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ABSTRACT
Integration of renewable energy resources into the power system has increased the financial and technical concerns for the market based transmission expansion planning. This paper proposes an algorithm for congestion management in a pool based electricity market base on particle swarm optimization (PSO). The proposed approach effectively relieves line overloads with minimum deviations in generations from initial market settlement. The proposed methodology is applied to the IEEE-30 Bus system to evaluate the feasibility and practicality of the developed planning strategy. The experimental results prove that the PSO is one among the challenging- optimization methods, which is indeed capable of obtaining higher quality solutions for the proposed congestion management problems.
INTRODUCTION
The power flow analysis is the essential and fundamental tool to power systems engineers. The congestion management is one of the most challenging operational problems with open access transmission. The congestion in power networks have been defined as if the transmission network is operated at or beyond one or more transfer limits. In deregulated power systems, because of the present trends of bilateral contracts in the electricity market, the role of independent system operator (ISO) is increasing. Under this scenario, the role of ISO is to create a set of rules that ensure sufficient control over producers and consumers to maintain an acceptable level of power system security and reliability. As the demand for deregulation of electric utilities is on the rise, the selection of the objective function for optimization of economic system operation is becoming more critical. After the restructuring of the electric power industry, profit generating companies have been developed to deliver electric energy in a competitive market. In such a case, independent regulated transmission system operators (TSOs) manage the operation of the transmission system. The congestion management is one of the central issues of centralized optimal power flow (COPF). The conventional benefit optimisations and congestion management methods have been mainly based on economic dispatch that enables to achieve minimum generation cost in a single utility environment. In order to achieve economical optimal dispatch with congestion management in the whole power system, a small amount of interchange of information is sufficient among the involved market players to obtain a global solution by setting up a common control centre. The congestion pricing and cost allocation-based methodology is also used in power system for benefit optimization.
Recently, researchers have shown interest in involving the demands in objective function to maximise their market profits. Also, the demand limits are incorporated with objective function of problems. In the early days of deregulation, customers were not having effective participation in power markets, and therefore they were not able to respond to the prices effectively. However, to have a complete competitive market, there should be enough motivations for customers to participate in power market operation.
The present investigation deals with the congestion management in centralised market structure with bilateral contracts between generators and costumers. The formulation of the problem is based on benefit maximisation with the role of consumer functions in problem objective. The line limits are also included in this formulation for congestion management. The solution is obtained by interior point (IP) method. This method has been extensively applied to solve large-scale OPF problems due to its fast computational speed and robustness. In IP OPF, the computation of gradient, Jacobian, and Hessian matrices of objective functions are constraint functions. Modified IEEE-30 bus system has been used to demonstrate the performance of the method proposed. The test results reveal that the proposed method gives good results including the losses in problem formulation. A coordinated real-time optimal dispatch method for unbundled electricity markets is proposed for system balancing and congestion management. With this method, almost all the possible resources in different electricity markets, including operating reserves and bilateral transactions, can be used to eliminate the real-time congestion according to their bids into the balancing market.
There has been a worldwide trend towards restructuring and deregulation of the power industry over the last decade. The competition in the wholesale generation market and the retail market together with the open access to the transmission network can bring many benefits to the end consumers, such as lower electricity prices and better services. However, this competition also brings many new technical problems and challenges to the operation of power system, which was regarded as "natural monopoly" due to the special characteristics of electricity as a commodity. On the other hand, this means real opportunities and challenges to power engineers and researchers. An important driving force behind this significant reform is the recent development of technology. At the end of the 20th century, many technological innovations are emerging.
REVIEW OF LITERATURE
The power market is represented with linear supply and demand curves. A stochastic dynamic programming algorithm [1] is used to solve the investment problem, where uncertainty in demand is represented as a discrete Markov chain. The stochastic dynamic model allows us to evaluate investment projects in new base and peak load power generation as real options, and determine optimal timing of the investments. The model builds upon real options theory, which has been developed over the last two decades specifically to evaluate investment projects under uncertainty. According to the real options theory, investment projects can be considered as options. The optimal timing of an investment does not occur until the value of the project itself exceeds the value of keeping the option to invest in the future. A similar description of the supply and demand of electricity is used in the theory of peak-load pricing. Peak-load pricing models were developed to find optimal pricing schemes and power generation expansion strategies for a regulated electric power utility, based on maximization of total social welfare. However, the traditional optimization models for peak load pricing, only find optimal investments for a given level of demand. Examples of dynamic formulations of the peak-load pricing problem exist, but these are deterministic. More recent analyzes of investments in competitive power markets also tend to be of a rather static and deterministic nature. The stochastic dynamic investment model presented in this workoffers a more comprehensive treatment of long-term uncertainties and their influence on optimal investment decisions. Our market description also facilitates a comparison of optimal investment strategies under centralized social welfare and decentralized profit objectives. Hence, the effect of market structure and regulations can be analyzed with the model. Such analyses of investments under uncertainty are important in order to better understand the long-term dynamics of investments, prices, and reliability in restructured power systems.
In a case study, we use the model to compare optimal investment strategies under centralized and decentralized decision making. Three very different methods of accomplishing the same task-managing the operation of the transmission system in the deregulated power system operating environment-have been implemented in [2] as deregulated market structures have been created around the world. Each has strengths and flaws, and there are some surprising inter-relationships. Each maintains power system security but differs in its impact on the economics of the energy market. No clearly superior method has so far emerged. Power system congestion is a major problem that the system operator (SO) would face in the post-deregulated era. Therefore, investigation of techniques for congestion-free wheeling of power is of paramount interest. One of the most practiced and an obvious technique of congestion management is rescheduling the power outputs of generators in the system. However, all generators in the system need not take part in congestion management.
Competition among suppliers of any commodity requires easy access to customers. In case of electric power competition requires that access to the transmission system by generators and loads be managed in a non-discriminatory and equitable manner. This concept has come to be known as transmission open access. However, two basic characteristics of electric power networks have to be The role of the transmission system became central to the restructuring debate when the California Public Utilities Commission (CPUC) introduced its proposal to introduce competition in the California electricity markets’. Two models dominated this debate. They are referred to here as the pool model and the bilateral mode, properly handled to achieve transmission open access; transmission congestion and transmission losses. This work is concerned with transmission congestion. Congestion is a consequence of network constraints characterizing a finite network capacity that precludes the simultaneous delivery of power from an associated set of power transactions. The second characteristic is related to the network’s transmission losses, i.e. the difference between the total supply and demand for power in the system. Both transmission congestion and transmission losses can result in an overall increase in the cost of power delivery. These increases in cost can be much greater in case of congestion than in the case of losses.
The PSO algorithm, reported [3] , handles the binding constraints by a technique different from the traditional penalty function method. [4] proposes a decentralized model for DC load flow based congestion management for the forward markets via Optimal Resource Allocation (ORA). The available thermal capacities of possible congested transmission lines are considered as commonly shared resources for all bilateral and multilateral transactions in the market. In our model, each transaction maximizes its profit under the limits of transmission line capacities allocated by the ISO. The ISO searches the optimal allocation of line capacities to each transaction.
Power markets have been developing rapidly in many parts of the world. However, the perfect design of power markets is still under the investigation for various reasons. The commodity of electricity should be transferred through the network and the transmission line capacity limits should be considered at all times. Congestion in a power system is a consequence of network constraints characterising a finite network capacity that limits the simultaneous transfer of power from all required transactions. The complicated issues of congestion management are market economic efficiency and system operation security.
Large scale nonlinear optimal power flow (OPF) problems have been efficiently solved by extensions from linear programming to nonlinear programming of the primal-dual logarithmic barrier interior-point method and its predictor-corrector variant. Motivated by the impressive performance of the nonlinear predictor-corrector extension, in [5] we extend from linear programming to nonlinear OPF the efficient multiple centrality corrections (MCC) technique that was developed by Gondzio. [6] proposes AC load flow-based decentralised model for congestion management in the forward markets using resource allocation technique. In this model, each transaction maximises its profit under the limits of transmission line capacities allocated by independent system operator. The voltage and reactive power impact of the system are also incorporated in the model. A covariance matrix adapted evolution strategy (CMAES) algorithm is used to solve decentralised congestion management problem for multilateral transactions. A framework for real-time congestion management under a marker structure similar to the newly proposed UK trading arrangement is presented in [7], in which not only resources in balancing market but also some bilateral contracts can be dispatched if necessary. The linearized model of a modified optimal power flow (OPF) is proposed to implement such a framework. A new optimal reactive power flow (ORPF) model in rectangular form is proposed in [8]. In this model, the load tap changing (LTC) transformer branch is represented by an ideal transformer and its series impedance with a dummy node located between them. The voltages of the two sides of the ideal transformer are then used to replace the turn ratio of the LTC so that the ORPF model becomes quadratic. The Hessian matrices in this model are constants and need to be calculated only once in the entire optimal process, which speed up the calculation greatly. The solution of the ORPF problem by the predictor corrector primal dual interior point method is described in [8]. A new algorithm for reactive-power optimization of large-scale power systems involving both discrete and continuous variables is presented in [9].
Congestion management problem can be generally considered as a centralised optimal power flow (COPF) problem with the objective of maximising social welfare with load flow and operation limit constraints. However, the COPF approach has some drawbacks in market environment. COPF requires the submission of detailed private information of market participants to the independent system operator (ISO) that may include their benefit/cost functions. In the market environment, such sensitive information is a commercial secret that market participants are unwilling to disclose to the ISO.
The COPF by the ISO lacks transparency to market participants, since the congestion price is likely to be set by the ISO, but not discovered through market mechanisms .Moreover, for the congestion management of inter-regional trades, this can share common resources (generation units,transmission lines and so on) across regions efficiently and increase the scale of economy. The decentralized optimal power flow (DOPF) approach is becoming more attractive for its possibility of using one agent for coordination and even without the existence of a real ISO for the entire system.
This algorithm realizes successive discretization of the discrete control variables in the optimization process by incorporating a penalty function into the nonlinear primal-dual interior-point algorithm. The principle of handling these discrete variables by the penalty function, the timing of introducing the penalty function during iterations, and the setting of penalty factors are discussed in detail. To solve the high-dimension linear correction equation speedily and efficiently in each iteration, a novel data structure rearrangement is proposed. Compared with the existing data structures, it can effectively reduce the number of nonzero fill-in elements and does not give rise to difficulty in triangular factorization. [10] Presents a new interior point nonlinear programming algorithm for optimal power flow problems (OPF) based on the perturbed KKT conditions of the primal problem. The proposed algorithm includes four kinds of objective functions and two different data structures. Extensive numerical simulations on test systems that range in size from 14 to 1047 buses, have shown that the proposed method is very promising for large scale application due to its robustness and fast execution time. The problem of ensuring that there is enough generation capacity to meet future demand has been an issue in market design since the beginning of the deregulation process. This results in a stabilization of the income of the generators and provides a clear incentive for new generation investment, with a minimum of regulatory intervention. Additionally, the method in [11] represents a market-compatible mechanism to hedge demand from the occurrence of high market prices. [13] proposes an approach for transmission congestion management (CM) in a deregulated power system. Transmission congestion mitigates network efficiency and results in increasing electricity price. Congestion can be effectively eliminated through several methods either by building a new transmission line or by increasing the capacity of the original line between congested zones. [13] evaluates the using of Demand Response (DR) programs in order to managing the congestion. For this purpose, a coordination process between GENCOs and the Independent System Operator (ISO) is considered. In the proposed approach, the coordination is modeled as a two-stage process. Electric power industries throughout the world have been restructured to introduce competition among the market participants and bring several competitive opportunities. [14] describes the assessment of ATC using AC Power transfer distribution factors (ACPTDFs) in combined economic emission dispatch (CEED) environment. The ACPTDFs are derived using sensitivity based approach for the system intact case and utilized to check the line flow limits during ATC determination. The obtained ATC results are compared with Newton Raphson Load Flow method (NRLF) to justify its accuracy. The design of a low-dispersion fiber Bragg grating (FBG) with an optimal grating length using covariance matrix adapted evolution strategy (CMAES) is presented in [15]. A novel objective function formulation is proposed for the optimal grating length low-dispersion FBG design. The CMAES algorithm employs adaptive learning procedure to identify correlations among the design parameters. The design of a low-dispersion FBG filter with 25-GHz (or 0.2 nm in the 1550-nm band) bandwidth is considered.
In this project work, to find the global solution an interior point (IP) based optimization method is proposed an optimization technique is proposed to release the congestion in the line and it is conducted on a modified IEEE 30 bus system with two market models.
PARTICLE SWARM OPTIMIZATION
3.1 INTRODUCTION
Particle swarm optimization, abbreviated as PSO, is based on the behaviour of a colony or swarm of insects, such as ants, termites, bees, and wasps; a flock of birds; or a school of fish. The particle swarm optimization algorithm mimics the behavior of these social organisms. The word particle denotes, for example, a bee in a colony or a bird in a flock. Each individual or particle in a swarm behaves in a distributed way using its own intelligence and the collective or group intelligence of the swarm. As such, if one particle discovers a good path to food, the rest of the swarm will also be able to follow the good path instantly even if their location is far away in the swarm. Optimization methods based on swarm intelligence are called behaviorally inspired algorithms as opposed to the genetic algorithms, which are called evolution-based procedures.
In the context of multivariable optimization, the swarm is assumed to beof specified or fixed size with each particle located initially at random locations inthe multidimensional design space. Each particle is assumed to have two characteristics: a position and a velocity. Each particle wanders around in the design space and remembers the best position (in terms of the food source or objective function value) it has discovered. The particles communicate information or good positions to each other and adjust their individual positions and velocities based on the information received on the good positions.
As an example, consider the behavior of birds in a flock. Although each bird has a limited intelligence by itself, it follows the following simple rules:
(i) It tries not to come too close to other birds.
(ii) It steers toward the average direction of other birds.
(iii) It tries to fit the “average position” between other birds with no wide
gaps in the flock.
Thus the behavior of the flock or swarm is based on a combination of three simple factors:
(i) Cohesion - stick together.
(ii) Separation - don’t come too close.
(iii) Alignment - follow the general heading of the flock.
The PSO is developed based on the following model:
(i) When one bird locates a target or food (or maximum of the objective function), it instantaneously transmits the information to all other birds.
(ii) All other birds gravitate to the target or food (or maximum of the objective function), but not directly.
(iii) There is a component of each bird’s own independent thinking as well as its past memory.
Thus the model simulates a random search in the design space for the maximum value of the objective function. As such, gradually over much iteration, the birds go to the target (or maximum of the objective function).
3.2 SWARM INTELLIGENCE
Particle swarm optimization may have some similarities with genetic algorithms and ant algorithms, but it is much simpler because it does not use mutation/crossover operators or pheromone. Instead, it uses the real-number randomness and the global communication among the swarm particles. In this sense, it is also easier to implement as there is no encoding or decoding of the parameters into binary strings as those in genetic algorithms which can also use real-number strings. This algorithm searches the space of an objective function by adjusting the trajectories of individual agents, called particles, as these trajectories form piecewise paths in a quasi-stochastic manner.
The movement of a swarming particle consists of two major components: a stochastic component and a deterministic component. Each particle is attracted toward the position of the current global best g*and its own best location xi*in history, while at the same time it has a tendency to move randomly.
When a particle finds a location that is better than any previously found locations, then it updates it as the new current best for particle i. There is a current best for all n particles at any time t during iterations. The aim is to find the global best among all the current best solutions until the objective no longer improves orafter a certain number of iterations. The movement of particles is schematically represented where xi*is the current best for particle i, and the current global best is given by
(3.1)
Fig.3.1 Schematic representation of the motion of a particle in PSO, moving towards the global best g* and the current best xi* for each particle i
3.3 BASIC FUNDAMENTALS OF PSO ALGORITHM
The basic fundamentals of the PSO technique are stated and defined as follows
1. Particle X(i): A candidate solution represented by a k-dimensional real valued vector, where k is the number of optimized parameters; at iteration i, the jth particle X (i, j) can be described as
(3.2)
where: x’s are the optimized parameters
xk(i,j) is the kth optimized parameter in the jth candidate solution d represents
the number of control variables
2. Population: This is a set of n particles at iteration i.
(3.3)
where n represents the number of candidate solutions.
3. Swarm: This is an apparently disorganized population of moving particles that tend to cluster together and each particle seems to be moving in a random direction.