Modelling of Wind Generators for WT3 Transient Stability Analysis in Networks

Modelling of Wind Generators for WT3 Transient Stability Analysis in Networks Tiago Câmara, Under Supervision of Prof. Pedro Flores Correia Abstract The influence of wind turbines in power systems is becoming increasingly important as wind generation grows. Hence the dynamic behaviour of WTGs (Wind Turbine Generators) should be thoroughly understood. The aim of this article is to study and program the dynamic model WT3 (Wind Turbine Type 3), applied in studies of transient stability. The behaviour of such models is governed by interactions between the continuous dynamics of state variables, and discrete events associated with limits. The model is developed inside an academic tool for transient electromechanical analysis. The program was implemented in MATLAB language and is a result of continuous work made by former IST students. The network system was tested with the presence of wind parks modelled accordingly with the WT3. The results were verified and validated by comparison with simulations made in PSS/E TM program. This article ends with a summary of the results achieved in this study and the conclusions drawn respectively. Index Terms Dynamic models, Transient Stability, Turbine- Governor, Wind Farms. R I. INTRODUCTION ENEWABLES have a growing presence in power systems nowadays. Within these, stands out the wind energy. In fact wind power is a renewable energy source with the highest growth rate, currently. The average annual growth rate of wind turbines installation is around 3%, during the last years []. Based on its strong growth (wind generation), there is a particular interest in the study of transient stability. The dynamic behaviour of wind turbine generators (WTGs) is quite different to that of synchronous generators. Therefore the implementations of WT3 models applies. Besides, WT3 is considered as a dominant technology for new wind farm developments. Such WTGs are also known as doubly fed induction generators (DFIGS) or doubly fed asynchronous generators. In this dissertation it is studied and implemented in an academic program, the generic WT3 model for transient electromechanical studies. The electrical characteristics of WT3s are governed by interactions between a wound-rotor induction machine and a back-to-back inverter. The inverter excites the rotor of the induction machine with a variable AC source. This provides control of the rotor flux frequency, enabling the rotor shaft frequency to optimally track wind speed. The dynamic behaviour of a WT3, as seen from the grid, is therefore dominated by controller response rather than physical characteristics. This is in marked contrast to traditional synchronous generators, where behaviour is governed by device physics. Further details are shown in Section II. Regarding the stability of power systems, the disturbances can be divided into two categories (a) small and (b) large. The tripping of a line may be considered as a small disturbance if the initial (pre disturbance) power flow on that line is not significant [2]. However, faults in which result in a sudden dip in the bus voltages, such as short-circuits, are large disturbances and require remedial action in the form of clearing the fault. These will be the only type of disturbances implemented in the software. The main objective of this dissertation is to expand the dynamic model library with wind generators (WT3), and simulate them in power grids. With this accomplishment it is easier to manipulate and change models as well as network data. It is important to refer that this work is the continuation of previous dissertations made by former IST students ([3] and [4]), and is aimed for academic purposes only. II. SOFTWARE The algorithm of the software is explained sequentially as follows. A. Simulation Data Acquisition The acquisition of data is made through the reading of two types of files, one of the power flow data and the other of the dynamic data. The first contains information regarding the network, such as, bus data, branch data, generation requirements and load demand data. The dynamic data file holds information regarding parameters of the WT3 models. The power flow file has the extension *.raw, while the dynamic files are terminated with *.dyr. This way the reading files for MATLAB are in compliance with the same ones used by the PSS/E TM. B. Power Flow Computation The initial power flow is used to obtain the results needed in loads and generators conversion, as well as the initial conditions required for dynamic simulation. Therefore it is an important process in transient stability analysis. The initial power flow is computed through Newton-Raphson method. Independently of the grid size, it converges in three to five iterations, as long as there are no reactive limits violations. It is important to underline that this type of power flow is only used in the initial process of the program (pre-simulation). When the simulation starts, the new computed power flow is executed with its converted loads in constant admittances, becoming a linear computation. C. Modelling of the Network Equations Having calculated the power flow, the modelling of the network equations takes the form of an admittance matrix,. Although this matrix was already built in the load flow calculation, a new matrix must be determined for the transient solution, so that the loads and generators are included in the computation. Regarding the load conversion, the constant admittance method was adopted. This method considers that the loads can be converted into pure equivalent admittances, by using (), and later added in the network admittance. The same

2 applies for the generator conversion, in order to compute the terminal voltages and currents at each generating bus. D. Calculation of Initial Conditions Before beginning the simulation, it is important to compute the initial conditions. In this section it is generally explained how the initial conditions are calculated:. The terminal current,, is calculated in the network reference. 2. The DFIGs rotor angle ( ) is computed. 3. The terminal voltages and currents are converted to the machine reference,. 4. The command voltage and current are computed ( ). 5. Lastly, based on the previous results it is calculated the torque and rotor speed ( ). E. Construction of the Matrices The matrices are then created through the algebraic equations, which are used in the digital numerical integration. These algebraic equations are obtained from the differential equations that represent the dynamics of each model. F. Dynamic Simulation After all the necessary preliminary calculations, the dynamic simulation begins. The digital computation is done through a discrete method in small time steps. In each iteration, it is computed new results for the state variables and for the grid power flow data. The simulation begins at. The initial conditions are the first set of solutions to compute the first set of system equations. Then the program verifies if the network admittance is changed. If it is, the network admittance is recalculated (fault occurred or cleared) otherwise the program continues. Later it is calculated the network power flow (linear). The algebraic variables are the voltages of each bus and the injected currents of each machine,. The injected currents before the machine equivalente impedance,, are computed and consequently obtained the voltages at each bus in (2), where is the matrix which accounts the admittance of each machine. The injected currents of each bus are calculated through equation (3). () (2) After the computation of the power flow, the state variables are checked to assess if they are within the limits established. Later on, it is computed the new states variables for the next time step (. The state variables are computed through the modified Euler-Cauchy method [5]. The program repeats the same procedure for the next time step until the time limit of simulation is reached. Lastly, when the simulation is completed the results are printed in the screen. III. DYNAMIC MODELS The WT3 model provided is a simplified generic model intended for bulk power system studies where a detailed representation of a WTG is not required. The model is for positive sequence phasor time-domain simulations. As referred, the domain of application of the model is the transient stability analysis of grid disturbances, e.g. faults, on the transmission system. The modelling of WT3 for load flow analysis is generally simple. Wind plants normally consist of a large number of individual WTGs. While the Wind Plant model may consist of a detailed representation of each WTG and the collector system, a simpler model is appropriate for most bulk system studies. Such model can be shown in Fig.. Fig.. Simplified Power Flow model [6]. The WECC WT3 wind turbine generator model is defined in [6]. The complete WTG is divided into four functional blocks, as indicated in Fig. 2. (6) (3) With the results of equations (2) and (3) the complex power is obtained by using (4), and consequently the generated active and reactive powers are computed. (4) (5) Fig. 2. WT3 dynamic model connectivity [6].

3 A. WT3G model This model is an equivalent of the generator and the field converter. It provides the interface between the WTG and the network. Unlike a conventional generator model, it contains no mechanical state variables for the machine rotor. Further, all of the flux dynamics have been eliminated in order to achieve rapid response to higher level commands from the electrical controls. The net result is an algebraic, controlled-current source that computes the required injected current into the network in response to the active current commands from the electrical control model. The model can be seen in Fig. 3. TABEL I Description Constant Reactive Power Control Wind Plant Reactive Power Control emulator - Constant Power Factor control Fig. 3. WT3 Generator model [6]. The windup and non-windup limits play an important role in dynamic simulation. These limits maintain the system in acceptable values in order to avoid possible damage. These limits are thoroughly documented in [7]. Assembling all the equations for the model gives (7) Fig. 4. WT3 Reactive Power Control model [6]. Regarding the active control, the active power and the rotors speed are analysed. Depending on its values, it is generated a current, a power and a speed signal. The function is typically modeled as a piece-wise affine function. WECC default parameters are provided in the Appendix - TABEL II. (8) (9) Fig. 5. WT3 Active Power Control model [6]. () The equations describing the WT3E model can be written: B. WT3E model The WT3E model dictates the active and reactive power to be delivered to the system. It is composed of two independent control functions, Active and Reactive. In Fig. 4 and Fig. 5 are shown the modelled control functions Active and Reactive, respectively. In the reactive control, the controller analyzes the generated reactive power and, consequently, creates a voltage signal which is sent to the WT3G model. This model contains two flags, and. The flag indicates which type of voltage control is made. In TABEL I it is described the function for each value of. The other flag ( ), indicates if it is used a closed loop terminal voltage control or not. () (2) (3) (4) (5)

4 (6) (23) (7) (8) (9) (24) (25) (26) (2) C. WT3T model The function of the turbine model is to extract the maximum power available from the wind without exceeding the limits of equipment. It can represent a single-mass (Fig. 6) or two-mass (Fig. 7) wind turbine model. The turbine model consist of two parts, ) simplified model of the aerodynamic relationship between blade pitch and mechanical power, and 2) a model of the shaft dynamics. D. WT3P model The pitch control model is shown in Fig. 8. The pitch angle function is to control the mechanical power, and consequently, the wind speed obtained by the turbine blade. For wind speeds below the nominal generated power value, the pitch blade is incremented to its fullest and vice-versa. Fig. 6. WT3 Turbine model (One-mass) [6]. Fig. 8. WT3 Pitch control model [6]. The WT3P model can be described by the following set of differential equations: (27) (28) (29) (3) Fig. 7. WT3 Turbine model (Two-mass) [6]. (3) For the single-mass model the differential equations can be written as: As for the double-mass model it is written as: (2) (22) IV. WT3E REACTIVE CONTROL The model described in Fig. 4 does not guarantee the stability of the system after a fault, when the signal is set to (Wind Plant Reactive Power Control emulator). The solution was to search for equivalent WT3 models that could show the possible differences. General Electrics (GE) had a similar model [8], and through it was possible to find the error.

Potência Ativa Gerada [pu] Tensão terminal [pu] Tensão barramento [pu] 5 As shown in Fig. 9, changes in the wind control emulator were made (in the Reactive Controller model): It was necessary to include a Windup limiter in the s3 block output and eliminate the Non-Windup limiter in the s4 block. The GE recommended and values, are fixed at. (p.u.). Since the limits were the only changes made, the differential equations remain the same as described in Section III.B..9.8.7.6.5 Tensão no barramento:.4.3.2 Fig. 9. Wind Control Emulator correction [8]. V. SIMULATION RESULTS For the validation of the developed program were performed three different simulations and compared with the PSS/E TM. The first simulation aims to validate the models described in Section III. The second simulation proves that the program can simulate grids with several WT3 models. Finally, the third simulation is intended to demonstrate the possibility of several WT3 models to be represented as a single one. After computing the non-linear power flow, the initial conditions are calculated and the dynamic simulation is started. The systems remains in steady state until, when a balanced three-phase short-circuit occurs in a line near a bus. The fault is eliminated in and the faulty line removed from the grid. The simulation proceeds until, when there are no more oscillations or variations on the power system. If the oscillations persist the system may be unstable, given the total simulation time. By definition all the simulations performed use the following parameters: Time step,. Network frequency,. System base,. In all figures the results of the MATLAB program and PSS/E TM are represented by a black and red continuous line, respectively. A. WT3 model validation For the WT3 model validation it is used a network with five buses including a substation, which can be seen in Fig.. To obtain accurate values all the models described in Section III need to be operating simultaneously. In this scenario the three-phase short circuit is applied in branch 2 next to bus. The fault is cleared by removing the faulty branch. The WT3 model has the signals and set to.. PSS/E TM MATLAB Fig.. Voltage magnitude, Bus.2..9.8.7.6.5.4.3.2 Fig. 2. Voltage magnitude, Bus 5.7.6.5.4.3.2. Fig. 3. Generator Active Power Tensão terminal do gerador: no barramento: 5 Potência Ativa Gerada do gerador: no barramento: 5 PSS/E TM MATLAB PSS/E TM MATLAB Fig.. Five bus Network including a substation.

Percentagem [%] Percentagem [%] Percentagem [%] Potência Reativa Gerada [pu] 6.35.3 Potência Reativa Gerada do gerador: no barramento: 5 PSS/E TM MATLAB In this case the short-circuit is applied in branch next to bus 4. The fault is cleared by removing the faulty branch..25.2.5..5 Fig. 4. Generator Reactive Power Fig. 6. Nine bus Network 5 4.5 4 3.5 3 2.5 2.5.5 Erro de Potência Ativa do gerador: no barramento: 2 Fig. 5. Generator Active Power Error 5 4.5 4 3.5 3 2.5 2.5.5 Erro de Potência Ativa do gerador: 3 no barramento: 3 Fig. 7. Generator Active Power group 3 Error When the three phase short-circuit is applied, the voltage magnitudes of bus and bus 5, and the generated active power instantaneously decay, as seen in Fig., Fig. 2 and Fig. 3 respectively. This happens because of the low impedances, which in turn are caused by the applied short-circuit. On the other hand, the reactive power hits its maximum peak value due to the voltage drop (Fig. 4). Regarding the program errors, it was only plotted the one who had the biggest differences with the PSS/E TM results, which was the generated active power (Fig. 5). The maximum error obtained was, which was during the fault period. This error decreases as the simulation tends to its end. Although it presents some small errors during the transitory regime it is an acceptable approximation, validating the WT3 model. B. WT3s validation In this scenario it is used a network with nine buses and three WT3 models as shown in Fig. 6. The objective is to validate the model for the operation of models in a network. 3 2.5 2.5.5 Erro de Potência Reativa do gerador: 3 no barramento: 3 Fig. 8.Generator Reactive Power group 3 Error Due to lack of space it is only represented the biggest errors obtained in this scenario, which were the Active and Reactive power of the third generator. The maximum error obtained was 5% as shown in Fig. 7 (Active Power), which occurred during

Potência Reativa [pu] V2 [pu] Potência Ativa [pu] V [pu] 7 the fault period. Regarding the reactive power, its maximum error obtained was, which ocurred during and after the fault period. Therefore the program is validated for WT3 models, based on these errors..9.8 Amplitude da Tensão no barramento 4 Geradores Gerador Eq C. In this case it is tested two scenarios with the same network presented in Fig., only differing on the load demand: Network with four WT3 models in the same bus. Network with one equivalent WT3 model. For the equivalent WT3 model was considered that its power base was four times higher when compared to each WT3 generator. This only applies if the equivalent reactance ( ) is the same. In the following plotted figures the coloured area represents the contribution of the four generators and the continuous black line represents the equivalent WT3 generator..7.6.5.4.3.2. Fig. 2.Voltage Magnitude in bus..9.8 Potência Ativa Gerada no barramento 5 Ger 4 Ger 3 Ger 2 Ger Ger Eq.9 Amplitude da Tensão no barramento 2 4 Geradores Gerador Eq.7.8.6.7.5.4.6.3.5.2. Fig. 9. Active Power in each generator versus equivalent generator..4.3.2..5 Potência Reativa Gerada no barramento 5 Ger 4 Ger 3 Ger 2 Ger Fig. 22.Voltage Magnitude in bus 2. Ger Eq.5 Fig. 2. Reactive Power in each generator versus equivalent generator. According to the Fig. 9 - Fig. 22 it is possible to conclude that the equivalent generator correctly modules the contribution of each WT3 generator. In Fig. 9 and Fig. 2 it is possible to verify that the sum of the power contribution of each generator is the same as the equivalent generator. In Fig. 2 and Fig. 22 the voltages magnitudes of the two scenarios are compared. The continuous red line represents the aggregate of four generators while the continuous black line represents the equivalent generator. The voltages are almost equal only containing a negligible error ( ). It is concluded that the WT3 model is possible to simulate several models with an equivalent one. VI. CONCLUSIONS This work had the goal of implementing a library of WT3 models in a transient stability simulator. Its purpose is only for academic studies. In this paper the importance of developing such a tool for WTGs was introduced. A brief explanation of the WT3 electrical characteristics were made, as well as for the stability of power systems. It was also referred that the program was the continuity of previous dissertations made by former IST students [3] and [4]. In Section II was discussed the algorithm of the program in small detail. The dynamic models presented

8 in the WT3 structure were thoroughly explained [6], as well as the differential equations that define their dynamic behaviour (Section III). It was taken to account that the Wind Control Emulator model ( presented in the WECC WT3E model, did not guarantee the stability of the power system after a fault. The GE presented a similar model [8] to the one studied in this paper that actually could stabilise the system. Section IV describes the changes made. Finally the results obtained through the MATLAB were compared with the PSS/E TM program (Section V). It was presented three different scenarios that validated the implemented WT3 model. The results obtained had a maximum difference of when compared to PSS/E TM. In the end, it is correct to say that the goals were achieved: Implementing a Wind Farm model in an academic tool for transient electromechanical analysis, with a level of precision close to a commercial simulator. APPENDIX TABEL II WECC DEFAULT PARAMETERS VALUES Parameters Values.69 (pu).78 (pu).98 (pu).2 (pu).74 (pu) Parameters REFERENCES Values.2 (pu) [] EWEA. (2) Demanda na UE. [Online]. http://www.ewea.org/index.php?id=8 [2] K. R. Padiyar, POWER SYSTEM DYNAMICS Stability and Control, Vol. I: Basic Concepts. Hyderabad, India: BS publications, 28. [3] André Paulo, A Library of Dynamic Models for Transient Stability, IST, Ed. Lisboa, Portugal, 28. [4] Pedro Araújo, Dynamic Simulations in Realistic-Size Networks, IST, Ed. Lisboa, Portugal, 29. [5] L. O. Chua T.S. Parker, Practical Numerical Algorithms for Chaotic Systems. New York: Springler-Verlag, 989. [6] PSS/E, Generic Type-3 Wind Turbine-Generator Model for Grid Studies, PSS/E, Ed. New York, 26. [7] P. Kundur, "Windup & Non-Windup Limits," in Power System Stability and Control. New York, USA: McGraw- Hill, Inc., 993, ch. 8.6, pp. 359-36. [8] General Electric, "Reactive Power Control," in Modelling of GE Wind Turbine-Generators for Grid Studies. New York, USA: General Electric International, April 6, 2, ch. 4.2., pp. 25-26.