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Asynchronous interconnection of two power systems by high voltage direct current transmissions (HVDCs) is a judicious choice to enhance the reliability of system operation and evade some risks. As one of the pioneers of asynchronous interconnection, the southern China power system encounters the challenge of coordinating generation of the sending-end and demand of the receiving-end. The day-ahead generation unit and tie-line scheduling problem is formulated as a two-stage mathematical optimization, in which the first-stage problem minimizes the variance of the remaining load series of receiving-end and generates a near-optimal interarea power transmission schedule, whereas the second-stage problem decides the production level of generation units and power flow of HVDC tie-lines with the objective of minimizing transmission losses. In the second-stage problem, discrete characteristics of HVDC power profile is explicitly modeled, and a quadratic loss function derived from historical data is used to calculate the overall loss of each HVDC, which is then piecewise linearized to form a tractable mixed integer linear programming. Numeric experiments based on realistic data of China Southern Power Grid are carried out. The feasibility and effectiveness of the proposed method is verified through comparing the optimized generation and transmission schedules with original ones which are generated based on expert knowledge.

Clean energies such as wind energy and solar energy have increased very fast in order to meet the environmental requirements. However, due to the uncertainties of wind and solar energy, the large-scale integration of new energy presents a great challenge to the power system economic dispatch. Thus, a multi-time-scale robust economic dispatch strategy of a multi-source hybrid power system based on the variable confidence level is proposed. The deterministic constraints of each time scale are transformed into robust constraints that take the uncertainty into account. Meanwhile, the robust level whose confidence level increases with the shortening of time scale is set to improve the scheduling conservative degree step by step. The selection principle of the robust level of each time scale is also presented. The proposed approach is applied to an IEEE 9-bus system. The calculation results are compared with those from the traditional multi-time scheduling method and show the effectiveness of the paper, which can reduce the uncertainty impact of wind, solar, and load forecast, as well as achieve a great balance of security, economic, and environmental benefits.

This paper discusses the implementation of a fully decentralized optimization for the multi-area stochastic dynamic economic dispatch (MASDED) of large scale power systems with wind power integrated. Firstly, the volatility of wind power is represented by sampling wind scenarios, and the consensus constraints of boundary buses’ phase angles among the forecast scenario and sampling scenarios are built. Secondly, the multi-area power system is decomposed into different areas by duplicating boarder variables. Finally, a bi-level iterative method that combines the modified analytical target cascading (ATC) method and the Benders decomposition method is applied to solve the MASDED in a fully decentralized way, and a coordination center turns out to be not necessary. The forecast scenario sub-problems and the sampling scenarios sub-problems of each area are solved iteratively, and the multipliers are updated in each area respectively. The 3-area IEEE RTS system and a 4-area 2298-bus system are tested to demonstrate the effectiveness of the proposed method.

Large-scale new energy incorporation presents great challenges to the power system economic dispatch. Complementary system can effectively enhance the accommodation of new energy. However, current complementary system day-ahead dispatch models have not considered the actual complementary and smoothing effect. Thus, a dynamic economic dispatch strategy based on multi-time-scale complementarity of wind, solar, hydro and thermal power is proposed. Wind, solar and hydro power is bundled as a virtual power (VP) according to their complementary features. The load tracking index is defined to represent the ability of the VP to track the load so that it can well follow the load curve. Meanwhile, a multi-time-scale complementary dispatch model is established, which includes a day-ahead 24h scheduling, an intra-day 4h rolling scheduling and a real-time 15min scheduling. According to the latest forecast, the day-ahead scheduling is amended continually, the VP output is adjusted continually to maintain its good tracking and the best complementary effect is also achieved. An example is calculated to verify that this strategy can effectively improve the actual complementary and smoothing effect of the complementary system, relieve the dispatch pressure as well as reduce the generation cost.

This paper proposes a rule based comprehensive approach to study distribution network reconfiguration (DNRC). The DNRC model with line power constraints is set up, in which the objective is to minimize the system power loss. In order to get the precise branch current and system power loss, a power summation based radiation distribution network load flow (PSRDNLF) method is applied in the study. The rules that are used to select the optimal reconfiguration of distribution network are formed based on the system operation experiences. The proposed rule based comprehensive approach is implemented in distribution network in Guiyang South Power Supply Bureau. For the purpose of illustrating the proposed approach, two distribution network systems are tested and analyzed in the paper.

This chapter comprehensively deals with various uncertain problems in power system operation such as uncertainty load analysis, probabilistic power flow, fuzzy power flow, economic dispatch with uncertainties, fuzzy economic dispatch, hydrothermal system operation with uncertainty, unit commitment (UC) with uncertainties, VAR optimization with uncertain reactive load, and probabilistic optimal power flow (P-OPF). Probabilistic analysis and fuzzy theory can be used to analyze the uncertainty load. A method of obtaining a stochastic model is to take a deterministic model and transform it into a stochastic model by (1) introducing random variables as inputs or as coefficients or as both; and (2) introducing equation errors as disturbances. The economy of UC of power systems is influenced by approximations in the operation planning methods and by the inaccuracies and uncertainties of input data.

Distribution networks are the most extensive part of the electrical power system. The goal of reconfiguration of the distribution network is to find a radial operating structure that minimizes power losses of the distribution system under normal operation conditions. Generally, distribution networks are built as interconnected networks, while in operation they are arranged into a radial tree structure. The distribution network reconfiguration (DNRC) model with line power constraints is set up, in which the objective is to minimize the system power loss. The basic idea of the heuristic branch exchange method is to compute change of power losses through operating a pair of switches. When the load flow distribution in a loop is an optimal flow, the corresponding network power losses will be minimal. In order to get a precise expression for system power loss, the branch power will be computed through a radial distribution network load flow (RDNLF) method.

Security-constrained economic dispatch (SCED) is a simplified optimal power flow (OPF) problem. It is widely used in the power industry. This chapter introduces several major approaches to solve the SCED problem, such as linear programming (LP), network flow programming (NFP), and quadratic programming (QP). Then, nonlinear convex network flow programming (NLCNFP) and the genetic algorithm (GA) are added to tackle the SCED problem. It also provides the implementation details of these methods and a number of numerical examples. The chapter presents a new NLCNFP model of economic dispatch control (EDC), which is solved by a combination approach of QP and NFP. It also presents a two-stage economic dispatch (ED) approach according to the practical operation situation of power systems. The first stage involves the classic economic power dispatch without considering network loss. The second stage involves ED considering system power loss and network security constraints.

This paper presents a new approach to study the optimal reactive power (VAR) control problem using a modified interior point (MIP) method. Basically, a two-step procedure is employed: computing a unified ranking process for optimal reactive power support sites using an analytic hierarchical process (AHP), and solving a optimal VAR control model for determining the values at the selected reactive power support sites. The AHP and sensitivity analysis methods are used to determine the sites of optimal VAR support service. The objective used in the optimal VAR control model is to minimize system real power losses and to penalize any new VAR utilization, so that the overall system VAR control options are optimized. The proposed approach is tested on the IEEE 14-bus and 30-bus systems, from which satisfactory results have been obtained.

This paper presents a new nonlinear optimization neural network approach to study the problem of security-constrained interconnected multiarea economic dispatch. It is a penalty-minimizing neural network approach with weights based on optimization theory and neural optimization method. In the paper the model of security-constrained multiarea economic dispatch is set up, in which tie-line security and transfer constraints in each area are considered. In addition, a simple analysis of buying and selling contract in a multiarea environment is made. The proposed method is tested on a system of three interconnected areas. The detailed results and analysis are given in the paper.

This paper presents an approach to calculate the price of reactive power (VAR) support service in a multi-area power system. The methods are cost-benefit analysis (CBA) and nonlinear convex network flow programming (NLCNFP). By using multiple cost-benefit indices, the VAR support benefits with respect to power delivery increases of tie lines are computed. These benefits are used to determine the VAR pricing in multi-areas environment. The multi-area optimization model with VAR pricing is solved by NLCNFP algorithm, which is a combined method of quadratic programming (QP) and network flow programming (NFP). The proposed VAR pricing scheme was tested on IEEE 118-bus system, which is divided into three areas.

This paper proposes an improved method to study distribution network reconfiguration (DNRC) based on a refined genetic algorithm (GA). The DNRC model, in which the objective is to minimize the system power loss, is set up. In order to get the precise branch current and system power loss, a radiation distribution network load flow (RDNLF) method is presented in the study. The refined genetic algorithm is also set up, in which some improvements are made on chromosome coding, fitness function and mutation pattern. As a result, premature convergence is avoided. The proposed approach is tested on 16-bus and 33-bus distribution networks. Study results are given in the paper.

This paper reports an application of the Everett optimization technique for value-based load shedding in naval-ship power system with network constraints and application of reliability constraints. A new congestion analysis index—expected contingency margin (ECM), which considers the probability of disturbance, and reliability indices loss of load probability (LOLP) and expected unserved energy (EUE) are presented to filter the critical outage and congestion cases. The optimal load shedding scheme carried out using the Everett optimization technique uses a utility function, which addresses the cost of allocating pay-off while satisfying the network and reliability constraints and generation capacity limits. The algorithm search for the optimal λ to form a fair pricing mechanism, which produces maximum pay-off and minimum load shedding while, satisfying system constraints. The proposed approach is examined on naval-ship power system and detailed results are shown.

Smart grid economic dispatch (SGED) is more complicated than the traditional economic dispatch since it involves the operation of the uncertain renewable energy resources, as well as chargeable and dischargeable storage. This paper presents an approach to solve the smart grid economic dispatch problem using a two-stage optimization method. The proposed SGED model contains wind power generation and the storage provider. The first stage involves the fixed wind power generation, which is estimated and also cannot be adjustable. The second stage involves smart grid economic dispatch considering network loss and security constraints, as well as adjustable wind energy, where the wind power generations are variable at some range. Three objectives may be used for the second stage. They are the minimization of the generation cost, the minimization of system loss, and the minimization of the movement of generator output from the first stage generation plans. A modified IEEE 30-bus system, which contains the wind farm and storage device, is used for testing. The test results show the effectiveness of the proposed two stage smart grid economic dispatch approach.

This paper presents a new nonlinear convex network flow programming (NLCNFP) model and algorithm for solving the security-constrained multi-area economic dispatch (MAED) problem. The tie-line security and transfer constraints in each area are considered in the MAED model. A simple analysis of a buying and selling contract in a multi-area environment is also made. The NLCNFP model of security-constrained multi-area economic dispatch was set up and solved by using a combined method of quadratic programming (QP) and network flow programming (NFP). The concept of maximum basis in the network flow graph was introduced to change the constrained model into an unconstrained QP model, which was easily solved by the reduced gradient method. The proposed approach is tested on a system of four interconnected areas with satisfactory results.

An integrated approach for reactive power price and control is developed. Reactive power price is divided into fixed and variable parts. The fixed part is the operational cost of reactive power service. The variable part of reactive power price is determined based on capability and contributions to the improvement of system performance such as security, reliability and economics. These contributions can be evaluated by computing sensitivity of objective function with respect to reactive power support. The optimal power flow (OPF) approach is used to carry out this purpose. For VAr planning (or control) purposes, three parallel indices are first presented to determine the sites of new VAr sources. They are benefit-to-cost ratio index, voltage reactive sensitivity index, and the bus voltage security index. The analytic hierarchical process is then used to comprehensively consider the effect of the three indices and the network topology for each candidate VAr source site. The proposed approach was tested on an IEEE 30-bus system with satisfactory results.

Since conventional optimal power flow (OPF) algorithms are limited and too slow for operational planning, power system operation and planning engineers have been seeking efficient OPF algorithms for three decades. The interior point method is one of the most efficient algorithms. In this paper, an improved quadratic interior point (IQIP) method is used to solve comprehensive OPF problems with a variety of objective functions, including economic dispatch, VAr planning and loss minimization. The IQIP method features a general starting point (rather than selected good point as in the general interior point method) and fast convergence. Consequently, the OPF package described in this paper offers huge improvements in speed, accuracy and convergence in solving multi-objective and multi-constraint optimization problems. It will be a very useful tool for the power industry.

This paper proposes a new method to study reactive power pricing and new VAr source selection using the analytic hierarchical process (AHP), and presents a price structure for providing reactive power service and control based on the OPF approach. The cost of reactive power support service is determined based on capability and contribution to improvement of system performance such as security, reliability and economics, by calculating sensitivity of objective function with respect to reactive power support. For VAr planning purpose, an analytic hierarchical process model is devised which comprehensively considers the network topology and all types of benefits including operating cost, system voltage and loss for each candidate VAr source site. The proposed approach for calculating VAr pricing and selecting the new VAr sources was tested on an IEEE 30-bus system. The calculation results are analyzed by the cost-benefit analysis (CBA) method.

A new approach in the power system analysis to automatic contingency selection (ACS) and ranking, using an analytic hierarchical process (AHP) is developed. ACS for the real and reactive power subproblems is solved by network flow programming, based on the existence of weak coupling between real and reactive quantities in power systems. The performance indices to assess the severity of contingencies are defined as the total real and reactive load to be curtailed. In the rank calculation, this paper takes into consideration the relative importance of transmission lines and the situation that the real and reactive power security constraints may be violated as the line outage appears, so that the precise information for the real time security analysis can be provided. The results on IEEE-14 bus test system are given in the paper

This paper presents an approach to reduce the transmission loss based on the practical system operation of North China Grid (NCG). The main idea is to handle the loss reduction issue using a new and practical angle from both a post-analysis perspective and a security constrained unit dispatch perspective. The objective of the proposed approach is to reduce the losses in the concerned dispatchable area as well as a list of specifically designated branches. The purpose of this paper is to analyze the past performances, and provide guidance for future operations. The proposed method for loss minimization and the related sensitivity calculation have been applied to NCG practical power system. The sample results and the practical analysis as well as future enhancements are also provided in the paper.

This paper presents a practical approach to implement the economic dispatch of the hydrothermal power system in Southern China. The proposed economic dispatch method first computes the initial generation plans for all generator units including hydro units, which are determined according to the equal incremental principal of hydrothermal system. The system loss is approximately considered during the calculation of the initial generation plan. Then, the mathematical model of the optimal dispatch, which considers the network loss and security constraints, is set up based on the initial operation point. The solution algorithm is the modified interior point method. For showing the effectiveness of the proposed approach, the practical hydrothermal power system in southern China is used for demonstration. The results show the feasibility of the proposed dispatch method.

This paper presents an approach to select the proper location of wind farm in power system. Two key factors for constructing wind farm are considered in this study. They are wind availability and wind speed. Because of the “undispatchable” nature of wind and the difficulty in forecasting, the wind availability and wind speed are random and uncertainty. Thus, the deterministic method is not appropriate to handle them. This paper uses fuzzy number to deal with the wind availability and wind speed. The term of average unavailable time (AUAT) is introduced in order to compute the probability of average wind availability. The proposed approach for selecting wind farm has been applied to the IEEE 30-bus test system.

This chapter selects several classic optimal power flow (OPF) algorithms and describes their implementation details. These algorithms include traditional methods such as Newton method, gradient method, linear programming, as well as the latest methods such as modified interior point (IP) method, analytic hierarchy process (AHP), and particle swarm optimization (PSO) method. The goal of OPF is to find the optimal settings of a given power system network that optimizes the system objective functions such as total generation cost, system loss, bus voltage deviation, emission of generating units, number of control actions, and load shedding while satisfying its power flow equations, system security, and equipment operating limits. The phase shifters are adjusted sequentially and their direction of adjustments are governed by the impact on the primary objective function of minimal line overload, in the search technique. This chapter focuses on applying PSO methods to solve the OPF problem.

This chapter contains sections titled: Introduction Linear Programming Method Quadratic Programming Method Network Flow Programming Method Nonlinear Convex Network Flow Programming Method Two-Stage Economic Dispatch Approach Security-Constrained ED by Genetic Algorithms Appendix: Network Flow Programming References ]]>

This chapter introduces the input-output characteristic of a power-generating unit as well as the corresponding practical calculation method. It presents several well-known optimization methods to solve the classic economic dispatch (ED) problem. The chapter discusses two general approaches to compute network losses and the corresponding incremental power losses. The first i.e. B-coefficient method, is the development of a mathematical expression for the losses in the network solely as a function of the power output of each of the unit. It discusses the equal incremental principle for classical ED. Finally, the chapter analyzes applications of the latest methods such as neural network and genetic algorithm to classic ED. This chapter also introduces several methods such as Gradient Method, Line Search, Newton-Raphson Optimization, Trust-Region Optimization, Newton-Raphson Optimization with Line Search, Quasi-Newton Optimization, Double Dogleg Optimization, Conjugate Gradient Optimization, Lagrange Multipliers Method and Kuhn-Tucker Conditions, used for economic power operation of power systems.

This chapter contains sections titled: Introduction Classic Method for Reactive Power Dispatch Linear Programming Method of VAR Optimization Interior Point Method for VAR Optimization Problem NLONN Approach VAR Optimization by Evolutionary Algorithm VAR Optimization by Particle Swarm Optimization Algorithm Reactive Power Pricing Calculation References ]]>

This paper presents a practical approach to implement the economic power dispatch of the power system in Southern China. The proposed economic dispatch method consists of two stages. The first stage involves the classic economic power dispatch without considering network loss, where the initial generation plans of the generator units are determined according to the rank of fuel consuming characteristic of the units or the principal of equal incremental rate. The second stage involves economic dispatch considering network loss and security constraints, where two objectives are proposed for the second stage. One is loss minimization, and another is the minimum movement of generator output from the initial generation plan. For showing the effectiveness of the proposed two stage economic dispatch approach, the IEEE 30-bus system is used for testing. The test results show the two stage dispatch method can not only reduce the system losses and system fuel consumption, but also control the movement of the generator output.

This paper proposes an application of the analytic hierarchy process (AHP) and analytic network process (ANP) for enhancing the selection of generating power units for appropriate price allocation in a competitive power environment. The scheme addresses adequate ranking, prioritizing, and scheduling of units before optimizing the pricing of generation units to meet a given demand. In the deregulated environment, the classical optimization techniques will be insufficient for the above-mentioned purpose. Hence, by incorporating the interaction of factors such as load demand, generating cost curve, bid/sale price, unit up/down cost, and the relative importance of different generation units, the scheme can be implemented to address the technical and nontechnical constraints in unit commitment problems. This information is easily augmented with the optimization scheme for an effective optimal decision. The scheme proposed is tested using the IEEE 39-bus test system.

This paper presents an implementation to alleviate the overload in the energy markets. The proposed alleviating overload (AOL) method is based on real time network analysis (RTNET), state estimator (SE), real time contingency analysis (RTCA), and the constraint shift factor (CSF) calculation in the energy management system (EMS). RTNET/SE is used to obtain real time data through state estimator and capture the real time data and compute loss sensitivities. RTCA/CSF is used to compute generator shift factors (or sensitivities) for the violated constraints both in base case and outage situations. The network data, loss sensitivities and the shift factors are passed to LMP system for dispatching the units and alleviating the constraints violations. The implementation of AOL and the test results for the constrained shift factor calculation are shown in the paper.

This paper proposes a rule based comprehensive approach to study distribution network reconfiguration (DNRC). The DNRC model with line power constraints is set up, in which the objective is to minimize the system power loss. In order to get the precise branch current and system power loss, a power summation based radiation distribution network load flow (PSRDNLF) method is applied in the study. The rules that are used to select the optimal reconfiguration of distribution network are formed based on the system operation experiences. For the purpose of illustrating the proposed approach, two distribution network systems are tested and analyzed in the paper.

This paper proposes a model of distribution network reconfiguration (DNRC) to minimize the system power loss. A refined genetic algorithm (GA) is set up, in which some improvements are made on chromosome coding, fitness function and mutation pattern. As a result, premature convergence is avoided. The proposed approach is tested on 16 bus and 33-bus distribution networks. Study results are given in the paper.

The paper develops a price structure for providing reactive power service and control based on optimal power flow (OPF) approach. The cost of reactive power support service is determined based on capability and contributions to the improvement of system performance such as security, reliability and economics, by computing sensitivity of objective function with respect to reactive power support. The OPF model, in which the objective function is minimization of system loss, is solved by the interior point approach. For VAr planning purpose, three parallel indices are first presented to determine the sites of new VAR sources, based on the cost benefit analysis, the sensitivity method and the voltage security margin method. Then, the analytic hierarchical process is used to comprehensively consider the effect of three indices and the network topology for each candidate VAr source site. The proposed approach was tested on an IEEE 30 bus system with satisfactory results.

A new idea using an analytic hierarchical process (AHP) is proposed for Var placement compensation. AHP uses parallel analytical criteria for selecting and ranking placement of Var compensation. Due to their independent nature these criteria are not necessarily the same although both aim to identify weak nodes in maintaining system voltages. AHP also considers quantitative criteria. It is especially suitable for problems that are difficult to analyse. AHP provides a simple, convenient and comprehensive means of selection and ranking. The proposed algorithms have been tested on the IEEE 14-bus and 30-bus systems with satisfactory results. The paper also proposes a new nonlinear optimisation neural network approach to study the reactive power problem. The approach is applied to Var control optimisation, in which the objective is to minimise the system voltage profile. The approach is a penalty-minimisation method with weights based on optimisation theory and neural optimisation methods. It is used to solve the nonlinear programming problem with equality and inequality constraints. The paper demonstrates that the energy function used is a Lyapunov function, and the equilibrium point of the proposed neural network corresponds to the optimal solution of a constrained optimisation problem.

A fully coupled active and reactive dispatch using linear programming and an analytic hierarchical process is developed. The purpose of combined active and reactive dispatch (CARD) is to achieve the overall objective of minimum generation cost and to improve the distribution of reactive power and voltage, subject to constraints which ensure system security. Security is defined as the maintenance of individual circuit flows, generator reactive power output and system voltages within limits under normal system conditions and contingency cases. The weighting factors of different kinds of objective functions are determined by an analytic hierarchical process (AHP), considering the relative importance of these objective functions. The developed method is demonstrated through its application to determine the combined active and reactive dispatch of a 713-node network representing a practical power system, provided by the National Grid Company plc (NGC). The calculation results show that a good balance can be achieved among the various objectives and a satisfactory generation pattern is obtained from the enhanced CARD program.