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This paper discusses the implementation of Load Frequency Control (LFC) in restructured power system using Hybrid Fuzzy controller. The formulation of LFC in open energy market is much more challenging; hence it needs an intelligent controller to adapt the changes imposed by the dynamics of restructured bilateral contracts. Fuzzy Logic Control deals well with uncertainty and indistinctness while Particle Swarm Optimization (PSO) is a well-known optimization tool. Abovementioned techniques are combined and called as Hybrid Fuzzy to improve the dynamic performance of the system. Frequency control of restructured system has been achieved by automatic Membership Function (MF) tuned fuzzy logic controller. The parameters defining membership function has been tuned and updated from time to time using Particle Swarm Optimization (PSO). The robustness of the proposed hybrid fuzzy controller has been compared with conventional fuzzy logic controller using performance measures like overshoot and settling time following a step load perturbation. The motivation for using membership function tuning using PSO is to show the behavior of the controller for a wide range of system parameters and load changes. Error based analysis with parametric uncertainties and load changes is tested on a two-area restructured power system.

Frequency regulation service in energy market is one of the profitable ancillary services. Its main objectives are to keep the tie-line power exchanges within the scheduled limits and to maintain zero change in frequency. Since frequency control in a complex and competitive environment is a tedious process, the control technique must be more intelligent and adaptive for a changing environment. More research work has been carried on Frequency control in restructured power system [

The Load Frequency Control (LFC) issue as an ancillary service represents an important role to maintain an acceptable level of efficiency, quality, and reliability in a deregulated power system environment. Many researchers have started to analyze possible new LFC schemes and regulation solutions, with paradigms suited for the energy market scenarios [

This paper is organized as follows: Generalized bilateral scheme is presented in section 2 and Generation Participation Matrix is defined in this section. System taken for investigation is defined in section 3. Fuzzy rule based control scheme for a bilateral based restructured power system is presented in section 4. Automatic membership function tuning using PSO based controller is discussed in section 5. Simulation results for different cases are presented in Section 6. The objective of this work is to formulate the dynamic LFC and evaluate and analyze the LFC based on different performance measures under parametric uncertainties.

Energy market scenarios are adapting changes every day to achieve the goal of better performance and efficiency in restructured power systems. In this paper, bilateral based market is taken for analysis. A general configuration for the LFC [

Bilateral based deregulated environment consist of an Independent System Operator (ISO), Distribution Companies (DISCOs), Generation Companies (GENCOs), and Transmission Companies (TRANSCOs). In the new environment, DISCOs may contract power from any GENCOs and ISO have to supervise these contracts

[_{ij} refers to ‘‘generation participation factor’’ and shows the participation factor of Genco i in total load following the requirement of DISCO j based on a specified bilateral contract [

New information signals due to possible various contracts between Disco i and other Discos and Gencos are shown as dashed arrows in

where

where ΔP_{di} (_{Loc-i} is the contracted load demand (contracted and uncontracted) in area i, and ΔP_{tie-I}_{,actual} is the actual tie-line power in area i. Using Equation (2), the scheduled tie-line power (ΔP_{tie-I}_{,scheduled}) can be calculated using Equation (7).

In the bilateral LFC structure, Control is highly decentralized. Each Load Matching Contract requires a separate control process, yet these control processes must cooperatively interact to maintain system frequency and minimize the area control error [

X_{i} Generator participation factor under contract.

Y_{i} Difference of import and export power.

Z_{i} Tie-line coefficient.

∆f_{i} frequency deviation.

B_{i} frequency bias.

∆P_{tie_i} net tie-line power flow.

∆P_{di} area load disturbance between areas i and j.

α area control error (ACE) participation factor.

∆P_{Li} contracted demand of area i.

∆P_{mi} power generation of Genco i.

∆P_{Loc_i} total local demand (contracted and uncontracted) in area i.

∆P_{tie_i}_{,actual} actual ∆P_{tie}__{i}._{ }

Consider the load frequency control problem for a two-area power system as shown in

The model is simple but captures the essential dynamics of a power system and has been widely used for LFC design purpose. The load frequency control problem for a multi-area power system requires that not only the frequency deviation of each area must return to its nominal value but also the tie-line power flows must return to their scheduled values. So a composite variable, the area control error (ACE), is used as the feedback variable to ensure the two objectives.

For Area #i, the area control error is defined as

and the feedback control for Area #i take the form

The transfer functions of the governor, the turbine, and the rotor inertia and load for Area #i are denoted by G_{gi}(s), G_{ti}(s), and G_{pi}(s), respectively. The transfer functions of the above mentioned are represented as

then the transfer function from u_{i} to ∆f_{i} can be easily found as

The transfer function for Area #i.

The system parameters taken for investigation [

Due to the increasing complexity and changing structure of power systems, it needs an intelligent controller as an alternative to the conventional control methodology. Fuzzy Logic Control would serve the better role in load frequency control in restructured power system. Fuzzy controller consists of three main stages, namely the Fuzzification interface, the Inference rules engine and Defuzzification interface.

For LFC, ACE and its derivative are chosen as inputs and Proportional and Integral Gains are taken as control outputs of the fuzzy controller. Gaussian Membership Functions (MFs) is chosen for obtaining fast response from the system. The MFs were named NL (Negative Large), NM (Negative Medium), NS (Negative Small), Z (Zero), PS (Positive Small), PM (Positive Medium) and PL (Positive Large) followed by error(E) and Derivative error (DE). In [_{P} & K_{i}) for area i are determined based on the experiments with classical (Ziegler-Nichols Tuned) PI controller. These two input signals are used as rule-antecedent in the formation of rule base, and the control outputs are used to represent the contents of the rule-consequent in performing the rule base [

Each fuzzy rule is in the form,

where MF_{nj} is a membership function and y_{n} and z_{n} are singleton values.

where C_{nj} is mean and σ_{nj} is standard deviation of the membership function.

AND operation is used and is given by

The output K_{P} and K_{I} calculated by

“k” refers total number of rules.

Based on the knowledge gathered from classical (Z-N) controller, fuzzy rules are formed and the appropriate rules for K_{i} and K_{p} are given in

NLE | NME | NSE | ZE | PSE | PME | PLE | |
---|---|---|---|---|---|---|---|

NLDE | PL | PL | PL | PM | PM | PS | Z |

NMDE | PL | PM | PM | PM | PS | Z | NS |

NSDE | PL | PM | PS | PS | Z | NS | NM |

ZDE | PM | PM | PS | Z | NS | NM | NM |

PSDE | PM | PS | Z | NS | NS | NM | NL |

PMDE | PS | Z | NS | NM | NM | NM | NL |

PLDE | Z | NS | NM | NM | NL | NL | NL |

PSO is a novel population based meta heuristic, which utilize the swarm intelligence generated by the cooperation and competition between the particles in a swarm and has emerged as a useful tool for engineering optimization. It has also been found to be robust in solving problems featuring nonlinearity, non-differentiability and high dimensionality.

In PSO, each particle is flown through the multidimensional search space, adjusting its position in search space according to its own experience or knowledge and that of neighboring particles. Therefore, a particle makes use of the best position encountered by itself and the best position of its neighbors to position itself toward an optimum solution. The effect is that particles fly toward the global minimum, while still searching a wide area around the best solution. The performance of each particle is measured according to a predefined fitness function which is related to the problem being solved [

PSO starts with a population of random solutions “particles” in a D-dimension space. The ith particle is represented by

sociated with the fittest solution it has achieved so far. The value of the fitness for particle i (pbest) is also stored

as

for acceleration toward p best and g best. The position of the ith particle is then updated according to Equation (16) [

It should be noted that choice properly fitness function is very important in synthesis procedure. Because different fitness functions promote different PSO behaviors, which generate fitness value providing a performance measure of the problem considered [

In order to illustrate the behavior of the proposed control strategy some simulations has been carried out. The system parameter of the test system is given in Appendix A.

Consider a system where all GENCOs in each area participate in LFC, i.e. ACE participation factors are

Case I: In this case it is assumed that all Gencos are participating in the LFC task as per contract. It is assumed that a large step load 0.05 p.u MW is demanded by each DISCOs in all areas. Frequency response for

both areas, tie line power exchange are shown in Figures 4-6. The actual power generated by each Gencos reach the desired value is given in _{nj}) and standard Deviation (σ_{nj}) before and after updation are given in

Case II: It is assumed that the rotating mass and load pattern parameters D_{i} and M_{i} have uncertain values in each control area. In addition to case I, 25% decrease in parametric uncertainties is taken. The results are shown in Figures 7-9. Simulation results show that all the Hybrid Fuzzy controllers track the load fluctuations possibly good. Their overshoot & settling time is better than conventional Fuzzy controllers.

Case III: Consider Case II, in addition to the specified contracted load demand and 25% decrease in D_{i} and M_{i}, a bounded random step load change (∆P_{di}) as an uncontracted demand appears in each control area.

The main aim of this test is to check the robustness of the proposed controller against uncertainties and random load disturbance. The load pattern applied to areas is shown in

The optimum values of the Proportional and Integral Gains of the different controllers for the aforementioned cases are shown in

Genco | 1 | 2 | 3 | 4 |
---|---|---|---|---|

∆P_{mi}(puMW) | 0.0525 | 0.0225 | 0.0975 | 0.0275 |

Membership Functions | Before PSO | After PSO | ||
---|---|---|---|---|

Mean(C_{nj}) | Standard Deviation(σ_{nj}) | Mean(C_{nj}) | Standard Deviation(σ_{nj}) | |

NL | −0.667 | 0.118 | −1 | 0.07786 |

NM | −0.3891 | 0.118 | −0.6833 | 0.04955 |

NDS | −0.1114 | 0.118 | −0.3 | 0.04247 |

Z | 0 | 0.118 | −0.05 | 0.04247 |

PS | 0.444 | 0.118 | 0.3117 | 0.0304 |

PM | 0.7221 | 0.118 | 0.6708 | 0.03575 |

PL | 1 | 0.118 | 1 | 0.0354 |

Case | Controller | Area1 | Area2 | ||
---|---|---|---|---|---|

Overshoot (Hz) | Settling Time (Sec) | Overshoot (Hz) | Settling Time (Sec) | ||

1 | Fuzzy | −0.0785 | 42 | −0.08 | 28 |

Hybrid Fuzzy | −0.048 | 25 | 0.05 | 20 | |

2 | Fuzzy | 0.13 | 48 | −0.13 | 42 |

Hybrid Fuzzy | −0.042 | 28 | 0.07 | 26 | |

3 | Fuzzy | 0.17 | - | 0.27 | - |

Hybrid Fuzzy | 0.1 | - | 0.2 | - |

Case | Gain | Fuzzy | Hybrid Fuzzy |
---|---|---|---|

1 | K_{P}_{1} | 0.175 | 0.225 |

K_{I}_{1} | 0.250 | 0.285 | |

K_{P}_{2} | 0.2331 | 0.203 | |

K_{I}_{2} | 0.3701 | 0.485 | |

2 | K_{P}_{1} | 0.20 | 0.267 |

K_{I}_{1} | 0.555 | 0.486 | |

K_{P}_{2} | 0.2051 | 0.165 | |

K_{I}_{2} | 0.685 | 0.455 | |

3 | K_{P}_{1} | 0.210 | 0.206 |

K_{I}_{1} | 0.545 | 0.525 | |

K_{P}_{2} | 0.2123 | 0.2 | |

K_{I}_{2} | 0.680 | 0.657 |

In this paper, automatic tuning of membership function of fuzzy controller using PSO is applied to bilateral LFC scheme. PSO is a popular search algorithm; it utilizes the swarm intelligence of cooperation and fast convergence to find the optimum value of the parameters of membership function used in fuzzy logic controller. Simulation results show the effectiveness of the proposed controller in damping the frequency oscillations and tie-line power very fast with less undershoot and overshoot. It is also seen from simulation results that under normal circumstances, Fuzzy and Hybrid Fuzzy using PSO-based controllers produce the better results. During parameter uncertainties and large load disturbance, Hybrid Fuzzy penalizes excessively over damped and excessively under damped responses and reduces overshoots. It has been therefore shown that Hybrid Fuzzy controller produces better performance in all testing environments.

P. Anitha,P. Subburaj, (2016) Hybrid Fuzzy Controller Based Frequency Regulation in Restructured Power System. Circuits and Systems,07,759-770. doi: 10.4236/cs.2016.76065

_{1} = 0.015 pu×MW/Hz; D_{2} = 0.016 pu×MW/Hz; M_{1} = 0.16667; M_{2} = 0.2012; B_{1} = 0.3483; B_{2} = 0.3827; T_{12} = 0.20.