A new approach to security-constrained generation scheduling of large-scale power systems with a piecewise linear ramping model

This paper presents a new and efficient approach to determine security-constrained generation scheduling (SCGS) in large-scale power systems, taking into account dispatch, network, and security constraints in pre and post-contingency states. A novel ramp rate limit is also modeled as a piecewise linear function in the SCGS problem to reflect more practical characteristics of the generating units. Benders decomposition is applied to this constrained solution process to obtain an optimal SCGS problem based on mixed-integer nonlinear programming (MINLP). The formulation can be embedded in two stages. First, a MIP is formulated in the master problem to solve a unit commitment (UC) problem. This stage determines appropriate on/off states of the units. The second stage, the subproblem, is formulated as a NLP to solve a security-constrained economic dispatch (SCED) problem. This stage is used to determine the feasibility of the master problem solution. It provides information to formulate the benders cuts that connect both problems. The proposed approach is tested in the IEEE 118-bus system to show its effectiveness. The simulation results are more realistic and feasible, whilst assuring an acceptable computation time.     

Combined heat and power economic emission dispatch using nondominated sorting genetic algorithm-II

This paper presents nondominated sorting genetic algorithm-II for solving combined heat and power economic emission dispatch problem. The problem is formulated as a nonlinear constrained multi-objective optimization problem. Nondominated sorting genetic algorithm-II is proposed to handle economic emission dispatch as a true multi-objective optimization problem with competing and noncommensurable objectives. The proposed algorithm is illustrated for two test systems and the test results are compared with those obtained from strength pareto evolutionary algorithm 2.     

Economic dispatch with generation contingency constraints

This paper presents a new model of the generation contingency constrained economic dispatch problem and proposes a method for its solution. The operating policy of Northern Ireland Electricity was the basis for the formulation, and software was implemented to support it. Since the Northern Ireland Electricity power system operates in relative isolation, the operating security criteria are rather stringent. In particular, it is required that loss of generation of any generating unit in the system must be covered by fast, 3 or 30 second generation reserves on other units in the system. The fast response unit reserve capabilities are represented by concave curves. The solution method is based a nonlinear version of Dantzig-Wolfe decomposition principle. Numerical results are presented     

基于通用分布的含风电电力系统随机动态经济调度

随着风电大规模并网,其不确定性给电力系统经济调度带来了新的挑战。文中利用通用分布模型拟合不同风电功率预测水平下的实际风电功率分布,并以此建立了考虑风电低估、高估成本的日前动态经济调度的随机优化模型。通过对目标函数和约束条件的转化与分析,将随机优化模型转化为一个非线性凸优化问题。结合二次规划算法和内点法,提出了一种两阶段优化算法用以求解对应的经济调度问题。最后,在含风电场的IEEE 30节点系统上,验证了所提基于通用分布的随机动态经济调度方法的有效性。     

基于模糊算法的水火系统双目标经济负荷分配的研究

本文建立了电力市场下以全网煤耗最小并成本节约最大为双目标的水火电力系统有功经济负荷分配模型,将模糊优化理论、大系统分解理论及线性规划方法有机结合,提出了求解双目标、大规模、非线性经济负荷分配问题的有效方法,得到了最佳满意度,协调了各目标间的冲突。仿真算例的结果验证了本文模型和算法的正确性和有效性。     

Operating strategies under emission constraints

The emission-constrained dispatch problem is formulated as a nonlinear constrained minimization problem. Consequently, the solution to the problem gives a continuous relationship between cost and annual emission for SO₂. It is shown that the power system should be operated at the same value of the Lagrangian multiplier, η, in every hour where η is defined as ∂(production cost)/∂(hourly emission). The addition of η as a proxy cost of emission in the economical dispatch procedure achieves this goal. It is shown that the emission-η relationship obtained by NLCM procedure can be used to make operating decisions, in particular, the trading of allowances     

Dynamic economic dispatch: feasible and optimal solutions

Dynamic economic dispatch is an extension of the conventional economic dispatch problem that takes into consideration the limits on the ramp rate of the generating units. This paper examines the factors that affect the feasibility and optimality of solutions to this problem. It proposes two new solution methods. The first is guaranteed to find a feasible solution even when the load profile is nonmonotonic. The second is an efficient technique for funding the optimal solution. The results obtained with these methods are compared with those obtained using previously published methods     

Economic dispatch with security-constrained rescheduling

A mathematical framework is described for the solution of the economic dispatch problem with security constraints, which can take into account the system corrective capabilities after an outage has occurred. The solution algorithm is based on mathematical programming decomposition techniques that allow the iterative solution of a ‘base-case’ economic dispatch and separate contingency analysis with generation rescheduling to eliminate constraint violations. The resulting dispatch has the same security level as the usual security-constrained dispatch, but with lower operating costs. Case studies with the system of Southern Brazil are presented. The extension of the methodology to include other corrective schemes is also discussed.     

A new approach to secure economic power dispatch

This article presents a new nonlinear convex network flow programming model and algorithm for solving the on-line economic power dispatch with N and N−1 security. Based on the load flow equations, a new nonlinear convex network flow model for secure economic power dispatch is set up and then transformed into a quadratic programming model, in which the search direction in the space of the flow variables is to be solved. The concept of maximum basis in a network flow graph was introduced so that the constrained quadratic programming model was changed into an unconstrained quadratic programming model which was then solved by the reduced gradient method. The proposed model and its algorithm were examined numerically with an IEEE 30-bus test system on an ALPHA 400 Model 610 machine. Satisfactory results were obtained.     

基于广义蚁群算法的电力系统经济负荷分配

提出了一种可用于求解一般形式的非凸、非线性约束优化问题的广义蚁群算法，以用于求解复杂的非凸、非线性电力系统经济负荷分配问题，与用于组合优化的蚁群算法类似，该算法运用了正反馈，分布式计算和贪婪式启发搜索，基于不动点理论，给出了该算法收敛的充分条件，多个算例结果表明，文中提出的算法是有效可行的。     

Value-Based Transmission Expansion Planning of Hydrothermal Systems Under Uncertainty

Transmission planning studies in hydrothermal systems deal with complex issues. Two include 1) the need for a robust grid that can accommodate a large number of economic dispatch patterns caused by differing hydrological conditions in the river basins and 2) the high cost of grid reinforcements due to the large distance from hydro plants to load centers and the required N-l security criterion. It is thus necessary to consider the tradeoff between supply reliability and reinforcement cost. The resulting planning problem is formulated as a large-scale mixed integer nonlinear optimization model. The objective function is to minimize the sum of investment costs and expected load-shedding costs. The constraints include linearized power flow equations, limits on circuit flows for all combinations of economic dispatch points (which capture hydrological variation), and circuit contingencies (which capture supply reliability). This paper describes a new solution scheme for this problem that is based on two techniques: 1) the extension of a binary disjunctive technique, which transforms the integer nonlinear problem into a linear one and 2) screening strategies, which allow a judicious choice of contingencies and candidate circuits. Planning studies for Brazil and Bolivia are presented and discussed.     

A new rooted tree optimization algorithm for economic dispatch with valve-point effect

This work proposes a new optimization method called root tree optimization algorithm (RTO). The robustness and efficiency of the proposed RTO algorithm is validated on a 23 standard benchmark nonlinear functions and compared with well-known methods by addressing the same problem. Simulation results show effectiveness of the proposed RTO algorithm in term of solution quality and convergence characteristics. In order to evaluate the effectiveness of the proposed method, 3-unit, 30 Bus IEEE, 13-unit and 15-units are used as case studies with incremental fuel cost functions. The constraints include ramp rate limits, prohibited operating zones and the valve point effect. These constraints make the economic dispatch (ED) problem a non-convex minimization problem with constraints. Simulation results obtained by the proposed algorithm are compared with the results obtained using other methods available in the literature. Based on the numerical results, the proposed RTO algorithm is able to provide better solutions than other reported techniques in terms of fuel cost and robustness.     

A new approach to generation scheduling in interconnected power systems using predictor-corrector proximal multiplier method

The purpose of this paper is to elaborate a new generation scheduling algorithm in the interconnected power systems. Typically, the generation scheduling problem as a mixed integer non-linear programming can be effectively solved by the generalized Benders decomposition technique which decouples an original problem into the master problem and subproblems to tremendously allow fast and accurate solutions of large-scale problems. In order to formulate efficient inter-temporal optimal power flow (OPF) subproblems, we will explore a regional decomposition framework based on predictor-corrector proximal multiplier method. In fact, this scheme can find the most economic generation schedules under the power transactions for a multi-utility system without the exchange of each utility’s own private information and major disruption to existing economic dispatch or OPF adopted by individual utilities.     

Dynamic optical economic dispatch under system availability constraints

In this paper we have developed a dynamic optimal economic dispatch policy based on a stochastic availability model of large-scale power systems and a piece-wise constant incremental fuel cost model. Using these models the optimal economic dispatch under given system availability constraint is formulated as a dynamic nonlinear optimization problem. The random variations of demands, available generation capacities and available tie line capacities are considered as constraints in the problem. In order to solve the optimization problem an efficient algorithm based on the rule of merit-order loading has been developed. The algorithm allows large dimensionality of the system and randomness of the system parameters. The algorithm can also be easily implemented on a dispatch computer. In order to illustrate the effect of the proposed method on system generation economy and availability, an example is presented giving detailed numerical results which are very encouraging. As far as the authors know, such an economic dispatch problem which maintains the system availability index at the highest possible level (under the given system environment) has never been considered in the literature before.     

An enhanced Lagrangian neural network for the ELD problems with piecewise quadratic cost functions and nonlinear constraints

This paper presents a new Lagrangian artificial neural network (ANN) and its application to the power system economic load dispatch (ELD) problems with piecewise quadratic cost functions (PQCFs) and nonlinear constraints. By restructuring the dynamics of the modified Lagrangian ANN [IEEE ICNN, 1 (1996) 537], stable convergence characteristics are obtained even with the nonlinear constraints. The convergence speeds are enhanced by employing the momentum technique and providing a criteria for choosing the learning rate parameters. Instead of having one convex cost function for each unit, which is normally the case in typical ELD problem formulations, more realistic multiple quadratic cost functions are used to reflect the effects of valve point loadings and possible fuel changes. In addition, the B matrix approach is employed for more accurate estimation of the transmission losses than treating them as a constant, which necessitate the inclusion of a nonlinear equality constraint. The effectiveness of the proposed ANN applied to the ELD problem is demonstrated through extensive simulation tests.     

Seeker Optimization Algorithm for Optimal Reactive Power Dispatch

Optimal reactive power dispatch problem in power systems has thrown a growing influence on secure and economical operation of power systems. However, this issue is well known as a nonlinear, multimodal and mixed-variable problem. In the last decades, computation intelligence-based techniques, such as genetic algorithms (GAs), differential evolution (DE) algorithms and particle swarm optimization (PSO) algorithms, etc., have often been used for this aim. In this work, a seeker optimization algorithm (SOA)-based reactive power dispatch method is proposed. The SOA is based on the concept of simulating the act of human searching, where the search direction is based on the empirical gradient by evaluating the response to the position changes and the step length is based on uncertainty reasoning by using a simple Fuzzy rule. In this study, the algorithm's performance is evaluated on benchmark function optimization. Then, the SOA is applied to optimal reactive power dispatch on standard IEEE 57- and 118-bus power systems, and compared with conventional nonlinear programming method, two versions of GAs, three versions of DE algorithms and four versions of PSO algorithms. The simulation results show that the proposed approach is superior to the other listed algorithms and can be efficiently used for optimal reactive power dispatch.      

Dynamic optimal economic dispatch under system availability constraints and transmission losses

In this paper we have developed a dynamic optimal economic dispatch policy on the basis of a stochastic availability model and a piece-wise constant incremental fuel cost model. Using these models the optimal economic dispatch under the system availability constraints and transmission losses is formulated as a dynamic nonlinear optimization problem. The problem is solved by an algorithm recently developed by the authors (Electr. Power Syst. Res., 9 (1985) 11–27). In order to illustrate the effectiveness of the proposed method, an example is presented with detailed numerical results.     

Reserve constrained economic dispatch with prohibited operatingzones

A method is described for solving the reserve constrained economic dispatch problem when some of the online generating units have prohibited operating zone(s). For a unit with prohibited zone(s), the zone(s) divide the operating region between the minimum generation limit (Pmin) and the maximum generation limit (Pmax) into disjoint convex subregions. These disjoint subregions form a nonconvex decisions space and the associated economic dispatch problem is thus a nonconvex optimization problem. As a result, the conventional Lagrangian relaxation (LR) approach (e.g. the λ-δ iterative approach) cannot be applied directly. The method proposed decomposes the nonconvex decision space into a small number of subsets such that each of the associated dispatch problems is either infeasible or one that can be directly solved via the conventional LR approach. Based on the decomposition, the optimal solution is the least costly one among all the feasible solutions of the associated dispatch problems. Examples are also given to illustrate the proposed method     

Evolutionary programming based economic dispatch of generators with prohibited operating zones

This paper presents a new approach using evolutionary programming for solving the economic dispatch (ED) problem of generators when some/all of the units have prohibited operating zones. In this method, additional constraints such as spinning reserve requirements and ramp-rate limits are also considered besides taking into account network losses. The proposed method is implemented for solving a few example dispatch problems. The results obtained by this new approach are compared with those obtained using traditional methods. The study results have shown that the approach developed is feasible and efficient.     

考虑风电不确定性的互联电力系统分散协调调度模型

针对含高比例风电的直流互联电力系统经济调度问题,采用鲁棒优化方法描述风电出力,提出了一种基于目标级联分析法的分散协调调度模型。首先,采用鲁棒优化方法中的多面体集合来描述风电出力的不确定性,为了降低问题求解的保守度,引入了鲁棒保守度调节因子。然后,根据分散协调算法的分解原理将待解决的经济调度问题分解为主问题和子问题。其中,主问题为上级调度中心协调优化互联电力系统之间的直流联络线功率,子问题为下级调度中心独立优化各区域电网的发电计划。最后,通过两个算例对所提模型的有效性进行了验证。结果表明,所提方法不仅可以弥补鲁棒优化方法偏于保守的不足,而且能够在应对风电出力不确定性的同时实现风电的跨区域消纳,适合中国电网目前的分层分区调度模式。