Dynamic Response of Large Wind Power Plant Affected by Diverse Conditions at Individual Turbines

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1 Dynamic Response of Large Wind Power Plant Affected by Diverse Conditions at Individual Turbines Marcelo A. Elizondo Pacific Northwest National Laboratory Seattle, Washington USA Shuai Lu, Guang Lin, and Shaobu Wang Pacific Northwest National Laboratory Richland, Washington USA {Shuai.Lu, Guang.Lin, Abstract Diverse operating conditions at individual wind turbine generators (WTG) within wind power plants (WPPs) can affect the WPP dynamic response to system faults. For example, individual WTGs can experience diverse terminal voltage and power output caused by different wind direction and speed, affecting the response of protection and control limiters. In this paper, we present a study to investigate the dynamic response of a detailed WPP model under diverse power outputs of its individual WTGs. Wake effect is considered as the reason for diverse power outputs. The diverse WTG power output is evaluated in a test system where a large 168-machine test WPP is connected to the IEEE-39-bus system. The power output from each WTG is derived from a wake effect model that uses realistic statistical data for incoming wind speed and direction. The results show that diverse WTG output due to wake effect can affect the WPP dynamic response activating specialized control in some turbines. In addition, transient stability is affected by exhibiting uncertainty in critical clearing time calculation. Index Terms-- Power system dynamic performance, power system stability, uncertainty quantification, wind power plant. I. INTRODUCTION Accurate representation of wind power plants (WPPs) in power system stability studies has gained importance because of two main reasons: the amount of installed wind generation is rapidly increasing around the world, and a large penetration of concentrated wind generation can affect the dynamic behavior of the power system [1] [2]. Power system stability studies require the solution of many dynamic models including the following components: transmission system, synchronous machines and its controls (e.g. turbine-governor, excitation controls), and wind power plants models (e.g. double-fed induction generators). In particular large WPPs are formed by many individual wind turbine generators (WTGs) that experience diverse conditions that can cause non-uniform response to system faults. In a large WPP, the main sources of diversity in individual WTG conditions are [3] [4]: a) the difference in incoming wind in each turbine, b) diversity in types of wind turbines used in the same WPP; c) diversity in controllers or control settings used in the individual wind turbines; and d) diversity in line impedance of the collector network between groups of wind turbines. This paper considers point a), the difference in incoming wind in each turbine, caused by wake effect. That is, individual turbines in a large WPP experience different wind speeds due to the uncertainty in wind speed and direction. The different wind power at each turbine sets an initial state that is different in each turbine of a large wind power plant. Wind speed and direction on a WPP is stochastic. Their corresponding probability functions can be estimated from historical data, as it was done in [5]. The different realizations of wind speed and direction cause different patterns of wake effect in a large power plant, resulting in different wind speeds at each individual turbine. The wake effect patterns can potentially change the dynamic response of the WPP to transmission system disturbances. In this paper, we present an analysis to investigate the dynamic response of a detailed WPP model under diverse power outputs of its individual WTGs. Wake effect is considered as the reason for diverse power outputs. The diverse WTG power output is evaluated in a test system with a large 168-machine test WPP connected to the IEEE-39-bus system. The power output from each WTG is derived from a wake effect model that uses realistic statistical data for incoming wind speed and direction. The results show that diverse WTG output due to wake effect can affect the WPP dynamic response activating specialized control in some turbines. In addition, transient stability is affected by exhibiting uncertainty in critical clearing time calculation. II. BACKGROUND This section reviews the models of elements of a WPP and a wake effect model used to introduce diversity in individual WTG conditions. A. Wind turbine generator model For offline stability studies, generic wind-turbine generator models have been developed [9]. Generic WTG models are based on a simplification of the detailed models, proposed in This work was supported by Advanced Scientific Computing Research (ASCR) program of U.S. Department of Energy (DOE) Office of Science. The Pacific Northwest National Laboratory is operated by Battelle for the US Department of Energy under contract DE-AC6-76RL /14/$ IEEE

2 [11] and [12]. The main purposes of the generic WTG models are to represent several vendors WTGs with a few generic models in dynamic simulations and to avoid using proprietary manufacturer-specific information. The simplifications are based on the assumption that the wind speed remains constant for a typical 3-second period of interest for offline simulations [13] [14]. The development of generic models is currently challenged by the representation of specific control functions of wind farms such as programmed inertia (control system to emulate the inertia of conventional synchronous generators), frequency support features (modification of power output in response to frequency deviations), and details of low-voltage ride through (reactive power control to withstand nearby transmission faults). The WTG generic models are classified into four types. Type 1 is a WTG with a fixed-speed conventional induction generator; Type 2 is a variable-slip induction generator with variable rotor resistance; Type 3 is variable-speed, doubly-fed induction generation with rotor-side converter; and Type 4 is a variable-speed asynchronous generator with full converter [9]. Fig. 1 shows the main structure and components of WTG models. Type 3 model is used in the simulations of this paper. Fig. 1. Dynamic WTG model; the diagram is general for the four types. Figure extracted from [1]. Details of equations and block diagrams of the components of the dynamic models can be found in [9], [1], [11], and [12]. As an example, in this section we briefly describe a shaft system model and some aspects of the models in turbine Type 3. Over/under-voltage active power reduction: During transients caused by faults, the active power generated by a WTG can be limited due to reactive current priority and operation outside standard voltage range [16] [17]. Reactive power priority and over/under-voltage active power reduction are implemented in the model used in this paper as follows [18]. The power controller is implemented with a PI controller that tracks a power reference determined by the speed control that ultimately depends on the incoming wind speed. The PI model is described with the following equations. p =P P, =K I p ; if V V V = T ; if V > V V (1) I _ =K p +x (2) Where P is the reference active power calculated from the speed control, P, is the total measured active power, is the power error, is the terminal voltage, is the steady state pre-disturbance voltage, is the PI state variable, is the integrator gain of the PI, and is the proportional gain of the PI, _ is the resulting active current reference for the rotor. The active current reference is farther limited by variable limiters, where the limits are chosen according to reactive power priority, i.e., maximum active current limit is reduced as a function of the total maximum current and the current reactive power output. As a result, the active power of the WTG is reduced when there is over and under voltage due to the change in logic in the PI controller and to give priority to reactive power control. B. Wind power plant model WPPs are composed of WTGs step-up transformer and a collector network that brings power to a point of interconnection where another transformer steps up the voltage to transmission levels. WTG usually generate power at a low voltage level (e.g. 575 V, 69 V). Each WTG has a stepup transformer that elevates the voltage to a medium voltage level (usually 34.5 kv) to connect the turbines to a collector network. The collector network, most commonly an underground cable, interconnects the WTGs in a daisy chain configuration. The collector network also connects the WTGs to a substation transformer that connects the WPP to the rest of the system at levels of 6kV or above [3] A full representation of the collector network is made using the well-known pi model to represent the underground cables. It also has transformer models for each step-up transformer and the substation transformer. C. Model of wake effect in a wind power plant In a WPP the wind that an individual WTG receives is affected by neighboring WTGs. The wind that passes through a WTG reaches the next WTG with reduced energy. This effect is called wake effect. Several wake effect models are available in the literature [6] [7] [8]. The model in [6] is among first models and the most used in the literature. Its simplicity is attractive for this work. The model is described as follows. The wind speed at the wake of a WTG is given by: = (3) Where, is the wind speed in [m/s] in the wake received at a distance in [m] from the WTG, is the original incoming wind speed in [m/s], is the radius of the WTG rotor in [m], and is the entrainment constant, which is set to.1 in this paper. The radius of the wake in [m] is given by: = + (4)

3 Equations (3) and (4) are generalized for the multi-wtg case as explained discussed in [6]. III. METHOD OF STUDY The process for the analysis is illustrated in Fig. 2. Samples of wind speed and direction are obtained from the statistical distribution of wind speed and direction. The samples are used in a wake effect model that gives the wind speed at each individual wind turbine, by modeling the WPP layout. The wind speed at each turbine is used as input data to each WTG in a detailed WPP model. A fault at the external transmission system is simulated to obtain the dynamic response of the WPP. The process is repeated for several sample pairs of wind speed and wind direction. The uncertainty on the dynamic response is then analyzed. A. Wake effect One case wake effect for the sample of 15.6 m/s wind speed and 125 direction angle for the incoming wind is shown in Fig. 4. to IEEE 39-bus system 84 WTGs WPP-MV 84 WTGs Fig. 3. Scheme of 168-turbine WPP model Wind speed [m/s] and direction at each WTG Fig. 2. Process of uncertainty analysis of detailed wind power plant model The wake effect produces diversity in terminal conditions of individual WTG in the detailed WPP model. There are two main differences in terminal conditions of each WTG in the full model: 1) each WTG experiences a different wind speed due to wake effect, and 2) each WTG experiences a different terminal voltage due to its location in the collector output and the pattern of power injections across the WPP. The characteristics and significance of the dynamic response of the WPP are analyzed in this paper. IV. SIMULATION EXAMPLE A 3-MW 168-machine wind power plant is used in this example; a scheme of the WPP is shown in Fig. 3. The WPP data is similar to real WPPs with a 34.5-kV collector system consisting of underground cable. The collector system is assumed to have a typical daisy chain configuration. Each chain consists in radial underground cables interconnecting 3 to 6 WTGs at a distance of 23 m between WTGs. The collector length from the substation to the first WTG in a daisy chain is assumed such that the WTGs can be arranged in a rectangular layout with 3 m between rows. As shown in the scheme of Fig. 3, 84 WTGs are assumed electrically farther away from the remaining 84 WTGs. Each group of 84 turbines has the collector characteristic described before. The rectangular layout of one of the 84 WTG groups is presented in Fig. 4. The rectangular layout was assumed for simplicity of modeling; however the method of study can be applied to other layouts. The WTGs are type 3 (DFIG) generic models available in the software DIgSILENT PowerFactory [18]. The WTGs are operated in constant reactive power mode. The WPP is connected to the IEEE 39-bus test system in bus 29. It is assumed that the power generated by the WPP directly displaces generation from the synchronous machine near the WPP (generator 9). In this way the initial power flow distribution on the test system is always the same. y coordinate [m] x coordinate [m] Fig. 4. Wind speed and direction at each wind turbine from wake effect model for assumed wind power plant layout B. Sampling of wind speed and direction for uncertainty analysis Fig. 5 shows histograms of 5 samples of wind speed and direction obtained from probability functions derived from historical data. The probability functions were derived by approximating to the historical data used in the reference [5]. Fig. 5. Histograms of 5 samples of wind speed and direction C. Uncertainty analysis of dynamic response to system fault For 5 samples of wind speed and direction, the full WPP model produces different power outputs as shown in Fig. 6. These total power outputs correspond to the different wind speed patterns determined by the wake effect model. The

4 different wake effect patterns produce different dynamic response as illustrated in Fig. 7, for a severe fault in line of 14 ms of duration. It can be seen in the figure that the voltage drops during the fault to about.4pu. After the fault the voltage is depressed until about 6 s, after this an overvoltage is observed between 6 and 7 seconds. This variation in voltage is related to the severity of the fault and the control settings on the WPP. This voltage behavior could be improved if a different voltage control strategy is or if additional equipment, such as static var compensators, is installed. However, the design of control is outside the scope of this paper. Instead, the uncertainty introduced by diverse operating conditions within the WPP is analyzed under the severe fault. Fig. 6. Initial total active power injected at point of interconnection for detailed WPP model for 5 samples of wind speed and direction. Voltage magnitud bus 29 [pu] wind speed [m/s] MW -5MW 5-1MW 1-15MW 15-2MW 2-25MW 25-3MW 3-35MW 35-4MW wind direction [deg] time1 [s] Fig. 7. Response of voltage at point of interconnection for detailed wind power plant model for 5 samples of wind speed and direction. D. Diversity in terminal conditions: action of limiters and WTG protection This section explores the diversity in terminal conditions at individual WTG in the full model. The two main differences in terminal conditions are: each WTG experiences a different wind speed due to wake effect, and a different terminal voltage due to location in the collector network and pattern of power injections across the WPP. The diverse action of overvoltage active power reduction in limiter is illustrated in this section. Fig. 8 shows the dynamic response of the detailed WPP model for initial power outputs between 35 and 4MW at the POI. Note characteristics of the response between 6 and 6.5 s of simulation. As shown in Fig. 9, not all of the individual WTGs activate the overvoltage active power reduction for a given wake effect and fault. The overvoltage active power reduction is either activated or not. Fig. 9 shows a case where the reduction occurs in the WTG electrically farther away from the POI. WPP active power[mw] range 35-4MW time1 [s] Fig. 8. Dynamic response of total active power from full WPP model. Effect of overvoltage active power reduction between 6 and 6.5 s. E. Impact on transient stability The impact on transient stability is analyzed using the concept of critical clearing time (CCT). CCT is the longest time a fault can be sustained (before being cleared by protection relays) without destabilizing the system. CCT was estimated running many simulations for different times of fault clearing (from 14 to 21 ms every 1 ms). When increasing the duration of the fault, the synchronous machines were the first to loose synchronism for the simulated scenarios. The stability was determined by monitoring mechanical speed and angle of the 1 synchronous machines of the IEEE-39-bus test system described before. Fig. 1 shows the critical clearing times (CCT) calculated for the detailed WPP model connected to the IEEE 39 bus test system. It is important to note that, for a given power output of the WPP, the external system has exactly the same conditions. The only factor affecting CCT is the initial power outputs of individual WTG inside the WPP due to wake effect. For example, observe uncertainty in CCT in Fig. 1 for WPP power output between 4 and 5 MW. V. DISCUSSION It can be seen in the previous section that the detailed WPP model shows uncertainty in transient responses. For low total WPP power output, the critical clearing time (CCT) is uncertain. For example for total WPP power output between 4 and 6 MW, CCT is between.16 and.19 s. This suggests that the diversity in initial power output in individual WTGs introduces uncertainty in WPP dynamic response when the WPP operates at low power outputs. Engineers should be aware of the uncertainty introduced by diverse WTG operating conditions in a large WPP. Additionally the detailed WPP model presents characteristics that are difficult to predict without detail representation, in particular because of protection and special

5 limiters of individual WTG. The main reason for this difficulty is that action of some protections in individual WTG depends on local terminal conditions. In transient stability studies, reduced or aggregated WPP representation of one or few WTGs are often used. The effect of diverse terminal conditions in the reduced WPP models should be studied. This is part of the ongoing research by the authors and it is outside of the scope of this paper. Additional work should be performed to validate the effects illustrated in this paper with data of large WPP in operation. Fig. 9. Action of overvoltage active power reduction (indicated by color) in individual WTGs for a given pattern of wake effect. Y-axis: initial terminal voltage at individual WTGs. X-axis: reactance in p.u. used as a proxi for electrical distance from WTGs to the point of interconnection (POI). Critical clearing time [s] initial voltage in pu reduction ON reduction OFF x to POI Total active power POI [MW] Fig. 1. Critical clearing time as a function of total power output for detailed WPP model with wake effect VI. CONCLUSIONS This paper analyzed the uncertainty introduced by diverse power output at individual wind turbine generators (WTGs) within a large wind power plant (WPP). The diversity in power output was assumed to be caused by wake effect. The effect on a detailed WPP model consisting of 168 machines was studied. Uncertainty in WPP dynamic response for transient stability assessment is analyzed. Results show that the critical clearing time of a system fault can change due to the WPP response uncertainty. Another challenge identified is the effect of protections and special limiters at individual WTGs affected by diversity in terminal conditions. Uncertainty quantification methods such as the method used in [15] can be applied to the WPP model. This is part of the authors ongoing research. The authors are also studying the uncertainty in WPP reduced model representation. 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