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Power system planning for modern distribution networks is undergoing a change because of distributed power generation and grid ancillary services. The vast electricity retail utility industry with many distribution network operators plans generation and transmission expansion planning for determining optimal investment decisions. This paper addresses this planning problem in a decentralized and distributed context. This paper introduces a coordinated decision making approach for optimal investments in generation and transmission expansion planning problems for distribution networks. The distribution networks are further classified into microgrids. Considering an agent as the functional information exchanging entity just like an energy meter with the objective to coordinate the expansion decisions of participants; a novel math-heuristic optimization model Coordinated Microgrid is presented. To simulate the coordination of information a multi-agent-system based coordinated decision making method is adopted and the value of coordination is investigated. The evolutionary vertical sequencing protocol, a heuristic method, is developed and implemented to simulate the coordination process among agents on the top level. The proposed protocol produces smart permutations of microgrids for coordination. On the bottom level, a two-stage chance-constrained stochastic MILP formulation for investment decisions with operational uncertainties is modeled. For market clearing a nodal-pricing scheme is adopted that maintains the Nash equilibrium among and across the microgrids for energy transactions. The proposed model is tested with consumption, network configuration data from three islands in west-coast of Norway. The models are solved to optimality and results lead to the observations that the value of coordination lies in profit increment of individual microgrid. The novel protocol proposed demonstrates an advantage of retrieving smart permutations from combinations of microgrids. In summary, CoMG is a novel expansion planning model for optimal investments in modern power distribution networks.

The main concern of Metering Systems Planning (MSP) for state estimation is the determination of the number, type and location to install metering devices to attend performance requirements related to observability and measurement redundancy. Due to financial constraints, the MSP is a multi-objective, combinatorial optimization problem, which involves conflicting objectives of investment cost and performance requirements. This paper proposes a multi-objective formulation for the MSP problem and a method for its solution. The method combines a Multi-Objective Evolutionary Algorithm based on subpopulation tables with the properties of the so-called HΔ matrix. The method can solve the MSP problem considering the existence of only measurements from supervisory control and data acquisition system, only from Phasor Measurement Units (PMUs) or both types of measurements. Using the concept of Pareto Frontier the method enables the project of reliable metering systems (those guaranteeing system observability during normal operating conditions and in the presence of contingency situations that cause the loss of one or two measurements or one remote terminal unit or one PMU) and other three types of metering systems with different performance requirements and costs in only one execution. Simulation results with IEEE test systems and a Brazilian system validate the paper propositions.

The paper addresses the well-known challenge of allocating storage units within the grid to minimize frequency deviations during transients. The current research is mainly motivated by a sequence of recent works that focus on location of inertia and storage units, considering the limitations of the transmission network, and its spatial effects. One possible drawback of these algorithms is their numerical complexity. To address this gap, this paper studies the storage distribution problem using the general framework of combinatorial optimization, and proposes algorithms to solve it. Among them, one solution is based on exhaustive search, while the others strongly rely on the cross-entropy method. We show that the latter is especially suitable for this application, since it can efficiently solve high-dimensional combinatorial optimization problems. Since the CE method may converge to sub-optimal solutions if the number of storage units increases significantly, this paper also proposes an enhanced CE method which solves the distribution problem considering the assumption that the locations of potential transients are known. In this regard, a key result is that the enhanced CE method convergences faster to the optimal solution and significantly reduces the number of computations.

Reliability is an overriding factor in power system operations. Corrective security-constrained economic dispatch (SCED) satisfying the “N − 1” criterion is difficult because of a large number of contingencies and the strict time limits for real-time operations. The existence of conflicting contingencies further complicates the problem. To overcome these difficulties, this paper develops a new iterative contingency filtering approach to manage “N − 1” transmission and generator contingencies via decomposition and coordination. Instead of always removing conflicting contingencies as in existing papers, we offer system operators an important option to keep them for increased reliability, enabled by identifying multiple conflicting contingencies simultaneously. To satisfy the strict time requirements in real-time operations, the computational performance of our approach is significantly enhanced by novel warm-start of subproblem models and by parallel computing. Numerical results demonstrate that our new approach is computationally efficient and scalable, and increases the system reliability. In particular, the Polish 2383-bus system with all transmission contingencies is solved within two minutes.

© 2016 Elsevier Ltd. All rights reserved. In this paper, authors propose a novel method to determine an optimal solution for profit based unit commitment (PBUC) problem considering emission constraint, under a deregulated environment. In a restructured power system, generation companies (GENCOs) schedule their units with the aim of maximizing their own profit by relaxing demand fulfillment constraints without any regard to social benefits. In the new structure, due to strict reflection of power price in market data, this factor should be considered as an important ingredient in decision-making process. In this paper a social-political based optimization algorithm called imperialist competitive algorithm (ICA) in combination with a novel meta-heuristic constraint handling technique is proposed. This method utilizes operation features of PBUC problem and a penalty factor approach to solve an emission constrained PBUC problem in order to maximize GENCOs profit. Effectiveness of presented method for solving non-convex optimization problem of thermal generators scheduling in a day-ahead deregulated electricity market is validated using several test systems consisting 10, 40 and 100 generation units.

This paper examines the effects of reactive power dispatch, losses, and voltage profile on the results of the interdiction model to analyze the vulnerability of the power system. First, an attacker-defender Stackelberg game is introduced. The introduced game is modeled as a bilevel optimization problem where the attacker is modeled in the upper level and the defender is modeled in the lower level. The AC optimal power flow (ACOPF) is proposed as the defender’s tool in the lower-level problem to mitigate the attack consequences. Our proposed ACOPF-based mathematical framework is inherently a mixed-integer bilevel nonlinear program (MIBNLP) that is NP-hard and computationally challenging. This paper linearizes and then transforms it into a one-level mixed-integer linear program (MILP) using the duality theory and some proposed linearization techniques. The proposed MILP model can be solved to the global optimum using state-of-the-art solvers such as Cplex. Numerical results on two IEEE systems and Iran’s 400-kV transmission network demonstrate the performance of the proposed MILP for vulnerability assessment. We have also compared our MILP model with the DCOPF-based approach proposed in the relevant literature. The comparative results show that the reported damage measured in terms of load shedding for the DCOPF-based approach is always lower than or equal to that for the ACOPF-based approach and these models report a different set of critical lines, especially in more stressed and larger power systems. Also, the effectiveness and feasibility of the proposed MILP model for power-system vulnerability analysis are discussed and highlighted.

To reduce the impact of wind power prediction error on power system operation, Credibility theory and Fuzzy chance constrained programming method are introduced while solving wind power inter-regional scheduling optimization problems. Firstly, the paper introduces the carbon trading (CT) and Tradable Green Certificates (TGC). Then, an energy independent external delivery model is constructed, which contains wind power independent delivery model and thermal power independent delivery model. Secondly, the paper put forward energy combined external delivery model considering CT and TGC. Meanwhile, Credibility theory and Fuzzy chance constrained programming method are used to deduce credibility distribution function of wind power prediction errors and define the feasible region under a certain confidence level, respectively. Since credibility distribution is applied as a measure function and the feasible region covers fuzzy event set, the optimal solution will be in the credible solution space. Thirdly, four scenarios are set according to CT and TGC. Finally, this paper uses six thermal power units and one wind farm as the simulation system. The simulation results show Credibility theory is applicable to overcome wind power uncertainty. Energy combined external delivery is better for improving system consuming wind power. CT and TGC could increase wind power grid-connection, but CT’s optimization effect is more obvious than TGC. The optimization effect reaches the optimum when both CT and TGC are implemented, and energy external delivery profits should be reasonable allocated for encouraging thermal power to participate in wind power delivery.

This paper investigates a novel real-time stochastic multi-period management strategy of a virtual power plant (VPP) using a three-layer language protocol based on computer program compiler principle, which takes advantage of the availability of the battery storage in a VPP to maximize the revenue of the VPP over the entire trading horizon considering the predicted prices in each slice of that horizon. When the conventional scenario tree method is used to solve the computational complexity of the multi-period stochastic optimization problem, it may cause the problem to become intractable when the problem-scale increases. This paper proposes a deterministic lookahead approach that makes use of a novel formal language that implements a special formal grammar to manage the real-time control on the battery storages of the VPP. The control of charging/discharging of the battery storages, which is driven by the real-time spot price and the rolling price prediction, is formalized by using the proposed recursive grammar and the corresponding non-deterministic finite automaton (NFA). For validation, the proposed approach is applied to a simple three-bus and an adapted IEEE 14-bus test system. The simulation results show that the proposed method can obtain optimal revenue by managing each battery in the VPP to operate as a local generator, a local load, an energy buyer, an energy seller, or by being in an idle state when the battery is full or empty.

Optimization tools are widely used for solving the short-term hydro scheduling (STHS) problem in a cascaded hydro system. In a mixed integer linear programming (MILP)-based formulation, the nonlinear and non-convex hydropower production function (HPF) is represented by piecewise linear approximation. However, instead of using a set of predefined curves with static breakpoints or a preprocessing phase to define the complete relationship between the power output, the net head, and the water discharge, this paper proposes a novel method in which the breakpoints in the linearization are determined dynamically, taking into account the time-varying head effect, intake loss, penstock loss, tailrace loss, and head-dependent turbine efficiency. Only one binary variable is needed to indicate the on/off status and power generation of a unit per period. Furthermore, there are few studies available on how to represent the HPF precisely for the hydraulic system where penstocks are shared by multiple generating units. In this paper, we investigate three heuristics to explicitly incorporate the nonlinear and state-dependent power loss in shared penstocks into the STHS problem. The method and heuristics have been implemented in an operational STHS tool used by many hydropower producers in Nordic countries. We use a simple hydro system to illustrate the method and heuristics and a real hydro system in Northern Norway to study calculation efficiency and solution quality. The numerical results indicate that the proposed method can precisely represent the head-dependent and nonlinear operating characteristics of the generating units. The accurate modeling of a system with multi-level shared penstock configurations is crucial for obtaining the optimal unit commitment. The heuristics can effectively handle the power loss in shared penstock in various operating conditions. © 2019 Elsevier Ltd Dynamic incorporation of nonlinearity into MILP formulation for short-term hydro scheduling © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).T

This paper develops a novel hybrid algorithm for solving transmission expansion planning (TEP) problems in electric power networks. Raising the awareness about immense contaminants produced by fossil fuels as well as depleting these resources have pushed energy companies toward considering more renewable energy resources (RERs). The RESs are beneficial for the society and the power system utility, however, taking into account the uncertainties, which are inherent in RERs, increase the complexity of the optimization problems. In this work, a Monte-Carlo simulation (MCS) is used to address the intermittent nature of wind energy. To handle the resulted model, by modifying and combining three well-known evolutionary algorithms such as shuffled frog leaping algorithm (SFLA), particle swarm optimization (PSO), and teaching learning-based optimization (TLBO), a potent hybrid MSFLA-MPSO-MTLBO, namely combinatorial heuristic-based profound-search algorithm (CHPSA), is proposed. A self-adaptive probabilistic mutation operator (SAPMO) is employed to enhance the effectiveness and computational efficiency of the CHPSA. Ten commonly-used benchmark problems are introduced to corroborate the performance of the CHPSA, while the IEEE RTS 24-bus test system is used to validate the model. Results show that the proposed CHPSA is capable of obtaining better solutions than other algorithms, either implemented in this paper or borrowed from the literature.

Gravitational search algorithm (GSA) is based on law of gravity and the interaction between masses. In GSA, searcher agents are collection of masses and their interactions are based on Newtonian laws of gravity and motion. In this paper, to further improve the optimization performance of GSA, opposition-based learning is employed in opposition-based gravitational search algorithm (OGSA) for population initialization and also for generation jumping. In the present work, OGSA is applied for the solution of optimal reactive power dispatch (ORPD) of power systems. Traditionally, ORPD is defined as the minimization of active power transmission losses by controlling a number of control variables. ORPD is formulated as a non-linear constrained optimization problem with continuous and discrete variables. In this work, OGSA is used to find the settings of control variables such as generator voltages, tap positions of tap changing transformers and amount of reactive compensation to optimize certain objectives. The study is implemented on IEEE 30-, 57- and 118-bus test power systems with different objectives that reflect minimization of either active power loss or that of total voltage deviation or improvement of voltage stability index. The obtained results are compared to those yielded by the other evolutionary optimization techniques surfaced in the recent state-of-the-art literature including basic GSA. The results presented in this paper demonstrate the potential of the proposed approach and show its effectiveness and robustness for solving ORPD problems of power systems.

This paper presents a methodology for the integration of dispatchable and nondispatchable renewable distributed generation (DG) units for minimizing annual energy losses. In this methodology, analytical expressions are first proposed to identify the optimal size and power factor of DG unit simultaneously for each location for minimizing power losses. These expressions are then adapted to place renewable DG units for minimizing annual energy losses while considering the time-varying characteristics of demand and generation. A combination of dispatchable and nondispatchable DG units is also proposed in this paper. The proposed methodology has been applied to a 69-bus test distribution system with different scenarios. The results demonstrate that dispatchable DG units or a combination of dispatchable and nondispatchable DG units can lead to a substantial reduction in annual energy losses when compared to nondispatchable DG units. The results also show that a maximum annual energy loss reduction is achieved for all scenarios proposed with DG operation at optimal power factor. (C) 2013 Elsevier Ltd. All rights reserved.

This paper is on the problem of short-term hydro scheduling (STHS), particularly concerning head-dependent reservoirs under competitive environment. We propose a novel method, based on mixed-integer nonlinear programming (MINLP), for optimising power generation efficiency. This method considers hydroelectric power generation as a nonlinear function of water discharge and of the head. The main contribution of this paper is that discharge ramping constraints and start/stop of units are also considered, in order to obtain more realistic and feasible results. The proposed method has been applied successfully to solve two case studies based on Portuguese cascaded hydro systems, providing a higher profit at an acceptable computation time in comparison with classical optimisation methods based on mixed-integer linear programming (MILP).

The medium-term operation planning (MTOP) of hydrothermal systems aims to define generation targets that minimize the expected operation cost over the planning period, considering a set of constraints with respect to the power system and the generating units. Mathematically, this problem can be characterized as a linear, stochastic and large scale, which requires the application of suitable optimization tools. The purpose of this paper is to apply the progressive hedging (PH) method to solve the MTOP problem. For that, two critical aspects of the PH are addressed: the use of warm start and the choice of a suitable penalty parameter. In addition, this paper compares the performance of the PH to other popular methods, the full high-scale linear programming problem, also known as deterministic equivalent, and the nested decomposition, when solving similar problems. As a result we show that the PH is a competitive method to solve the MTOP problem.

Data interruption may cause the centralized energy management system of a microgrid (MG) to collapse. To solve this problem, a hybrid prediction-based energy management strategy is proposed in this paper to predict interrupted data for the centralized dispatching process of an MG. This hybrid prediction method is designed following a combination of model predictive control and extreme learning machine techniques. Based on the predicted data of distributed energy resources and three types of loads from demand-side response, an optimization model is formulated to minimize the operational cost. If some predicted data are interrupted during transmission, then a prospect vulnerability assessment method is applied to select a neighboring device to predict the interrupted data. In the end, an improved particle swarm optimization algorithm is proposed with the help of genetic algorithms to accelerate convergence to global optimal solutions for the proposed MG energy management problem. The effectiveness of the proposed models and solution methods is also verified by a case study.

Made available in DSpace on 2019-10-06T16:31:34Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-12-01 The Network-Constrained Nonsmooth Economic Dispatch (NCNS-ED) is formulated as a nonsmooth, nonconvex and multimodal optimization problem. Nonsmoothness is generally associated with valve-point loading effects in the cost function of thermal units. Due to nonsmoothness, gradient-based approaches cannot be used directly for solving NCNS-ED problems. Hence, heuristic approaches have been used as the main methodologies for solving this problem. In this paper, we propose a reformulation for the NCNS-ED problem that enable its solution by means of gradient-based approaches. This formulation is based on the definition of an equivalent nonlinear programming problem where the modular terms are eliminated by using artificial variables and inequality constraints. We propose a primal–dual modified log-barrier function approach for solving the reformulated problem, where each inequality constraint is penalized by using a piecewise function that involves the modified barrier functions of Polyak and Jittortrum-Osborne-Meggido. Numerical results involving small-, medium- and large-scale power systems, have shown that the proposed reformulation enables eliminating nonsmoothness in the NCNS-ED problems. The method proposed, which is compared to some methods described the literature, has shown robustness for solving real large-scale NCNS-ED problems with acceptable computation times. Department of Electrical Engineering Faculty of Engineering-FEB Unesp-Univ. Estadual Paulista Department of Mathematics Faculty of Sciences-FC Unesp-Univ. Estadual Paulista Department of Electrical Engineering Faculty of Engineering-FEB Unesp-Univ. Estadual Paulista Department of Mathematics Faculty of Sciences-FC Unesp-Univ. Estadual Paulista

International audience; Primary frequency control is the automatic mechanism implemented on power systems to regulate the power balance through frequency and hence, its action should be taken into account when modelling any contingency state leading to a modification of the active power balance (e.g. generator failures). This paper presents a fully distributed method to solve the DC security constrained power flow (DC-SCOPF) that takes into account the automatic primary frequency response of generators after an incident. In more detail, we extend existing distributed DC-SCOPF formulations by: (1) introducing a new variable representing the frequency deviation; and (2) enhancing the local problem of each generator to consider how it adjusts its production after each contingency according to its primary frequency control compensation factor. The computation of the frequency deviations in the DC-SCOPF problem is formulated into a suitable form (i.e. in the form of a general consensus problem) so that smaller problems, corresponding to individual sub-regions or actors, can be solved and coordinated via the alternating direction method of multipliers (ADMM) in a distributed manner. In this way, actors of the system do not need to exchange any confidential information with other actors during the optimization procedure. A salient feature of our approach is that it can consider contingencies that lead to area separation without any prior specification of the topology and thus can adapt to many kinds of situations that are of interest in interconnected systems. Extensive simulation results on several standard IEEE systems show the good performance of the proposed model and algorithm in terms of convergence speed and accuracy as well as its capacity to deal with the disconnection of areas in interconnected systems.

With the integration of large-scale renewable energy sources to power systems, many optimization methods have been applied to solve the stochastic/uncertain transmission-constrained unit commitment problem. Among all methods, two-stage and multi-stage robust optimization-based methods are the most widely adopted ones. In the two-stage methods, non-anticipativity of economic dispatch (ED) decisions are not considered. While in multi-stage methods, explicit decision rules (like affine decision rules) are adopted to guarantee non-anticipativity of ED decisions, the computational burden can be heavy and the optimality of the solution is affected. In this paper, a multi-stage robust TCUC formulation with implicit decision rules is proposed, as well as a decomposition framework to solve it. The solutions are proved to be multi-stage robust and non-anticipativity of ED decisions is guaranteed. Meanwhile, a computationally efficient time-decoupled solution method for the feasibility check subproblems is also proposed, such that the method is suitable for large-scale TCUC problems with uncertain power injections. Numerical tests are conducted on IEEE 118-bus system and Polish 2383-bus system. The proposed method outperforms the multi-stage robust method with explicit decision rules in solution’s economic performances, and is more computationally efficient than the all-scenario-feasible method. The effectiveness of time-decoupled solution method is also verified.

Made available in DSpace on 2019-10-06T16:12:39Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-06-01 Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) This paper proposes a multistage convex distribution system planning model to find the best reinforcement plan over a specified horizon. This strategy determines planning actions such as reinforcement of existing substations, conductor replacement of overloaded feeders, and siting and sizing of renewable and dispatchable distributed generation units. Besides, the proposed approach aims at mitigating the greenhouse gas emissions of electric power distribution systems via a monetary form. Inherently, this problem is a non-convex optimization model that can be an obstacle to finding the optimal global solution. To remedy this issue, convex envelopes are used to recast the original problem into a mixed integer conic programming (MICP) model. The MICP model guarantees convergence to optimal global solution by using existing commercial solvers. Moreover, to address the prediction errors in wind output power and electricity demands, a two-stage stochastic MICP model is developed. To validate the proposed model, detail analysis is carried out over various case studies of a 34-node distribution system under different conditions, while to show its potential and effectiveness a 135-node system with two substations is used. Numerical results confirm the effectiveness of the proposed planning scheme in obtaining an economic investment plan at the presence of several planning alternatives and to promote an environmentally committed electric power distribution network. Electrical Engineering Department São Paulo State University (UNESP), Ilha Solteira Department of Electrical Engineering and Automation Aalto University, Maarintie 8 Electrical Engineering Department São Paulo State University (UNESP), Ilha Solteira FAPESP: 2015/21972-6 CNPq: 305318/2016-0

Made available in DSpace on 2019-10-04T12:33:54Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-03-01 Technological University of Pereira (Universidad Tecnologica de Pereira), Colombia This paper presents a new model for optimal integrated planning of medium and low voltage distribution systems with penetration of distributed generation (DG) in the low voltage network. The proposed bilevel model takes into account in the upper and the lower levels, the medium and low voltage network planning respectively. This approach considers as conflict between these two agents (upper and lower levels), the size and location of the distribution transformers (DT), ie. the incidence in both networks of the power flow circulating from the primary to the secondary system. The main objective of this approach is to find a joint global solution that establishes a balance to benefit the planning of both networks, by decomposing the problem in two subproblems (or levels). The upper and lower levels involve the costs of installing and upgrading the new and existing elements (branches, DT, substations and DG) and the cost of the energy technical losses. This problem is formulated as a mixed integer non-linear model, and is solved using a tabu search algorithm (TSA). To verify the efficiency of the proposed methodology, three cases of study are compared: (i) traditional integrated planning, (ii) bilevel integrated planning and (iii) bilevel integrated planning with DG in the LV network. The obtained results show the importance of considering both networks in a simultaneous way in the electric distribution system planning, which allows finding answers of lower global costs. Technol Univ Pereira, Dept Elect Engn, Carrera 27 10-02, Pereira, Colombia Univ Estadual Paulista, Dept Elect Engn, Av Brasil 56 Ctr, Ilha Solteira, Brazil Univ Estadual Paulista, Dept Elect Engn, Av Brasil 56 Ctr, Ilha Solteira, Brazil Technological University of Pereira (Universidad Tecnologica de Pereira), Colombia: 6-13-4

Made available in DSpace on 2019-10-06T16:52:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-03-01 This paper presents a data-driven spatial net-load forecasting model that is applied to the distribution network expansion problem. The model uses population census data with Information Theory-based Feature Selection to predict spatial adoption patterns of residential electric vehicle chargers and photovoltaic modules. Results are high-resolution maps (0.02 km2) that allow distribution network planners to forecast asymmetric changes in load patterns and assess resulting impacts on installed HV/MV substation transformers in distribution systems. A risk analysis routine identifies the investment that minimizes the maximum regret function for a 15-year planning horizon. One of the outcomes from this study shows that traditional approaches to allocate distributed energy resources in distribution networks underestimate the impact of adopting EV and PV on the grid. The comparison of different allocation methods with the presented diffusion model suggests that using conventional approaches might result in strong underinvestment in capacity expansion during early uptake and overinvestment in later diffusion stages. INESC TEC and University of Porto UFABC – Federal University of ABC, Santo André INESC TEC UNESP – São Paulo State University, Ilha Solteira UNESP – São Paulo State University, Ilha Solteira

In this paper, the integration of intermittent distributed generation (wind and solar) is dealt with by proposing a multi-objective multistage distribution network expansion planning formulation based on e-constraint method. This approach allows the planners to obtain pareto-optimal solutions based on the two objective functions: (1) installation costs of distributed generation, substations, feeders, maintenance costs of assets, costs of energy purchased from substations, cost of unserved energy and (2) utilization of renewable distributed generation. To represent the intermittent nature of load and renewable distributed generation, several time blocks are utilized, and its effectiveness is compared with an existing approach. The overall problem is formulated as a mixed-integer linear programming and a linear equation-based substation price is utilized within the optimization framework to reduce the size of the problem. The proposed method is applied to the modified 24-nodes test network for different cases to analyse the utilization of renewable distributed generation from different point of views and it is inferred from the results that the proposed model yields a variety of planning solutions which are better to increase the utilization of renewable distributed generation.

At the stage of planning distributed generation (DG) for a distribution network, the network configuration is a key factor in increasing the DG hosting capacity. The determination of a configuration that maximizes the hosting capacity is a highly complex, nonlinear combinatorial optimization problem. No existing method can yield the global optimal solution for practical-scale networks. Therefore, this paper proposes a scalable optimization method. Specifically, the proposed method enumerates all optimal configurations while simultaneously considering optimal DG placement. The proposed method first optimizes the DG placement for possible partial networks using a second-order cone programming technique. Next, it enumerates possible combinations of the partial networks while avoiding a combinatorial explosion using a highly compressed data structure. Finally, it finds the optimal configurations by exploring solutions over the data structure. In experiments involving a large-scale network containing 235 switches, our enumeration method obtained 1.49 × 10 18 global optimal configurations in 17.1 h. Another powerful feature of our method is that it enables distribution system operators to select the preferred optimal configuration interactively.

This paper proposes a framework to determine capacity profiles in smart buildings. In this scheme the users choose a level of power capacity to account for their stochastic demand while paying the corresponding electricity prices through a flexible time-and-level-of-use pricing policy. We formulate a two-stage stochastic optimization model that minimizes the total cost of booking a power capacity level and meeting the energy demand for the planning horizon. We present two approaches to select the scenarios for the stochastic optimization. In the first approach, we assume that the probability distributions of the start times of the loads are known, and the scenarios are generated using those distributions. In the second approach, we assume that only historical consumption data is available and we propose a new algorithm to build the scenarios using this data. Our simulation experiments validate the performance of both approaches and report cost savings of up to 16%.

Unbalanced distribution of single-phase customers among the three phases is an important factor in causing unbalance in low-voltage (LV) distribution systems. This unbalance phenomenon has some important consequences as higher losses in the distribution system, increasing voltage unbalance, and higher neutral wire current. The key challenge is that these networks only have the monthly reading of customers’ meters which is called data-scarce distribution systems due to the lack of enough information. In this paper, a method is proposed in order to have a balanced distribution of single-phase customers between the phases based on particle swarm optimization (PSO) algorithm to reduce the average-load losses (which is calculated losses in the average load of all of the customers and is an attainable data in real-world data-scarce distribution systems). First, a comparative study is performed between two load balancing methods. In the first method, the transformer neutral wire current is reduced. This method is used generally in electricity distribution companies. In the second method, the balancing is performed in order to reduce the losses in the average-load. Then, a probabilistic approach is proposed in order to manage the uncertainty of single-phase customer's consumption, which is an important issue in low-voltage distribution systems balancing. Numerical studies are performed on a practical system and the results show that the proposed method has higher performance comparing to the first method used by distribution companies. Also, it is observed that by rephasing of some single-phase customers, losses are reduced significantly.

With the growing level of uncertainties in today’s power systems, the vulnerability analysis of a power system with uncertain parameters becomes a must. This paper proposes a two-stage adaptive robust optimization (ARO) model for the vulnerability analysis of power systems. The main goal is to immunize the solutions against all possible realizations of the modeled uncertainty. In doing so, the uncertainties are defined by some pre-determined intervals defined around the expected values of uncertain parameters. In our model, there are a set of first-stage decisions made before the uncertainty is revealed (attacker decision) and a set of second-stage decisions made after the realization of uncertainties (defender decision). This setup is formulated as a mixed-integer trilevel nonlinear program (MITNLP). Then, we recast the proposed trilevel program to a single-level mixed-integer linear program (MILP), applying the strong duality theorem (SDT) and appropriate linearization approaches. The efficient off-the-shelf solvers can guarantee the global optimum of our final MILP model. We also prove a lemma which makes our model much easier to solve. The results carried out on the IEEE RTS and modified Iran’s power system show the performance of our model to assess the power system vulnerability under uncertainty.

Based on the data collected from smart meters, electricity pricing models can be developed to balance power supply and demand in each time slot and obtain the optimal consumption loads and prices. However, in real life, users’ reserved consumption requirement loads sometimes deviate significantly from the optimal consumption loads obtained from models, which results in overloaded power systems or even power cuts. To address this issue, an Engineering Process Control monitoring strategy has been proposed in this paper to minimize the difference between the optimal and the users’ reserved consumption requirement loads. We proposed an exponential weighted moving average model to predict the load difference in future time slots, and also developed a novel quadratic function based demand response mechanism to adjust the power price for power providers. The demand response mechanism can be used to adjust the price in the future time slots when the predicted demand exceeds the upper or lower boundary. Simulation results indicate that the quadratic function adjustment strategy has excellent performance in a practical power market in Singapore. Compared with the linear function based adjustment method, the proposed quadratic function based adjustment method decreases the adjustment times and standard errors of residuals, and increases the social welfare and power suppliers’ profits under the same boundary conditions. In addition, the performance of the proposed strategy demonstrated its competency in peak-cutting and valley-filling and balancing energy provision with demands.

Flexible ramping products (flexiramp), provided by entitled resources to meet net demand forecast error, are the underpinning for the accommodation of the substantial uncertainties associated with variable wind power. This paper proposes an enhanced flexiramp modeling approach, cast in a hybrid stochastic/deterministic multi-timescale framework. The framework employs a chance-constrained day-ahead scheduling method, as well as deterministic scheduling on intra-hourly basis (real-time scheduling), to allow optimal procurement planning of the flexiramp products in both timescales. A stepwise and piecewise demand price curve is also proposed to calculate the flexiramp surplus procurement price. Non-generation resource (NGR), referring to energy storage, is implemented to provide extra flexibility. Additionally, cycling ramping cost (cycliramp), introduced to model operational and maintenance costs and reduce the wear and tear of generators, is also included as a penalty. Numerical tests are conducted on 6-bus and 118-bus systems. Results demonstrate the merits of the proposed scheduling model as well as the effects of flexiramp and cycliramp costs in the multi-timescale scheduling.

Dynamic economic dispatch with valve-point effects (DED-VPE) is a non-convex and non-differentiable optimization problem that is difficult to solve efficiently. In this paper, a hybrid approach combining mixed-integer linear programming (MILP) and the interior point method (IPM), abbreviated as MILP-IPM, is proposed to solve a DED-VPE problem in which complicated transmission loss is also included. Due to the non-differentiable nature of the DED-VPE problem, the classical derivative-based optimization methods can no longer be used. With the help of model reformulation, a differentiable non-linear programming (NLP) formulation that can be directly solved using the IPM is derived. However, if the DED-VPE problem is solved using the IPM in a single step, the optimization can easily become trapped in a poor local optimum due to its non-convex nature and multiple local minima. To obtain a better solution, an MILP method is required to solve the DED-VPE problem without transmission loss, yielding a good initial point for the IPM to improve the quality of the solution. Simulation results demonstrate the validity and effectiveness of the proposed MILP-IPM approach for solving the DED-VPE problem.

The Energy Hub has become an important concept for formally optimizing multi-carrier energy infrastructure to increase system flexibility and efficiency. The existence of energy storage within energy hubs enables the dynamic coordination of energy supply and demand against varying energy tariffs and local renewable generation to save energy cost. The battery lifetime cost may be included in the optimization objective function to better utilize battery for long term use. However, the operational optimization of an interconnected energy hub system with battery lifetime considered presents a highly constrained, multi-period, non-convex problem. This paper proposes Particle Swarm Optimization (PSO) hybridised with a numerical method, referred to collectively as the decomposition technique. It decouples the complicated optimization problem into sub-problems, namely the scheduling of storage and other elements in the energy hub system, and separately solves these by PSO and the numerical method ‘interior-point’. This approach thus overcomes the disadvantages of numerical methods and artificial intelligence algorithms that suffer from convergence only to a local minimum or prohibitive computation times, respectively. The new approach is applied to an example two-hub system and a three-hub system over a time horizon of 24 h. It is also applied to a large eleven-hub system to test the performance of the approach and discuss the potential applications. The results demonstrate that the method is capable of achieving very near the global minimum, verified by an analytical approach, and is fast enough to allow an online, receding time horizon implementation.

Optimal transmission switching is proposed in recent years to optimize the power system operational cost in deterministic studies. With the rapid growth of renewable generations, the grid uncertainties have greatly increased, which cannot be ignored in the decision-making of optimal transmission switching problems. This paper proposes a novel two-stage stochastic optimization formulation with a convex relaxation for AC optimal transmission switching problems. A generalized Benders decomposition based algorithm, including an inner loop and an outer loop, is proposed to solve the AC optimal transmission switching problem with grid uncertainties. The optimal switching plan and the expected system cost will be found in the iterative calculation without any sacrifice of accuracy. Numerical studies on the IEEE 118-bus system and the South Carolina 500-bus confirm the effectiveness of the proposed decomposition approach in solving the AC optimal transmission switching problems with grid uncertainties. The scalability analysis shows the proposed approach is efficient in dealing with a large number of scenarios.

Power grids are evolving toward 100% renewable energy interfaced by inverters. Virtual inertia and damping provided by inverters are essential to synchronism and frequency stability of future power grids. This paper numerically addresses the problem of dispatch of virtual inertia and damping (DID) among inverters in the transmission network. The DID problem is first formulated as a nonlinear program (NLP) by the Radua collocation method which is flexible to handle various types of disturbances and bounds constraints. Since the NLP of DID is highly non-convex, semi-definite programming (SDP) relaxation for the NLP is further derived to tackle the non-convexity, followed by its sparsity being exploited hierarchically based on chordality of graphs to seek enhancement of computational efficiency. Considering high dimension and inexactness of the SDP relaxation, a feasibility-embedded distributed approach is finally proposed under the framework of alternating direction method of multipliers (ADMM), which achieves parallel computing and solution feasibility regarding the original NLP. Numerical simulations carried out for five test power systems demonstrate the proposed method and necessity of DID.

Due to high fuel efficiency and environmental friendliness combined cooling, heating and power (CCHP)-based microgrids (MGs) become much more popular. To reduce the total operating costs of CCHP-based MG cluster, an incentive-based multi-energy trading mechanism is proposed to facilitate multi-energy trading among independent CCHP-based MG operators (CMGOs). Motivated by the mechanism, multi-energy trading is carried out among a number of neighboring CMGOs. In practice, CMGOs may belong to different economic entities. Besides, there is usually no coordination center. Therefore, a fully decentralized distributed solution based on the alternating direction method of multipliers decomposition technique is proposed. Especially, to achieve fair benefit allocation, a novel index termed as contribution rate is first proposed to identify CMGO’s contributions to multi-energy trading. Then, asymmetric Nash bargaining theory is used to determine the benefits obtained by each CMGO. Besides, a payment chain is designed to implement the benefit allocation mechanism proposed in this paper. Each CMGO gets the corresponding benefits according to their contribution rates. The simulation results demonstrate the effectiveness of the proposed mechanism.

Energy hubs, which integrate multiple energy vectors through converters, can enhance the value of Integrated Local Energy Systems (ILES) via increased flexibility and reduced costs. However, uncertain renewable energy and the non-convex, non-linear properties of energy flows complicate the modelling and operation of energy hub systems. This paper develops chance-constrained optimization methods for planning and operation of energy hub systems under uncertainty. The non-linear formulations of power and gas flows are relaxed by convexification methods, leading to a formulation of Second Order Cone Problem (SOCP), which can be efficiently solved to global optimality. The correlation between geographically close wind generators connected to the hub systems is modelled by establishing their relation using Gaussian copula. The proposed chance-constrained optimization is demonstrated on a six-hub system within a multi-vector energy distribution network with 7 electrical buses and 7 gas nodes. The value of different levels of system integration through the installation of energy hubs is investigated. The results show that by combining system integration via energy hubs with chance constrained operation, the proposed method can reduce operating costs and increase renewable energy yields, thereby benefitting hub system operators and customers with reduced energy infrastructure investment and energy costs.

When a distribution system encounters a major outage due to extreme events, an efficient sequential service restoration (SSR) strategy is required to restore the outage system. However, uncertainties associated with renewable energy generation and load demands pose significant and complex challenges for the optimization of SSR strategies. This paper proposes a robust multiple power source co-optimization approach for the SSR of an outage distribution system. First, network configuration and sequential switching actions are jointly optimized to sequentially form microgrids (MGs). Second, multiple types of power sources, such as distributed generators and energy storage units, are re-energized and coordinated to pick up critical loads in parallel restored MGs. In addition, uncertainties associated with renewable energy generation and load demands are considered during the restoration process, thereby requiring a robust SSR scheme to increase the reliability of MG operations, The mathematical problem is modelled as a mixed-integer tri-level programming problem with inner-level binary variables. Thus, the extended column-and-constraint generation (EC&CG) algorithm is employed to solve the proposed robust model. The numerical results demonstrate the effective performance of the proposed approach and its robustness and advantages compared to existing models that do not consider uncertainties.

Energy hub systems integrate various energy sources and interconnect different energy carriers in order to enhance the flexibility of the system. In this paper, a cooperative framework is proposed in which a network of energy hubs collaborate together and share their resources in order to reduce their costs. Each hub has several sources including CHP, boiler, renewable sources, electrical chiller, and absorption chiller. Moreover, energy storages are considered for electrical, heating, and cooling systems in order to increase the flexibility of energy hubs. Unlike the methods based on Nash-equilibrium points, which find the equilibrium point and have no guarantee for optimality of the solution, the employed cooperative method finds the optimal solution for the problem. We utilize the Shapley value to allocate the overall gain of the hub’s coalition based on the contribution and efficiency of the energy hubs. The proposed method is modeled as a mixed integer linear programming problem, and the cost of network energy hubs are decreased in the cooperative operation, which shows the efficiency of this model. The results show 18.89, 10.23, and 8.72% improvement for hub1, hub2, and hub3, respectively, by using the fair revenue mechanism.

In this paper, two approaches are proposed for transactive energy systems with competitive market in order to detect anomalies that occur in the process of information exchange during market interactions. The first approach fully exploits the property of monotonicity associated with the supply or demand curves of rational market participants. It only relies on the data that are normally exchanged through market interaction and does not require any extra information. Therefore, it can be easily adopted by existing system implementation. When the gradients of the supply (or demand) curves have positive lower (or negative upper) bounds, a second approach can be further developed for more accurate anomaly detection if the knowledge of these bounds become available. For both approaches, the impacts of power flow constraints are also taken into account. The detailed simulation studies illustrate the performance and effectiveness of the proposed approaches in detecting anomalies caused by cyberattacks.

Power system emergency control is one key defense strategy in contingencies for protecting the system from cascading blackout. Under Frequency Load Shedding (UFLS) is one such strategy to ensure system stability by shedding load to retrieve balance between power supply and demand. Novel UFLS scheme design and a scheme optimization approach are proposed in this paper to find the optimal load-shedding schemes for different network partition resulted from contingencies. To obtain all possible UFLS schemes for a certain area, a candidate scheme set design algorithm based on value assigning of scheme parameters is proposed and then a relatively complete candidate scheme set is constructed. Considering network splitting caused by protection, several subsystems may exist from the reconstruction of independent network areas. The concept of homological area is defined and a graph-based method is used to analyse system topology change. Then, a multi-attribute decision-making (MADM) algorithm is introduced for order preference by similarity to an ideal solution (TOPSIS) for global optimizing candidate schemes. Optimal schemes for an area in both isolated area and homological area cases can be derived from all feasible UFLS schemes by MADM method. Simulation results demonstrate that the UFLS schemes can effectively restore system frequency in different network topologies.

Aggregations of flexible loads can provide several power system services through demand response programs, for example load shifting and curtailment. The capabilities of demand response should therefore be represented in system operators' planning and operational routines. However, incorporating models of every load in an aggregation into these routines could compromise their tractability by adding exorbitant numbers of new variables and constraints. In this paper, we propose a novel approximation for concisely representing the capabilities of a heterogeneous aggregation of flexible loads. We assume that each load is mathematically described by a convex polytope, i.e., a set of linear constraints, a class which includes deferrable loads, thermostatically controlled loads, and generic energy storage. The set-wise sum of the loads is the Minkowski sum, which is in general computationally intractable. Our representation is an outer approximation of the Minkowski sum. The new approximation is easily computable and only uses one variable per time period corresponding to the aggregation's net power usage. Theoretical and numerical results indicate that the approximation is accurate for broad classes of loads., Supporting appendix is available on request for additional details on proofs or preconditioning techniques

Large-scale smart grids call for online algorithms that are able to achieve the most accurate estimates. This paper shows how to achieve both the scalability and near globally optimal results for bad data and topology error detection and identification problems, by conducting fully distributed algorithms over convexified problem formulations. The proposed distributed decomposition is realized by (1) reducing a large network into much smaller network “cliques” which do not need extensive information exchange; (2) performing a Lagrangian dual decomposition in each clique and passing messages between cliques; and (3) conducting alternative coordinate descent optimization for robustness. To reduce the relaxation error in the convexification procedure, a nuclear norm penalty is added to approximate original problems. Finally, we propose a new metric to evaluate detection and identification results, which enables a system operator to characterize confidence for further system operations. We show that the proposed algorithms can be realized on IEEE test systems with improved accuracy in a short time.

Made available in DSpace on 2018-12-11T17:03:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2016-11-01 This paper presents a new methodology to solve the reconfiguration problem of electrical distribution systems (EDSs) with variable demand, using the artificial immune algorithm Copt-aiNet (Artificial Immune Network for Combinatorial Optimization). This algorithm is an optimization technique inspired by immune network theory (aiNet). The reconfiguration problem with variable demand is a complex problem of a combinatorial nature. The goal is to identify the best radial topology for an EDS in order to minimize the cost of energy losses in a given operation period. A specialized sweep load flow for radial systems was used to evaluate the feasibility of the topology with respect to the operational constraints of the EDS and to calculate the active power losses for each demand level. The algorithm was implemented in C++ and was evaluated using test systems with 33, 84, and 136 nodes, as well as a real system with 417 nodes. The obtained results were compared with those in the literature in order to validate and prove the efficiency of the proposed algorithm. Electrical Engineering Department Campus of Ilha Solteira Unesp Univ Estadual Paulista, Av. Brazil 56 INESC TEC, Av. Dr. Roberto Frias, 378 Faculty of Economics University of Porto, Av. Dr. Roberto Frias, s/n Faculty of Engineering University of Porto, Av. Dr. Roberto Frias, s/n Electrical Engineering Department Campus of Ilha Solteira Unesp Univ Estadual Paulista, Av. Brazil 56

This paper presents a new framework for vulnerability analysis. Under this framework, we can identify the vulnerable components and the critical components of a power grid. Distinct from previous work, our model considers the interaction between the components of the power system, and models the dynamic evolving process of cascading failures. The impact of a component failure on the system is dynamically changing as the failure propagates. We analyze the vulnerability of a power grid using an optimization model based on game theory, and use linear programming method to solve it. Since instability is the reason of power outage, we use an instability index to measure the negative impact to the system. The results from this optimization problem suggest which component of the system is critical since its failure can most negatively impact the cyber-physical system.