Adaptive multi objective differential evolution with fuzzy decision making in preventive and corrective control approaches for voltage security enhancement

https://doi.org/10.1016/j.jfranklin.2018.04.043Get rights and content

Highlights

  • Multi Objective Differential Evolution (MODE) based voltage security enhancement through combined preventive–corrective control strategy.

  • Load shedding, generation rescheduling and optimal utilization of FACTS devices are considered for voltage security enhancement.

  • Minimization of cost of FACTS devices, minimization of load shedding for stability improvement.

  • Proposed algorithm employs DE/randSF/1/bin strategy with self tuned parameter.

  • A fuzzy based decision making algorithm is employed to get the best compromise solution from the non dominated solutions.

Abstract

This paper presents a multi objective differential evolution (MODE) based voltage security enhancement through combined preventive-corrective control strategy. Load shedding, generation rescheduling and optimal utilization of FACTS devices are considered for security enhancement. Maximum l-index of load buses is taken as the indicator of voltage stability. Minimization of cost of FACTS devices, minimization of amount of load shedding along with improvement in voltage stability are the objectives of this multi objective optimization problem. The optimal location of FACTS devices are selected using modal analysis technique. The buses for load shedding are selected based on the minimum eigen value of load flow Jacobian. The proposed MODE algorithm employs DE/randSF/1/bin strategy scheme with self tuned parameter which employs binomial crossover and difference vector based mutation. A fuzzy based decision making algorithm is employed to get the best compromise solution from the non dominated solutions. The proposed MODE is also tested with statistical performance metrices. The proposed methodology is implemented on IEEE 30 bus and IEEE 57 bus test systems. The proposed MODE method provides better solutions in the pareto optimal front than the other optimization techniques such as MOGA and NSGA II under combined preventive–corrective control approach. In IEEE 30 bus system, the amount of load shedding is reduced by 40% and voltage stability is improved by 15% and in IEEE 57 bus system, the amount of load shedding is reduced by 15.4% and voltage stability is improved by 13% by the proposed approach. Hence the simulation results show that the proposed approach provides considerable reduction in the amount of load shedding and enhancement of voltage stability by including generation rescheduling and utilization of FACTS devices.

Introduction

Voltage instability [1], [2] is the inability of the power system to maintain acceptable voltage profile under normal conditions and even after being subjected to disturbances. The approaches for voltage stability assessment can be classified into static and dynamic approaches. In this work, l-index [3] one of the static voltage stability index is used for assessing voltage stability of the system.

There are two different strategies available for voltage stability enhancement: preventive and corrective control approaches [4]. Preventive control is applied so as to ensure that the operating point is away from point of voltage collapse in anticipation of credible contingencies. The corrective control action on the other hand is activated only after the occurrence of contingency. Corrective control is considered as economic one in the market environment, nevertheless preventive control is also needed to reduce system interruption. Hence, the preventive and corrective control approaches have to be combined in an optimal manner to enhance voltage stability of the system. Chattopadhyay and Chakrabarti [5] presents preventive/corrective control model to prevent and correct for voltage instability taking into account the load shed dynamics. A mixed integer programming preventive model and a linear programming corrective model are proposed which significantly reduces the computational requirement for the contingency constrained preventive model and enables the corrective model to be linearized. Vaahedi et al. [6] proposed formulations for preventive/corrective controls and VAR planning considering voltage security in the normal and post contingent states. The formulations using Benders decomposition where several number of iterations are required to get a solution due to the fact that Benders cuts, which are added to the main problem are linear constraints. Xu et al. [7] address the optimal coordination between preventive–corrective security constrained optimal power flow model. The objective is to minimize the total expected security control cost which is the sum of the costs of preventive and corrective controls considering the probability of the contingencies. Suitable combinations of preventive and corrective control for Voltage Stability Enhancement (VSE) have not been reported in many literatures. Hence in this paper, combined preventive and corrective control strategy is considered for voltage stability enhancement.

When the power system is under stressed condition, the occurrence of contingencies may lead to voltage instability in the system. Suitable control actions have to be taken to avoid the occurrence of voltage instability in power system. The control actions include generation rescheduling, load shedding and adjustment of FACTS devices. Generation rescheduling [8], [9] has been recognized as one of the effective control ways for improving stability problems. Generation rescheduling is necessary to change the real power settings from base case to contingency state in order to maintain the stability of the system. But the generation units require time to ramp up their levels according to the type and size of the units. Abido [10] proposed an effective scheme involving generation rescheduling by minimizing the real power control variable adjustments for VAR dispatch problem. Surrender Reddy [11] proposed an optimal reactive power scheduling problem using cuckoo search algorithm in deregulated power system. Mohapatra et al. [12] proposed coordinated preventive and corrective rescheduling actions to make the system correctively secure with respect to line and generator outages. In addition, to alleviate the emergency state as early as possible, generation rescheduling alone may not be sufficient. Hence, the other corrective controls like load shedding and incorporating FACTS devices are also considered in this work.

When the operating state is near to instability, if the control strategies such as rescheduling of generators are exhausted, the only alternative way is load curtailment at some buses to avoid voltage collapse. Load shedding is one of the possible corrective actions aimed at forcing perturbed system to a new stable equilibrium state. Load shedding [5], [13], [14] can be defined as the amount of load that must almost instantly be removed from a power system to keep the remaining portion of the system operational. Load shedding is a coordinated set of controls which results in decrease in electric load in the system. Under emergency conditions, system operators have to decide in a very short time which load circuits are to be shed in stressed system conditions so that power balance can be regained and the nominal value of frequency and voltage can be regained. Buses which have larger sensitivities (ranked in descending order) is the change in proximity indicator with respect to load shed (real and reactive power at load buses).

Subramanian [15] proposed sensitivity based approach for load shedding problems in which weighted error criterion is considered for limiting the size of the loads being dropped. In [13], an LP based optimization algorithm has been proposed to determine the amount and location of the minimum load shedding to improve the load margin to voltage collapse. In this work, optimal load shedding strategy is carried out by identifying optimal locations using sensitivity matrix and amount of load shedding is decided using evolutionary algorithms.

To ensure voltage security of the system, FACTS devices based on power electronics technology are a good choice due to their fast and flexible control. Flexible Alternating Current Transmission System (FACTS) devices [16] are included as the additional corrective action which greatly minimizes the other corrective controls such as amount of load shedding and generation rescheduling in contingency states. To obtain good performance from these controllers, proper placement and sizing of these devices is crucial. In practical system, suitable allocation of FACTS devices depends on system stability and other factors such as installation cost and conditions also need to be considered [16], [17]. The optimal location and control of FACTS devices like SVC and TCSC using real coded genetic algorithm to enhance available transfer capability in deregulated power system is studied in [18]. Saravanan et al. [19] proposed the application of PSO technique for optimal placement and sizing of FACTS devices with minimum cost of installation and to improve system loadability. Phadke et al. [20] proposed fuzzy performance index based on fuzzy logic and real coded GA to determine the optimal placement and sizing of FACTS devices. This paper applies modal analysis method [21] to find the optimal location of multi-type FACTS devices namely: SVC and TCSC to enhance voltage stability. In this paper, a techno economic assessment of multi type FACTS devices is proposed as the corrective control strategy for voltage stability improvement. Surender Reddy et al. [22] presents multiobjective optimization approaches for optimal choice, location and size of FACTS controllers in deregulated power system to relieve the congestion under different system states are studied.

In this work, traditional OPF problem is extended to multi objective OPF problem including generation rescheduling, adjustment of multi type FACTS devices and load shedding for improvement in system stability. Because of the presence of conflicting objectives, a multi objective optimization problem results in a number of optimal solutions known as pareto optimal solutions [23]. In multi objective optimization, effort must be made in finding the set of trade off pareto solutions by considering all objectives to be important. In [24], [25], the OPF problem has been solved using evolutionary algorithms considering cost and emission as objectives. A multiobjective OPF problem using the concept of incremental power flow model considering generation cost, system losses and voltage stability is discussed in [26]. Basu [27] proposed multi objective differential evolution to solve multi-objective optimal power flow to minimize cost of generation, emission and active power transmission loss of FACTS device equipped power systems. Varadarajan and Swarup [28] proposed differential evolution to solve multi objective optimal power flow which is subdivided into active and reactive power dispatch. In [29], a multi objective adaptive immune algorithm for solving the combined economic and environmental dispatch problem is proposed. Rosehart et al. [30] proposed a technique to optimize active and reactive power dispatch while maximizing voltage security in power systems. The use of interior point methods together with goal programming and linearly combined objective functions are the optimization techniques used to solve the multi objective OPF problem. In [31], multi objective VSCOPF is studied using NSGA II with fuel cost minimization and voltage stability enhancement. Marinescu [32] proposed coordinated automatic control and voltage regulation in power system in two different levels: static and dynamic level. In [33], multi objective differential evolution for reactive power planning problem including voltage stability enhancement is proposed. In [34], a congestion management approach by using generation rescheduling and load shedding with voltage dependent load modeling is considered. Basu [35] proposed MODE for multi objective reactive power dispatch problem by minimizing active power transmission loss and maximizing voltage stability. In [36], a recurrent MODE is proposed for non linear constrained reactive power management problem in which the algorithm has been repeated using the available Pareto optimal solutions and reinitializing the remaining population. In many of the literature papers, combination of control actions like generation rescheduling, load shedding and FACTS devices are not considered. Hence in this paper, suitable combinations of corrective controls are studied under multi objective optimal power flow for voltage stability enhancement.

The ability of evolutionary techniques like Differential Evolution to find multiple solutions in one single simulation run makes them unique in solving multi objective optimizations. The multi objective optimization algorithm seems to converge very fast to the vicinity of the true Pareto front but problem is to actually reach it and to spread solutions along the front. This seems to indicate that multi objective differential evolution with additional mechanisms is needed to maintain diversity. Hence this paper proposes multi objective differential evolution (MODE) with self tuned parameters for VSCOPF problem. DE/randSF/1/bin scheme [37] is used for the OPF problem in which mutation scheme uses a randomly selected vector and only one weighted difference vector is used to perturb it. The mutation scheme is combined with binomial type crossover and with random scale vector. Due to the convergence speed, simplicity and robustness by MODE to reach the optimal solutions makes it suitable for large scale optimization problem like VSCOPF problem. The quality of the proposed MODE is also tested with statistical performance matrices that is not reported in many literatures.

This paper is organized as follows: The modeling and placement of FACTS devices are presented in Section 2. The problem formulation for multi objective optimization problem for combined preventive–corrective control strategy are presented in Section 3. Section 4 gives the brief introduction of multi objective differential evolution along with selection of best compromise solution by fuzzy decision making strategy is explained. The performance metrics of multi objective evolutionary algorithms for testing the quality of the MODE is presented in Section 5. The results and discussions showing the effectiveness of the proposed method in IEEE 30 bus system and IEEE 57 bus system are presented in Section 6. The major contributions and conclusions are discussed in Section 7.

Section snippets

Modeling of SVC and TCSC

Static Var Compensator (SVC) have been extensively used in power system applications to provide the controlled reactive power and voltage stability improvement. SVC is a shunt compensator and is modeled as series capacitor bank shunted by Thyristor Controlled Reactor (TCR) as shown in Fig. 1. It can be used for both inductive and capacitive compensation. In this work, SVC is modeled as ideal reactive power injection at bus i: ΔQi=Qsvc

The SVC is modeled as a variable reactance that can generate

Problem formulation

The task of voltage security enhancement is formulated as a multi objective optimization problem with minimization of L-index, amount of load shedding, FACTS investment cost and minimum adjustment of real power settings of generators from base case to contingency state as the objectives. Adjustment of generator outputs in the base case and the rescheduling of generators in the contingency state, amount of load shedding and adjustment of FACTS devices are considered as control parameters to

Multi objective differential evolution

In 1995, Price et al. [37] proposed a new floating point encoded evolutionary algorithm for global optimization and named it DE owing to a special kind of differential operator which they invoked to create new offspring from parent chromosomes instead of classical crossover and mutation. Easy methods of implementation and minimum parameter tuning made the algorithm popular very soon. DE employs a greedy selection process that is the best new solution or its parent wins the competition providing

Performance measures of multi objective optimization algorithms

Another important aspect to consider is how to evaluate the quality of the obtained non dominated front. Among these aspects there are (1) the number of non dominated solutions obtained, (2) the closeness between the obtained front and the true pareto optimal front and (3) the coverage of the Pareto front i.e. the spread and distribution of the non dominated solutions.

The performance measures [23] should be designed to reflect the property in terms of how well the computed non dominated front

Results and discussion

The proposed combined preventive and corrective control approach for voltage stability enhancement is implemented on IEEE 30 bus and IEEE 57 bus systems and the results are presented. The generators are modeled as PV buses with reactive power limits and the loads are represented by constant PQ loads. The power system is stressed by simulating single line outages and increase in load. (N-1) contingency analysis is performed considering the outage of lines and selecting the severe contingency

Conclusion

This paper has presented an optimal strategy to improve the voltage stability of the power system during emergency condition through combined preventive and corrective control approaches such as generation rescheduling, load shedding and installation of FACTS devices. The voltage stability margin of the system is calculated using L-index, which is a quantitative measure for the estimation of the distance of the actual state of the system to the stability limit and describes the stability of the

References (39)

  • T Van Cutsem et al.

    Voltage Stability of Electric Power Systems

    (1998)
  • LeeB.H. et al.

    A study on voltage collapse mechanism in electric power system

    IEEE Trans. Power Syst.

    (1997)
  • P Kessel et al.

    Estimating the voltage stability and loadability of power systems

    IEEE Trans. Power Deliv.

    (1996)
  • FengZ. et al.

    A comprehensive approach for preventive and corrective control to mitigate voltage collapse

    IEEE Trans. Power Syst.

    (2000)
  • E. Vaahedi et al.

    Dynamic security constrained optimal flow/var planning

    IEEE Trans. Power Syst.

    (2001)
  • XuY. et al.

    Solving preventive–corrective SCOPF by a hybrid computational strategy

    IEEE Trans. Power Syst.

    (2014)
  • WangR et al.

    Re-dispatching generation to increase power system security margin and support low voltage bus

    IEEE Trans. Power Syst.

    (2000)
  • V.H. Quintana et al.

    Overload and voltage control of power systems by line switching and generation rescheduling

    Canad. J. Electr. Comput. Eng.

    (1990)
  • M.A Abido

    Multiobjective optimal VAR dispatch considering control variable adjustment costs

    Int. J. Power Energy Convers.

    (2001)
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