Load frequency control in deregulated power system with wind integrated system using fuzzy controller

Abstract

This paper presents the analysis of load frequency control (LFC) of a deregulated two-area hydro-thermal power system using fuzzy logic controller, with doubly fed induction generators (DFIGs) integrated into both the control areas. The deregulation of power sector has led to the formation of new companies for generation, transmission and distribution of power. The conventional two-area power system is modified to study the effects of the bilateral contracts of companies on the system dynamics. Deregulation creates highly competitive and distributed control environment, and the LFC becomes even more challenging when wind generators are also integrated into the system. The overall inertia of the system reduces, as the wind unit does not provide inertia and isolates from the grid during disturbances. The DFIGs integrated provide inertial support to the system through modified inertial control scheme, and arrests the initial fall in frequency after disturbance. The inertial control responds to frequency deviations, which takes out the kinetic energy of the wind turbine for improving the frequency response of the system. To enhance the participation of the doubly fed induction generator (DFIG) in the frequency control, optimal values of the speed control parameters of the DFIG-based wind turbine have been obtained using integral square error (ISE) technique. The dynamics of the system have been obtained for a small load perturbation, and for contract violation using fuzzy controller.

Keywords

frequency regulation / fuzzy controller / de-regulated power system / doubly fed induction generator (DFIG) / bilateral contract

Introduction

Load frequency control (LFC) is one of the most important ancillary services to be maintained for smooth and secure operation of any power system. After deregulation, new organizations viz., generation companies (GENCOs), transmission companies (TRANSCOs), distribution companies (DISCOs), and independent system operators (ISO) have emerged, which are responsible for maintaining the real-time generation-load balance so as to operate the system stably under highly competitive and distributed control environment [1]. The practical power system comprises of a generation mix of thermal, hydro, wind, solar etc. Nowadays, the focus has shifted towards inclusion of cleaner sources of energy, of which wind power has the potential to displace the conventional generation to a certain extent. However, with large penetration of the wind power into the power system, the grid frequency will be more prone to disturbances, as the wind units do not participate in the frequency regulation services. Thus, as the wind penetration level increases, it is essential to use the DFIG-based wind turbine in the system frequency regulation along with the conventional generating units. Such problems become severe in isolated areas with large wind units. In deregulated power system, the load frequency problem becomes even more challenging when wind units are also integrated. There must be perfect coordination among the new utilities to maintain the real time power balance, regulate line flows and facilitate their bilateral contracts. Any inertial support from the wind units can reduce the adverse effects of load perturbation and contingency on the system [2,3].

The control capabilities of the variable speed wind turbine have been improved with the advancements in technology. The DFIG-based wind turbine can now be used efficiently for frequency control services. The wind units contribute towards system frequency regulation through inertial control, pitch control, and speed control [4]. The power (pitch+ speed) control scheme is applied on the DFIG to use it in the frequency regulation services. The DFIG operates according to a deloaded optimum power extraction curve, such that the active power injected increases or decreases according to the variations in the system frequency [5]. The dynamic participation of the DFIG in the frequency control is analyzed through modified inertial control which responds proportionally to the frequency deviation and uses the kinetic energy of the turbine blades to improve the frequency [6-8].

The present restructured power sector comprises of many power producing units of different types. The inertial and the dynamic characteristics of these new power generating sources differ from those of the conventional generating units. Thus, in the restructured power system, LFC becomes a very important ancillary service to be maintained for real time power balance, to minimize tie-line deviations, to facilitate bilateral contracts of the GENCOs and DISCOs in different areas, and to ensure the steady and secure operation of the power system. The automatic generation control (AGC) or LFC has been presented for two-area deregulated hybrid power system in Ref. [9]. The studies provide detailed review over these issues, and also explain the simulation of the LFC problem under deregulated environment. The role of the power electronics controllers in the form of thyristor controlled phase shifter (TCPS) and SMES to stabilize the system frequency, and to reduce the tie-line power oscillations have also been discussed for deregulated power system in Refs. [10,11].

Many types of controllers have been tested in the conventional two-area LFC problem to regain the normal state of the operation of the power system after any disturbance. These controllers for AGC are the proportional and integral (PI), the proportional-integral-derivative (PID), and the optimal controller. In addition to these controllers, the fuzzy logic controller is also used quite often. The design steps for fuzzy logic controller as used for the AGC problem have been elaborated in Ref. [12]. It has been applied in a number of control applications in the power system. The fuzzy controller is used to provide ancillary services in competitive market structure through price based mechanisms [13]. A fuzzy based automatic generation controller with a flexible alternating current transmission (FACTS) device is also proposed for frequency control in an open access market scenario [10]. The controller based on frequency linked pricing is also effective in frequency regulation and stabilizes the response much faster [14]. The fuzzy logic controller is an efficient controller, but in very few cases only, it has been used to evaluate the LFC in a hybrid system under deregulated environment.

The objective of the paper is to analyze the LFC problem in a two-area hydro-thermal interconnected deregulated system with the DFIGs-based wind turbine integrated into both areas. The DFIGs operate according to the deloaded optimum power extraction curve and incorporate the frequency deviation signals to inject the electrical powers. In this way, the active power injected by the DFIG is kept on, while the frequency deviation stands, therefore, contributing to frequency control. A wind penetration level of 10% has been applied, and frequency responses for a load perturbation of 2% have been obtained with optimized parameters of the DFIG controller. The bilateral contracts between Gencos and Discos have been considered using distribution participation matrix (DPM). In addition to small load perturbation in one area, a case of contract violation has also been simulated, and generator (thermal and hydro) responses have been presented. Simulation experiments have been conducted using SIMULINK in MATLAB and system responses have been obtained and analyzed through fuzzy controller.

Deregulated power system

The electrical power system is quite complex and dynamic in nature. This sector was largely in hands of vertical integrated utilities (VIUs), which own generation, transmission and distribution system that supply power to consumers at regulated rates. After restructuring, new organizations viz., generation companies (GENCOs), transmission companies (TRANSCOs), distribution companies (DISCOs), and independent system operators (ISO) have emerged. The restructuring also encourages independent power producers (IPPs) by making generation license free. Under deregulation the first step was to separate the generation of power from transmission and distribution, thus putting the generation on the same footings as the IPPs. The Gencos and IPPs can compete in the competitive market to sell their power. The Gencos and Discos can also have bilateral contract among each other with in area and with interconnected Gencos and Discos of the system.

Disco participation matrix (DPM) is used to express the contracts between various Gencos and Discos in matrix form. This helps in easy visualization of these contracts [2]. Equation (1) represents the DPM for the two-area system, each having two Gencos and two Discos.

(1)\left(\begin{array}{llll}cp{f}_{11}\hfill & cp{f}_{12}\hfill & cp{f}_{13}\hfill & cp{f}_{14}\hfill \\ cp{f}_{21}\hfill & cp{f}_{22}\hfill & cp{f}_{23}\hfill & cp{f}_{24}\hfill \\ cp{f}_{31}\hfill & cp{f}_{32}\hfill & cp{f}_{33}\hfill & cp{f}_{34}\hfill \\ cp{f}_{41}\hfill & cp{f}_{42}\hfill & cp{f}_{43}\hfill & cp{f}_{44}\hfill \end{array}\right).

Any entry cp{f}_{\mathrm{12}} in Eq. (1) corresponds to the fraction of the total load power contracted by Disco ₂ from Genco₁. The number of rows in DPM matrix corresponds to Gencos and number of columns equal to the number of Discos. cpf refers to contract participation factor and in general:

(2){\displaystyle \sum _{i}cp{f}_{ij}=\mathrm{1.0}}.

Figure 1 shows the block diagram representation of two-area hydro-thermal deregulated system for LFC with DFIGs integrated into both of the areas. Under steady state conditions the power flows on the tie-line is given by

(3)\mathrm{\Delta }{P}_{tie\; 12}^{\mathrm{sch}}=cp{f}_{\mathrm{12}}\mathrm{\Delta }{P}_{L2}-cp{f}_{\mathrm{21}}\mathrm{\Delta }{P}_{L\mathrm{1}}.

The actual power flow through tie-line is given as

(4)\mathrm{\Delta }{P}_{tie\; 12}^{\mathrm{act}}={\displaystyle \frac{\mathrm{2}\pi T_{\mathrm{2}}}{s}}(\mathrm{\Delta }{f}_{\mathrm{1}}-\mathrm{\Delta }{f}_{\mathrm{2}}).

The tie line power error at any instant can be calculated as

(5)\mathrm{\Delta }{P}_{tie\; 12}^{\mathrm{err}}=\mathrm{\Delta }{P}_{tie\; 12}^{\mathrm{act}}-\mathrm{\Delta }{P}_{tie\; 12}^{\mathrm{sch}}.

When the final steady state is attained, the \mathrm{\Delta }{P}_{\mathrm{tie}12}^{\mathrm{err}} becomes zero. The error signal is used to generate respective area control error (ACE) as in the case of the conventional system.

(6){\mathrm{ACE}}_{\mathrm{1}}=B_{\mathrm{1}}\mathrm{\Delta }{f}_{\mathrm{1}}-\mathrm{\Delta }{P}_{\mathrm{tie}12}^{\mathrm{err}},

(7){\mathrm{ACE}}_{\mathrm{2}}=B_{\mathrm{2}}\mathrm{\Delta }{f}_{\mathrm{2}}-a_{\mathrm{12}}\mathrm{\Delta }{P}_{\mathrm{tie}12}^{\mathrm{err}}.

For a two-area system, the contracted power supplied by the ith Genco is given by

(8)\mathrm{\Delta }{P}_i={\displaystyle \sum _{j=\mathrm{1}}^{N_{\mathrm{Disco}=\mathrm{2}}}cp{f}_{ij}}\mathrm{\Delta }{P}_{Li}-ap{f}_i{\displaystyle \sum \mathrm{\Delta }{P}_{\mathrm{UC}i}},

where \mathrm{\Delta }{P}_i is the desired total power generation, \mathrm{\Delta }{P}_{\mathrm{UC}i} is the un-contracted demands, and \mathrm{\Delta }{P}_{Li} is the load change in the system.

DFIG modeling

Traditionally, the wind units do not participate in load frequency control. But, now with advanced control, the kinetic energy stored in the mechanical system of the wind turbines can be extracted with variable speed generators. The DFIG-based wind turbines can produce power with variable mechanical speed and extract kinetic energy to support the primary frequency regulation. Although, the steady-state active power delivered to the grid by a DFIG depends on the wind speed, the power can be dynamically controlled to a certain extent by utilizing the stored mechanical energy. In this paper, the dynamic model depicted in Fig. 2 and discussed in Refs. [6] and [14] has been used for the study of frequency regulation which has the essence of emulation control [15].

An additional control signal is created to adapt the power set points \mathrm{\Delta }{P}_f^{\ast }as a function of deviation and rate of change of frequency in emulation control of the DFIG. The controllers try to keep the turbine at its optimal speed in order to produce the maximum power. A power set point \mathrm{\Delta }{P}_{\omega }^{\ast } based on measured speed and measured electrical power is provided by the controller. The ΔP_NC has two components; \mathrm{\Delta }{P}_f^{\ast } the additional reference point based on the frequency change Eq. (12), and \mathrm{\Delta }{P}_{\omega }^{*} which is based on optimum turbine speed as a function of wind speed and given as

(9)\mathrm{\Delta }{P}_{\omega }^{\ast }=-K_{\mathrm{wp}}({\omega }^{*}-\omega )+K_{\mathrm{wi}}{\displaystyle \int ({\omega }^{*}-\omega )dt},

(10)\mathrm{\Delta }{P}_{\mathrm{NC}}=\mathrm{\Delta }{P}_f^{\ast }+\mathrm{\Delta }{P}_{\omega }^{\ast },

where K_{\mathrm{wp}} and K_{\mathrm{wi}} are constants of PI controller, which provides fast speed recovery and transient speed variation, which helps non conventional generators to supply the required active power to reduce deviations, respectively. The contribution of the DFIG towards system inertia is given by

(11)$$\begin{gathered} {\displaystyle \frac{\mathrm{2}H}{f}}{\displaystyle \frac{d\mathrm{\Delta }f}{dt}}=\mathrm{\Delta }{{\displaystyle P}}_f-D{{\displaystyle \mathrm{\Delta }}}_f \\ =\mathrm{\Delta }{{\displaystyle P}}_g+\mathrm{\Delta }{P}_{\mathrm{NC}}-\mathrm{\Delta }{{\displaystyle P}}_{\mathrm{12}}-\mathrm{\Delta }PD-D\mathrm{\Delta }f. \end{gathered}$$

The swing Eq. (11) gives an idea about the contribution of the DFIG towards system inertia. It has an additional reference power setting which is built based on the change in frequency using a washout filter with time constant T_w, that relies on a conventional primary regulation performance in a transient.

(12)\mathrm{\Delta }{R}_f^{*}={\displaystyle \frac{\mathrm{1}}{R}}(\mathrm{\Delta }{X}_{\mathrm{2}}),

where, R is the droop constant as used conventionally and \mathrm{\Delta }{X}_{\mathrm{2}} is the frequency change measured where the wind turbine is connected to the network.

The DFIG responds to frequency deviations during transients by using their stored kinetic energy, and cannot act in a permanent system frequency deviation. For this reason, the frequency term (\mathrm{\Delta }{X}_{\mathrm{2}}) used in Eq. (12) is the result of a washout filter, as illustrated in Fig. 2. In this approach, the DFIG inertia contributes to that of the rest of the system. The controller proposed makes use of the frequency deviations instead of the derivative of frequency as in the control law to provide fast active power injection control. The active power injected by the wind turbine is ΔP_NC. The power injected is compared with ΔP_NCref so as to obtain the maximum power output, which is obtained by maintaining reference rotor speed where maximum power is obtained.

Design of fuzzy logic controller

The design of the fuzzy logic controller involves three basic steps, namely, input parameter allocation, framing of rules associated with inputs, and defuzzifying of the output in to a real value. The ACE is the main parameter in the regulation component of the LFC. The ACE and the rate of change of the ACE (ΔACE) are considered as the inputs to the fuzzy logic controller and Δu is the output. The fuzzy controller has the essence of the conventional PI controller, which is given as

(13)u=K_{p}e+K_i{\displaystyle \int edt},

where K_p and K_i are the proportional and integral gains respectively and e is the error signal. Taking the derivative of Eq. (13) w.r.t. time, u can be expressed as

(14)\dot{u}=K_p\dot{e}+K_{i}e.

Both the ACE and ΔACE are divided in to seven control areas based on magnitudes and sign. The areas are NL, NM, NS, Z, PS, PM and PL which stand for negative large, negative medium, negative small, zero, positive small, positive medium, and positive large respectively. The mathematical formula applied is the “Min/Max” rule for ‘and’ and ‘or’ respectively. This reduces calculation complexity and time. Symmetrical triangular membership function is considered for all the variables.

Table 1 lists the rules that are framed through the behavior of the system response after a small load perturbation. Each fuzzy variable is quantized into seven fuzzy sets; there are 49 rules that are required to generate a fuzzy output. The rules for the controller are decided based on the value of the ACE, e and change in the ACE Δe. If the value of e is positive and Δe is negative, the system will reduce the error itself, which means the output in that case should be zero.

The most important step in the controller design is defuzzification. The output of the inference system is a fuzzy value. However, the physical process cannot deal with the fuzzy value. Therefore, it is essential to covert this fuzzy value in to a real value. The center of gravity method is used for defuzzification due to its simplicity. The detailed procedure on fuzzy controller formation is described in Refs. [9] and [10].

System investigated

The objective of the LFC is to restore the frequency to its nominal value as soon as possible and to regulate the tie-line power flow fluctuations between neighboring control areas. The simulations have been conducted on the two-area hybrid interconnected system under an open access market as demonstrated in Fig. 1. Area-1 consists of two thermal generating units and area-2 contains two hydro units. The DFIGs are connected to both the areas and they contribute to frequency regulations by providing inertial support to the system. The fuzzy logic controller is used to generate proportional accurate signal for any incoming ACE as a result of any load change. Figure 3 displays the block named as fuzzy controller in Fig. 1. A load perturbation of 2 percent in area-1 at the time of t = 1 s is applied. To enhance the participation of the DFIG in frequency control in response to system disturbances, optimal values of the speed control parameters (K_wp and K_wi) of the DFIG-based wind turbine have been obtained. The ISE technique is used for obtaining the optimum values of K_wp and K_wi to minimize the objective function defined as “Performance Index J”:

(15)J={\displaystyle \sum [\mathrm{\Delta }{f}_{\mathrm{1}}^{\mathrm{2}}+\mathrm{\Delta }{f}_{\mathrm{2}}^{\mathrm{2}}+\mathrm{\Delta }{P}_{\mathrm{tie}}^2]}\mathrm{\Delta }T,

where ΔT is a given time interval for taking samples, Δf_i is the discrete value of incremental change in frequency for the ith area and ΔP_tie is the value of incremental change in tie-line power. The sample values are obtained from their respective plots derived through transfer function analysis. The optimal values of the DFIG speed controller parameters are obtained by searching for the minimum value of J.

Simulation results and discussion

The simulations have been conducted in a two-area hydro thermal system in an open access environment to investigate the role of the DFIG in system frequency control. The model constants used for the DFIG-based wind turbine are given in Ref. [6]. The simulations have been conducted with the fuzzy logic toolbox in Simulink in MATLAB 7.0 using Mamdani type fuzzy inference system (FIS). The interaction between the DFIG-based wind turbine and traditional plants has been investigated for a load perturbation of 2% in area-1 for wind penetration of 10 percent. In an open access market scenario, the Gencos and the Discos have bilateral contract agreements. The Discos contract with the Gencos as per the DPM discussed in Section 2. In this case the DPM has been taken as follow:

(16)\mathrm{DPM}=\left(\begin{array}{cccc}0.5& 0.5& 0& 0\\ 0.5& 0.5& 0& 0\\ 0& 0& 0.5& 0.5\\ 0& 0& 0.5& 0.5\end{array}\right).

Frequency responses of the two-area deregulated power system are presented in Fig. 4 for a load perturbation of 2% in area-1 with the penetration of the DFIGs in both areas. The results indicated that the frequency response of both areas have smaller lower excursions when the DFIG is participating in the frequency control. However, without the DFIG, the overshoots (OS) and the undershoots (US) are higher and the settling time also is larger. The undershoot in area-1, where the load perturbation takes place is higher as compared to that in area-2. Table 2 provides the OS, US and performance index, and J values of the two-area interconnected system with and without the DFIG integrated into it.

Figure 5 shows the response of the conventional generators in area-1 and area-2. The hydro units react fast as compared to the thermal units. The response of the hydro units decreases initially following a load change, due to the delay in valve opening mechanism. The DFIGs act more swiftly as compared to hydro units and it can be seen that peak excursions are higher in the system without the DFIG and much lower when the DFIG provides frequency support (Fig. 5(b)). The DFIG provides system frequency support in initial intervals of disturbance, which delays the response of the thermal generators. As the inertia of the thermal units is large, they change their generations afterward. This can be seen from the results in Fig. 5(a), where generations of the thermal units are lower when the DFIG is providing inertial support. This confirms the participation of the DFIG in the frequency control.

Figure 6(a) presents the generation response of the DFIG in area-1 and 2 for a load change of 2% in area-1. It can be observed that the DFIG in area-1 increases its generation more as compared to the DFIG in area-2 where load change has taken place. The DFIG provides system frequency support in initial intervals of disturbance only, and final generation is taken over by the conventional units. Figure 6(b) shows the speed variations of the DFIGs of both areas. As the DFIG in area-1 provides higher active power support, the decrease in its kinetic energy is slightly high. The DFIG releases the kinetic energy stored in its rotating masses to provide quick frequency support by decreasing its speed. The presence of the DFIG in the system helps to reduce the tie-line oscillations between the two control areas. This can be seen in Fig. 7, where the tie-line oscillations die down faster when the DFIG is providing support following a load change in area-1.

Area control errors (ACEs) for area-1 and area-2 following a step load perturbation in area-1 are presented in Figs. 8(a) and 8(b) respectively. It is observed that there are much lesser errors when the DFIG is participating in the frequency control. The OS is smaller, but the settling time rises slightly due to deviation of wind turbine from its optimal speed.

An additional case of bilateral contract violation is also simulated by introducing an additional load change of 1 percent at the time of t = 4 s. The generators in both areas respond to these violations depending upon performance characteristics. It can be observed from the responses that the conventional generators are burdened less when the DFIGs are supplying frequency support. The peak OS and the settling times in the case of the hydro units (Figs. 9(a) and 9(b)) and thermal generators (Figs. 9(c) and 9(d)) are better with the DFIG support even after contract violation. The frequency responses for both areas are obtained for the contract violation at the time of t = 10 s. Improved response is observed with the DFIGs providing frequency support during contract violations in area-1 (Fig. 10(a)), and in area-2 (Fig. 10(b)).

Figure 11 compares the performance index value of the LFC when the DFIG is connected to the power system, and when there are no DFIGs available. It can be seen that the inclusion of the DFIG into the system for providing the inertial support during disturbance stabilizes the frequency deviations efficiently. This is confirmed by the performance index value which is much lower when the DFIGs are providing frequency support. The responses of the frequency, tie-line power flow and power generations generators confirm the participation of the DFIG in the LFC.

Conclusions

This paper investigates the role of DFIG-based wind turbine towards LFC in a two-area hydro-thermal power system in an open access environment. The modified inertial control scheme is used for the DFIG which provides inertial support to the system during transients and arrests the fall in frequency. The parameters of the DFIG controller have been optimized to enhance its participation in the frequency regulation. The DFIG responds a bit faster than the hydro and the thermal units which sometimes delay the reaction time of the conventional generators after disturbance. The conventional generators increase their generations based on their response characteristics. The DFIG reacts during initial instants and provides inertial support by decreasing its speed momentarily. The final generation, however, is taken over by the conventional units only. The peak frequency variations of the control areas are reduced and the settling time is also improved when the DFIG-based wind turbines participate in the frequency regulation along with the conventional generators. The DFIGs are also very effective in settling frequency excursions during bilateral contract violation by companies. In the complex restructured power system, where it is difficult to obtain an exact mathematical model for the system, the fuzzy controller can be used to control the process even with small knowledge of the system. The frequency responses of the two-area system, the generation response of the conventional generators and the tie line fluctuations confirm the participation of the DFIG in load frequency regulation.

Appendix

System data

T_p1,T_p2 = 20 s; K_p1, K_p2 = 120 Hz/pu MW; P_r1, P_r2 = 1200 MW; T_t = 0.3 s; T_g=0.08 s; T_w=1 s, T_r = 5 s, T₁ = 41.6 s, T₂ = 0.513 s; R₁, R₂ = 3 Hz/pu MW; T₁₂ = 0.0866 s; B₁, B₂ = 0.4249 Hz/pu MW; T_ps =0.1 s.

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