Evaluation of production costs of two interconnected electric power systems by the segmentation method

This paper develops the methodology, based on the segmentation method, to evaluate the production costs of two interconnected systems. The demand plane is divided into a grid structure, or segments, of equal size. Each segment contains the joint probability of the occurrence of load in the range of the selected segment as well as the first moments, or expected values, of load, or equivalent load, and residual tie line capacity for each system. The methodology proposed is accurate and computationally efficient. The method is applied to the evaluation of expected energy generation, unserved energy as well as production costs of two interconnected systems. The impact of tie line capacity variations, forced outage rate changes as well as joint ownership of generation is investigated.     

Load management: impacts on the reliability and production costs of interconnected systems

With the increasing recognition that load management could be beneficial to a utility, the planner has an added alternative in generation expansion planning in deciding whether to construct a new plant, to purchase power from a neighbouring utility or to implement a load management scheme. This paper evaluates the impacts of load management strategies on the reliability as well as on the production costs of two interconnected systems. Investigation has been made to find the equivalence, in terms of reliability improvement and production cost benefit, between the tie-line capacity and the percentage reduction of the peak demand. In the simulation, the correlation between the loads of two inteconnected systems is considered. The segmentation method is utilized in the numerical simulation.     

Reliability of two interconnected systems with jointly owned units

The installation of a large size generating unit requires a huge investment. In some cases, utilities share the ownership of a unit among the neighbouring utilities to face the problem of this cost. This paper presents a methodology to evaluate the reliability of two interconnected systems with a jointly owned unit (JOU). The methodology is capable of evaluating the reliability of two interconnected systems with a multi-state JOU as well as with more than one JOU. The concept of appropriate modification of transfer as well as the installed capacities to incorporate the transfer of shares from one system to another is introduced in this paper. The method is applied to evaluate the reliability of two interconnected systems with JOUs. In the numerical evaluation, the segmentation method is used.     

Unit commitment by genetic algorithm with specialized search operators

An approach for solving the unit commitment problem based on genetic algorithm with new search operators is presented. These operators, specific to the problem, are mutation with a probability of bit change depending on load demand, production and start-up costs of the generating units and transposition. The method incorporates time-dependent start-up costs, demand and reserve constraints, minimum up and down time constraints and units power generation limits. Repair algorithms or penalty factors in the objective function are applied to the infeasible solutions. Numerical results showed an improvement in the solution cost compared to the results obtained from genetic algorithm with standard operators and other techniques.     

A method for optimal pricing of electric supply including transmission system considerations

Determining real-time electricity rate structures is currently receiving a great deal of attention. In this paper, a strategy for pricing electricity supply is formulated and evaluated. Unlike other methods which use only the variation of fuel cost for generation to estimate the rate structures, the proposed pricing algorithm incorporates the optimal allocation of transmission system operating costs based on time-of-use pricing. The transmission costs are obtained by assigning a price k to each unit of power flow in the network. The assignment does not discriminate between participants located at differing parts of the network. The real-time pricing reflects the instantaneous cost of production and functions as a load management tool because this interacts with consumer behavior. The demand for power flows and transmission on an electricity supply system, like the demand for any bundle of economic goods depends upon the assigned transmission prices, together with the economic benefit to the consumer. It is assumed that there are no privately owned generating plants and that all plants and transmission lines are operated by the utility. The modeling scheme is applied to the IEEE standard 5, 14, 30 and 57 bus power systems and involves solving a modified optimal power flow problem (OPF) iteratively using the MINOS package. It is concluded that the method has a wide potential application in electricity supply pricing.     

Stochastic models for power generation system production costs

Production costing models are widely used in the electric power industry for the purpose of generation capacity expansion planning, fuel management, and operational planning. These models account for the load variation over time and generator outages. A widely used model, due to Balériaux and Booth, yields a prediction of the expected production costs and is based on the load duration curve and forced outage rate of the generating units. This paper highlights the fact that, in order to obtain a more detailed characterization of the probability distribution costs beyond the expected value, a model involving the stochastic processes underlying the generator outages is necessary. A stochastic model is considered as an enhancement to the traditional Balériaux model. It is shown that Monte Carlo simulation can be routinely used on the enhanced model to provide answers concerning the distribution of production costs. Monte Carlo methods avoid the problems associated with the complexity of the analytical methods. Numerical examples are given using the enhanced model where load is considered to be either a deterministic or stochastic time-varying function. An example is given using decision analysis where a possible use of the more detailed information on the probability distribution of production costs in generation system planning is illustrated.     

一种基于负荷分解的随机生产模拟新方法

本文提出了一种随机生产模拟新方法,该方法根据负荷分布密度函数曲线的峰谷特性将其表达为若干个Gram-Charlier展开式的凸组合,发电系统的停运容量分布也以Gram-Charlier展开式描述,由此推导出机组的期望发电量、系统可靠性指标的计算公式。在IEEE-RTS和我国河南系统中的应用表明:本文提出的方法计算结果要比累积量法准确得多,同时保留了累积量法运算速度快的优点,更适用于我国电力系统。     

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.     

综合考虑网络结构不确定性的概率潮流计算方法

目前,在概率潮流计算方法中,不确定性因素多数仅考虑了负荷的不确定性及发电机的随机故障,而不计及网络结构的变化。文中提出一种概率潮流计算新方法,综合考虑了负荷、发电机、网络结构不确定性对潮流结果的影响。文中推导了线路故障时节点注入功率与各支路有功功率的线性关系,应用半不变量法和Gram-Charlier级数展开式求取各支路潮流的概率分布,避免了复杂的卷积运算;结合补偿法及全概率理论来处理网络结构变化的随机因素,建立了综合考虑负荷随机变化、发电机随机故障和网络结构随机变化的概率潮流计算模型,可以快速求得各支路潮流的概率分布函数(CDF)和概率密度函数(PDF)。通过对IEEE 39节点及某区域电网实际系统的算例分析,表明网络结构的不确定性对待求量的概率分布有显著影响。因此,利用所提方法得到的概率潮流结果能为规划人员提供更准确和全面的信息。通过与蒙特卡罗方法进行比较,验证了该方法的快速性与准确性,说明所提方法具有实际应用前景。     

基于机会约束规划的电力系统安全成本优化计算

提出了一种基于机会约束规划计算电力系统安全成本的新方法。安全成本模型由发电侧备用成本、可中断负荷成本、再调度成本和期望失稳损失等因素构成。在求解该模型的过程中,应用遗传算法和蒙特卡罗仿真技术,将发电侧备用容量和可中断负荷作为随机变量并用概率的形式表示约束条件,从而得到最优安全成本费用。最后通过IEEE30节点测试系统验证了该方法的有效性。     

Features that influence composite power system reliability worthassessment

Reliability worth assessment using customer interruption costs is an important element in electric power system planning and operation. This paper deals with two features that affect the composite generation-transmission system reliability worth assessment. One feature is the incorporation of temporal variations in the cost of interruption. This paper illustrates the effect on the expected annual system outage cost of temporal variation in the interruption costs for the residential, agricultural, industrial, commercial and large user sectors. The other aspect considered in this paper is using a probability distribution approach to represent the cost of interruption model. The conventional customer damage function approach utilizes average customer costs while the probability distribution approach recognizes the dispersed nature of the customer outage data. These two methods of cost evaluation are applied to reliability worth assessment in this paper. A sequential Monte Carlo approach incorporating time varying loads is used to conduct all the studies. Case studies performed on two composite test systems show that incorporating time varying costs of interruption for the industrial sector resulted in a significant reduction in the expected outage cost. A comparison of the reliability worth obtained using the customer damage function method (CDF) with the probability distribution approach suggests that using the CDF method may significantly undervalue the reliability worth by a factor of three to four     

Evaluation of the marginal outage costs in interconnected andcomposite power systems

The structure of electric utilities is undergoing dramatic changes as new and expanded service options are added. The concepts of unbundling the electric service and offering customers a range of new services that more closely track actual costs are expanding the options open to customers. Spot pricing provides the economic structure for many of these new service options. An important component of spot prices is the marginal outage cost incurred by customers due to an incremental change in load. This paper presents a formalized approach of calculating the marginal outage cost in interconnected generating systems and composite generation and transmission systems using quantitative reliability techniques. The effects of selected pertinent factors on the marginal outage cost in composite systems are also presented. The proposed methods are illustrated by application to the IEEE-Reliability Test System (IEEE-RTS)     

一种基于模糊途径的发电系统可靠性评估

介绍了用模糊数学计算发电系统可靠性的一种新方法。该方法用隶属函数表现发电机组故障率和修复率的不确定性和不精确性,将系统负荷数据“模糊化”,同时在机组追加算法的基础上进行模糊修正,通过负荷的模糊聚类简化计算,提高了计算效率。该算法以概率分布特征表述可靠性指标,符合概率统计特征。     

Time-dependent factorial cumulants in interacting nano-scale systems

We discuss time-dependent factorial cumulants in interacting nano-scale systems. Recent theoretical work has shown that the full counting statistics of non-interacting electrons in a two-terminal conductor is always generalized binomial and the zeros of the generating function are consequently real and negative. However, as interactions are introduced in the transport, the zeros of the generating function may become complex. This has measurable consequences: With the zeros of the generating function moving away from the real-axis, the high-order factorial cumulants of the transport become oscillatory functions of time. Here we demonstrate this phenomenon on a model of charge transport through coherently coupled quantum dots attached to voltage-biased electrodes. Without interactions, the factorial cumulants are monotonic functions of the observation time. In contrast, as interactions are introduced, the factorial cumulants oscillate strongly as functions of time. We comment on possible measurements of oscillating factorial cumulants and outline several avenues for further investigations.     

Impact analysis of static voltage assessment based on three‐phase probabilistic load flow with correlated wind power

Impact analysis based on the three‐phase probabilistic load flow (PLF ) algorithm is proposed in this paper to evaluate the effect on static voltage of an unbalanced power system. Correlations between adjacent wind power resources are considered. An improved cumulants method with correlated variables is proposed and applied to the unbalanced system. Cornish–Fisher expansion is used to obtain the cumulative distribution function of bus voltage and line flow. The impacts for wind turbines , which include rated capacity, power factor, and correlation on PLF, are studied, and the relations of the means and standard deviations between three‐phase unbalanced and balanced systems are analyzed. A 25‐bus and a 33‐bus system are studied as examples to show the effectiveness of proposed method, and results of cumulants method are compared with those of Monte Carlo simulations. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

抽水蓄能电站及其系统运行优化的概率模拟算法

在随机生产模拟中运用负荷曲线分解技术和动态规划方法,提出了抽水蓄能电站及其系统运行优化的概率模拟算法。该算法以系统发电运行成本与缺电损失之和最小为目标,满足了电站水库蓄水及库容限制条件和日或周的抽水-发电循环电力电量平衡条件,计及了抽水蓄能电站在抽水和发电方式下随机停运的影响。算例证明了该算法的可行性,并且可在电源规划、发电计划和系统运行优化中更准确地模拟、分析和优化抽水蓄能电站及其所在系统运行状况。     

Generation expansion planning by considering energy-efficiency programs in a competitive environment

Restructuring of the electricity industry and the development of energy efficiency solutions are the two major developments of the recent power systems. Implementation strategies in the use of energy efficiency can be made by utilizing more energy-efficient equipment or increasing penetration rate of production of new sources of energy at the generating side. These new sources of energy can be renewable sources, especially wind resource and energy storage instruments such as grid-connected electric vehicles. The vehicles can be charged during the low load and discharged during peak load. In this study, wind resources and grid-connected electric vehicles are considered as an approach for energy efficiency strategies in generation expansion planning. But, because of high investment cost, great uncertainty of wind resources’ productivity and uncertainty of their supportive policies no one will invest on them without proper supportive policies in a competitive environment. So support policies for wind resource are also considered. One of the fundamental problems of supportive policies is financial support in a competitive environment. Therefore, as an innovation of the paper, grid-connected electric vehicles is used to solve the problem. In the paper, the impact of these vehicles is considered in a way that they act integrated with wind resources and thus increases the capacity factor of wind resources.     

Cost-Related Reliability Evaluation of Interconnected Bulk Power Systems Using An Equivalent Approach

This paper presents a technique to calculate cost-related reliability indices of a composite power system at the load points and for the overall system. An adequacy equivalent approach is utilized to effectively reduce the required computation times for interconnected composite system analysis. The cost-related reliability indices are calculated in the form of both annualized and annual values. System studies conducted on two interconnected reliability test systems are presented which provide insight into the values of the indices in different situations. The cost reliability indices are important factors in determination of the optimal reliability level at which the reliability investment achieves the best results to reduce the customer damage costs due to power supply interruptions.