The impact of wind uncertainty on the strategic valuation of distributed electricity storage

The intermittent nature of wind energy generation has introduced a new degree of uncertainty to the tactical planning of energy systems. Short-term energy balancing decisions are no longer (fully) known, and it is this lack of knowledge that causes the need for strategic thinking. But despite this observation, strategic models are rarely set in an uncertain environment. And even if they are, the approach used is often inappropriate, based on some variant of scenario analysis—what-if analysis. In this paper we develop a deterministic strategic model for the valuation of electricity storage (a battery), and ask: “Though leaving out wind speed uncertainty clearly is a simplification, does it really matter for the valuation of storage?”. We answer this question by formulating a stochastic programming model, and compare its valuation to that of its deterministic counterpart. Both models capture the arbitrage value of storage, but only the stochastic model captures the battery value stemming from wind speed uncertainty. Is the difference important? The model is tested on a case from Lancaster University’s campus energy system where a wind turbine is installed. From our analysis, we conclude that considering wind speed uncertainty can increase the estimated value of storage with up to 50 % relative to a deterministic estimate. However, we also observe cases where wind speed uncertainty is insignificant for storage valuation.     

Outsourcing and capacity planning in an uncertain global environment

Firms employing offshore outsourcing strategies may face both exchange rate and demand uncertainties. In this paper, we show that the firms may benefit from operational option to switch production by keeping capacities with both domestic and foreign suppliers. The value of the operational option increases as the exchange rate uncertainty or demand uncertainty increases. In addition, when the firms become risk-averse, they may use domestic capacity to hedge against offshore capacity. As a result, the firms may choose to hold local capacity even if it exhibits negative marginal contribution to the profit. Furthermore, risk-averse firms may keep more total capacity than risk-neutral firms.     

基于实物期权定价方法的林业碳汇项目投资决策仿真研究

文章针对林业碳汇项目投资决策的复杂性、动态性和不确定性过程,利用林业—碳汇共同经营决策模型计算林业碳汇项目在投资期内的期望价值,采用实物期权定价方法对不同阶段不同策略下的林业碳汇项目价值进行评估,同时提出了多主体仿真建模方法,利用NetLogo仿真软件对林业碳汇项目投资决策过程进行动态模拟。仿真系统中涉及到的主体有林地、CO₂和投资者,投资者主要是作为观察者的身份,在不同阶段会做出不同的投资策略。模拟仿真三种不同状态下投资者的决策变化:一是传统林业投资动态模拟,不包含碳汇和期权因素动态模拟;二是引入碳汇市场后的林业投资动态模拟;三是引入碳汇市场和期权后林业投资动态模拟。NetLogo仿真分析结果表明引入碳汇市场可以提高投资者的收益并改变投资者的经营策略,同时引入期权,不仅增加了投资者的积极性而进行扩张投资,还可以更好地发挥林木碳汇功能,体现林业的生态价值及经济价值。     

The Assessment of Diurnal Storage Requirements for Gas Supply Systems

The British Gas Corporation is preparing for substantial capital expenditure to provide additional gas storage capacity, which is required to balance out the within-day variations of demand, Conversion to natural gas, with its higher calorific value, resulted in a substantial increase in the effective volume of gas storage available. This surplus has been eroded by the rapid growth in demand over the decade since conversion, and new investment in storage will be required if current forecasts of growth are correct. The assessment of the storage requirements has therefore become more important, and more sophisticated methods are being developed. In this paper the factors affecting the need for storage are examined, the methods adopted in incorporating these factors into a simulation model are discussed, and the results from the models are presented. Consideration is given to the national policy aspects of the problem and to the interactions between O.R. and other staff within B.G.C. during the development of the project.     

Uncertain Product Quality, Optimal Pricing and Product Development

A firm is developing a new product. However, the firm is uncertain as to how consumers will perceive the product's desirability or quality. Using a general model of product quality, conditions for an increase in uncertainty to increase the optimal price are derived. General conditions are derived under which the firm prefers the less risky project, the one with lower quality variability. However, if at the optimal price the firm only has positive demand for high quality realizations, then the firm prefers a more risky project. As the uncertainty exists in the consumers' preferences, welfare effects can be determined, unlike in previous work examining uncertainty.     

Managing production with flexible capacity deployment for serial multi-stage manufacturing systems

This paper presents a model for serial multi-stage manufacturing systems facing variability from two sources. One source is demand uncertainty; the other is manufacturing uncertainty associated with all manufacturing stages. A production control policy based on the planned lead time and the manufacturing capacity requirement is developed. It is shown that this production control policy has the effect of reducing the variance of production output for all manufacturing stages. Some specific analyses are provided to illustrate the production control policy developed. The model developed provides a vehicle for examining the interrelationships among the production output, the planned lead time and the actual manufacturing flow time. The risk-pooling value over both demand randomness and manufacturing uncertainty, which is achieved through consolidating some manufacturing capacity and deploying flexible capacity among the manufacturing stages, is analyzed. This risk-pooling value can be realized in the form of either reduced manufacturing flow time or increased effective capacity to meet more demand. It is shown that the risk-pooling value increases as the planned lead time decreases.     

Incorporating demand uncertainty and forecast error in supply chain planning models

This paper develops a framework for examining the effect of demand uncertainty and forecast error on unit costs and customer service levels in the supply chain, including Material Requirements Planning (MRP) type manufacturing systems. The aim is to overcome the methodological limitations and confusion that has arisen in much earlier research. To illustrate the issues, the problem of estimating the value of improving forecasting accuracy for a manufacturer was simulated. The topic is of practical importance because manufacturers spend large sums of money in purchasing and staffing forecasting support systems to achieve more accurate forecasts. In order to estimate the value a two-level MRP system with lot sizing where the product is manufactured for stock was simulated. Final product demand was generated by two commonly occurring stochastic processes and with different variances. Different levels of forecasting error were then introduced to arrive at corresponding values for improving forecasting accuracy. The quantitative estimates of improved accuracy were found to depend on both the demand generating process and the forecasting method. Within this more complete framework, the substantive results confirm earlier research that the best lot sizing rules for the deterministic situation are the worst whenever there is uncertainty in demand. However, size matters, both in the demand uncertainty and forecasting errors. The quantitative differences depend on service level and also the form of demand uncertainty. Unit costs for a given service level increase exponentially as the uncertainty in the demand data increases. The paper also estimates the effects of mis-specification of different sizes of forecast error in addition to demand uncertainty. In those manufacturing problems with high demand uncertainty and high forecast error, improved forecast accuracy should lead to substantial percentage improvements in unit costs. Methodologically, the results demonstrate the need to simulate demand uncertainty and the forecasting process separately.     

A dynamic programming model of energy storage and transformer deployments to relieve distribution constraints

We introduce a stochastic dynamic programming (SDP) model that co-optimizes multiple uses of distributed energy storage, including energy and ancillary service sales, backup capacity, and transformer loading relief, while accounting for market and system uncertainty. We propose an approximation technique to efficiently solve the SDP. We also use a case study with high residential loads to demonstrate that a deployment consisting of both storage and transformer upgrades decreases costs and increases value relative to a transformer-only deployment.     

电力市场环境下计及V2G和多类型需求响应的综合能源系统多目标优化模型

园区综合能源系统(Park integrated energy system,PIES)是满足用户多种用能需求的一种重要途径,但由于内部分布式能源机组出力具有不确定性,且与负荷在时间维度上存在一定的不匹配性,限制了能源利用效率和经济效益的提升.因此,本文首先在构建耦合热电的PIES的基础上,构建了多类型需求响应模型;其次,构建了考虑风光机组出力不确定性的以系统净收益、清洁能源弃能率为多目标函数的优化模型;然后,构建了"不确定性处理-多目标处理-单目标处理"的三阶段求解模型,最后,以V2G和需求响应为考虑条件,设计多情景.算例结果表明:V2G可以为清洁能源不稳定发电提供有效备用,在一定程度上提供清洁能源利用效率;引入电热需求响应,能够改变用户负荷,增加经济效益.     

Stockpiling under price uncertainty and storage capacity constraints

A model is presented for the operation of an agent whose responsibility is to purchase and perhaps stockpile sufficient quantities of a certain commodity in order to satisfy an exogenous constant demand per time period. This is the situation faced by a state agency which is responsible for the purchasing of oil products to satisfy the demand of a country in which demand for energy has stabilized at a certain level.An important feature of the model is that the price of the commodity is described by a stochastic process. This reflects the volatility of prices of oil products. Furthermore, the model takes storage capacity constraints explicitly into account, and thus can help to assess the optimal level of storage capacity expansion.The relevant stochastic dynamic programming equations are derived and solved for the least cost function, which turns out to be piecewise linear in the inventory level. The storage capacity enters only in the computation of the constant term of the value function. The solution of the dynamic programming equation leads also to the optimal purchasing strategy of agencies with different levels of flexibility in their policy: in the model, an agency can be allowed or not to resell from the stock and it can have finite or infinite storage capacity.     

基于博弈论的节能量保证型EPC合同决策分析

合同能源管理(EPC)是一种以未来节约的能源费用支付节能项目成本的节能管理机制。节能量保证型EPC模式中,耗能企业负责为项目融资,节能服务公司提供项目的全程服务并向客户企业保证一定的节能效益。若达不到承诺值,节能服务公司向客户进行补偿,若超出承诺值,客户给予节能服务公司一定的奖励。合同决策问题是该模式应用中的重要问题。本文以节能量保证型EPC合同中初始项目投资、合同期限和超额节能效益奖励的决策问题为研究对象,建立了客户和节能服务公司之间的决策博弈模型,分析二者的最优合同决策。数值试验结果表明,该方法不仅能让客户企业和节能服务公司均受益,还可以有效提高项目的投资报酬率,并且较高的节能服务公司技术水平和客户初始耗能水平能产生更高的节能效率。     

A note on issues of over-conservatism in robust optimization with cost uncertainty

We identify and discuss issues of hidden over-conservatism in robust linear optimization, when the uncertainty set is polyhedral with a budget of uncertainty constraint. The decision-maker selects the budget of uncertainty to reflect his degree of risk aversion, i.e. the maximum number of uncertain parameters that can take their worst-case value. In the first setting, the cost coefficients of the linear programming problem are uncertain, as is the case in portfolio management with random stock returns. We provide an example where, for moderate values of the budget, the optimal solution becomes independent of the nominal values of the parameters, i.e. is completely disconnected from its nominal counterpart, and discuss why this happens. The second setting focusses on linear optimization with uncertain upper bounds on the decision variables, which has applications in revenue management with uncertain demand and can be rewritten as a piecewise linear problem with cost uncertainty. We show in an example that it is possible to have more demand parameters equal their worst-case value than what is allowed by the budget of uncertainty, although the robust formulation is correct. We explain this apparent paradox.     

基于不确定理论的铁路货运需求预测

合理预测铁路货运需求是铁路管理部门建设、运营等决策基础。为应对铁路货运需求的复杂变化,基于Pearson相关性分析方法筛选出铁路货运需求的七个具有关键影响的因素,并结合不确定理论建立不确定多元线性回归模型,相应的铁路货运预测结果由传统单一值变成可能的需求区间范围,更加符合处于不确定环境下的铁路货运需求实际情况。选取国家统计局2004~2016年相关数据进实证研究,并与回归模型以及BP模型的预测结果对比分析,实验表明不确定多元线性回归的预测结果更加精确。     

基于小波神经网络的中国能源需求预测模型

通过分析影响我国能源需求的主要因素,建立了基于小波神经网络的需求预测模型.采用定性与定量相结合的方式,分析了影响我国能源需求的主要因素,通过将人口总数、GDP、产业结构变化以及能源消费量的一阶滞后作为输入变量,建立基于小波神经网络的我国能源需求非线性预测模型.实验结果表明,该非线性预测模型与多元回归模型相比更加合理,具有更高的预测精度.     

A simple recourse model for power dispatch under uncertain demand

Optimal power dispatch under uncertainty of power demand is tackled via a stochastic programming model with simple recourse. The decision variables correspond to generation policies of a system comprising thermal units, pumped storage plants and energy contracts. The paper is a case study to test the kernel estimation method in the context of stochastic programming. Kernel estimates are used to approximate the unknown probability distribution of power demand. General stability results from stochastic programming yield the asymptotic stability of optimal solutions. Kernel estimates lead to favourable numerical properties of the recourse model (no numerical integration, the optimization problem is smooth convex and of moderate dimension). Test runs based on real-life data are reported. We compute the value of the stochastic solution for different problem instances and compare the stochastic programming solution with deterministic solutions involving adjusted demand portions.This research is supported by the Schwerpunktprogramm Anwendungsbezogene Optimierung und Steuerung of the Deutsche Forschungsgemeinschaft.     

A dependent project evaluation and review technique: A Bayesian network approach

The Program Evaluation and Review Technique (PERT) dates back to 1959. This method evaluates the uncertainty distribution of a project’s completion time given the uncertain completion times of the activities/tasks comprised within it. Each activity’s uncertainty was defined originally by a unique two parameter beta PERT distribution satisfying what is known to be the PERT mean and PERT variance. In this paper, a three-parameter PERT family of bounded distributions is introduced satisfying that same mean and variance, generalizing the beta PERT distribution. Their additional flexibility allows for the modeling of statistical dependence in a continuous Bayesian network, generalizing in turn the traditional PERT procedure where statistical independence is assumed among beta PERT activity durations. Through currently available Bayesian network software and the construction of that PERT family herein, the coherent monitoring of remaining project completion time uncertainty given partial completion of a project may become more accessible to PERT analysts. An illustrative example demonstrating the benefit of monitoring of remaining project completion time uncertainty as activities complete in that Bayesian fashion shall be presented, including expressions and algorithms for the specification of the three prior parameters for each activity in the project network to adhere to classical the PERT mean and PERT variance and a degree of statistical dependence between them.     

Integrated facility location and production scheduling in multi-generation energy systems

In this paper, we investigate the energy system design problems with the multi-generation technologies, i.e., simultaneous generation of multiple types of energy. Our results illustrate the economic value of multi-generation technologies to reduce spatio-temporal demand uncertainty by risk pooling both within and across different facilities.     

Proactive data envelopment analysis: Effective production and capacity expansion in stochastic environments

Demand fluctuations that cause variations in output levels will affect a firm’s technical inefficiency. To assess this demand effect, a demand-truncated production function is developed and an “effectiveness” measure is proposed. Often a firm can adjust some input resources influencing the output level in an attempt to match demand. We propose a short-run capacity planning method, termed proactive data envelopment analysis, which quantifies the effectiveness of a firm’s production system under demand uncertainty. Using a stochastic programming DEA approach, we improve upon short-run capacity expansion planning models by accounting for the decreasing marginal benefit of inputs and estimating the expected value of effectiveness, given demand. The law of diminishing marginal returns is an important property of production function; however, constant marginal productivity is usually assumed for capacity expansion problems resulting in biased capacity estimates. Applying the proposed model in an empirical study of convenience stores in Japan demonstrates the actionable advice the model provides about the levels of variable inputs in uncertain demand environments. We conclude that the method is most suitable for characterizing production systems with perishable goods or service systems that cannot store inventories.     

不确定环境下基于资金约束的技术授权策略

技术创新的价值实现需要后续的商业化开发,市场需求不确定会影响商业化投资的价值评估,在企业商业化受到资金约束时如果进行资金筹集就会有一定困难,而合理设计的授权合约这时可以作为项目的融资途径之一。本文研究了企业的最优授权策略在无资金约束时和资金约束时的差异,试图通过技术授权合约的设计进行筹资,发现利用授权合约的预付金可以满足部分融资需要,但是使用授权合约融资的成本较高,影响融资额度的主要因素包括接受授权企业的研发成本、市场需求的预期、单位产品税的承诺等。     

基于可信性理论的PPP项目特许期-价格联合调整策略研究

需求预测误差是影响PPP项目收益预测准确性的主要因素。为减少谈判争议,确保风险和收益的动态均衡,本文基于模糊数学可信性理论,构建了考虑需求不确定的特许期-价格联合调整模型。将项目运营期间的需求预测误差作为模糊变量,将运营期内特许期和价格的联合调整策略作为决策变量,通过模糊模拟求解出不同特许期和价格调整组合下的期望收益误差以及正收益预期下的可信性,进而得到特许期和价格的联合调整策略可行解集。并将该模型应用于某污水项目中,结果表明,该模型能够有效地解决需求不确定性风险对特许期测算影响的问题,弥补了目前PPP项目特许期和价格调整决策研究中未考虑需求预测误差的不足,对PPP项目特许期和价格的调整决策有着重要的参考意义。