Monte Carlo stochastic simulation of electric power generation system production costs under time-dependent constraints

Probabilistic production costing models are widely used in the electric power industry to forecast the cost of producing electricity. A widely used model due to Balériaux and Booth provides an analytical formula for the expected production costs using the load duration curve (LDC) in place of chronological sequence of loads and the forced outage rates of the generating units. Since the chronological information is lost in the LDC, it cannot accurately simulate those aspects of production cost that are time dependent in nature. The paper points out that, in addition to the need for a chronological simulation of load to capture the time-dependent constraints, it is also necessary to model the frequency and duration of the generation outages. Monte Carlo results are given for a Markovian model for the frequency and duration of the outages where several unit commitment constraints are considered. It is shown that the mean and variance of the production costs may differ significantly if the failure and the repair rates of the generating units are changed although the respective forced outage rates remain unaltered. The paper also highlights the simplicity of using continuous-time simulation in the Markov model.     

Computation of power generation system production costs

This paper considers the problem of computing the expected value of generating system production costs. First, using a stochastic model for the frequency and duration of generation outage, it provides an efficient Monte Carlo procedure for the evaluation of the Baleriaux formula. Secondly, it points out the need for using a stochastic model for estimating production costs with time-dependent constraints via Monte Carlo. Lastly, it considers a model where the chronological load also has a random component and obtains an expression for expected production costs for this situation     

Security-constrained expansion planning of fast-response units for wind integration

This paper proposes a stochastic expansion planning of fast-response thermal units for the large-scale integration of wind generation (WG). The paper assumes that the WG integration level is given and considers the short-term thermal constraints and the volatility of wind units in the planning of fast-response thermal units. The new fast-response units are proposed by market participants. The security-constrained expansion planning approach will be used by an ISO or a regulatory body to secure the optimal planning of the participants’ proposed fast-response units with the WG integration. Random outages of generating units and transmission lines as well as hourly load and wind speed forecast errors are modeled in Monte Carlo scenarios. The Monte Carlo simplification methods are introduced to handle large-scale stochastic expansion planning as a tradeoff between the solution accuracy and the calculation time. The effectiveness of the proposed approach is demonstrated through numerical simulations.     

A Probability Model for the Electricity Price Duration Curve Under an Oligopoly Market

In this paper, we propose a new formulation for the “price duration curve” (PDC) using probability considerations and provide a procedure for constructing it. This curve is expected to be useful in the long-term prediction of market prices and is similar in spirit to the load duration curve. It shows the proportion of time over a given time horizon during which the real-time market price of electricity is expected to exceed specified dollar amounts. The price over a long term is a stochastic quantity that depends on physical factors such as production cost, load, generation availability, unit commitment, and transmission constraints. It also depends on economic factors such as strategic bidding and load elasticity. We illustrate a procedure for constructing a stochastic system-based model for the PDC, taking into account the randomness associated with load and generator outages. The effects of unit commitment, transmission congestion, and transmission outages are not considered. We use two economic models. One is due to Bertrand and represents perfect competition. The other model is due to Rudkevich who have given a closed-form expression for the market- clearing price in an oligopoly consisting of several identical firms.     

Monte Carlo computation of power generation production costs underoperating constraints

This paper highlights the need for considering the stochastic processes associated with the frequency and duration of generating unit outages for assessing the mean and variance of production costs under operating constraints. A numerical example based on a Markov model is given to show that Monte Carlo estimates of these quantities may be incorrect if only the forced outage rates are used in place of the stochastic parameters underlying the outage frequency and duration. Additionally it describes a variance reduction procedure whereby the Monte Carlo estimates can be obtained with a much smaller sample size than would be required otherwise. A numerical example is given for a small system     

Optimization technique for long-term generation expansion planning using the maximum principle and the Gaussian distribution function

This paper presents a new approach to optimal long-range generation planning. A completely new analytical approach to the production costing model and reliability measure is developed under the assumption of a Gaussian probability distribution for the random load fluctuations and plant outages. The long-range generation investment problem is formulated as an optimal control problem to determine optimally the annual investment in new generation capacity. The Hamiltonian minimization is performed by using a version of the gradient projection method.     

Market-clearing with stochastic security-part I: formulation

The first of this two-paper series formulates a stochastic security-constrained multi-period electricity market-clearing problem with unit commitment. The stochastic security criterion accounts for a pre-selected set of random generator and line outages with known historical failure rates and involuntary load shedding as optimization variables. Unlike the classical deterministic reserve-constrained unit commitment, here the reserve services are determined by economically penalizing the operation of the market by the expected load not served. The proposed formulation is a stochastic programming problem that optimizes, concurrently with the pre-contingency social welfare, the expected operating costs associated with the deployment of the reserves following the contingencies. This stochastic programming formulation is solved in the second companion paper using mixed-integer linear programming methods. Two cases are presented: a small transmission-constrained three-bus network scheduled over a horizon of four hours and the IEEE Reliability Test System scheduled over 24 h. The impact on the resulting generation and reserve schedules of transmission constraints and generation ramp limits, of demand-side reserve, of the value of load not served, and of the constitution of the pre-selected set of contingencies are assessed.     

不确定性环境下考虑弃风的电力系统日前调度

为尽可能减少弃风,将弃风电量期望作为最小化优化目标加入日前调度模型。该优化目标与原有模型中的发电成本最小互相矛盾,为协调这两个子优化目标,通过隶属度函数分别将它们模糊化,构建了基于最大满意度的单目标优化模型,并采用遗传算进行了求解。风电并网增加了系统的不确定性,模型采用基于风险指标失负荷概率的机会约束代替传统的旋转备用约束。失负荷概率与弃风电量期望计算过程中考虑了负荷、风功率随机预测误差以及常规机组随机强迫停运。基于IEEE 118节点系统的仿真实验表明,该调度模型可给出兼顾发电成本与风电接纳水平的日前调度计划,为系统调度人员提供参考。     

考虑隐性故障的继电保护重要度分析方法

提出基于电力系统连锁故障风险评估的继电保护隐性故障重要度分析的新方法。首先通过继电保护隐性故障概率模型得到保护设备的隐性故障概率,然后将风险评估理论与母线孤立、负荷失电和电力损失期望3个指标结合,最终建立起电网的Monte Carlo仿真模型,利用继电保护重要度分析方法,得出电网中保护设备引发电网连锁故障的重要度排序。IEEE14节点系统的应用结果证明了该方法的可行性和正确性。     

基于EMTDC配电馈线中电压暂降概率评估

电压暂降概率评估的结果可以用于判断电力系统网络结构是否合理。与电压质量监测相比,随机预估方法能够在短期内得到负荷处公共连接点的电压暂降特征量。在配电馈线系统中,三相不平衡负荷沿输电线分布,且负荷类型不尽相同。如何准确地评估配电馈线网络的电压暂降概率,关键是对馈线系统的模型和故障类型进行仿真。采取蒙特卡洛法(Monte-Carlo)模拟和电磁暂态仿真软件EMTDC相结合的评估方法对配电网系统进行评估,算法通过对蒙特卡洛法随机产生的各种故障形态进行仿真计算,最后分析统计得到公共连接点的电压暂降概率。     

含电动汽车负荷的分布式风电源优化配置

分布式风电(distributed wind generation,DWG)出力、系统负荷功率以及电动汽车(electric vehicles,PEV)无序充电功率的随机性和时序性波动为配电网中DWG的优化配置带来更多的不确定性。为此,利用季节场景与时段划分法处理DWG出力与负荷大小的时序特性,并对PEV的随机性进行概率建模。对各时段采用机会约束规划方法建立了以年度综合成本为目标的DWG优化配置模型。利用蒙特卡洛模拟嵌入保留精英策略的遗传算法的方法对典型算例进行求解,结果验证了所提模型与方法的正确性和有效性。     

GENCO's Risk-Based Maintenance Outage Scheduling

This paper presents a stochastic model for the optimal risk-based generation maintenance outage scheduling based on hourly price-based unit commitment in a generation company (GENCO). Such maintenance outage schedules will be submitted by GENCOs to the ISO for approval before implementation. The objective of a GENCO is to consider financial risks when scheduling its midterm maintenance outages. The GENCO also coordinates its proposed outage scheduling with short-term unit commitment for maximizing payoffs. The proposed model is a stochastic mixed integer linear program in which random hourly prices of energy, ancillary services, and fuel are modeled as scenarios in the Monte Carlo method. Financial risks associated with price uncertainty are considered by applying expected downside risks which are incorporated explicitly as constraints. This paper shows that GENCOs could decrease financial risks by adjusting expected payoffs. Illustrative examples show the calculation of GENCO's midterm generation maintenance schedule, risk level, hourly unit commitment, and hourly dispatch for bidding into energy and ancillary services markets.     

考虑延迟期权的增量配电网源网协调规划方法

考虑增量配电网中的负荷电价变化等不确定性因素,将延迟期权理论融入到增量配电网源网规划模型之中,提出一种考虑延迟期权的增量配电网源网协调规划方法。首先在期望负荷增长率的基础上构建增量配电网分布式电源的选址定容模型,并通过序优化算法得到分布式电源规划可行方案的帕累托前沿;然后在此基础上通过蒙特卡洛模拟,得出增量配电网负荷及电价的变化路径,在此基础上构建考虑延迟期权的分布式电源最优投资时间决策模型,最终得到增量配电网最优投资规划策略。基于IEEE30节点系统的仿真验证了本文方法的有效性和可行性。     

基于离散概率潮流的大风电接入后的电网规划

利用离散概率模型描述风功率及负荷不确定性导致的网络潮流不确定性,利用Monte Carlo模拟技术分析并网风功率的概率分布特性,并利用正态分布描述负荷的不确定性.以一定的精度将风功率及负荷的概率密度函数离散化,并在此基础上结合线性直流潮流模型推导支路潮流的概率密度函数.规划模型以线路投资费用最少为优化目标,利用机会约束处理规划方案在正常运行及N-1情况下的过负荷.利用基本遗传算法（genetic algorithm,GA）对规划模型进行了求解.基于改进Garver6节点系统的仿真试验证明所提算法及模型的有效性.     

基于几何分布的微电网孤岛运行可靠性快速概率评估

微电网内间歇性分布式电源和负荷的波动性使孤岛运行可靠性评估变得复杂。而避免负荷频繁投切的实际短时孤岛切负荷策略增强了负荷状态的时序关联性,该策略下序贯蒙特卡洛仿真计算量大。针对上述问题,文中基于几何分布模型和概率计算,提出了快速准确计算微电网负荷点停电时间概率分布的解析公式,可综合计算负荷点和系统可靠性指标。以改造的配电系统为例,通过评估微电网孤岛运行可靠性将所提方法与蒙特卡洛评估方法进行了对比分析,论证了所提方法的快速性和有效性;对源荷功率波动性和切负荷策略对微电网孤岛运行可靠性的影响进行分析,进一步验证了所提计算模型的合理性。     

Estimating the variance of production cost using a stochastic loadmodel

The purpose of this paper is to provide a realistic load variation model to be used in short-term (one to three years) planning studies. A stochastic model is proposed, and this model is used to quantify the variation of the estimated production cost that is directly affected by the load uncertainty. The paper presents a method of estimating the variation of production cost. This is the first paper to use a Gauss-Markov stochastic model of load with a chronological production simulation model. This load model captures the stochastic load variation behavior and the correlation between weekly peak demand and weekly energy. A weekly Gauss-Markov sampling scheme is incorporated in the proposed approach to model load variation. This stochastic load model is used to generate sample chronological load profiles that represent the annual load variation in weekly detail. These load profiles are then used in annual Monte Carlo production simulation. Case studies illustrate the implementation of this stochastic load variation modeling. These case studies illustrate that load uncertainty has a significantly larger effect on cost uncertainty than does uncertainty in unit availability     

考虑负荷和风电出力不确定性的输电系统机会约束规划

提出了一种考虑负荷和风电场输出功率不确定性、基于机会约束规划的输电系统规划方法。将Monte Carlo方法与解析的概率潮流计算方法相结合,得到含风电场电网输电线路的有功概率潮流分布。通过改进经典的输电系统规划模型,得到考虑负荷和风电场有功出力的概率分布、基于概率潮流计算的输电系统机会约束规划模型。为了有效求解该模型,设计了一种两步式遗传算法。该方法可以有效处理输电系统规划中的不确定性,并为规划人员提供比传统方法更丰富的信息。算例证明了该方法的有效性。     

含分布式电源与充电站的配电网协调规划

分布式电源与电动汽车充电站共同接入配电网,对配电网规划和运行具有重要的影响。提出一种综合协调规划方法,该方法能够实现分布式电源选址定容、充电站位置及容量、配电网架建设和改造的综合优化规划。考虑风光资源和负荷的随机波动性,以配电系统投资、运行维护和环境成本的随机期望值最小为目标,建立了含分布式电源与充电站的配电网协调规划模型,采用改进遗传算法进行求解。以一个待扩展的辐射状配电网络为例,仿真计算结果表明,对含分布式电源与充电站的配电网进行综合协调规划,能够提高电网的经济和环境效益,得到的规划方案更为合理。     

基于生成对抗网络的综合能源负荷场景生成方法

综合能源负荷场景生成是研究能源计量、规划运行等领域问题的基础,具有重要意义。但由于数据采集困难、综合能源负荷多能耦合等因素的限制,综合能源负荷场景的多样化生成仍是一大难题。提出了一种基于生成对抗网络(generative adversarial networks, GAN)的综合能源负荷场景生成方法。首先建立梯度惩罚优化的Wasserstein生成对抗网络模型,解决综合能源负荷的高随机性可能带来的不收敛或模式崩溃问题。其次,基于深度长短期记忆(long short-term memory, LSTM)的循环神经网络构建生成对抗网络的生成器和判别器,使模型更适用于复杂综合能源负荷数据生成。算例结果表明,所提模型的生成负荷场景在概率分布、曲线标志性特征和冷热电负荷之间相关性等方面相较于蒙特卡洛法和原始生成对抗网络均获得了较好结果,可以在不同模式下生成具有多样性且逼真的负荷场景。     

A new approach of point estimate method for probabilistic load flow

This paper analyses the power system load flow using new point estimate method considering uncertainties, which may happen in the power system. These uncertainties may arise from different sources, such as load demands or generation unit outages. A novel probabilistic load flow based on new point estimate method has been proposed in this paper. The proposed method surpasses the previous point estimate methods when generalizing the approach to multiple random variables with various probabilistic distributions. Addressing the results of Monte Carlo simulation method as reference, the new point estimate method is applied to IEEE 14-bus test system and the advantages of this new method have been presented. The results reveal that the proposed point estimate method has less computational burden and time comparing than Monte Carlo simulation method while the accuracy remains at a high level.