Multi-area power systems economic dispatch using nonlinear convex network flow programming

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.     

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。     

A new model and algorithm of secure and economic automatic generation control

This paper presents a new nonlinear convex network flow programming (NLCNFP) model and algorithm for solving the on-line economic power dispatch and automatic generation control (AGC) with security and economy. Two AGC functions—load frequency control (LFC) and economic dispatch control (EDC) are modeled on the same timescale as EDC. This new AGC modeling and solution algorithm meets not only the control requirement of frequency and tie-line power as in the conventional load frequency control, but also the line security and system economy. The proposed approach is tested on an IEEE 30-bus system with satisfactory results.     

基于原-对偶内点法和混合整数规划法的机组组合问题研究

电力系统机组组合能带来显著的经济效益,随着电力市场的不断发展,在电力系统优化运行中变得尤为重要。然而电力系统机组组组合问题是一个大规模、非凸、非线性混合整数优化问题,至今仍然没有找到一种理想的优化算法。因此针对其特点,采用了原-对偶内点法和混合整数规划法相结合的算法,首先利用混合整数规划法形成伴随规划来处理离散变量,再通过内点法求解伴随规划子问题和负荷经济分配,充分发挥了两种算法在求解机组组合问题上的优势。文中对标准10机组24时段系统算例进行了仿真测试并与之前的各种优化算法进行了对比,结果表明了本文算法模型解决机组组合问题的有效性和优越性。     

基于风速预测和随机规划的含风电场电力系统动态经济调度

随着风力发电在电力系统中比重的持续增加,在电力系统经济调度中需要考虑风电场的影响;而并网风电场具有动态、随机、容量大等特点,传统的经济调度方法已不再适用。针对风电场出力的随机性,在风速预测的基础上,应用随机规划理论建立了考虑机组组合的含风电场电力系统动元网络和遗传算法的混合智能算法,提高了算法的收敛速度和搜索性能。以含风电场的IEEE30节点系统为算例验证了所提方法的可行性和有效性。     

变负荷条件下追踪电力系统安全最优运行轨迹的参数化方法

提出一种追踪线性约束下凸可分规划问题最优解轨迹的参数化方法。该参数优化算法可在对偶松弛凸可分规划算法的主循环之外,通过少量参数化扩展得到。参数分析表明最优解轨迹的性态是一条分段线性曲线,解轨迹上的破点和不可行现象存在密切关系。将这种方法应用到电力系统有功最优潮流问题中,得到一种统一经济调度和安全约束调度的参数化安全约束调度(security constrained economic dispatch,SCED)新算法,它可快速追踪变负荷条件下系统安全最优运行轨迹。算法在IEEE14-300节点测试系统及2个省级实际系统上通过测试,数值试验和几何分析表明了该方法的计算特性和物理内涵,同时清楚地显示了目前调度模式中存在的问题和改进方向。     

A nonlinear fractional programming approach for environmental–economic power dispatch

A nonlinear fractional programming approach is provided for addressing the environmental–economic power dispatch problems in the thermal power dispatch systems. The objective of this study is to simultaneously minimize the total fuel cost and total emissions of the power dispatch systems, which is realized by two simultaneous models with nonlinear constraints. The first model is to minimize the quotient of two competing and conflicting functions (i.e. [total emission function]/[total fuel cost function]), and the second one is to minimize the total fuel cost expressed by a quadratic objective function. In particular, the process of solving the first model uses Dinkelbach’s algorithm to convert the minimization problem with the nonlinear fractional objective function into a sequence of non-fractional minimization problems. The effectiveness of this approach is demonstrated through applying to the standard IEEE 30-bus test system. Comparison between the present approach and other existing approaches shows that the proposed approach can generate superior decision alternatives from the view point of realizing a more environmentally friendly and cost-effective scheme and/or considering the power transmission loss rate in the power dispatch systems.     

Economic dispatch of active power by quadrativ programming using a sparse linear complementary algorithm

A new method for economic dispatch of active power is presented. Formulation of the problem as a quadratic program allows the inclusion of a linear network model and operational constraints together with an explicit representation of the cost incurred by transmission losses. The problem is solved by a linear complementary pivoting algorithm which takes full advantage of the sparse form of the objective function and constraints. Computational experience indicates that the method is highly efficient and is capable of solving realistic problems in elapsed times that are compatible with online applications using minicomputer hardware.     

考虑气电联合需求响应的气电综合能源配网系统协调优化运行

在未来多能互补、综合能源系统的背景下,传统配电网和配气网独立调度运行的模式已经不能满足多种能源互补的运行要求。为此,该文提出气电综合能源配网系统最优潮流的凸优化方法,即利用二阶锥规划方法对配电网潮流方程约束进行处理,并提出运用增强二阶锥规划与泰勒级数展开相结合的方法对天然气潮流方程约束进行处理,进而将非线性的气电综合能源配网系统优化调度问题转化为混合整数二阶锥规划模型,为气电综合能源配网的气/电协调优化运行和规划设计提供支撑。同时在配网系统中引入气电联合需求响应来提高系统调度的可控性和灵活性,从而更好的消纳新能源,以达到配网系统的优化运行。仿真结果表明,运用增强二阶锥规划与泰勒级数展开相结合的方法能更好提高配气网的二阶锥松弛精度,且考虑气电联合需求响应能够提高综合能源配网系统运行的经济性和新能源的消纳能力。     

基于半定规划的{0,1}-经济调度

基于内点半定规划,提出一种直接求解{0,1}-经济调度问题({0,1}-ED)的新方法.通过引入辅助变量,该方法将原整数变量约束转化为凸二次约束,进而将{0,1}-ED问题转化为半定规划问题,并用内点法进行求解.对于大系统整数变量的微小偏差,应用简单的启发式技术调整.ED-420等9个测试系统的仿真结果表明,所提方法能够有效地处理{0,1}-经济调度,对于大多数问题都可以得到较精确的结果,计算时间具有多项式复杂性.     

机会约束随机动态经济调度的凸松弛迭代求解法

大规模风电并网给电力系统运行带来了重大技术挑战,其出力的随机性和波动性增加了线路传输能力和备用调节能力不足的风险,传统的确定性经济调度方法已不完全适用。首先提出了一种基于混合高斯分布的机会约束随机动态经济调度模型,该模型将最小备用约束和线路传输容量约束建模为机会约束,并引入调频机组的仿射控制策略以实时平衡风功率的波动。然后提出了一种机会约束规划的松弛迭代求解方法,将随机调度模型转化为二次规划模型以实现快速有效求解。利用中国西南某省25个风电场的现场数据以及IEEE 118节点系统进行算例分析,验证了混合高斯分布对风电预测误差的拟合精度,以及所提方法的可行性。     

基于SOCP的综合能源系统日前调度概率最优能量流

随着能源危机的加重,再电气化成为破解能源发展难题的必然选择。根据电气互联综合能源系统作为再电气化的一种新思路,提出利用二阶锥规划求解综合能源系统日前优化调度概率最优能量流的方法。首先,利用电力系统、天然气系统和能源集线器构建综合能源系统日前调度概率模型;然后,将综合能源系统日前调度概率模型放缩为凸模型;接着,采用点估计法求解综合能源系统日前调度概率最优能量流;最后,利用典型算例在MATLAB上的YALMIP平台验证此算法的正确性与有效性。     

配电网重构的凸模型

推导出了配电网重构的混合整数二次规划模型、二次规划二次约束模型和二阶锥规划模型,并提出有连续凸松弛的AC潮流问题。所提各模型可由标准商业软件可靠、有效地解决最优性问题。在推导各模型的过程中,得到了放射性网络潮流的近似原始二次约束模型和二阶锥规划模型。     

Semi-definite Programming Approach to Stochastic Combined Heat and Power Environmental/Economic Dispatch Problem

This article presents a solution to the stochastic multi-objective combined heat and power environmental/economic dispatch problem using the semi-definite programming formulation. The vector objective is reduced to an equivalent scalar objective using the weighted sum method. The resulting optimization problem is formulated as a convex optimization via semi-definite programming relaxation. The convex optimization problem was solved to obtain Pareto-optimal solutions. Improvement in the distribution of solution set was achieved through non-linear selection of the weight factor. Simulation was performed on a test problem to investigate the effectiveness of the proposed approach. Results showed that the semi-definite programming based weighted sum method has inherently good convergence property and can have its diversity property improved through weight adaptation.     

考虑配电网电能质量改善的分布式光伏优化调度方法

针对配电网中存在的电压越限、谐波畸变、三相不平衡等问题,从综合改善多电能质量问题的角度出发,研究了一种配电网分布式光伏优化调度模型及其求解方法。首先,分析了分布式光伏并网逆变器进行无功功率、谐波电流及不平衡功率补偿的控制方案;在此基础上,以可调度分布式光伏的三相功率及谐波电流输出为控制变量,基于配电网三相基波及谐波潮流方程,建立了最小化网络损耗、不平衡电压以及谐波电压的最优潮流模型;然后,提出了一种潮流计算与优化计算交替迭代的两阶段优化求解算法,对非凸非线性的最优潮流模型进行变量削减,并将其转换为凸二次约束二次规划模型从而实现高效求解;最后,通过一个162节点三相配电网进行算例分析,结果表明,根据最优潮流模型结果对分布式光伏进行调度后,配电网谐波畸变、三相不平衡以及电压越限问题得到了有效改善,且两阶段优化求解算法的计算效率也满足配电网调度时间要求,验证了所提分布式光伏优化调度方法在改善配电网电能质量方面的有效性。     

考虑配电网电能质量改善的分布式光伏优化调度方法

针对配电网中存在的电压越限、谐波畸变、三相不平衡等问题,从综合改善多电能质量问题的角度出发,研究了一种配电网分布式光伏优化调度模型及其求解方法。首先,分析了分布式光伏并网逆变器进行无功功率、谐波电流及不平衡功率补偿的控制方案;在此基础上,以可调度分布式光伏的三相功率及谐波电流输出为控制变量,基于配电网三相基波及谐波潮流方程,建立了最小化网络损耗、不平衡电压以及谐波电压的最优潮流模型;然后,提出了一种潮流计算与优化计算交替迭代的两阶段优化求解算法,对非凸非线性的最优潮流模型进行变量削减,并将其转换为凸二次约束二次规划模型从而实现高效求解;最后,通过一个162节点三相配电网进行算例分析,结果表明,根据最优潮流模型结果对分布式光伏进行调度后,配电网谐波畸变、三相不平衡以及电压越限问题得到了有效改善,且两阶段优化求解算法的计算效率也满足配电网调度时间要求,验证了所提分布式光伏优化调度方法在改善配电网电能质量方面的有效性。     

基于网损因子迭代的安全约束机组组合算法

针对考虑安全约束的机组组合(security constrained unit commitment,SCUC)问题,在传统SCUC模型的基础上,建立考虑有功网损及其在电网中分布的SCUC模型,提出一种基于网损因子迭代的SCUC算法。此算法每次迭代先解固定网损因子的SCUC问题,求得机组的运行状态,然后进行交流潮流计算,更新网损因子,进入下一次迭代。针对可能出现的网损因子振荡问题,提出SCUC和经济调度相结合的方法,选择对应发电成本较小的机组启停状态,进行经济调度优化和网损因子迭代计算,直至算法收敛。对IEEE 30和IEEE 118节点系统进行的仿真计算验证了所提算法的正确性和有效性。     

Real-time economic dispatch with line flow and emission constraintsusing quadratic programming

The presence of multiple constraints due to network line flow limits and emission allowances in the economic dispatch of modern power systems makes the conventional Lambda-Delta iterative approach no longer effective. This paper proposes a practical strategy based on quadratic programming (QP) techniques to solve the real-time economic dispatch problem. It formulates the problem with a quadratic objective function based on the unit's cost curves in quadratic or piecewise-quadratic forms. The operation constraints are modeled as linear equality/inequality equations, resulting in a typical QP problem. Goal programming techniques are also incorporated in the formulation which guarantees the best available solution even under infeasible conditions. In addition, the proposed strategy formulates the problem in the second phase dispatch in real-time by including a set of emergency control variables to provide effective control strategies for properly relieving constraint violations if they exist. The effectiveness of the proposed strategy is demonstrated by an example power dispatch problem     

A bi-objective DC-optimal power flow model using linear relaxation-based second order cone programming and its Pareto Frontier

The DC optimal power flow (DC-OPF) plays an important role in the operation and planning of modern power systems. In this paper, a bi-objective DC-OPF model minimizing both network losses and generation costs is introduced, which can further be converted into a single objective model via the weighted sum method. Furthermore, the Pareto Frontier is employed to solve this problem. In the mathematical view, the model is a special non-convex quadratic constraints quadratic programming problem. In order to obtain a continuous Pareto Frontier, the original non-convex feasible region is relaxed to its convex hull using a linear relaxation-based second order cone programming method. Compared with the semi-definite relaxation method, the proposed method can greatly reduce the number of dummy variables and the complexity of solutions. Finally, simulations on eight small systems and four practical, large systems are performed, in addition to the comparison of a Monte Carlo simulation. The results verify the effectiveness of the proposed algorithm.     

一种安全约束经济调度的广义网络流规划算法

本文分析了一般网络流规划算法在潮流分布、网络损失与安全约束等方面所存在的问题,提出了一种安全约束经济负荷分配的广义网络流规划模型与算法。并讨论了广义网络流规划的模型与非线性解法。对例题进行计算,验证了本文方法的有效性。