Produção Nacional
Revisado por pares
Short‐term operation of a distribution company: A pseudo‐dynamic tabu search‐based optimisation
2018; Institution of Engineering and Technology; Volume: 12; Issue: 12 Linguagem: Inglês
10.1049/iet-gtd.2017.0731
ISSN1751-8695
AutoresMarcel Chuma Cerbantes, Ricardo Fernández‐Blanco, Miguel A. Ortega‐Vazquez, José Roberto Sanches Mantovani,
Tópico(s)Microgrid Control and Optimization
ResumoIET Generation, Transmission & DistributionVolume 12, Issue 12 p. 2995-3004 Research ArticleFree Access Short-term operation of a distribution company: A pseudo-dynamic tabu search-based optimisation Marcel Chuma Cerbantes, Corresponding Author Marcel Chuma Cerbantes marcel.chuma@gmail.com Department of Electrical Engineering, Universidade Estadual Paulista, Ilha Solteira, Brazil Instituto Federal de Mato Grosso do Sul, Três Lagoas, BrazilSearch for more papers by this authorRicardo Fernández-Blanco, Ricardo Fernández-Blanco Department of Applied Mathematics, University of Malaga, Malaga, SpainSearch for more papers by this authorMiguel A. Ortega-Vazquez, Miguel A. Ortega-Vazquez orcid.org/0000-0002-7601-4455 Grid Operations and Planning, Electric Power Research Institute, Palo Alto, USASearch for more papers by this authorJosé Roberto Sanches Mantovani, José Roberto Sanches Mantovani Department of Electrical Engineering, Universidade Estadual Paulista, Ilha Solteira, BrazilSearch for more papers by this author Marcel Chuma Cerbantes, Corresponding Author Marcel Chuma Cerbantes marcel.chuma@gmail.com Department of Electrical Engineering, Universidade Estadual Paulista, Ilha Solteira, Brazil Instituto Federal de Mato Grosso do Sul, Três Lagoas, BrazilSearch for more papers by this authorRicardo Fernández-Blanco, Ricardo Fernández-Blanco Department of Applied Mathematics, University of Malaga, Malaga, SpainSearch for more papers by this authorMiguel A. Ortega-Vazquez, Miguel A. Ortega-Vazquez orcid.org/0000-0002-7601-4455 Grid Operations and Planning, Electric Power Research Institute, Palo Alto, USASearch for more papers by this authorJosé Roberto Sanches Mantovani, José Roberto Sanches Mantovani Department of Electrical Engineering, Universidade Estadual Paulista, Ilha Solteira, BrazilSearch for more papers by this author First published: 22 May 2018 https://doi.org/10.1049/iet-gtd.2017.0731Citations: 6AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This work presents a probabilistic sequential framework for short-term operation of distribution companies (DisCos) participating in the day-ahead (DA) and real-time (RT) markets. In the proposed framework, the DisCo's operating decisions are sequentially optimised; first, in a DA operation stage, and then in RT. The DA decisions are driven by the DisCo's profit maximisation, while the DisCo aims to minimise the actions required to accommodate deviations from forecasted quantities (i.e. the DA decisions) in the RT operation stage. This sequential approach considers realistic voltage-sensitive loads and full ac power flow equations to represent the realistic network's active and reactive power injections. In addition, the operation of stationary batteries and the demand elasticity under time-varying retail prices are explicitly modelled. The two resulting models are large-scale highly non-linear non-convex mathematical problems with continuous and discrete variables. A pseudo-dynamic tabu-search-based solution algorithm is used as an alternative to conventional optimisation solvers in order to tackle the problem in an effective manner, without linearisations. Numerical results from 69- and 135-bus distribution systems illustrate the performance and the scalability of the proposed approach. 1 Introduction Modern distribution companies (DisCos) are power system agents that simultaneously deliver electrical energy to consumers, and operate the distribution network [1]. In short-term operation, DisCos are profit-seeking entities that strive to maximise the difference between the revenue from the energy sold to consumers and the total cost of supply [2]. To attain such goal, the DisCo buys energy from the wholesale electricity market and from investor-owned distributed generators (DGs) and sells energy to consumers, while operating the network efficiently within technical limits [2, 3]. The DisCo participates in both day-ahead (DA) and real-time (RT) markets to meet the load-generation power balance in the short-term. However, trading in RT is usually risky due to the high volatility of the RT prices which may lead to monetary losses [1–4]. Therefore, the DisCo seeks to settle all its transactions on the DA operation, and use RT markets as last resort to accommodate deviations from DA quantities [4]. Within the context of a restructured electricity sector, the DisCo's operation problem has taken particular interest over the last few years, specially due to the integration of distributed energy resources (DERs) into distribution networks [5–8]. Algarni and Bhattacharya [5] propose DisCo's short-term decision models for DA and RT operations under a two-stage sequential framework. This model relies on simple deterministic formulations, thus disregarding the stochastic nature of market-clearing prices, demand, and production of renewable sources. In [6], it is proposed a sequential stochastic framework to model the DisCo's DA and RT operations. However, it is assumed that the DA market-clearing prices are known. Safdarian et al. [7] present a DisCo's short-term decision model including price-based demand response. The authors rely on approximated linear models to enforce active and reactive power flow constraints. Finally, a RT operation framework for a DisCo with aggregator-based demand response resources is proposed in [8]. The problem is formulated as a bilevel model to capture the rational aggregators’ behaviour and then it is reformulated as a single-level mixed-integer non-linear program. The works by the authors in [5–8] also neglect the operation of network devices such as step voltage regulators (SVRs) and energy storage devices (i.e. stationary batteries), which drastically impact on the DisCo's short-term operation. In fact, the operating costs are lower when the operation of such network devices is properly optimised [9]. In addition, they assume a constant power load representation (i.e. the practical voltage-sensitive behaviour of active and reactive power loads is neglected), which may lead to suboptimal solutions. The effect of constant power and voltage-sensitive load models in distribution planning is analysed in [10–13]. In [10], experimental results show that line losses are increased after improving the power factor and voltage profile of the substation when switching a shunt capacitor bank (SCB). Singh et al. [11] and Qian et al. [12] investigate the impact of load models on the planning of DG units. Singh et al. [11] demonstrate that the location and size of DG units can be significantly affected when considering practical voltage-sensitive load models. As a consequence, the results are inaccurate when a constant power load model is assumed. In [12], the authors claim that a constant power load model is no longer appropriate in networks with high penetration of DERs. In fact, the quantification of operation benefits strongly depends on the models of power flow analysis. Also, Padilha-Feltrin et al. [13] show that the network's Volt-VAR management is more effective when realistic voltage-sensitive load models are assumed. Therefore, voltage-sensitive load models are more accurate and better suited to represent load injections in distribution networks. This work proposes realistic DA and RT operational planning models for a DisCo based on a probabilistic sequential framework [5, 6]. The DA model is driven by profit maximisation, while the DisCo aims to minimise the active power adjustment costs of deviations from DA forecasts in the RT model. The main contributions of this work are: This paper proposes lifelike models for the DisCo's DA and RT operations. As customarily done in current power systems where DA and RT markets are separately run, the DisCo's DA and RT short-term operation models are implemented sequentially. An important aspect is the incorporation of realistic voltage-sensitive models for loads [11] and full ac power flow equations to represent the real-life nature of the network's active and reactive power injections. The proposed model includes the operation of SVRs, SCBs, and DERs, such as dispatchable/intermittent DG units and stationary batteries; and the demand elasticity as an explicit function of time-varying retail prices. The resulting models are characterised as large-scale highly non-linear non-convex programs with continuous, binary, and discrete variables due to the ac power flow nature, voltage-sensitive loads, and elastic demand. An effective pseudo-dynamic tabu search (TS)-based solution procedure [14] is proposed. This method is capable of handling non-continuous variables, time-coupled constraints, and the nonlinearities that characterise the problem efficiently, without resorting to linear proxies that would degrade the accuracy of the solutions. TS has proven efficiency when applied to large-scale complex planning problems in the power system literature [15–19]. Finally, a probabilistic power flow based on a fast and efficient point estimate method (PEM) [20] is used to tackle uncertainties of demand, renewable resources, and market-clearing prices. To the best of the authors’ knowledge, this is the first time that full ac power flow constraints with practical voltage-sensitive loads are assumed to assess the effects of Volt-VAR control provided by DERs and network devices in the DisCo's DA and RT operations. Thus, the accuracy of the DisCo's decisions in both operating stages is improved, i.e. a much more practical solution is obtained. One of the major obstacles in viable application of conventional optimisation solvers is the existing computational complexity associated with the non-linear terms of the resulting model plus its stochastic nature. In fact, the proposed models may not be solved by conventional optimisation techniques. Non-linear optimisation solvers would lead to intractability as the number of binary and discrete variables increases. Moreover, approximated linearisation techniques could be applied to this problem in order to yield a mixed-integer linear program. However, those techniques have two potential disadvantages: (i) they come at expense of increasing the number of constraints and variables, which may lead to intractability; and (ii) approximations unavoidably lead to inaccuracies. The performance of the proposed approach is evaluated on a 69-bus distribution test feeder [21] and a 135-bus distribution network [22] is used for scalability purposes. In [19], the accuracy and capability of TS is successfully assessed over a conventional convex optimisation technique such as second-order conic programming. The rest of this work is organised as follows. Section 2 addresses the problem formulation. Section 3 describes the solution approach. Section 4 analyses the numerical results. Finally, relevant conclusions are drawn in Section 5. 2 Problem formulation The DisCo is assumed to own and operate the distribution network while behaving as a price-taker that can procure energy from the wholesale electricity market and DG units [3]. Within this context, the DisCo seeks to maximise its profits from the DA transactions. In a typical US-style forward (i.e. DA) electricity market, profits are given by the difference between the energy sold to customers and the purchases from the market and DG units. In RT, the objective is to minimise the adjustments required to accommodate deviations from quantities forecasted in the DA operation stage [5, 6]. Fig. 1 depicts the DisCo's decision timeline for the current day D in the proposed sequential framework. In DA, the 24 h operating decisions for the current day D are optimised a day-ahead before the DA market closes. Then, the deviations from DA decisions are adjusted in RT for each time t of the current day D based on the transactions in the RT market [23]. Fig. 1Open in figure viewerPowerPoint DisCo's decision timeline for current day D in the proposed sequential framework In the proposed model, the following assumptions are made: The DisCo's transactions are performed in terms of active power procurement only [3]. DG units are investor-owned. Dispatchable DG units have full control of active and reactive power production. The production of intermittent DG units is fully injected into the network; and reactive control is possible [24]. DG owners are paid based on the retail prices [25], i.e. the same price that consumers pay to the DisCo when consuming electricity. Time-varying retail prices are assumed the same for all types of consumers (i.e. residential, commercial, and industrial) [26]. The network is equipped with the required communication and metering technology, which allows for a better integration of network devices and DERs. Batteries are utility-owned and can perform arbitrage. The deterministic formulation of the proposed models is described next assuming hourly time periods. 2.1 DA operating stage In DA operation, the DisCo needs to determine: (i) the amount of energy to be purchased from the DA market, (ii) the active power production of DG units, and (iii) the time-varying retail prices within a real-time pricing (RTP) scheme to better reflect the DA market-clearing prices; while optimising Volt-VAR control provided by DG units and network devices, such as SCBs and SVRs. These decisions are made once a day considering the uncertainties of demand, renewable resources, and DA market-clearing prices. As a consequence, deviations between the DA energy procurement and the actual energy balance may arise. It is assumed that all deviations from DA transactions are balanced in the RT operating stage. In a compact way, the DA model can be formulated as follows: (1) (2) where is the profit function of the DisCo in the DA operation, is the set of control variables in the DA operation, is the set of dependent variables in the DA operation, is the set of random parameters in the DA operation, and is the feasibility set of the optimisation problem modelling the DisCo's DA operation. The objective function (1) is driven by the maximisation of the DisCo's profit and constraint (2) represents the feasibility set of the DisCo's DA optimisation problem. The DisCo's profit can be defined as: (3) where N is the set of buses; T is the set of time periods; is the retail price that consumers pay at time t for active power considering an RTP scheme; is the active power load at bus j and time t ; G is the set of DG units; is the price that DG unit g is paid at time t ; is the active power produced by DG unit g at time t ; S is the set of substations; is the DA market-clearing price at time t ; and is the active power purchased from external grid in the DA market at substation s and time t. The objective function (3) comprises three terms. The first term is the total revenue for active energy sold to consumers. The second term represents the cost of the active energy produced by the DG units. Note that . Finally, the third term represents the cost of active energy purchased in the DA market. The feasibility set in (2) includes the modelling of these constraints: Power flow equations: The ac active and reactive power flow equations from [27] are modified to include the DA injection, production of DG units, charging/discharging of stationary batteries, and SCBs injections. Voltage-sensitive load model: A realistic voltage-sensitive load model [11] is used in this work. The active and reactive power demands depend on the active and reactive power demands at nominal voltage before response to time-varying retail prices and non-linearly with the corresponding voltage. Specific parameters are used in the voltage-sensitive load models to represent the behaviour of residential, commercial, and industrial loads and can be found in [28]. Demand elasticity: The demand elasticity of consumers is modelled in terms of the time-varying retail prices, active and reactive power demands at nominal voltage before response to those prices, the price elasticity coefficients, and the daily average retail price [7, 28]. The daily average retail price can be agreed with consumers based on a contract [26] and the price elasticity coefficients can be divided into two different groups: (i) self-elasticity and (ii) cross-elasticity. Self-elasticity relates the demand response to prices associated with the same hour, whereas cross-elasticity associates the demand response to prices at different hours [29]. In this work, these coefficients are assumed to be known. Retail prices: The retail prices for active power consumption are held within minimum and maximum bounds and the daily average of the retail prices must be equal to a fixed daily average retail price, which can be agreed with consumers based on a contract [26]. Nodal voltage limits: These limits ensure acceptable voltage levels at all buses. The voltage at the substation buses is held constant and equal to the nominal value, similar to the concept of slack buses used in transmission power flow calculations. Substation capacity limit: This constraint enforces the capacity limits of the substation transformers. Line current limits: These constraints enforce bounds on line current capacities. Production limits of DG units: These constraints ensure the capacity limits of DG units’ active and reaction power production. In addition, the reactive power production of DG units is limited by the operating power factor limits. Finally, the power output calculation of intermittent wind turbines and PV units is done as described in [30]. Volt-VAR control of DG units: The Volt control is performed by minimising the voltage magnitude mismatch so that the production of reactive power of the DG unit is based on the desired operating voltage magnitude [31]. The VAR control is based on the optimisation of the operating power factor angle within acceptable limits [31]. Stationary batteries: These constraints ensure the operation of utility-owned stationary batteries. In this work, the DisCo acts as a battery aggregator to control the charging/discharging of its storage facilities [32]. SVRs: The operation of type-B SVRs [33] is enforced by modelling the tap position of SVR on each line and time period. SCBs : These constraints ensure the reactive power limits of SCBs by optimising the position of switched capacitors of the SCBs. The interested reader is referred to Appendix 1 for the detailed formulation of the constraints associated with the DisCo's DA optimisation problem. 2.2 Real-time operating stage In RT, the DisCo seeks to minimise the cost of adjustments that are required to accommodate deviations from forecasted quantities determined in the DA stage. That is, the DisCo needs to determine the required adjustments of active power production of DG units and re-optimise Volt-VAR control provided by DG units, SCBs, and SVRs. The RT operation decisions are determined prior (e.g. 5 min) to time t, the current hour, in order to be applied at the beginning of time t [34], as depicted in Fig. 1. We consider a rolling window operating planning horizon of 24 h, covering the current time t and the following time periods, as in [32]. Note that the decisions for time t and subsequent time periods are determined by considering the information on the actual realisation of the demand, renewable resources, and RT market-clearing prices. The RT approach is then formulated from t and considers all the remaining periods. In a compact way, the RT operation of the DisCo can be formulated as: (4) (5) where is the cost function of adjustments of the DisCo in RT operation, is the set of control variables in RT operation, is the set of dependent variables in RT operation, is the set of random parameters in RT operation, and is the feasibility set of the optimisation problem modelling the DisCo's RT operation. The objective function (4) is driven by the minimisation of the cost of adjustments of the DisCo and constraint (5) represents the feasibility set of the DisCo's RT optimisation problem. The DisCo's deviations can be defined as: (6) where is the active power adjustment in RT of DG unit g at time , which is calculated as in (7); is the RT market-clearing price at time ; and is the active power purchased from external grid in the RT market at substation s and time . (7) and where is the power purchased from DG unit g at time in DA; and symbol indicates the best-known solution. It should be noted that (i.e. for the set of intermittent DG units). The first term of the objective function (6) represents the cost of active energy produced by investor-owned DG units. The dispatchable DG units are always compensated for any deviation of the decisions taken in DA. The second term is the cost of active energy purchased in the RT market. The absolute value of in the second term reduces the DisCo's incentives for gaming in the RT market, which prevents market distortions. The feasibility set in (5) also includes power flow equations, voltage-sensitive load models, demand elasticity of consumers to time-varying prices, nodal voltage limits, line current capacity, production limits and Volt-VAR control of DG units, operation of stationary batteries, operation of SVRs, and the reactive power limits of SCBs. Unlike constraints (2) which are defined for the whole DA time frame, the feasibility set in (5) is defined for the corresponding rolling horizon. The active power balance is also modified to consider the power purchases in the DA market and the RT injections. Finally, it is also assumed that the total active power imported from the external grid . The interested reader is referred to Appendix 2 for the detailed formulation of the constraints associated with the DisCo's RT optimisation problem. 3 Solution approach In this section, we describe the proposed pseudo-dynamic TS-based method to solve the resulting large-scale non-linear programs with continuous and discrete variables, as described in Section 2. This proposed model includes the probabilistic approach based on a Hong's PEM [20] to handle uncertainties. 3.1 TS-based method TS is a metaheuristic that uses a local heuristic search process to iteratively find the best-known candidate solution until a stopping criterion is met. This criterion is based on the number of iterations wherein the best-known solution remains unchanged. TS algorithm allows non-improving moves for a broader exploration of the solution space. To avoid recurring to previously assessed solutions and then overcoming local optima, TS uses a memory-based strategy called tabu list [14], which significantly improves the effectiveness of its search procedure. Its efficiency depends on two main features: (i) codification and (ii) neighbourhood. An effective decimal representation of the control variables is assumed to implement the operating decisions [16]. New candidate solutions (i.e. the neighbourhood) are generated at each iteration based on a combination of small changes to the control variables of the previously assessed solution. A pseudo-dynamic approach is used to create efficient neighbourhood structures, i.e. the neighbourhoods are designed based on the particularities of each resulting sub-problem as in [18, 19]. These features exhibit some advantages of TS over traditional metaheuristics [14]. The interested reader is referred to [14] for further details. 3.1.1 DA solution We propose a pseudo-dynamic iterative three-stage solution process, which enforces the time-coupled constraints. The first stage is related to the interactions with the transactions on the DA operation and Volt-VAR control. The second stage addresses the operation of stationary batteries. Finally, the third stage optimises the time-varying retail prices. Then, the set of DA control variables is divided into three subsets, i.e. , as described in Appendix 3. Fig. 2Open in figure viewerPowerPoint Flowcharts of the proposed TS-based solution procedures for the DisCo's short-term operation (a) DA operating stage, (b) RT operating stage Note that subscripts and t, respectively, refer to iteration and time period and they have been added for the sake of clarity Each subset comprises the DA decision control for each stage, i.e. DA sub-problem 1 (DA-SP1) solves for , DA sub-problem 2 (DA-SP2) for , and DA sub-problem 3 (DA-SP3) for . At each stage, the TS algorithm is applied to solve the corresponding sub-problem based on its efficiently designed neighbourhood structure. The subsets associated with the remaining sub-problems are fixed. The resulting DA TS-based solution process is presented in Fig. 2 (a), wherein is the iteration counter and represents the difference between the fitness of the DA overall best-known solution and DA-SP1. Note that the fitness includes the value of the objective function and a term penalising the infeasible constraints. Thus, the fitness represents the quality measure of a candidate solution; and it is computed after solving an ac probabilistic power flow to determine . 3.1.2 Real-time solution A similar pseudo-dynamic iterative two-stage solution procedure is proposed to enforce the time-coupled constraints through efficient neighbourhoods. Therefore, the set of RT control variables is divided into two subsets to represent each stage (or sub-problem): (i) the subset related to the interactions with the transactions on the RT operation and Volt-VAR control (), solved in RT-SP1; and (ii) the one related with the optimisation of the operation of stationary batteries (), in RT-SP2. The description of each subset can be found in Appendix 3. Fig. 2 (b) describes all the steps of the proposed TS-based solution procedure in RT. Note that is calculated as the difference between the fitness of the overall best-known solution and the solution of RT-SP1 at each iteration. Again, the computation of the fitness is possible when is obtained. 3.2 PEM-based probabilistic scheme In order to handle the uncertainties of market-clearing prices, demand, and renewable resources considered in both DA and RT operating stages, we implement a fast and efficient PEM-based probabilistic power flow algorithm [20]. This scheme provides the best performance when considering a high number of input random parameters (m). It can be seen that evaluations of the objective function are required only, unlike other methods based on time-consuming Monte Carlo simulations. Therefore, the proposed approach is suitable for solving large-scale power system operational planning problems. 4 Case study The effectiveness of the proposed approach is evaluated on a 69-bus distribution feeder [21] to examine the impacts of realistic voltage-sensitive loads in the DisCo's short-term operation. A 135-bus distribution system [22] is then used to test the scalability of the proposed method. 4.1 69-bus distribution system The 69-bus 12.26 kV radial distribution system [21] consists of 48 buses with loads, three DG units, two SCBs, one SVR, and one substation located at bus . The total system active and reactive loads are 3801.9 kW and 2694.1 kVAr. For illustrative purposes, the technical and economic data are based on that provided in [18] with the following modifications: (i) DG unit at bus 21 is a 300 kVA PV unit; (ii) the production limit of the dispatchable DG unit at bus 62 is 500 kVA; (iii) the DG's power factor limits are set to 0.8 for both leading and lagging conditions; and (iv) there are two SCBs located at buses 18 (300 kVAr fixed and two 150 kVAr switched capacitors) and 52 (600 kVAr fixed and two 300 kVAr switched capacitors). Simulation data for demand and market-clearing prices are taken from [23]; while statistical information of wind speed and solar irradiation are obtained from [35]. The proposed DA and RT operational planning models are applied to four cases of network load profiles: (i) case 1: 50% residential, 25% commercial, 25% industrial; (ii) case 2: 25% residential, 50% commercial, 25% industrial; (iii) case 3: 25% residential, 25% commercial, 50% industrial; and (iv) case 4: constant power load. The values of , which is the percentage of load type l at bus j in the realistic voltage-sensitive load model (where ), are assumed the same at all buses [13]. Note that the first three cases are voltage-sensitive load models with non-zero values of and , which are the active and reactive exponents of load type l at bus j and time t. The values of these exponents for residential, commercial, and industrial load types can be found in [28]. 4.1.1 Effect of voltage-sensitive loads In this subsection, the effect of voltage-sensitive loads in the DisCo's short-term operation is examined. For all cases, the solutions are attained in less than 24 min. Table 1 provides the total energy procurement that the DisCo should buy to maximise profits in DA and minimise costs in RT for each load profile. This table shows also their itemised quantities, such as the energy purchased in the DA market, in the RT market, and from DG units. The energy bought from DG units includes the purchases decisions made in both the DA and RT stages. As can be seen, the DisCo's total energy procurement is always lower in the cases wherein the voltage-sensitive behaviour of loads is assumed (ca
Referência(s)