The natural hedge of a gas-fired power plant

Electricity industries worldwide have been restructured in order to introduce competition. As a result, decision makers are exposed to volatile electricity prices, which are positively correlated with those of natural gas in markets with price-setting gas-fired power plants. Consequently, gas-fired plants are said to enjoy a “natural hedge.” We explore the properties of such a built-in hedge for a gas-fired power plant via a stochastic programming approach, which enables characterisation of uncertainty in both electricity and gas prices in deriving optimal hedging and generation decisions. The producer engages in financial hedging by signing forward contracts at the beginning of the month while anticipating uncertainty in spot prices. Using UK energy price data from 2006 to 2011 and daily aggregated dispatch decisions of a typical gas-fired power plant, we find that such a producer does, in fact, enjoy a natural hedge, i.e., it is better off facing uncertain spot prices rather than locking in its generation cost. However, the natural hedge is not a perfect hedge, i.e., even modest risk aversion makes it optimal to use gas forwards partially. Furthermore, greater operational flexibility enhances this natural hedge as generation decisions provide a countervailing response to uncertainty. Conversely, higher energy-conversion efficiency reduces the natural hedge by decreasing the importance of natural gas price volatility and, thus, its correlation with the electricity price.     

安全约束条件下的经济调度优化模型研究

发电侧放开竞争的电力系统需要更加有效、准确的决策工具对有限的资源进行调度规划。短期经济调度优化问题是一个混合整数非线性规划问题,很难得到有效最优解,尤其是对于大规模电力系统。为了提高求解效率,本文提出了一个考虑安全约束的经济调度优化模型(Security-Constrained Economics Dispatch,SCED),主要采用线性化思想处理经济调度优化问题的模型以及各种约束,采用基于校正的交替求解方法,使得调度优化结果在运行成本最小化的前提下满足系统的安全稳定约束。同时,将本文方法运用到IEEE 30节点系统进行测试,从而验证本文方法有效性。     

Unit commitment in electricity pool markets

We consider an electricity generator making offers of energy into an electricity pool market over a horizon of several trading periods (typically a single trading day). The generator runs a set of generating units with given start-up costs, shut-down costs and operating ranges. At the start of each trading period the generator must submit to the pool system operator a new supply curve defining quantities of offered energy and the prices at which it wants these dispatched. The amount of dispatch depends on the supply curve offered along with the offers of the other generators and market demand, both of which are random, but do not change in response to the actions of the generator we consider. After dispatch the generator determines which units to run in the current trading period to meet the dispatch. The generator seeks a supply function that maximizes its expected profit. We describe an optimization procedure based on dynamic programming that can be used to construct optimal offers in successive time periods over a fixed planning horizon.     

A shortage probability metric for battery depletion risk

In this paper, we propose a battery depletion risk (BDR) metric that evaluates the probability of depleting an energy storage system in the context of a centralized power system with stochastic demand and supply for electricity across multiple consecutive time periods. This newly proposed reliability metric informs battery sizing decisions to mitigate outage risks. We demonstrate the applicability of this metric by embedding it in an economic dispatch model with thermal generation units and a centralized energy storage system.     

计及需求响应不确定性的综合能源系统多目标优化调度管理

需求响应作为电力系统的重要调节手段,可显著提升系统灵活性和经济性。利用价格弹性构建了包含价格与激励措施的需求响应模型,并在此基础上考虑需求响应的不确定性,以综合能源系统经济性和环保性为优化目标,构建了综合能源系统多目标优化调度模型。利用E约束法将多目标优化模型转化为单目标优化模型,得到Pareto最优解集,运用模糊决策法从中选取最优方案。基于实际案例进行测算,结果表明价格型与激励型需求响应手段的结合能够实现削峰填谷,有效降低系统的运行成本和碳排放量。     

The gas analysis modeling system (GAMS)

This paper gives an overview of a large integrated model of the natural gas industry in the United States. The system described has been used to evaluate the impacts of natural gas legislation before the U.S. Congress. Many common operations research tools such as linear programming, dynamic programming and network flow theory are used at various stages in the model.     

A Benders decomposition algorithm for a multi-area,multi-stage integrated resource planning in power systems

The aim of this paper is to propose an integrated model for resource planning in power systems by taking into account both supply and demand sides options simultaneously. At supply-side, investment in generation capacity and transmission lines is considered. Demand side management (DSM) technologies are also incorporated to correct the shape of the load duration curve in terms of peak clipping and load shifting programmes. A mixed integer non-linear programming model is developed to find the optimal location and timing of electricity generation/transmission as well as DSM options. To solve the resulting complex model, nonlinearity caused by transmission loss terms are first eliminated using the piecewise linearization technique. Then, a Benders decomposition (BD) algorithm is developed to solve the linearized model. The performance of the proposed BD algorithm is validated via applying it to the 6-bus Garver test system and a modified 21-bus IEEE reliability test system.     

O.R. and U.K. natural gas depletion strategy

This paper describes two models using operational research techniques to explore alternative strategies for the depletion of U.K. natural gas reserves. The first is a linear programming formulation of the problem of matching annual supply and demand for gas over the indefinite future. The second evaluates the financial implications of the matches produced by the first. The key variables which affect results from the model are discussed as are some of the ways in which results are used. These results have an influence on decisions ranging from detailed peak shaving policy to considerations of national fuel policy and the balance of energy supplies in the U.K. in the longer term.     

电网输电分配与阻塞管理的数学模型

研究发电机组供电与电网各线路的有功潮流之间的输电分配和阻塞管理的优化问题.用多元线性回归理论拟合各线路上的有功潮流关于各发电机组出力的近似表达式,建立关于电力市场输电阻塞管理的二次规划数学模型.分别以预报电荷982.4MW和1052.8MW为例进行实证分析.     

智能电网下考虑风险的供电企业购电优化模型

针对智能电网带给供电企业购电决策的影响,提出了一种考虑风险的购电优化决策方法。智能电网建设并开展运营,发电侧考虑接纳更多的可再生能源发电,用电侧智能用电设备的使用导致主动负荷的出现等,这一系列变化给智能电网环境下供电企业购电决策带来一定程度的风险。首先,考虑了智能电网下负荷与风电出力不确定性给供电企业经营带来的风险,采用风险元传递理论与多目标规划理论,建立智能电网购电优化模型。然后,提出采用约束多目标粒子群优化算法(CMOPSO)对模型进行求解思路;最后,算例说明该模型的可行性,研究成果为我国智能电网运营风险管理提供新方法、新思路。     

国际天然气价格驱动因素的结构性变化

页岩气开采技术的大规模应用增加了非常规天然气供应潜力,对国际天然气市场供需格局产生了较大冲击。本文利用带结构断点的协整检验、时变系数模型和条件误差修正模型等方法系统地研究了天然气价格与原油价格的动态关系,以及库存、天气和投机等短期因素对气价变化的影响。结果显示,国际天然气价格与原油价格间的协整关系在2005年飓风季与2008年金融危机期间发生了结构性变化,而且原油价格对天然气价格的影响强度呈现倒U型结构。此外,极端天气、突发性事件及投机等短期因素对气价存在显著的短期影响。不过,随着天然气供应出现过剩局面,天然气价格对这些短期因素的敏感性已大幅降低。     

Spatial dependencies of wind power and interrelations with spot price dynamics

Wind power has seen strong growth over the last decade and increasingly affects electricity spot prices. In particular, prices are more volatile due to the stochastic nature of wind, such that more generation of wind energy yields lower prices. Therefore, it is important to assess the value of wind power at different locations not only for an investor but for the electricity system as a whole. In this paper, we develop a stochastic simulation model that captures the full spatial dependence structure of wind power by using copulas, incorporated into a supply and demand based model for the electricity spot price. This model is calibrated with German data. We find that the specific location of a turbine – i.e., its spatial dependence with respect to the aggregated wind power in the system – is of high relevance for its value. Many of the locations analyzed show an upper tail dependence that adversely impacts the market value. Therefore, a model that assumes a linear dependence structure would systematically overestimate the market value of wind power in many cases. This effect becomes more important for increasing levels of wind power penetration and may render the large-scale integration into markets more difficult.     

Robust responses to climate change via stochastic MARKAL: The case of Québec

Future patterns of climate change and economic growth are critical parameters in long-term energy planning. This paper describes a multi-stage stochastic programming approach to formulate a flexible energy plan. The plan incorporates multiple future scenarios and provides for mid-course corrections depending upon the actual realizations of future uncertainties. Results are derived from the stochastic version of Extended MARKAL (MARKet ALlocation) model for Québec, developed for this purpose. The analysis indicates significant savings of overall system cost in using a hedging strategy over any of the perfect foresight ones. With a 50% probability of implementing stringent carbon mitigation measures after 15 years, the emission trajectory takes the middle path till this uncertainty is resolved. Prior to resolution, electricity supply follows the middle path, natural gas and renewable energy tend to follow the low mitigation trajectory, and oil supply approaches the high mitigation trajectory. A set of specialized hedging technologies has been identified, which emerges more competitive in the hedging strategy than in any of the perfect foresight ones. The paper concludes that such treatment of future uncertainties can give insights that are beyond the scope of an analysis based on deterministic scenarios.     

Contract design and supply chain coordination in the electricity industry

In this article we propose a model of the supply chain in electricity markets with multiple generators and retailers and considering several market structures. We analyze how market design interacts with the different types of contract and market structure to affect the coordination between the different firms and the performance of the supply chain as a whole. We compare the implications on supply chain coordination and on the players’ profitability of two different market structures: a pool based market vs. bilateral contracts, taking into consideration the relationship between futures and spot markets. Furthermore, we analyze the use of contracts for differences and two-part-tariffs as tools for supply chain coordination. We have concluded that there are multiple equilibria in the supply chain contracts and structure and that the two-part tariff is the best contract to reduce double marginalization and increase efficiency in the management of the supply chain.     

Connectivity-and-hop-constrained design of electricity distribution networks

This paper addresses the problem of designing the configuration of an interconnected electricity distribution network, so as to maximize the minimum power margin over the feeders. In addition to the limitation of feeder power capacity, the distance (as hop count) between any customer and its allocated feeder is also limited for preventing power losses and voltage drops. Feasibility conditions are studied and a complexity analysis is performed before introducing a heuristic algorithm and two integer linear programming formulations for addressing the problem. A cutting-plane algorithm relying on the generation of two classes of cuts for enforcing connectivity and distance requirements respectively is proposed for solving the second integer linear programming formulation. All the approaches are then compared on a set of 190 instances before discussing their performances.     

Toward net-zero carbon manufacturing operations: an onsite renewables solution

A growing number of manufacturing firms are striving to achieve eco-friendly operations through onsite wind or solar generation. This paper proposes a zero-carbon power supply model to guide the integration of onsite renewable energy into manufacturing facilities. We intend to address two fundamental questions: (1) Is it cost-effective to deploy onsite wind turbines and solar photovoltaics (PVs) systems to achieve net-zero carbon environmental performance? (2) Is the renewable generation system able to meet the electricity demand despite the power intermittency? To answer these questions, we formulate a stochastic optimization model to minimize the levelized cost of onsite renewable energy. The goal is achieved by optimizing the sizing of wind and solar generating units. The proposed energy solution is tested in ten cities around the world under diverse climatic conditions. While PV is still expensive, we conclude that manufacturers could realize zero-carbon emissions at affordable cost provided the local wind speed is above 5 m/s.     

Planning the production of a fleet of domestic combined heat and power generators

This paper describes a planning problem, arising in the energy supply chain, that deals with the planning of the production runs of micro combined heat and power (microCHP) appliances installed in houses, cooperating in a fleet. Two types of this problem are described. The first one is the Single House Planning Problem (SHPP), where the focus is on supplying heat in the household. The second one combines many microCHPs into a Fleet Planning Problem (FPP) and focuses on the mutual electricity output, while still considering the local heat demand in the individual households. The problem is modeled as an ILP. For practical use a local search method is developed for the FPP, based on a dynamic programming formulation of the SHPP.     

GAMBIT-A Linear Programming Model to Balance Transmission Investment and Market Options<Superscript>†</Superscript>

Since the discovery of large-scale reserves of natural gas in the North Sea, the Gas Council has been given extended powers to purchase gas and to transmit it in bulk to the twelve Area Gas Boards. One of the functions of the Gas Council's Economic Planning Division is to determine the economic balance of the revenue obtainable from the large industrial markets and the costs of purchasing gas and constructing a national transmission system to supply the load. The paper describes the formulation of one of the mathematical models being used for planning studies and discusses the reasons for the choice of a linear programming package and the selection of objective function. The paper also describes a series of studies undertaken and the results obtained, together with some conclusions as to the effectiveness of the model as a planning tool.     

深圳市供水量的最优组合预测

城市供水系统是一个复杂的大系统,供水量受多种因素的共同影响。本文以深圳市最近20多年的供水量历史数据为基础,建立了深圳市供水量的最优组合预测模型。该模型具有较高的预测精度,组合预测的预测效果优于任意一种单一预测的预测效果,供水量预测结果对深圳市未来供水的短期或长期规划能起到重要的宏观指导作用。     

Non-convex power plant modelling in energy optimisation

The European electricity market has been deregulated recently. This means that energy companies must optimise power generation considering the rapidly fluctuating price on the spot market. Optimisation has also become more difficult. New production technologies, such as gas turbines (GT), combined heat and power generation (CHP), and combined steam and gas cycles (CSG) require non-convex models. Risk analysis through stochastic simulation requires solving a large number of models rapidly. These factors have created a need for more versatile and efficient decision-support tools for energy companies.We formulate the decision-problem of a power company as a large mixed integer programming (MIP) model. To make the model manageable we compose the model hierarchically from modular components. To speed up the optimisation procedure, we decompose the problem into hourly sub-problems, and develop a customised Branch-and-Bound algorithm for solving the sub-problems efficiently. We demonstrate the use of the model with a real-life application.