Transmission congestion and voltage profile management coordination in competitive electricity markets

This paper describes a generalized active/reactive iterative coordination process between GENCOs and the Independent System Operator (ISO) for active (transmission congestion) and reactive (voltage profile) management in the day-ahead market. GENCOs apply priced-based unit commitment without transmission and voltage security constraints, schedule their units and submit their initial bids to the ISO. The ISO executes congestion and voltage profile management for eliminating transmission and voltage profile violations. If violations are not eliminated, the ISO minimizes the transmission and voltage profile violations and sends a signal via the Internet to GENCOs. GENCOs reschedule their units taking into account the ISO signals and submit modified bids to the ISO. The voltage problem is addressed and a linear model is formulated and used in the proposed method. The voltage problem is formulated as a linear programming with a block-angular structure and Dantzig-Wolfe decomposition is applied to generate several smaller problems for a faster and easier solution of large-scale power systems. Two 36 unit GENCOs are used to demonstrate the performance of the proposed generalized active/reactive coordination algorithm.     

Augmented Lagrange Hopfield network based Lagrangian relaxation for unit commitment

This paper proposes an augmented Lagrange Hopfield network based Lagrangian relaxation (ALHN-LR) for solving unit commitment (UC) problem with ramp rate constraints. ALHN-LR is a combination of improved Lagrangian relaxation (ILR) and augmented Lagrange Hopfield network (ALHN) enhanced by heuristic search. The proposed ALHN-LR method solves the UC problem in three stages. In the first stage, ILR is used to solve unit scheduling satisfying load demand and spinning reserve constraints neglecting minimum up and down time constraints. In the second stage, heuristic search is applied to refine the obtained unit schedule including primary unit de-commitment, unit substitution, minimum up and down time repairing, and de-commitment of excessive units. In the last stage, ALHN which is a continuous Hopfield network with its energy function based on augmented Lagrangian relaxation is applied to solve constrained economic dispatch (ED) problem and a repairing strategy for ramp rate constraint violations is used if a feasible solution is not found. The proposed ALHN-LR is tested on various systems ranging from 17 to 110 units and obtained results are compared to those from many other methods. Test results indicate that the total production costs obtained by the ALHN-LR method are much less than those from other methods in the literature with a faster manner. Therefore, the proposed ALHN-LR is favorable for large-scale UC implementation.     

静态安全约束下基于Benders分解算法的可用传输容量计算

在电力市场环境下，可用传输容量(ATC)是反映输电线路可用于交易的剩余容量的重要指标。文中以最优潮流为基础，采用Benders分解方法将考虑静态安全约束的ATC计算问题分解为一个基态主问题和一系列与各预想事故有关的子问题。主问题用来处理基态潮流和相应约束以及由子问题所返回的Benders割(cut)约束，而各子问题用来处理各预想事故和形成相应的静态安全约束。文章给出了相应的数学模型，并提出了两种改进的求解策略。4节点和IEEE30节点系统的计算结果表明了该方法和求解策略的有效性。     

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 comprehensive strategy for transmission switching action in simultaneous clearing of energy and spinning reserve markets

There is a great resolution calling for smart grids in recent years. Introduction of new technologies, that make the network flexible and controllable, is a main part of smart grid concept and a key factor to its success. Transmission network as a part of system network has drawn less attention. Transmission switching as a new transmission service can release us from load shedding and remove the constraints’ violations.Transmission switching can provide economic benefits compared to other control methods such as generation unit rescheduling or load shedding for contingency management.Utilizing a stochastic mix-integer nonlinear programming (SMINLP) model, transmission switching is used during contingencies and steady state to determine optimal required energy and reserve values.Stochastic joint energy and reserve markets with transmission switching considering dynamic constraints has been proposed to minimize the cost of supplying load, security expenses.Considering dynamic constraints in proposed model avoid the occurrence of transient instability when opening the line in transmission switching action.A network reduction method based on modified Jacobean AC Newton–Raphson technique power flow considering switchable line in technique is used for speeding up the calculation, efficiency and simplicity.To investigate the efficiency of the proposed strategy IEEE 14 bus test and IEEE 57 bus test system are studied. According to the obtained results, this strategy decreases energy and reserve marginal prices, as well as security cost.     

On the self-scheduling of a power producer in uncertain trading environments

This work presents a scenario-based approach to the self-scheduling problem of a price taker power producer in a DA market. It concentrates on three categories of uncertainty including price, forced outage and generation reallocation and analyses their effects on the producer revenue. To tackle the uncertainties a set of price scenarios are so generated that their means and covariance matrix are the same as the base-case scenario. Forced outage and generation reallocation of generator for each price scenario are appropriately modeled through a probabilistic methodology. In this work Downside Risk (DR) is employed as the risk measure which quantifies the downside violations from a specified target. A risk-constrained self-scheduling problem is therefore formulated and solved as a mixed integer linear programming problem. Numerical results for a case study are discussed.     

考虑输电网络影响的火电机组优化组合的一种实用算法

提出一种考虑输电网络损耗及线路过负荷的火电机组优化组合的实用算法。用动态规划法建立一个初始解,运用启发式手法对初始解进行修正,使之逐个满足各约束条件,得到运行可能解,并通过更新发电机起动优先顺序使此过程反复进行直至得到(准)最佳解。在求解过程中引入最优潮流计算,使考虑输电网络损耗及线路过负荷等网络因素对发电机组优化组合的影响成为可能,并提出一种调节发电机出力和改变发电机组合相结合的消除线路过负荷的方法。在IEEE-118母线(36机)系统上对所提出的算法进行了各种条件下的仿真计算,考察了网络损耗及线路过负荷对发电机组优化组合的影响,验证了所提算法对解决考虑输电网络因素影响的发电机组优化组合问题的有效性。     

考虑网络安全约束的机组组合新算法

市场机制驱使电网运行于安全极限的边缘,考虑网络安全约束的机组组合问题变得尤为重要,基于对偶原理的拉格朗日松弛法是解决这一问题的有效途径。文章提出了一种解决网络安全约束下的机组组合问题的新算法,在拉格朗日对偶分解的基础上结合变量复制技术,通过引入附加人工约束将网络约束嵌入单机子问题中,实现在机组组合中考虑网络安全约束。该算法摆脱了现有各种处理手段在解决网络安全约束的机组组合问题时将网络安全约束与机组启停相分离的不足,揭示了安全经济调度和安全约束下的机组组合在概念上的区别和联系。     

A solution method using neural networks for the generator commitment problem

This paper studies the feasibility of applying the Hopfield-type neural network to unit commitment problems in a large power system. The unit commitment problem is to determine an optimal schedule of what thermal generation units must be started or shut off to meet the anticipated demand; it can be formulated as a complicated mixed integer programming problem with a number of equality and inequality constraints. In our approach, the neural network gives the on/off states of thermal units at each period and then the output power of each unit is adjusted to meet the total demand. Another feature of our approach is that an ad hoc neural network is installed to satisfy inequality constraints which take into account standby reserve constraints and minimum up/down time constraints. The proposed neural network approach has been applied to solve a generator scheduling problem involving 30 units and 24 time periods; results obtained were close to those obtained using the Lagrange relaxation method.     

Security-constrained optimal generation scheduling for GENCOs

This paper presents an approach for maximizing a GENCO's profit in a constrained power market. The proposed approach considers the Interior Point Method (IPM) and Benders decomposition for solving the security-constrained optimal generation scheduling (SC-GS) problem. The master problem represents the economic dispatch problem for a GENCO which intends to optimize its profit. The formulation of the master problem does not bear any transmission network constraints. The subproblem will be used by the same GENCO to check the viability of its proposed bidding strategy in the presence of transmission network constraints. In this case if the subproblem does not yield a certain level of financial return for the GENCO or if the subproblem results in an infeasible solution of the GENCO's proposed bidding strategy, the GENCO will modify its proposed solution according to the Benders cuts that stem out of the subproblem. The study shows a more flexible scheduling paradigm for a GENCO in a competitive arena. The proposed approach proves practical for modeling the impact of transmission congestion on a GENCO's expected profit in a competitive environment.     

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.     

一种计及网络约束和禁止运转区影响的经济负荷分配算法

建立了考虑发电机禁止运转区和电力系统网络约束的经济负荷分配问题的数学模型,引入了GENOCOP遗传算法进行求解:初始种群由问题的可行解组成,遗传操作所产生的个体仍在约束条件定义的可行解空间内.采用直流潮流表示电力系统网络约束,将系统线路损耗处理成系统总负荷的线性函数,但在考虑禁止运转区时,问题的约束条件仍不能保持线性特性.定义机组在禁止运转区上的耗量特性是一个远大于机组正常耗量的常数,故在约束中不需考虑禁止运转区的影响,进而应用上述算法在含问题可行解空间的最小线性空间内寻优.算例分析表明,文中算法能有效求解具有复杂数学模型的经济负荷分配问题,提高了寻优效率与解的质量.     

A method for unit commitment with transmission losses and flow constraint

Researches on the unit commitment with transmission network have been reported recently. However, most of these researches mainly discussed the security constrained unit commitment, while the relationship between unit commitment and transmission losses was not considered. However, from the standpoint of operating reserve for ensuring power supply reliability, a unit commitment considering transmission losses is required. Further, under the deregulation and liberalization of the electric power industry, not only the line's security but also transmission losses are expected to play an important role in calculating the network access charge, and unit commitment taking into account transmission losses is also desired from this viewpoint. In this paper, a unit commitment approach with both transmission losses and line flow constraint is presented. Based on a heuristic iterative optimization method, first, an initial schedule is created by using a successively decommitting unit approach that is proposed in this paper. Then, we determine constraints included in the unit commitment schedule by a heuristic iterative optimization approach, in which an algorithm able to get rid of line overload by DC optimal power flow is developed. Through numerical simulations on two test power systems, the effectiveness of the proposed method is shown. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 142(4): 9–19, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10116     

Evolutionary programming based security constrained optimal power flow

This paper presents an algorithm for solving security constrained optimal power flow problem through the application of evolutionary programming (EP). The controllable system quantities in the base-case state are optimised to minimize some defined objective function subject to the base-case operating constraints as well as the contingency-case security constraints. An IEEE 30-bus system is taken for investigation. The security constrained optimal power flow results obtained using EP are compared with those obtained using conventional security constrained optimal power flow. The investigations reveal that the proposed algorithm is relatively simple, reliable and efficient and suitable for on-line applications.     

一种计及静态安全约束机组组合的有效算法

以直流潮流模型为基础,将计及电网静态安全约束的机组组合问题分解为无安全约束的机 组组合问题和计及电网静态安全约束的优化潮流问题2个子优化问题。通过在后者中引入虚拟变 量来反映机组组合对输电元件传输限制的牵制及影响,并借用虚拟变量和发电转移因子,构建前者 与后者间关联的补充约束条件,从而形成前者随后者变化的影响机制及优化方向的修正手段,由此 提出了2个子优化问题间交替求解的算法。该算法充分兼容现有成型方法,符合电力系统实际,对 解决电网静态安全对机组组合制约现象,以及对机组组合方案评价,有良好的适应性。     

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     

Neural networks approach for solving economic dispatch problem withtransmission capacity constraints

This study presents a new approach using Hopfield neural networks for solving the economic dispatch (ED) problem with transmission capacity constraints. The proposed method is based on an improved Hopfield neural network which was presented by Gee et al. (1994). The authors discussed a new mapping technique for quadratic 0-1 programming problems with linear equality and inequality constraints. The special methodology improved the performance of Hopfield neural networks for solving combinatorial optimization problems. The authors have now modified Gee and Prager's (GP) method in order to solve ED with transmission capacity constraints. Constraints are handled using a combination of the GP model and the model of Abe et al. (1992). The proposed method (PHN) has achieved efficient and accurate solutions for two-area power systems with 3, 4, 40 and 120 units. The PHN results are very close to those obtained using the quadratic programming method     

Nodal price control: a mechanism for transmission network cost allocation

This paper presents an approach for the allocation of transmission network costs by controlling the nodal electricity prices. The proposed approach introduces generation and nodal injection penalties into the traditional economic dispatch so as to create nodal price differences that recover the required transmission revenue from the resulting congestion rent. As a consequence, the new electricity prices reflect not only the marginal costs of production subject to transmission constraints but also the capital costs of the network. This is the approach commonly adopted with most commodities whose price includes the unit cost of the good itself as well as the transportation cost from the production centers to the final consumer.     

A probabilistic approach to generation maintenance scheduler with network constraints

Most generating unit maintenance scheduling packages consider the preventive maintenance schedule of generating units over a one or two year operational planning period in order to minimize the total operating cost while satisfying system energy requirements and maintenance constraints. In a global maintenance scheduling problem, we propose to consider network constraints and generating unit outages in generation maintenance scheduling. The inclusion of network constraints in generating unit maintenance will increase the complexity of the problem, so we decompose the global generator scheduling problem into a master problem and sub-problems using Benders decomposition. At the first stage, a master problem is solved to determine a solution for maintenance schedule decision variables. In the second stage, sub-problems are solved to minimize operating costs while satisfying network constraints and generators’ forced outages. Benders cuts based on the solution of the sub-problem are introduced to the master problem for improving the existing solution. The iterative procedure continues until an optimal or near optimal solution is found.     

考虑输配协同的电网机组组合与技改计划联合优化模型

进行考虑输配协同的电网机组组合与技改计划联合优化,对于提高输配整体新能源消纳率、保障系统中短期可靠经济运行具有重要意义。分别构建输电网、配电网的机组组合与技改计划联合优化模型。针对中短期优化中新能源随机性较大的问题,采用机会约束规划进行处理并将约束转化为确定性约束。分析输配分立式优化、集中式协同优化、分布式协同优化求解模型的可行性,综合比较后采用基于目标级联分析法的分布式协同优化算法实现模型的输配解耦与并行求解。算例分析表明,所提模型能够合理安排输配电网的机组启停机状态及技改项目的施工计划,并验证了目标级联分析法对于解决输配协同优化问题的有效性。