + 0.5Z xf H20850 H20648 H208490.5Z xf + Z C H20648 Z gen