Application of chaos-based chaotic invasive weed optimization techniques for environmental OPF problems in the power system

This paper presents efficient chaotic invasive weed optimization (CIWO) techniques based on chaos for solving optimal power flow (OPF) problems with non-smooth generator fuel cost functions (non-smooth OPF) with the minimum pollution level (environmental OPF) in electric power systems. OPF problem is used for developing corrective strategies and to perform least cost dispatches. However, cost based OPF problem solutions usually result in unattractive system gaze emission issue (environmental OPF). In the present paper, the OPF problem is formulated by considering the emission issue. The total emission can be expressed as a non-linear function of power generation, as a multi-objective optimization problem, where optimal control settings for simultaneous minimization of fuel cost and gaze emission issue are obtained. The IEEE 30-bus test power system is presented to illustrate the application of the environmental OPF problem using CIWO techniques. Our experimental results suggest that CIWO techniques hold immense promise to appear as efficient and powerful algorithm for optimization in the power systems.     

Supply Function Equilibrium in Electricity Spot Markets with Contracts and Price Caps

In electricity wholesale markets, generators often sign long term contracts with purchasers of power in order to hedge risks. In this paper, we consider a market where demand is uncertain, but can be represented as a function of price together with a random shock. Each generator offers a smooth supply function into the market and wishes to maximize his expected profit, allowing for his contract position. We investigate supply function equilibria in this setting, using a model introduced by Anderson and Philpott. We study first the existence of a unique monotonically increasing supply curve that maximizes the objective function under the constraint of limited generation capacity and a price cap, and discuss the influence of the generators contract on the optimal supply curve. We then investigate the existence of a symmetric Nash supply function equilibrium, where we do not have to assume that the demand is a concave function of price. Finally, we identify the Nash supply function equilibrium which gives rise to the generators maximal expected profit. This work was supported by the Australian Research Council Grant RMG1965The authors would like to thank three anonymous referees for their helpful comments     

An adaptive model with joint chance constraints for a hybrid wind-conventional generator system

We analyze scheduling a hybrid wind-conventional generator system to make it dispatchable, with the aim of profit maximization. Our models ensure that with high probability we satisfy the day-ahead power promised by the model, using combined output of the conventional and wind generators. We consider two scenarios, which differ in whether the conventional generator must commit to its schedule prior to observing the wind-power realizations or has the flexibility to adapt in near real-time to these realizations. We investigate the synergy between the conventional generator and wind farm in these two scenarios. Computationally, the non-adaptive model is relatively tractable, benefiting from a strong extended-variable formulation as an integer program. The adaptive model is a two-stage stochastic integer program with joint chance constraints. Such models have seen limited attention in the literature because of the computational challenges they pose. However, we develop an iterative regularization scheme in which we solve a sequence of sample average approximations under a growing sample size. This reduces computational effort dramatically, and our empirical results suggest that it heuristically achieves high-quality solutions. Using data from a wind farm in Texas, we demonstrate that the adaptive model significantly outperforms the non-adaptive model in terms of synergy between the conventional generator and the wind farm, with expected profit more than doubled.     

计及多重阻塞的电动汽车移动储能特性建模

为实现城市交通电力耦合系统在城市道路、充电设施、输电线路阻塞环境下的优化运行,提出了计及多重阻塞的动态交通电力流联合优化方法。首先,基于时空网络模型,提出了计及电动汽车移动、静止、充电、排队模式的队列时空网络模型,构建了适用于电动汽车的车辆调度模型,进而形成动态交通分配模型,以减少交通出行损失。其次,通过优化发电机组、储能等的出力和备用计划,计及城市电网安全、备用约束,构建了安全约束动态经济调度模型,以降低碳排放及发电成本。随后,形成多目标动态优化模型,并将其转换为混合整数凸二次规划问题。最后,在耦合IEEE-30、Sioux Falls系统中验证了所提模型的有效性。     

Interior point models for power system stability problems

In this paper, a detailed analysis of the use of optimization techniques in the study of voltage stability problems, leading to the incorporation of voltage stability criteria in traditional Optimal Power Flow (OPF) formulations is presented. Optimal power flow problems are highly nonlinear programming problems that are used to find the optimal control settings in electrical power systems. The relationship between the Lagrangian Multipliers of the OPF problem and the classification of the maximum loading point level of the system is given. Finally, the paper presents a sequential OPF technique to enhance voltage stability using reactive power and voltage rescheduling with no increase in real (active) generation cost.     

Market Price Calculations in Restructured Electricity Markets

In the traditional organisation of the power market, the generation Unit Commitment and Dispatch problem was solved as a cost minimisation problem. After deregulation of the electricity sector, the problem must be solved as a profit maximising problem. It is necessary to find feasible market prices. This is difficult, because simple marginal cost based prices not always cover startup and operation-independent costs, with the result that the generator would choose not to run with such prices. In this paper a market structure is proposed with a central market operator computing the market equilibrium for both energy and reserves, based on generator offers and consumer bids. It is shown that it is possible to find feasible market prices. Using a simple test system, it is shown that demand elasticity can have a profound impact on prices and generator revenues and profits during peaking hours.     

Multi-machine power system state-space modelling for small-signal stability assessments

This work presents a general state-space representation of a multi-machine, multi-order power system model, which may be used to carry out small-signal stability assessments. Computational software coded in MATLAB has been developed in order to find and analyse the solution of an arbitrary number of synchronous generators in the network. Each generator is represented by a pre-defined model. The model choice is tailored to fit the available data for each generator. The software has provisions for conducting power flow solutions and the calculation of the initial state that the generators keep prior to the disturbance. The state-space representation and the equivalent transfer function matrix of the system are generated automatically. Eigenvalue analysis may be carried out using the standard MATLAB functionality. The paper is one of a tutorial nature and in order to check on the sanity of the results given by the new software, two text-book networks have been examined. The results were also compared with those generated using commercial industrial-grade software.     

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.     

Economic order quantity model and Taguchi’s cost of poor quality

In this paper we consider defective products and Taguchi’s cost of poor quality in the economic order quantity (EOQ) model. We assume that the product quality performs a normal distribution function, and the Taguchi’s poor quality cost has been involved. From our analysis, it has been found that the annual profit will be decreased if the poor quality of product and Taguchi’s quality cost are involved in the model. It has also been found that economic order quantity in our model is larger than that in a traditional EOQ model.     

可再生能源配额制下异质权力发电商的绿色生产决策研究

基于可再生能源配额的政策背景,本文构造了发电商三种不同市场权力结构下的绿色生产决策模型。讨论了敏感参数对异质权力发电商最优决策结果的影响,基于参数范围分析了不同权力结构下的最优决策效果。通过消费者效用、发电成本、环境保护的社会福利函数,识别出了参数最优取值范围内的最优决策效果的市场结构。结果显示:当绿证交易价格、最低配额比例超过最低临界值时,绿色发电商能够实现最优决策效果,但对传统发电商的最大利润产生了显著的“挤出”效应。若绿证交易价格和电力需求价格弹性系数在最佳区间内,则传统和绿色发电商既能够达到最优决策效果,又可以最大限度促进社会福利效用的单调增加,即存在绿色发电商主导的最优市场决策结构,但不存在最优纳什决策结构。     

部分延迟订购的易变质品联合定价与生产策略

构建了一个需求同时依赖于销售价格和库存水平,生产率和变质率均为常数,允许缺货且缺货量部分延迟订购的易变质品联合定价与生产控制模型。首先证明了在销售价格给定的情况下,系统的总利润函数是关于生产计划的严格凹函数,平均利润函数是严格的伪凹函数,即存在唯一的最优解,并给出其充分条件。接着给出问题的一个数值求解算法。最后通过算例,展示了模型及相关算法的应用,并对相关参数进行了灵敏度分析,结果显示:当产品的生产成本、缺货成本和机会成本增加时,系统的平均利润将下降;生产成本和延迟订购阻力系数对最优定价和生产策略以及平均利润的影响较大。     

Using agents for solving a multi-commodity-flow problem

We investigate a commodity trading problem in a flow network with arbitrary topology where sinks combine commodities into bundles in order to generate profits. Our focus is the profit maximization problem for the trading network under both central and distributed control. We compute solutions for the central control problem using an integer linear program while we compute solutions for the distributed case by implementing the nodes in the network as software-agents that exchange messages in order to establish profitable trades. We report on computational results using both methods and demonstrate that there is a connection between agent profits and a centrality measure developed for the problem. We also demonstrate that with our current agent strategy, there is a trade-off between the agents acting too quickly before enough information is available and waiting too long and thus giving each agent too much information and thus too much power over the outcome.     

Optimization of two-step investment in a production process

We consider the problem of optimizing the control of a production process. The control parameters are the capacity utilization and the investment in the growth of the production capacity. We assume that the investments are divided into two parts: initial investment aimed at creating production facilities, and investment aimed at increasing the capacity during the production process. The initial and increased capacities and the moment of changing the capacity are variable parameters to be specified. The price of the product is assumed to be a random process. The problem is to optimize the production process and to construct a control strategy that maximizes the average discounted profit. We propose an approach to the construction of an optimal adaptive strategy for controlling the production. The approach is based on the dynamic programming method.     

A stochastic inventory problem with fuzzy shortage cost

Up to now, many inventory models have been considered in the literature. Some assume stochastic demands and others consider the deterministic case. Though they include a shortage cost due to lost sales, it is usually assumed to be known concretely and a priori. This paper introduces fuzziness of shortage cost explicitly into the classical newsboy problem. That is, we investigate the so-called fuzzy newsboy problem where its shortage cost is vague and given by an L shape fuzzy number. Then the total expected profit function also becomes a fuzzy number. Finally, we find an optimal ordering quantity realizing the fuzzy max order of the profit function (fuzzy min order considering the profit function) and compare it with the optimal ordering quantity of the non-fuzzy newsboy problem.     

The ability to compensate for suboptimal capacity decisions by optimal pricing decisions

Certain companies have high capacity cost and rather moderate production cost. These companies usually assume that deciding about their capacity is quite critical. Frequently, however, they are able to adjust the demand for their products to the available capacity by setting appropriate prices, that is higher (lower) than current prices in the presence of under-capacity (over-capacity). We argue that appropriate prices can reduce the adverse effects of non-optimal capacities. We analyze the sensitivity of profit in such a situation for a company in a monopolistic market, selling a non-storable product and facing fluctuating but interdependent demand across two time periods which allows to profitably differentiate prices. Therefore, we state optimality conditions for prices in situations of variable and given capacities and describe a procedure to determine them. The main suggestion of this analysis is that, within the bounds of the normative models and specific parameters examined, optimal prices can substantially reduce the adverse effects of capacity deviating from its optimum. In this way, profit is rather insensitive to deviations of capacity from its optimum. The implications of this finding are discussed for a number of situations.     

Mixing properties of modified additive generators

We develop amatrix-graph approach to estimating themixing properties of bijective shift registers over a set of binary vectors. Such shift registers generalize, on the one hand, the class of ciphers based on the Feistel network and, on the other hand, the class of transformations of additive generators (the additive generators are the base for the Fish, Pike, andMush algorithms). It is worth noting that the original schemes of additive generators are found insecure due to their weak mixing properties. The article contains the results of investigations for the mixing properties of modified additive generators. For the mixing directed graph of a modified additive generator, we define the sets of arcs and cycles, obtain primitivity conditions, and give a bound for the exponent. We show that, the determination of parameters for the modified additive generator allows us to achieve a full mixing in a number of iterations that is substantially less than the number of vertices in the mixing digraph.     

A model and approach to the challenge posed by optimal power systems planning

Currently, there is a need to plan and analyze the electric power transmission system in greater detail and over larger geographic areas. Existing models approach the problem from different perspectives. Each model addresses different aspects of and has different approximations to the optimal planning process. In order to scope out the huge challenge of optimal transmission planning, this paper presents a new modeling approach for inter-regional planning and investment in a competitive environment. This modeling approach incorporates the detailed generator, topology and operational aspects found in production cost planning models into a larger framework that can find optimal sets of transmission expansion projects. The framework proposed here can be used in an auction to award investment contracts or as a part of a more general policy analysis. The solution yields the set of transmission projects that have the highest expected benefits, while also representing generic generation expansions under the same objective. The model is a two-stage, mixed-integer, multi-period, N-1-reliable model with investment, unit commitment, and transmission switching. The combination of combinatorial, stochastic and operational elements means this model may be computationally intractable without judicious modelling aggregations or approximations to reduce its size and complexity. Nevertheless we show via a dual problem that analysing the economics and sensitivity of the solution is computationally more straightforward.     

The unit commitment model with concave emissions costs: a hybrid Benders’ Decomposition with nonconvex master problems

We present a unit commitment model which determines generator schedules, associated production and storage quantities, and spinning reserve requirements. Our model minimizes fixed costs, fuel costs, shortage costs, and emissions costs. A constraint set balances the load, imposes requirements on the way in which generators and storage devices operate, and tracks reserve requirements. We capture cost functions with piecewise-linear and (concave) nonlinear constructs. We strengthen the formulation via cut addition. We then describe an underestimation approach to obtain an initial feasible solution to our model. Finally, we constitute a Benders’ master problem from the scheduling variables and a subset of those variables associated with the nonlinear constructs; the subproblem contains the storage and reserve requirement quantities, and power from generators with convex (linear) emissions curves. We demonstrate that our strengthening techniques and Benders’ Decomposition approach solve our mixed integer, nonlinear version of the unit commitment model more quickly than standard global optimization algorithms. We present numerical results based on a subset of the Colorado power system that provide insights regarding storage, renewable generators, and emissions.     

The uncapacitated facility location problem with demand-dependent setup and service costs and customer-choice allocation

We consider a generalization of the uncapacitated facility location problem, where the setup cost for a facility and the price charged for service may depend on the number of customers patronizing the facility. Customers are represented by the nodes of the transportation network, and facilities can be located only at nodes; a customer selects a facility to patronize so as to minimize his (her) expenses (price for service + the part of transportation costs paid by the customer). We assume that transportation costs are paid partially by the service company and partially by customers. The objective is to choose locations for facilities and balanced prices so as to either minimize the expenses of the service company (the sum of the total setup cost and the total part of transportation costs paid by the company), or to maximize the total profit. A polynomial-time dynamic programming algorithm for the problem on a tree network is developed.     

低碳电网扩张策略:以南方电网公司为例

研究了需求随机环境下电力企业关于电源建设与电力调度的最优决策;考虑电源机组的能源结构约束与运营发电期内的碳排放总量约束,构建了以总成本最小化为目标的带补偿二阶段随机规划模型;定性分析了模型的最优解与装机容量等其它参数之间的联系;以南方电网公司为例,基于真实的数据并考虑政府的规划建议与企业自身的低碳化发展要求,利用情景生成法求解随机规划模型。结果反映了电力系统发展过程中环保绩效与总成本之间的矛盾之外,为企业在实践运作中计划期的电力建设决策以及运营期的发电决策提供了一些有价值的建议。