Day-ahead optimal reactive power ancillary service procurement under dynamic multi-objective framework in wind integrated deregulated power system
Introduction
The restructuring of the electric power system has changed the operational and control strategies. The services that were part of the vertically integrated electric system previously are now considered separate services [1]. Such services are now being handled independently and are known as ancillary services (AS). In the deregulated system, the AS provider plays a vital role in maintaining power system security. Reactive power (VAr) support, an ancillary service essential to uphold the power flow in the transmission lines with an acceptable voltage at PQ buses [2]. The necessity of VAr support changes with the changing topology of the system and other conditions. Therefore, the judicious procurement of reactive power has emerged as the foremost issue in the operation of a deregulated power system.
In the reactive power procurement, the system operator (SO) procures reactive power from sources ensuring maximum social benefit and regulates the bid prices for all the market participants [3]. The procurement of reactive power utilized the reactive ancillary service pricing approach [4,5]. Different aspects of reactive power pricing in power markets were addressed considering the impact of VAr procurement on real generation [6]. The reactive power pricing was investigated in real-time using locational marginal price-based theory [7]. Locational marginal prices (LMPs) are described as the marginal costs of consuming active and reactive power at any specific bus at that instant. The impact of different factors was analyzed on reactive power marginal price under deregulation [8]. A comprehensive study was reported for reactive power marginal pricing in the competitive electricity market [9,10]. The active and reactive power cost was allocated using marginal price approach [11]. The improved pricing structure of reactive power was developed by considering lost opportunity cost and inclusion of location characteristics of produced reactive power [12]. A price-based reactive power dispatch was solved to optimize the VAr generation cost [13].
The optimal real and reactive power dispatch was studied extensively for the conventional thermal units [[14], [15], [16], [17], [18], [19], [20], [21]]. A combination of classification based evolutionary algorithm and decision making was used to solve multi-objective optimal VAr dispatch problem [22]. A modified social spider optimization was utilized for optimal VAr dispatch considering different objectives [23]. The increasing penetration of widely distributed and abundantly available wind energy necessitates power flow studies to emphasize on VAr procurement issues. The SO must accommodate the intermittent nature of wind generation reliably and cost-efficiently in the deregulated environment [24]. Doubly fed induction generators and permanent magnet synchronous generators are generally utilized in wind farms owing to their capability to generate power at varying speeds and provide reactive power [[25], [26], [27]]. The wind farm owners need to be paid for supplying the reactive power service [28].
The uncertainty of wind generation was accounted in modeling the VAr capability of wind farms [29]. The influence of high wind penetration on power system operation was analyzed for different scenarios comprising variable wind generation share [30]. The optimum real and reactive power dispatch was solved to maximize the wind power output and improve economic efficiency [31]. A statistical method was presented to analyze the impact of wind integration on voltage quality [32]. The modification in market formulation [33] was analyzed for AS procurement for a system with variable renewable energy sources in the competitive electricity market.
A single objective probabilistic VAr dispatch problem was analyzed to minimize active power losses under the wind generation uncertainties [34,35]. An optimal VAr dispatch was investigated using an adaptive differential evolutionary search algorithm to optimize active power loss and aggregate voltage deviation individually [36]. A fast reactive power dispatch tool was developed utilizing a hybrid particle swarm optimization algorithm [37] for frequent VAr setting in a wind farm to minimize active power losses. A stochastic multi-objective VAr dispatch problem in an incorporated wind system was solved for the co-optimization of active power loss and voltage stability index using ε-constraint technique [38]. The multi-objective optimal real and reactive power dispatch problems involving wind generation and load uncertainties were solved by enhanced firefly algorithm [39] and biogeography based optimization [40]. A stochastic multi-objective optimal VAr dispatch was solved by lexicographic optimization and augmented ε-constraint method involving wind generation to co-optimize market payment, VAr reserves, and loading margin [41].
The artificial electric field algorithm (AEFA) is a metaheuristic optimization algorithm inspired by the Coulomb’s law of electrostatic force. It has been used to solve benchmark non-linear test functions. It requires the creation of charge function and Coulomb’s constant to maintain the search space accuracy [42]. The algorithm requires adjustment of only two parameters and has fast convergence towards the global optimum solution. It also has better exploration and exploitation capability and less computation complexity [43].
In this paper, a multi-objective artificial electric field algorithm (MO-AEFA) is developed to solve day-ahead optimal reactive power dispatch for the procurement of VAr ancillary service in a wind integrated pool-based deregulated system. The algorithm considers the Pareto optimality condition and nondominance concept. Two mutation operators, namely, sign and reorder mutation operators, are added to the original AEFA. These mutation operators help escape from being trapped in local optima and avoid premature convergence and maintain diversity amongst particles [44].
In the literature, there are efforts to solve optimal VAr dispatch problems for single as well as multi-objectives in wind integrated systems but these are not formulated as the dynamic optimization problem for VAr AS procurement. Overall, there is a paucity of work on dynamic multi-objective optimization problems to procure reactive power support ancillary services in a wind integrated system. Thus, the paper focuses on the procurement of VAr support ancillary services in a multi-objective dynamic framework including wind generation uncertainties in the pool-based deregulated system using MO-AEFA approach. The results are compared with the multi-objective particle swarm optimization (MOPSO), multi-objective gravitational search algorithm (MOGSA), and multi-objective grey wolf optimizer (MOGWO). The main contributions of the paper are briefed as below:
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Problem formulation for procurement of VAr AS in a deregulated environment considering uncertainties in wind generation under a multi-objective dynamic framework.
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Implementation of the nondominated sorting MO-AEFA approach for VAr AS procurement with the co-optimization of total reactive power procurement (RPP) cost and voltage deviation.
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Investigating the impact of wind power penetration on RPP cost and voltage deviation.
Section snippets
Problem formulation
In the paper, the day-ahead VAr dispatch problem is formulated as a dynamic optimal power flow problem to optimize the total RPP cost and voltage deviation. The problem formulation is briefed hereunder as:
Optimal switching operations based on location marginal price
The locational marginal price (LMP) of reactive power at a bus is described as the minimum cost to supply the next incremental reactive load demand. If the value of LMP is high at a bus, it means that the load at that bus requires extra reactive power and vice versa. In this work, it is assumed that the VAr output of shunt capacitors providing reactive power AS depends on the forecasted LMP of the bus. The number of switching instants in a day is kept fixed ( = 5) in the paper as it is not
Artificial electric field algorithm (AEFA)
The AEFA optimization algorithm works on the principle of Coulomb’s law of electrostatic force [42]. In this algorithm, agents are treated as charge particles and their performance is measured by their charges. Each particle experiences attraction owing to an electrostatic charge that leads to the movement in the agent’s direction with the greatest charge. The greatest charges represent good solutions, and their movement is slower than the lower charges in the search space and guarantee the
Performance metrics
In multi-objective optimization, both the convergence to Pareto optimal set and maintaining diversity or distribution are important [48], which are measured through various performance metrics [22,49,50]. In this paper, distance and diversity metrics are utilized for the purpose. These metrics are described as:
Simulation results
The optimization investigations have been realized for the day-ahead VAr dispatch problem for minimizing total RPP cost and voltage deviation. The scheduling is carried out for one-day through 24 intervals of 1 h each. The investigation has been carried out on two test systems: Test system 1: IEEE 30-bus and Test system 2: IEEE 118-bus. Multi-objective artificial electric field algorithm (MO-AEFA) has been developed for the simultaneous optimization of objectives. The parameters considered for
Computational burden
In this work, a fast Newton power flow program employing sparse matrix techniques is used to exploit the sparsity of system admittance and Jacobian matrices and reduce the computational effort, owing to the requirement of less computer storage and running time [52]. The computational time expended by all the algorithms i.e. MOPSO, MOGSA, MOGWO, and MO-AEFA is calculated for both IEEE 30-bus and IEEE 118-bus test systems using both conventional power flow and fast Newton power flow techniques.
Conclusions
The problem of a day-ahead dynamic multi-objective reactive power ancillary service procurement has been investigated in this work for co-optimization of total VAr procurement cost and voltage deviation in wind integrated deregulated power system. The VAr dispatch is analyzed for different wind penetration levels. The volatile nature of wind generation is accounted via imbalance penalties due to over-estimation and under-estimation costs. A Pareto based MO-AEFA algorithm is presented for the
CRediT author statement
Akanksha Sharma: Methodology, Software, /Writing - original draft. Sanjay K. Jain: Supervision, Writing - review & editing.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors acknowledge the financial support from the Department of Science and Technology (DST) under Innovation in Science Pursuit for Inspired Research (INSPIRE) Fellowship, INSPIRE Code- IF170542, to carry out this research work.
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