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Performance index based analysis is made to examine and highlight the effective application of Particle Swarm Optimization (PSO) to optimize the Proportional Integral gains for Load Frequency Control (LFC) in a restructured power system that operates under Bilateral based policy scheme. Various Integral Performance Criteria measures are taken as fitness function in PSO and are compared using overshoot, settling time and frequency and tie-line power deviation following a step load perturbation (SLP). The motivation for using different fitness technique in 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 are tested on a two-area restructured power system. The results of the proposed PSO based controller show the better performance compared to the classical Ziegler-Nichols (Z-N) tuned PI and Fuzzy Rule based PI controller.

In general LFC role is to ensure reliable operation of interconnected power systems by adjusting generation to minimize frequency deviations and regulate tie-line flows. Operating the power systems in a new environment will certainly be more complex than in the past, due to restructuring and a considerable degree of technical and economical interconnections. LFC and relative control strategies mostly remained similar to before deregulation except that services provided by participants are now classified as ancillary [

The 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. Possible issues in Frequency control in energy market were discussed in [

This paper is organized as follows: Generalized bilateral scheme is presented in Section 2 and GPM 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. PSO based controller is discussed in Section 5 and the motivation of using different fitness function is discussed in this section. The objective of this work is to formulate the dynamic LFC and evaluate and analyze the LFC based on different performance criteria under parametric uncertainties.

New market concepts were adapted 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 [

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 [

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

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 are given [

Conventional control methods may not give satisfactory solutions, because of increasing complexity and changing structure of power systems. Fuzzy logic control is an excellent alternative to the conventional control methodology when the processes are too complex for analysis by conventional mathematical techniques. Fuzzy Logic Control 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. The Membership Functions (MFs) were chosen to be triangular for obtaining fast response from the system. The MFs were named LN (Large Negative), MN (Medium Negative), SN (Small Negative), Z (Zero), SP (Small Positive), MP (Medium Positive) and LP (Large Positive). In [

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 optima- zation. 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

tion, obtained thus far by any particle in the population. PSO consists of, at each step, changing the velocity of each particle toward its pbest and gbest according to Equation (15). The velocity of particle i is represented as

for acceleration toward pbest and gbest. The position of the ith particle is then updated according to Equation (16), [

Ace/dAce | LN | MN | SN | Z | SP | MP | LP |
---|---|---|---|---|---|---|---|

LN | LP | LP | LP | MP | MP | SP | Z |

MN | LP | MP | MP | MP | SP | Z | SN |

SN | LP | MP | SP | SP | Z | SN | MN |

Z | MP | MP | SP | Z | SN | MN | MN |

SP | MP | SP | Z | SN | SN | MN | LN |

MP | SP | Z | SN | MN | MN | MN | LN |

LP | Z | SN | MN | MN | LN | LN | LN |

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 [

The optimization problem is based on the minimization of the Fitness Function subject to the conditions that the PI gains k_{p} and k_{i} of both the controllers will lie within the minimum and the maximum limits as given below.

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 α_{1} = 0.75, α_{2} = 1 − α_{1} = 0.25; α_{3} = 0.5, α_{4} = 1 −α_{3} = 0.5

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 and Power generation of Gencos are shown in Figures 4-6. It is observed that PSO based controller has low overshoot and less settling time compared to Fuzzy Rule based PI(FPI) Controller. It is noted that PSO-ITAE and PSO-ITSE has better performance than PSO-IAE, PSO-ISE and PSO-MSE. The actual power generated by each Gencos reach the desired value is given in

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

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

Case II: It is assumed that the rotating mass and load pattern parameters Di and Mi have uncertain values in each control area. In addition to case I, 25% decrease in parametric uncertainties is taken. The chane in frequency deviation for both areas are shown in

Case III: Consider Case II, in addition to the specified contracted load demand and 25% decresase in D_{i} and M_{i}, a bounded random step load change (∆P_{di}) as a 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. Frequency deviation for two areas are given in

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

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

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

Classical Z-N(Z-N) | +0.162 | 66 | +0.141 | 62 |

Fuzzy PI(FPI) | +0.126 | 43 | +0.120 | 45 |

PSO-MSE | +0.045 | 52 | −0.125 | 40 |

PSO-ISE | +0.046 | 34 | −0.115 | 24 |

PSO-IAE | +0.045 | 49 | −0.115 | 32 |

PSO-ITSE | +0.042 | 34 | −0.110 | 29 |

PSO-ITAE | +0.05 | 34 | −0.115 | 35 |

Controller | Area 1 | Area 2 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Case 1 | Case 2 | Case 3 | Case 1 | Case 2 | Case 3 | |||||||

K_{P1 } | K_{I1 } | K_{P1 } | K_{I1 } | K_{P1 } | K_{I1 } | K_{P2 } | K_{I2 } | K_{P2 } | K_{I2 } | K_{P2 } | K_{I2 } | |

Z-N | 0.2405 | 0.715 | 0.197 | 0.605 | 0.195 | 0.625 | 0.345 | 0.745 | 0.3210 | 0.7127 | 0.3205 | 0.5421 |

FPI | 0.175 | 0.250 | 0.20 | 0.555 | 0.210 | 0.545 | 0.2331 | 0.3701 | 0.2051 | 0.685 | 0.2123 | 0.680 |

PSO-ISE | 0.325 | 0.4205 | 0.301 | 0.4265 | 0.3250 | 0.4135 | 0.2505 | 0.5214 | 0.2765 | 0.4157 | 0.2706 | 0.4710 |

PSO-ITSE | 0.3015 | 0.4175 | 0.3105 | 0.4956 | 0.320 | 0.3915 | 0.2831 | 0.5001 | 0.2871 | 0.4101 | 0.2801 | 0.4611 |

PSO-IAE | 0.2971 | 0.4103 | 0.310 | 0.7101 | 0.3221 | 0.4001 | 0.2768 | 0.510 | 0.2715 | 0.4423 | 0.2900 | 0.4733 |

PSO-ITAE | 0.3197 | 0.4123 | 0.3321 | 0.5191 | 0.3210 | 0.4200 | 0.2899 | 0.5021 | 0.2665 | 0.4741 | 0.2899 | 0.4777 |

PSO-MSE | 0.4550 | 1.012 | 0.3001 | 0.9123 | 0.4000 | 0.920 | 0.9245 | 1.3232 | 0.7001 | 1.0219 | 0.6748 | 1.0114 |

In this paper, PSO based PI tuning are applied to bilateral LFC scheme. Simulation results indicate 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 all the PSO-based controllers produce the better results. During parameter uncertainties, the proposed controller with ISE penalizes large initial and final error. During large load disturbance, it penalizes excessively over damped oscillations and hence PSO-ISE consecutively produces optimum result in all testing conditions.

P. Anitha,P. Subburaj, (2016) Integral Performance Criteria Based Analysis of Load Frequency Control in Bilateral Based Market. Circuits and Systems,07,1021-1032. doi: 10.4236/cs.2016.76086

R_{1} = R_{3} = 3%;

R_{2} = R_{4} = 2.73%;

T_{g}_{1} = T_{g}_{3} = 0.08s;

T_{g}_{2} = T_{g}_{4} = 0.06s;

T_{t}_{1} = T_{t}_{3} = 0.4s;

T_{t}_{2} = T_{t}_{4} = 0.44s;

K_{r}_{1} = K_{r}_{2} = K_{r}_{3} = K_{r}_{4} = 0.5;

T_{r}_{1} = T_{r}_{2} = T_{r}_{3} = T_{r}_{4} = 10s;

D_{1} = 0.015pu MW/Hz;

D_{2} = 0.016pu MW/Hz;

M_{1} = 0.16667;

M_{2} = 0.2012;

B_{1} = 0.3483;

B_{2} = 0.3827;

T_{12} = 0.20.