Coordinated design of fuzzy‐based speed controller and auxiliary controllers in a variable speed wind turbine to enhance frequency control
2016; Institution of Engineering and Technology; Volume: 10; Issue: 9 Linguagem: Inglês
10.1049/iet-rpg.2015.0405
ISSN1752-1424
AutoresAlireza Ashouri‐Zadeh, Mohammadreza Toulabi, Ali Mohammad Ranjbar,
Tópico(s)Wind Energy Research and Development
ResumoIET Renewable Power GenerationVolume 10, Issue 9 p. 1298-1308 Research ArticleFree Access Coordinated design of fuzzy-based speed controller and auxiliary controllers in a variable speed wind turbine to enhance frequency control Alireza Ashouri-Zadeh, Corresponding Author Alireza Ashouri-Zadeh ashorizadeh_a@ee.sharif.edu Center of Excellence in Power System Management and Control, Sharif University of Technology, Tehran, IranSearch for more papers by this authorMohammadreza Toulabi, Mohammadreza Toulabi Center of Excellence in Power System Management and Control, Sharif University of Technology, Tehran, IranSearch for more papers by this authorAli Mohammad Ranjbar, Ali Mohammad Ranjbar Center of Excellence in Power System Management and Control, Sharif University of Technology, Tehran, IranSearch for more papers by this author Alireza Ashouri-Zadeh, Corresponding Author Alireza Ashouri-Zadeh ashorizadeh_a@ee.sharif.edu Center of Excellence in Power System Management and Control, Sharif University of Technology, Tehran, IranSearch for more papers by this authorMohammadreza Toulabi, Mohammadreza Toulabi Center of Excellence in Power System Management and Control, Sharif University of Technology, Tehran, IranSearch for more papers by this authorAli Mohammad Ranjbar, Ali Mohammad Ranjbar Center of Excellence in Power System Management and Control, Sharif University of Technology, Tehran, IranSearch for more papers by this author First published: 14 July 2016 https://doi.org/10.1049/iet-rpg.2015.0405Citations: 19AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This paper proposes novel controllers for doubly fed induction generator (DFIG)-based wind turbines. These controllers not only optimize the transient behaviour of DFIGs, but also realize their participation in the power system frequency control task. The proposed controllers include one main speed controller as well as two auxiliary controllers. The main speed controller is a fuzzy-based controller which their parameters are optimized using the genetic algorithm (GA) to achieve the optimal transient response. It applies the rotational speed signal and causes the DFIG to return to the maximum power point (MPP) quickly after any turbulent in the wind speed. Moreover, two smart auxiliary controllers, i.e., frequency deviation and wind speed oscillations controllers are suggested. The frequency deviation controller enables the DFIG frequency support and the wind speed oscillations controller alleviates the impacts of wind speed fluctuations on the wind turbine output power both with utilizing the wind turbine kinetic energy. To investigate the efficiency of main controller, two case studies are considered. Moreover, some time domain simulations are performed on IEEE 39-bus system to evaluate the influences of the auxiliary controllers on the load frequency control task. Results confirm the effectiveness and superiority of the proposed controllers. Nomenclature Sb base power Vb base voltage fb base frequency ωb base angular speed ωs, ωr stator and rotor angular speeds s rotor slip H inertia constant Tm, Te turbine and electric torques vd s, vq s, vd r, vq r d–q components of stator and rotor voltages id s, iq s, id r, iq r d–q components of stator and rotor currents Rs, Rr stator and rotor resistances Xss, Xrr stator and rotor self-reactances Xm magnetising reactance 1 Introduction Nowadays, wind energy has become more important worldwide due to the environmental concerns. Until 2010, the world wind turbine installed capacity was ∼200 GW. By the end of 2014, this value has grown to 369.5 GW [1]. Therefore, evaluating the effects of wind turbines on the power system operation and control is necessary in different wind power penetration levels. Wind turbines can generally be decomposed into two main categories, i.e. fixed speed wind turbines and variable speed with turbines (VSWTs) [2]. The VSWTs has become the dominant type during the past few years due to their higher efficiencies. However, this type of wind turbine imposes many adverse impacts on the power system. On one hand, the generated power of VSWTs varies with the wind speed fluctuations and this results in the frequency deviations [3]. On the other hand, they cannot contribute in the power system frequency regulation due to application of convertors in their structure [4]. Thus, in recent years, there has been a growing interest in investigating the impacts of VSWTs on the power system frequency control. The effects of wind turbines on the power system frequency have been studied in [5, 6]. In [7, 8], it is found that the VSWTs can contribute in the power system frequency control through an auxiliary controller. Using VSWTs to deal with the grid frequency deviations is presented in [9-11]. In [12, 13], the stored kinetic energy of VSWTs has been utilised to emulate the inertial response. Bevrani and Daneshmand [14] propose a new fuzzy logic-based load frequency control (LFC) scheme which minimises the system frequency deviations as well as tie-line power changes in the power systems with high penetration of wind power. Model predictive LFCs in the power systems with VSWTs are suggested in [15, 16]. Toulabi et al. [17] introduce a new LFC structure with dynamic participation of VSWTs in the frequency regulation. More recently, application of modern intelligent controllers such as artificial neural networks and fuzzy logic controllers has been expanded. Fuzzy controllers are used in nearly all fields of science and technology due to their robustness, simplicity, and reliability. In contrast to the conventional controllers which are based on the linear mathematical models of the systems, the fuzzy control methodology tries to construct a controller based on the measurements, experiences, and knowledge of experts/operators [18]. The performance of fuzzy logic-based controllers are determined with their membership functions. The membership function parameters are usually optimised to insure acceptable transient response. On the basis of the complexity and non-linearity of the defined optimisation problem, the population-based stochastic optimisation techniques such as genetic algorithm (GA), imperialist competitive algorithm, and particle swarm optimisation can be utilised in the optimisation problem. To achieve an optimal transient response, this paper proposes a main fuzzy logic-based speed controller. The parameters of this controller are tuned using GA. Moreover, two auxiliary controllers are also suggested here. The wind speed oscillations controller alleviates the adverse impacts of VSWTs on the power system and the frequency deviation controller facilitates the participation of VSWTs in the frequency regulation. The proceeding sections of this paper are organised as follows. In Section 2, a complete wind energy conversion system (WECS) model with a new fuzzy-based controller is presented. The fuzzy logic and fuzzy controller are described in Section 3. Description of the optimisation algorithm is given in Section 4. In Section 5, the design of the smart auxiliary controllers is explained. Section 6 includes some time-based simulations with a detailed discussion and analysis. Finally, the conclusion is given in Section 7. 2 Wind energy conversion system Generally, the VSWTs are divided into two types, i.e. doubly fed induction generator (DFIG) type and fully rated converter (FRC) type. The DFIG-based wind turbines contain a wound rotor induction generator. However, the FRC-based wind turbines can apply either an induction generator or a permanent magnet synchronous generator. In this paper, a DFIG has been utilised in the WECS structure. The WECS consists of four important subsystems which are explained below. 2.1 Turbine model VSWTs are used in order to extract maximum power from the wind. The provided power by WECS, i.e. PWECS, is given in (1) (1) where CP, ρ, A, and V are the power coefficient, air density in kilograms per cubic metres, turbine swept area in square metres, and wind speed in metres/seconds, respectively. CP can be calculated as below [19] (2) where λ and θ are the tip speed ratio and pitch angle, respectively. c1 to c9 are constant coefficients which their values depend on the wind turbine type. The tip speed ratio is defined by (3) where ω is the rotational speed in radians/seconds and R is the rotor radius in metres. Fig. 1a shows the power coefficient Cp as a function of wind speed and rotational speed. It is assumed that pitch angle is zero. Besides, Fig. 1b illustrates the power coefficient dependency on the pitch angle and tip speed ratio. As it can be seen, the greater pitch angle results in the smaller power coefficient. Moreover, for one particular pitch angle, there exists an optimal tip speed ratio which maximises the power coefficient [20]. Fig. 1Open in figure viewerPowerPoint Power coefficient (a) Cp as a function of the wind speed V and of the rotational speed ω, (b) Cp as a function of the pitch angle θ and of the tip speed ratio λ 2.2 Blade pitch control Blade pitch angle control is a feature of nearly all large modern horizontal-axis wind turbines. The purpose of this controller is to adjust the blade pitch and keep the rotor speed within the operating limits as the wind speed changes. The pitch control scheme which is used in this paper is shown in Fig. 2a. As this figure shows, if the output power is greater than PMax, the blade pitch increases to reduce the output power. Fig. 2Open in figure viewerPowerPoint DFIG control scheme (a) Blade pitch controller, (b) Speed controller, (c) Terminal voltage controller 2.3 Doubly fed induction generator In this paper, DFIG is modelled using the state space representation in [21]. The rotor and stator currents have been utilised as the state variables in this model. The state space representation is defined in (4). It should be noted that the bar in the notation indicates per unit values (4) where (5) and (6) Moreover, , , , , , and . It is worth noting that α1, α2, βs, and βr depend on the generator slip. The rotor swing (7) is used to calculate the slip as shown below (7) where Tm is the turbine torque and Te is the electric torque. The electric torque is defined in (8) (8) 2.4 Terminal voltage and rotor speed controller The d and q components of the rotor voltage are used to control the DFIG terminal voltage and torque, respectively. On the basis of (7), the rotor speed can be regulated by controlling the torque. Therefore, the rotor speed can be adjusted by regulating the rotor voltage q component [22]. Fig. 2 shows the DFIG control scheme used in this paper. As it is shown, both terminal voltage and speed controllers use the fuzzy logic-based controllers. Fig. 2b illustrates the proposed speed controller which causes the WECS to extract the maximum power from the wind. This controller applies the maximum power curve calculated by (2) and (3). In fact, the rotor speed is first measured and the corresponding maximum reference power is then generated. In the next stage, the output power of the wind turbine is compared with the reference power and the fuzzy controller changes Vq r such that the optimal speed is achieved. The performance of the proposed controller is similar to the fixed-point algorithms [23]. Fig. 3 shows the complete WECS model. Fig. 3Open in figure viewerPowerPoint WECS model 3 Fuzzy logic Summing up, the fuzzy controller consists of three stages. The first stage is the fuzzification which is the process of converting a real scalar value into a fuzzy value. This is achieved with different types of membership functions (fuzzifiers). Gaussian and bell membership functions are more popular due to their smoothness and concise notation. The second stage is the fuzzy inference system (FIS). The FIS is a system that maps inputs to outputs using the fuzzy set theory. The final stage is the defuzzification which converts fuzzy values to non-fuzzy values using strategies such as centroid, mean max, and weighted average. These three stages are displayed in Fig. 4a. Fig. 4Open in figure viewerPowerPoint Fuzzy controller (a) Fuzzy controller scheme, (b) Input membership functions, (c) Output membership functions Heuristic methods are frequently used to design fuzzy control systems [24]. In this case, the mathematical model of the plant is required. Four steps should be followed to design a fuzzy logic controller for a dynamical system: Identifying the relevant input and output variables of the controller and their variation ranges with respect to the system dynamic behaviour. Defining the proper fuzzy set and membership function for each variable. Setting up the rule base. Determining the defuzzification method. In this paper, the input signals of the speed controller are ΔP and its derivative, and the input signals of the voltage controller are ΔV and its derivative. Using proper gains, the inputs and outputs are limited in reasonable ranges. The Mamdani-type FIS is applied, and as shown in Fig. 4, symmetric five-segments triangular membership functions are used as input (Fig. 4b) and output (Fig. 4c) variables. The membership functions are defined as HN, LN, Z, LP, and HP. In this survey, the triangular membership function is used due to its fast response. The rule base is presented in Table 1. The GA is used for tuning fuzzy systems membership function parameters. the mathematical equation of triangular membership function μx(xi) is defined as follows: (9) where x and c are the mean and spread of the fuzzy set X, respectively, and xi is a crisp variable. Table 1. Fuzzy rule base err HN LN Z LP HP δerr HN HN HN LN LN Z LN HN LN LN Z LP Z HN LN Z LP HP LP LN Z LP LP HP HP Z LP LP HP HP 4 Genetic algorithm GA is a method for solving constrained and unconstrained optimisation problems based on a natural selection process that mimics biological evolution. The algorithm repeatedly modifies a population of individual solutions (chromosomes). At each step, the GA randomly selects individuals from the current population and uses them as parents to produce children for the next generation. Over successive generations, the population evolves toward an optimal solution. The GA can be used to solve problems that are not well suited for standard optimisation algorithms including problems in which the objective function is discontinuous, non-differentiable, stochastic, or highly non-linear. Owing to the mutation operator, GA is more suitable algorithm to find the global optimum in comparison with the other heuristic methods [25]. As shown in Fig. 5a, application of GA for tuning the fuzzy membership function involves the following six main steps [26]: Initialisation: Each of N chromosomes in the population is set randomly. Table 2 shows the structure of each chromosome. As it is shown, each chromosome has five genes. (A1, A2), (A1d, A2d), and B are the membership function parameters associated with the input signal, input derivative signal, and output signal, respectively. It is obvious from Figs. 4b and c that (A1, A2, A1d, A2d) and B affect the input and output triangular membership functions, respectively. It should be noted that the membership functions of input signal and input derivative signal are the same. In this step, some modification maybe required. This is due to the fact that A2 must always be greater than A1 (Fig. 4a). Evaluation: The quality of each chromosome, qi, is evaluated according to WECS operation. It is calculated as follows: (10) where N is the number of the chromosomes in the population and (11) where Pmi(opt) and are the mechanical input power at the optimum operating point and the electrical output power of WECS with the i th fuzzy controller system, respectively. PLoss are the total electrical and rotational losses which are assumed to be constant. Fig. 5Open in figure viewerPowerPoint GA (a) GA flowchart, (b) Selection algorithm flowchart, (c) Mutation algorithm flowchart Table 2. Structure of each chromosome Gene 1 Gene 2 Gene 3 Gene 4 Gene 5 A1 A2 A1d A2d B The main goal of the proposed approach is an enhancement in the transient performance of WECS. In this paper, integral time-weighted squared error (ITSE) criteria are used. In ITSE, the squared errors are weighted with time to distinguish between early and late errors. Thus, using ITSE criteria can result in more enhancement in both settling time and overshoot. iii. Selection: Chromosomes are randomly picked to create the next generation based on their quality. In this paper, the fitness-proportionate selection method has been used. In this method, qi is utilised to allocate a probability of selection associated with each chromosome. The chromosome probability of being selected is as follows: (12) The cumulative probability distribution (CDF) based on the list of chromosomes and their selection probabilities are first generated. Then, a uniform random number between 0 and 1 is applied. The corresponding inverse CDF represents a chromosome. This procedure is repeated N/2 times. This operation is shown in Fig. 5b. iv. Cross-over: Some chromosomes (more than one) are combined and produce new chromosomes. Equation (13) is used for this purpose (13) where chi and chi+1 are the i th and i + 1 th selected chromosomes in the step of selection, respectively. Equation (13) represents that each gene of the child is the mean of the parent genes. The cross-over is done for all selected chromosomes. V. Mutation: All chromosomes are subjected to mutation with the probability 0.02. This probability should be equal to a low number due to the fact that the mutation introduces diversity and too high probability leads to the primitive random search. The mutation algorithm is shown in Fig. 5c. Correction maybe required similar to the first step. Vi. Termination checking: The algorithm repeats steps 2–5 until a given termination criterion is met such as a predefined number of generations. By running several simulations and observing the results, a population size of 50 is used in this particular case. Moreover, with this population size, there is no further improvement in the quality function after generation 100. Therefore, the population size, N, and the maximum number of generations are set to be 50 and 100, respectively. 5 Smart auxiliary controllers Wind turbine output power oscillations as well as power system frequency deviations can be reduced by using the stored kinetics energy of the rotor. Two controllers are proposed here to achieve these goals. The first controller uses the power system frequency as a control signal and improves the system frequency behaviour. The second one alleviates the impact of wind speed oscillations on the WECS output power. The input signal of the second controller is the WECS output power. The effects of both auxiliary controllers are explained in detail in the following sections. 5.1 Frequency deviation controller Owing to the massive inertia of the rotor, the amount of stored kinetic energy in the rotor is considerable. This energy can be utilised in the emergency conditions. For example, when a power plant is tripped, the power system frequency starts to drop. Owing to power system lags, the governor control systems cannot respond to the disturbance quickly. In unfavourable conditions, this frequency deviation may cause of tripping the frequency relays. VSWTs can be used to reduce these frequency deviations. In other words, the system frequency behaviour can be improved by transferring the rotor kinetic energy to the power system. Similarly, during a large load trip, the frequency excursions can be avoided by increasing the wind turbine rotational speed. Some important concerns must be considered in designing the frequency support controller. As shown in Fig. 1, the efficiency of the WECS decreases as the rotor speed deviates from the maximum power point (MPP). Thus, there exists a critical speed, ωc, in which no additional power is provided by further decrement in the rotational speed. In other words, below the critical speed, though more speed reduction causes more transfer of power, the WECS total provided power decreases. This is due to the power coefficient decrement. In this situation, not only WECS can help the frequency regulation task, but also its energy conversion efficiency is highly decreased. The critical speed corresponding to each operating point must be taken into account if WECS is equipped with the frequency support controller. Total energy provided by WECS as a result of rotational speed variations is as follows: (14) where J is turbine–generator moment of inertia and ωnew and ωold are the rotational speeds corresponding to the new and old operating points, respectively. Here, ωnew can be calculated as follows: (15) where is the maximum allowable rate of change of wind turbine speed. The value of ωc can be calculated using the fact that in this speed the additional power provided by the kinetic energy decrement is equal to the decrease in wind power extraction due to the efficiency reduction, i.e. dEWECS = 0. In this situation, ωnew = ωc. It should be noted that due to the control system delays and uncertainties, dt is considered to be a couple of seconds. High dt results in the conservative critical speed, and thus the WECS can deliver less kinetic energy to the power system. Fig. 6a shows the critical and optimum speed curves. Fig. 6Open in figure viewerPowerPoint Smart auxiliary controllers (a) Optimum and critical speed curves, (b) Frequency deviation controller, (c) Wind speed oscillations controller, (d) Co-operation between the main controller and two auxiliary controllers It is worth noting that this concern does not exist in the power system frequency increment. This is due to the fact that both rotor speed increment and energy conversion efficiency decrement result in the power system frequency reduction. Thus, the upper limit of rotational speed is only determined by the protection schemes, i.e. ωu. Another concern in the frequency support controller is about the rate of return to the optimal operating point. This time interval is known as the recovery period. It should be noted that in both directions this rate should be as low as possible. If this rate is not appropriately selected, returning the energy that is either stored in or extracted from the rotor will lead to the second subsequent frequency deviation. This is not obviously preferable and careful attention should be paid in the selection of this parameter. The proposed frequency deviation controller is shown in Fig. 6b. It consists of three main components as follows: A dead band block which filters small deviations (<0.002 pu or 0.1 Hz). An acceleration limiter block which restricts the rate of wind turbine speed variations. A speed limiter block which maintains the wind turbine rotational speed in the proper range, i.e. (ωc, ωu). This range depends on the operating point of wind turbine. For example, the critical speed corresponding to the wind speed 10 m/s is equal to 0.7 pu. This controller reacts to the frequency excursions. The power system frequency fs is monitored continuously. If the frequency deviates more than 0.1 Hz, the dead band block is activated. The produced control signal is then fed to the acceleration limiter which confines the rate of change of rotational speed. The next block prevents the rotational speed violation during the frequency support period. 5.2 Wind speed oscillations controller Turbulence is absolutely key in the performance of WECS. The loads affecting the WECS parts can be influenced by the control system. For example, an auxiliary controller can be designed to alleviate the impact of the wind speed oscillations on the WECS output power. This can be accomplished by using the stored kinetic energy of the rotor. In other words, the required power in order to smooth the WECS output power can be stored in or extracted from the rotor kinetic energy. The structure of this controller is depicted in Fig. 6c. This controller is comprised of four components. A high-pass filter is utilised to remove the steady-state component of output power. A proportional-integral (PI) controller is applied to compensate the tracking error. Similar to the frequency deviation controller, acceleration and speed limiters are considered here to manage both wind turbine rotational speed and efficiency. The operation of this controller can be explained as follows. The output power passes through a high-pass filter and its steady-state and low-frequency components are eliminated. The generated signal is then fed into a PI controller. The PI controller causes the rotor to change its speed. To restrict the rate of wind turbine speed variations, this signal is passed through an acceleration limiter next. Similar to the frequency deviation controller, a speed limiter block is finally utilised to supervise the rotational speed and keep the rotational speed in the pre-calculated range. It should be noted that the cost of this smoother output power is the additional stresses on the different parts of WECS structure. Therefore, from a practical point of view, a compromise should be considered between the power system frequency variations and the mechanical stresses. Thus, maximum acceptable stress value must be taken into account in VSWTs equipped with the proposed controller. It is worth noting that the bandwidth of filter significantly affects the mechanical stresses. The higher cut-off frequency results in the lower mechanical stress. However, the activity of wind speed oscillation controller is reduced, and thus WECS output power variations increase. The co-operation between the main controller and two auxiliary controllers is depicted in Fig. 6d. As shown, the main controller and wind speed oscillations controller operate jointly in the normal conditions. The main controller tracks the MPP trajectory and the wind speed oscillations controller restricts the impact of the wind speed fluctuations on the output power. However, the frequency deviation controller causes the VSWT to provide the frequency support, and thus enhances the power system frequency behaviour. When a large disturbance occurs in the power system, the frequency deviation controller detects the frequency deviations and sends a signal which causes the main controller as well as the wind speed oscillations controller to be disabled. As the power system frequency is restored, this controller becomes disabled and the main controller and the wind speed oscillations controller activate again. It is worth noting that the operating point of VSWT as well as its specifications affect the efficiency of the two auxiliary controllers. It is intuitively obvious that the wind turbines can participate more effectively in the regulation task in the higher wind speed. Similar behaviour can be imagined in the wind turbines with higher moment of inertia. This is due to their higher stored kinetic energy. Thus, wind turbines can release more power in emergency conditions. 6 Simulation and discussion This section investigates the performance of WECS main speed and auxiliary controllers. It should be noted that in order to simplify the analysis, the magnitudes of the bus-bar voltages are assumed to be constant. This is due to the fact that the flow of active power and reactive power in the transmission network are almost independent of each other and they are studied separately for large class of problems [27-29]. 6.1 Main speed controller performance verification As the first case study, it is assumed that the wind speed increases from 6 to 15 m/s with a constant acceleration (Fig. 7a). Fig. 7b illustrates the output power of WECS versus its rotor angular speed for different wind speeds. As it is shown in Fig. 7b, the fuzzy-based controller successfully follows the MPP trajectory. The WECS output power (Pout) and corresponding control signal (Vq r) for both proposed fuzzy controller and the conventional one are shown in Figs. 7c and d, respectively. In the conventional control schemes, a PI controller is used as the speed controller. The PI controller parameters, i.e. KP and KI are set to be 0.3 and 0.5, respectively [30]. It can be seen that the fuzzy controller tracks the MPP faster, and thus the performance of the proposed controller is superior than the conventional one. This enhancement in the performance is magnified as the rate of change of wind speed increases. Therefore, it can be concluded that the fuzzy-based controller is more appropriate for the WECS. The specifications of induction generator are given in Table 4 in the Appendix. Table 4. Induction generator specifications [21] Symbol Dimension Sb 2 MVA Vb 690 V fb 50 Hz ωb 2πfb H 3.5 s Rs 0.00488 pu Rr 0.00549 pu Rd 0.2696 pu Xl s 0.09241 pu Xl r 0.09955 pu Xm 3.95279 pu Fig. 7Open in figure viewerPo
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