A New Meta-heuristic Technique Based on Robust Power System Stabilizer with Wind Power Penetrations

In this paper a robust Power System Stabilizer (PSS) is proposed based on inverse additive perturbation in a power system with wind farms. The proposed controller designed by new Improve Bacteria Foraging Algorithm (IBFA) to achieve robustness of this strategy where the optimization process is formulated based on an enhancement of system robust stability margin. The designed optimal PSS is based on Fuzzy Logic Controller (FLC). The effectiveness of the proposed technique is tested over ten macine 39 buses New England power system. Obtained results demonstrate the superiority of proposed technique over conventional PSS.


Introduction
Some of the earliest power system stability problems included spontaneous power system oscillations at low frequencies. These Low Frequency Oscillations (LFOs) are related to the small signal stability of a power system and are detrimental to the goals of maximum power transfer and power system security. Once the adjustment of using damper windings on the generator rotors and turbines to control these oscillations was found to be satisfactory, the stability problem was thereby disregarded for some time [1]. But, as power systems began to be operated closer to their consistency limits, the weakness of a synchronizing torque among the generators was distinguished as a major cause of system instability [2]. Automatic Voltage Regulators (AVRs) helped to improve the steady-state stability of the power systems, but transient stability started a concern for the power system operators. With the development of large, interconnected power systems, another concern was the transfer of large amounts of power across extremely long transmission lines. The addition of a supplementary controller into the control loop, such as the introduction of Power System Stabilizers (PSSs) to the AVRs on the generators, supplies the means to reduce the inhibiting effects of low frequency oscillations [3]. Most of the time the PSSs and AVRs are locally controlled; which means that, the controller is designed to act on measurements such as bus voltage, generator shaft speed, or rotor angle of the associated machine's controls as presented in Figure 1. In the recent years, renewable electrical energy such as wind power generations, have achieved a significant level of penetration in the power systems due to infinite availability and low impact to environment. However, wind power generation is staggering in nature. Matching the supply and the demand is often a problem. The power output fluctuations from wind power generations cause a problem of low frequency oscillation, deteriorate the system stability and make the power system operation more difficult. The power frequency and the tie-line power deviations persist for a long term. In this status, the governor system may no longer be capable to absorb the frequency fluctuations due to its slow response [4].
Actually, several plants prefer to employ conventional lead-lag structure PSSs, due to the ease of online tuning and reliability [5]. However, the revenue of these controllers doesn't have good behavior in different load conditions. For this reason, a lot of intelligent algorithms have been introduced to optimal tuning of the PSSs parameters such as Ant Colony (AC) [6], Genetic Algorithm (GA) [7], Particle Swarm Optimization [8], Artificial Bee Colony [9] and etc.
The proposed algorithms are strong in optimization procedure but, they have some advantages and disadvantages. For instance, GA is a powerful optimization technique, independent on the complexity of problems where no prior knowledge is available. Also GA is very sufficient in finding global or near global optimal solution of the problem, it requires a very long run time that may be several minutes or even several hours depending on the size of the system under study [10][11].
To tackle of the mentioned backwards, in this paper a new Improve Bacteria Foraging Algorithm (IBFA) is presented based on fuzzy controller. The inverse additive perturbation is applied to represent unstructured system uncertainties. For tuning the optimal rule base of fuzzy controller, the concept of enhancement of system robust stability margin is formulated as the optimization problem. Also, the proposed IBFA is considered as a solution technique to problem. The obtained simulation results over ten machine-39 bus New England power system demonstrate the robustness of the proposed strategy.
The remaining parts of the paper are organized as follows. In the second section, the formulation of power system modeling is presented. The proposed controller structure is introduced in section three. The proposed IBFA and its application for the solution of the low oscillation problem with wind are presented in section four. Obtained numerical results from New England power system are presented in section five and compared with the other recently published methods. Section six concludes the paper.

Problem Statement
In this paper a multi-machine power system is considered as a test case where the third order model is presented in [12]. Actually, the proposed power system consists of ten generators and the electrical and mechanical part of ith generator is modeled as follow: Where, ∆Pei is the state deviation in generator electromagnetic power for the ith subsystem ∆ωi is the state deviation in rotor angular velocity for the ith subsystem, ∆Vti is the state deviation in the terminal voltage of the generator for the ith subsystem

A. Mechanical Oscillation Frequency
The linearized rotor motion equation for synchronous generator can be described as: Where, ∆Tm is the mechanical input torque ∆Te is the electromagnetic torque and ∆Te =K1∆δ+ K2∆δ, By neglecting the K2∆E'q the formulation can be described as; ∆Te =K1∆δ+ ∆TD D is the natural damping constant Accordingly the above equation after Laplace transformer and ∆w=s∆δ/w0 can be described as; Which can be described as; Accordingly, we can achieve the following equation from above equations; Where, ξn is the damping factor wn is the undamped mechanical oscillation frequency Usually the value of D is small, so the system damping is low. In order to enhance the system damping for suppressing the low frequency oscillation, the positive damping term is added by PSS.

B. Power System Model
A 10-machine 39-bus power system with wind farms is considered as a test case for this paper which is presented in Figure 2. To assess the effectiveness and robustness of the proposed method over a wide range of loading conditions, different operation conditions are considered. Details of the system data and operating condition are given in Ref. [13]. The proposed power system is divided to four area with connected wind farm as shown in Figure 2.

C. Wind Power Model
It is clear that the output power of wind generator depends on wind velocity. The wind speed model chosen in this study consists of four-component model [14], that is defined as; The base wind velocity component is represented in literature as: Where KB is a constant and assumed to presenting the wind power. The gust wind velocity can be defined as; MAXG is the gust peak TG is the gust period T1G is the gust starting time (1-cosine) gust is an essential component of wind velocity for dynamic studies The ramp wind velocity component is described as:

Bulletin of EEI
This component may be used to approximate a step change with T2R >T1R. Also, the random noise component can be described as:  is a random variable with uniform probability density on the interval 0 to 2π and the spectral density function can be defined as: Where KN is the surface drag coefficient which is considered 0.004 and F is turbulence scale which is considered 2000, and μ is the mean speed of wind at reference height. Various study have shown that values of N=50, and ∆ω = 0.5-2.0 rad/s provide results of excellent accuracy.
D. Characteristic of wind generator output power The output power of studied wind generator is expressed by a nonlinear function of the power coefficient Cp as function of blade pitch angle, β, and tip speed ratio, γ. The tip speed ratio is presented as follow: The power coefficient can be presented as:  At the end, the output of mechanical power for wind generator is: Where, ρ (=1.25 kg/m3) is the air density and Ar (=1735 m2) is the swept area of blade.

Fuzzy Logic Controller
In classical control, the value of control is determined in relation to a number of data inputs using a set of equations to express the entire control process. Expressing human experience in the form of a mathematical formula is a very difficult task, if not an impossible one. Accordingly, Fuzzy Logic Controller (FLC) provides a simple tool to interpret this experience into reality [15]. FLCs are rule-based controllers with resembles structure with a knowledge based controller except that the FLC utilizes the principles of the fuzzy set theory in its data representation and its logic. The classic structure of FLC can be simply presented in Figure 3. A set of fuzzy rules represents the FLC mechanism for adjusting the effect of certain system stimuli. Thus, the aim of fuzzy control systems is to replace a skilled human operator with a fuzzy rules-based system. The FLC also provides an algorithm which can convert the linguistic control strategy, based on expert knowledge, to automatic control strategies.
Thus, to reduce fuzzy system effort cost, in this paper proposed an intelligent technique for optimal tuning of fuzzy controller. Figure 4, shows the structure of the proposed IBFA-FPSS to improve power system stability.

The IBFA Technique
In this part, the proposed improved Bacteria Foraging Algorithm (IBFA) is presented for the solution of the power system oscillation with wind farm effects. The BFA is an efficient population based stochastic search technique recently developed by Passino [16] which has found an increasing interest in the recent years as an optimization technique due to its high ability to search the promising areas of the solution space. The concept of this technique is based on the foraging mechanism of E. coli bacteria that are present in human intestines. The classic BFA technique is briefly illustrated in the flowchart of Figure 1 and can be described as the following step by step: Step 1) The classic BFA consist of three main loop as; chemotaxis, reproduction and elimination-dispersal. To generate the initial population, i.e.  Step 2) Set the counter of bacteria, denoted by i, to one (i=1) to implement the chemotaxis loop.
Step 3) For bacterium i, the cost function of BF, denoted by CF(i,j,k,l), is computed as follows: CF(i,j,k,l)=AOF(i,j,k,l)+JCC(i,j,k,l) Where AOF(i,j,k,l) represents augmented objective function of the proposed problem including its objective function The constructed AOF should be minimized. Where, JCC(i,j,k,l) is defined as follows:   ) for bacterium i.
Step 5) The objective function of bacterium i for the next iteration of the chemotaxis loop (j+1) is computed as; CF(i,j+1,k,l) = AOF(i,j+1,k,l) + JCC(i,j+1,k,l) Step 6) This step whichi is named as swim an inner counter m is initialized to zero (m=0) and a parameter Jlast is set as Jlast = CF(i,j,k,l).
Step 7) If i<NS, go to step 8; otherwise go to step 9.
Step 8) Increment i (i=i+1) and go back to step 3.
Step 10) If j < Nch, go back to step 2. Otherwise, go to the next step.
Step 11) Set the counter of bacteria to one (i=1) to implement the outer loop, i.e. reproduction.
Step 13) If k < Nre, go to step 14; Otherwise; go to step 15.
Step 14) Set j=0 and go back to step 2.
Step 15) Set i=1 to implement the outermost loop of BF.
Step 17) If l < Ned, go to step 18; otherwise got to step 19.
Step 18) Set j=0 and k=0 and go back to step 2. Step 19) The BF algorithm is terminated and the best bacterium of the population owning the lowest value of the objective function CF is returned as the final solution of the optimization problem.
In this paper, a new version of BFA is presented to enhance the exploration capability and diversity of the search process of classic BFA [17]. Accordingly, to avoid generating similar search directions and enhance the diversity of the search process, mutation operation is modified as follows:   On the other hand, the proposed IBFA can benefit from both variable search directions and variable tumble steps (with high diversities) leading to higher search capability of the IBFA. Furthermore, βmax is adaptively changed along the iterations of the reproduction loop of the IBFA to enhance its convergence behavior: Thus, the proposed IBFA begins with a high value of βmax(k,l) to search different regions of the solution space with high exploration. After a number of executions of the reproduction loop, when the bacteria enter the promising area, βmax(k,l) is adaptively reduced, limiting the range of variations of β(i,j,k,l), to search the area with higher resolution.

Simulation Results
In this paper, an IBFA-FPSS is proposed, which combines the advantage of the IBFA and fuzzy control techniques to achieve good robust performance. It should be mentioned that obtaining the optimal decision-making logic for the proposed IBFA fuzzy control strategy is very important to achieve the desired level of robust performance [9], because it is a computationally expensive combinatorial optimization problem. Usually, the rule-base sets are determined by experience and control knowledge of a human expert. However, experts may not always be available and even when available it is a trial-and-error process that takes much time and cost [9]. The results of the fuzzy rule-base sets are listed in Tables 1-3. In the proposed rule-base optimization problem, the membership function sets for the KPi, KIi and Kdi are defined as triangular partitions with five segments from 0 to 1 [18]. In this study the controllers are connected to G2 -G10 in the test system. Evaluation of the Integral of the Time multiplied Absolute value of the Error (ITAE) and Figure of Demerit (FD) based on the system performance characteristics are defined as [19]:     The wind velocity in four area is presented in Figure 7. Also, wind power generations are presented in Figure 8, and  In this paper two scenarios are presented to test the proposed control strategy in New England power system. For the first scenario, it is very important that, the performance of the proposed controller is tested under transient conditions by applying a 6-cycle three-phase fault or increasing the mechanical torque. So, in this scenario a 6-cycle three-phase fault is applied in line 26-29 and bus 29. The responses of generators 1, 3, 7 and 9 are presented in Figure 12. Also the numerical results of FD and ITAE are presented in Table 4. In the second scenario a 0.1 step is applied over the torque of generators. The tie-line response of power system is presented in Figure 13-15. Also, the responses of 1, 3, 7 and 9 generators are presented in Figure 16. The numerical results of FD and ITAE are presented in Table 5.

Conclusion
In this paper, a design scheme of robust PSS ten-machine New England power system using by considering inverse additive perturbation in a power system with wind farms is presented through hybrid technique of fuzzy controller and improved BFA. By proposed IBFA, the rule based of fuzzy controller is optimized to damp power system oscillation where. The proposed technique is tested in various load condition for the solution of the low frequency oscillation problem in power system. The proposed test case is compared with Classic PSS through different load conditions and numerical results of ITAE and FD. Obtained numerical results and simulation results demonstrate that the proposed strategy satisfied the stability of multi-machine power system.