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Soft open points (SOPs) are power electronic devices which provide interconnection between two feeders in place of normally open points in electricity distribution networks. SOPs can continuously control active power flow between feeders and inject reactive power controllably at both nodes, which can be used to provide substantial capacity support to the system. This paper provides a reliability-based method to quantify the capacity value (the additional load which can be accommodated without reducing reliability) of SOPs using the Effective Load Carrying Capability method within a Monte Carlo Simulation (MCS). Optimization of post-fault active/reactive power injections by SOPs to minimize energy not supplied is formulated (directly in matrix form) as a second-order cone programming problem. This results in very low computational times which enables embedding of the optimization problem within the MCS. The proposed methodology is applied to a modified real-world distribution network considering three different SOP sizes (5 SOPs totalling 2.5, 5, 10 MVA) across three redundancy levels (N-1, N-0.75, N-0.5), and on an unbalanced network with distributed generation. Results demonstrate capacity values ranging from 2.4–12.84 MVA. When operating under a relaxed redundancy level, the capacity value of a given SOP capacity can more than double relative to N-1. [ABSTRACT FROM AUTHOR]

This paper proposes a new scheme for bulk system restoration considering the available black-start resources (BSRs) in the distribution system (DS). The DS assisted generator start-up sequence (D-GSS) scheme is realized in a decentralized way, so that it does not only benefit the bulk system GSS by utilizing available BSRs in the DS, but also respects the independent operation of the transmission system operator (TSO) and distribution system operators (DSOs). First, the decentralized D-GSS scheme is presented including the interaction of the TSO and DSOs and the corresponding compact models. The models of the decentralized D-GSS scheme are built with the bulk system GSS modeled as a mixed-integer quadratic program (MIQP), the DS multi-step operation modeled as mixed-integer second-order conic programs (MISOCPs) and reliable power supply assessments of renewable energy sources as linear programs (LPs). Finally, a projection function based analytical target cascading (P-ATC) method is developed to iteratively solve the decentralized models with model complexity reduction. The P-ATC algorithm can handle integer variables and improve the computational efficiency of the iterative calculation process. The effectiveness of the proposed method is validated using the small-scale T6D2 system and large-scale T118D5 system, showing good GSS performance and computation efficiency. [ABSTRACT FROM AUTHOR]

Day-ahead scheduling has played a significant role in the operation of distribution systems, aiming at minimizing the total operation cost. With the excessive integration of information and communication technologies and intelligent electronic devices, distribution system operators may seek to optimally control the active management elements to increase the economic and technical performance of future smart distribution systems. This paper focuses on an integrated day-ahead scheduling scheme that is formulated as a mixed integer second-order cone programming problem to obtain the optimal solution by means of the relaxed power flow model (RPFM). The detailed technical constraints for all the elements are accommodated based on the RPFM-based optimization method. Meanwhile, active management cost and punishment cost of wind power curtailed and customer energy not supplied are also considered in the design objectives of this paper. In order to address the uncertainties, a stochastic robust optimization method is first introduced to decide the active management elements (including capacitor bank, electrical storage system, controllable load, and switch) as the robust decision scheme. Afterwards, the column-and-constraint generation algorithm is applied to solve the proposed stochastic robust two-stage optimization model. Numerical results based on the IEEE 33-bus, PG&E 69-bus, and practical 152-bus systems are obtained to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The unit commitment is still a widely studied problem, especially when more renewable energy of stochastic character is being added to power systems. This paper proposes a model for weekly planning of systems involving hydro, wind, and thermal energy under a stochastic perspective. The proposed model follows the endogenous reserve determination criterion to achieve a simultaneous optimization of energy and reserves considering wind uncertainty, forced outages of equipment, a dc Flow model of the network, and cascaded head sensitive hydro systems, among others. The paper also develops a practical solution methodology based on outer approximation and benders decomposition. Testing has been conducted over four systems, and computational results demonstrate that the proposed model and solution are useful and effective. [ABSTRACT FROM AUTHOR]

In the restructured power industry, bulk energy storage may play a crucial role to provide the flexibility required by system operators to cater for the unprecedented levels of uncertainty. Within the context of co-optimized electricity markets for energy and reserves under wind uncertainty, this paper addresses the incorporation of bulk energy storage units in day-ahead network-constrained energy and reserve scheduling. A novel two-stage robust optimization approach is presented whereby the nonconvex and time-coupled operation of storage devices is precisely modeled while accounting for the anticipativity of the two-stage setting. The resulting robust counterpart is cast as a mixed-integer trilevel program with lower-level binary variables. In order to address the nonconvexity of the recourse problem, this paper proposes the application of an exact nested column-and-constraint generation algorithm. Numerical results illustrate the effective performance of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents a methodology for generating restoration sequences in distribution systems and microgrids with emphasis on deriving optimal switching times for remote control switches. Microgrid architecture considered are assumed to be operating in islanded single master mode. Control methods for handling the unbalance inherent in distribution systems using single-phase controlled PQ inverters were developed and incorporated in the proposed method. The problem of considering simultaneously both energy optimization and dynamic stability of the system, which is lacking in existing methods, was addressed by studying the transient behavior of microgrids based on extended electromagnetic transients program (EMTP) simulations and then approximate and incorporate these behaviors into the optimization formulation for restoration. The approach is based on multi-objective optimization of final restored load and total restoration time. The methodology was studied on a modified IEEE 123 node test feeder. An EMTP simulation in PSCAD of the formed microgrids was used to validate the accuracy of the dynamic and steady-state characteristics of the resulting systems. By considering the transient behavior of distributed generators (DGs) during restoration, a better restoration sequence that does not trigger protection relays could be realized. [ABSTRACT FROM AUTHOR]

Voltage control plays an important role in the operation of electricity distribution networks, especially with high penetration of distributed energy resources. These resources introduce significant and fast varying uncertainties. In this paper, we focus on reactive power compensation to control voltage in the presence of uncertainties. We adopt a chance constraint approach that accounts for arbitrary correlations between renewable resources at each of the buses. We show how the problem can be solved efficiently using historical samples analogously to the stochastic quasi-gradient methods. We also show that this optimization problem is convex for a wide variety of probabilistic distributions. Compared to conventional per-bus chance constraints, our formulation is more robust to uncertainty and more computationally tractable. We illustrate the results using standard IEEE distribution test feeders. [ABSTRACT FROM AUTHOR]

Smart inverters provide additional control capability to help optimize the operation of distribution systems. This paper proposes a framework for exact optimal active and reactive power dispatch of distributed photovoltaic (PV) generation, switched capacitors, and voltage regulators in large multi-phase unbalanced distribution systems. The objectives of the optimal dispatch are minimization of the energy loss, PV active power curtailment, and operations of capacitors and voltage regulators, in addition to elimination of voltage violations and reverse power flow. The optimization problem is formulated in rectangular coordinates as a nonlinear, nonconvex problem. Effective computational strategies are proposed to allow the application of predictor-corrector primal-dual interior point method to solve optimization problems in real-time with a large number of constraints and variables, including discrete variables corresponding to switched capacitors and voltage regulators. The accuracy of the numerical solution and the ability to implement the proposed framework are validated using the unbalanced multi-phase IEEE 34-bus and EPRI 2,998-bus distribution systems with 15-minute load and PV data. The results show a significant loss reduction and elimination of both voltage violations and reverse power flow. [ABSTRACT FROM AUTHOR]

Demand-response aggregators are faced with the challenge of how to best manage numerous and heterogeneous distributed energy resources (DERs). This paper proposes a decentralized methodology for optimal coordination of DERs. The proposed approach is based on Dantzig–Wolfe decomposition and column generation, thus allowing to integrate any type of resource whose operation can be formulated within a mixed-integer linear program. We show that the proposed framework offers the same guarantees of optimality as a centralized formulation, with the added benefits of distributed computation, enhanced privacy, and higher robustness to changes in the problem data. The practical efficiency of the algorithm is demonstrated through extensive computational experiments, on a set of instances generated using data from Ontario energy markets. The proposed approach was able to solve all test instances to proven optimality, while achieving significant speed-ups over a centralized formulation solved by state-of-the-art optimization software. [ABSTRACT FROM AUTHOR]

This paper discusses the application of the recently proposed augmented Lagrangian alternating direction inexact Newton (aladin) method to non-convex ac optimal power flow problems (ac-opf) in a distributed fashion. In contrast to the often used alternating direction of multipliers method (admm), aladin guarantees locally quadratic convergence for ac-opf. Numerical results for 5–300 bus test cases indicate that aladin is able to outperform the admm and to reduce the number of iterations by about one order of magnitude. We compare aladin to numerical results for the admm documented in the literature. The improved convergence speed comes at the cost of increasing the communication effort per iteration. Therefore, we propose a variant of aladin that uses inexact Hessians to reduce communication. Additionally, we provide a detailed comparison of these aladin variants to the admm from an algorithmic and communication perspective. Moreover, we prove that aladin converges locally at a quadratic rate even for the relevant case of suboptimally solved local nonlinear programs. [ABSTRACT FROM AUTHOR]

Multienergy systems are flexible energy systems that can benefit from energy resources to supply different energy demands. Due to the capabilities of multienergy systems in generating different energy carriers, these systems have been rapidly expanded in power systems. After restructuring in power system in recent years and appearance of competent energy markets, energy systems operated within such environments have been usually exposed to uncertainties of various parameters, such as price, demand, etc. In this paper, a novel optimization framework based on hybrid scenario-based/interval/information gap decision theory method is developed to investigate the optimal operation of smart energy hubs (S. E. Hubs) subject to economic priorities, technical constraints of the distribution network and uncertainties. Considering energy hubs equipped to smart facilities, demand-side management programs including price response and load response services have been available to motivate electrical consumers to revise their consumption pattern in order to satisfy economic priorities of energy hubs. By using the results of employed hybrid uncertainty modeling approach, the operator of S. E. Hubs can decide either to take risk-averse or risk-seeking strategy against the uncertainties. Uncertainty based integration of S. E. Hubs into distribution network is evaluated regarding the IEEE 33-bus test system and the results obtained from simulations are presented for comparison. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of how best to coordinate, or “stack,” energy storage services in systems that lack centralized markets. Specifically, its focus is on how to coordinate transmission-level congestion relief with local, distribution-level objectives. We describe and demonstrate a unified communication and optimization framework for performing this coordination. The congestion relief problem formulation employs a weighted ${\ell _{1}\text{-norm}}$ objective. This approach determines a set of corrective actions, i.e., energy storage injections and conventional generation adjustments, that minimize the required deviations from a planned schedule. To exercise this coordination framework, we present two case studies. The first is based on a 3-bus test system, and the second on a realistic representation of the Pacific Northwest region of the United States. The results indicate that the scheduling methodology provides congestion relief, cost savings, and improved renewable energy integration. The large-scale case study informed the design of a live demonstration carried out in partnership with the University of Washington, Doosan GridTech, Snohomish County PUD, and the Bonneville Power Administration. The goal of the demonstration was to test the feasibility of the scheduling framework in a production environment with real-world energy storage assets. The demonstration results were consistent with computational simulations. [ABSTRACT FROM AUTHOR]

Volt/var control (VVC) is one of the primary functions of the distribution management system aiming at optimum operation of power distribution networks while respecting all of their operational and security constraints. However, the recent huge integration of highly stochastic distributed generation (DG) sources with the grid presents a significant challenge to the traditional VVC schemes, which assume the future to be perfectly known. This paper presents a two-stage chance constrained optimization scheme to handle these nodal power uncertainties and guarantees that the operational and security constraints are respected for almost all realizations of the uncertainty. The chance constrained model is solved by collecting enough randomly chosen samples from the probability spaces of the uncertain parameters so that the class of the problem, a mixed integer second-order cone program, is not elevated. The algorithm not only dispatches the optimum schedule for discrete controlling devices like transformers and shunt capacitors but also optimizes the predefined decision rules for reactive power control of DG sources, thus falling in line with the requirement laid down in the revised IEEE 1547 Standard. Numerical simulations on three different test systems show the superiority of the proposed algorithm over the traditional deterministic methods. [ABSTRACT FROM AUTHOR]

This paper presents a new methodology based on multiobjective optimization techniques to perform an optimized, coordinated, and selective allocation of control and protection devices in distribution networks with distributed generation (DG). The proposed mathematical model consists of two objective functions that consider economic issues and the network continuity index. Physical and operational constraints are taken into account, with emphasis on the set of constraints based on practical rules of distribution companies and international technical standards, which require the specification, coordination, and selectivity of the protection devices installed in the network. The possibility of load transfer from neighboring feeders and islanded DG operation is also considered. The proposed model is a mixed integer nonlinear programming, and we use NSGA-II (Nondominated Sorting Genetic Algorithm) to solve it. The proposed methodology is applied in a real 135-bus system found in the literature. [ABSTRACT FROM AUTHOR]

In this paper, the coordinated investment in transmission and storage systems under uncertainty is addressed from the perspective of a central planner. The problem is formulated with the objective of achieving an effective expansion of both transmission and storage that minimizes the investment cost, while achieving an effective operation of a power system with high penetration of renewable power. The problem is stated within an adaptive robust optimization framework that incorporates stochastic modeling. Future available generation capacity and peak load in the target year (long-term uncertainty) are modeled using a robust set, while daily operating conditions (short-term uncertainty) are represented with a scenario set. The expansion tradeoff between transmission and storage systems is analyzed using the IEEE RTS 24-bus and IEEE 118-bus networks. [ABSTRACT FROM AUTHOR]

In order to support an appropriate level of resource adequacy in the long term and also to achieve a reliable operation in the short term, a new pricing design and mechanism is needed as a key success factor of real-time energy-only market. This paper proposes optimization-based mathematical models to explore operating reserve demand curves (ORDCs) and two price adders in real-time energy-only market, including dispatch correction and extended security-constrained economic dispatch. The Lagrangian multipliers of the dispatch correction problem are used to construct the ORDCs. Then, the derivative of the ORDCs’ social welfare is formulated as real-time online reserve price adders such as the scarcity adder and the price-lift adder. In case studies, we justify the effectiveness of the proposed ORDCs and two price adders by a simple example with two aggregated units and the Electric Reliability Council of Texas data. [ABSTRACT FROM AUTHOR]

The penetration of distributed renewable energy sources in the distribution grid is increasing considerably in the last years. This is one of the main causes that contributed to the growth of technical problems in both transmission and distribution systems. An effective solution to improve system security is to exploit the flexibility that can be provided by distributed energy resources (DER), which are mostly located at the distribution grids. Their location combined with the lack of power flow coordination at the system operators interface creates difficulties in taking advantage of these flexible resources. This paper presents a methodology based on the solution of a set of optimization problems that estimate the flexibility ranges at the distribution and transmission system operators (TSO-DSO) boundary nodes. The estimation is performed while considering the grid technical constraints and a maximum cost that the user is willing to pay. The novelty behind this approach comes from the development of flexibility cost maps, which allow the visualization of the impact of DER flexibility on the operating point at the TSO-DSO interface. The results are compared with a sampling method and suggest that a higher accuracy in the TSO-DSO information exchange process can be achieved through this approach. [ABSTRACT FROM AUTHOR]

Distributed energy storage (DES) offers a number of benefits to improve the power system reliability. This paper presents an improved corrective security constrained optimal power flow (CSCOPF) with DES system. The proposed DES model takes into account the current state of charge (SOC) and the energy capacity model of the DES. The corrective control actions employed in the paper include not only the traditional long-term rescheduling control actions, but also the short-term post-contingency fast corrective control of the DES. A hybrid method is developed to solve the improved CSCOPF problem, and the effectiveness of the proposed method is evaluated and demonstrated in the paper by three example power systems. [ABSTRACT FROM AUTHOR]

Recent years have witnessed significant interest in convex relaxations of the power flows, with several papers showing that the second-order cone relaxation is tight for tree networks under various conditions on loads or voltages. This paper shows that ac-feasibility, i.e., to find whether some generator dispatch can satisfy a given demand, is NP-hard for tree networks. [ABSTRACT FROM AUTHOR]

This paper defines flow control algorithms for loop flow cancellation based on the allocation and tracing of bilateral transactions and loop flows. In Part I of this paper, we have shown that the main difference between transportation and electrical networks is caused by the existence of loop flows. We have introduced a distributed framework for the modeling and tracing of bilateral transactions and the corresponding loop flows. Its zooming-out capability provides a valuable mechanism for representing external (inter-area) loop flows based on simplified topologies of individual areas. The tracing information accurately allocates bilateral transactions with associated contract paths to line flows and loop flows. Furthermore, this information can be used for determining the set points of control equipment so that loop flows are minimized. In this framework, phase angle regulators (PARs), commonly used for line flow control, are represented through their effects on loop flows. We define sufficient conditions for achieving complete loop flow cancellation. A new distributed algorithm for determining PAR set points in a coordinated way without revealing operating conditions of individual areas is introduced in this part. Finally, complete loop flow cancellation and the distributed algorithm for finding PAR set points are demonstrated in the Reliability Test System (RTS) 96-bus system with wheeling loop flows. [ABSTRACT FROM AUTHOR]

This paper proposes a data-driven affinely adjustable distributionally robust method for unit commitment considering uncertain load and renewable generation forecasting errors. The proposed formulation minimizes expected total operation costs, including the costs of generation, reserve, wind curtailment, and load shedding, while guaranteeing the system security. Without any presumption about the probability distribution of the uncertainties, the proposed method constructs an ambiguity set of distributions using historical data and immunizes the operation strategies against the worst case distribution in the ambiguity set. The more historical data is available, the smaller the ambiguity set is and the less conservative the solution is. The formulation is finally cast into a mixed integer linear programming whose scale remains unchanged as the amount of historical data increases. Numerical results and Monte Carlo simulations on the 118- and 1888-bus systems demonstrate the favorable features of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a methodology for integrated planning of real-life medium-voltage networks based on the utility planning concepts. The research is motivated by the need to develop a methodology that would line-up with utility day-to-day businesses and could be applied in real-life. Its core is a two-stage optimization process, where the first stage solves the static investment optimization and the second stage considers operational problem. A probabilistic decision tree approach is proposed for the solution of the entire problem to consider uncertainties in the planning period. The overall formulation is given first, which is followed by details of the investment model and outlines of the proposed operation planning. The novelty of the investment problem, which determines optimal network reinforcements, is explicit modeling of network security constraints of radially operated networks, whilst considering different operating regimes. Additional novel features include modeling of real-life supply restoration rules through network reconfiguration and optimal placement of new switching devices, as well as consideration of “customer flows” on the network. Connection of new distributed generation and demand centers and construction of circuits on new corridors are also included. Two investment models are formulated as mixed-integer nonlinear optimization problems, tested on several MV networks and compared with established methods. The proposed operational problem is solved in two stages, quality-of-supply and operation cost optimization. Computational aspects are also presented. [ABSTRACT FROM PUBLISHER]

This paper provides a reformulation of the scenario-based two-stage unit commitment problem under uncertainty that allows finding unit-commitment plans that perform reasonably well both in expectation and for the worst case. The proposed reformulation is based on partitioning the sample space of the uncertain factors by clustering the scenarios that approximate their probability distributions. The degree of conservatism of the resulting unit-commitment plan (that is, how close it is to the one provided by a purely robust or stochastic unit-commitment formulation) is controlled by the number of partitions into which the said sample space is split. To efficiently solve the proposed reformulation of the unit-commitment problem under uncertainty, we develop two alternative parallelization and decomposition schemes that rely on a column-and-constraint generation procedure. Finally, we analyze the quality of the solutions provided by this reformulation for a case study based on the IEEE 14-node power system and test the effectiveness of the proposed parallelization and decomposition solution approaches on the larger IEEE 3-Area RTS-96 power system. [ABSTRACT FROM PUBLISHER]

To coordinate electric vehicle (EV) charging, the EV aggregator (EVA) is usually assumed to obtain the privilege from EV owners (EVOs) to determine the EV charging profile, and complex communication between EVA and EVOs is demanded, which poses difficulties for practical applications. In contrast, this paper proposes the concept of an EV chargeable region to evaluate the distribution network (DN) EV hosting capacity, i.e., how much EV charging demand can be accommodated in a DN, within which the technical constraints of DN (e.g., voltage deviation) are guaranteed and EVOs’ charging requests are maximally ensured. The optimization of the EV chargeable region is formulated as a two-stage robust optimization model with adjustable uncertainty set. The EV chargeable region and DN decision variables are optimized in the first stage and the feasibility in the real-time worst-case scenario is checked in the second stage, considering the uncertainty of EV charging demand and DN active and reactive power. A modified column and constraint generation and outer approximation method is adopted to address the proposed problem. Simulations on an IEEE 123-node DN demonstrate the effectiveness of the proposed model. [ABSTRACT FROM PUBLISHER]

Security-constrained optimal power flow (SCOPF) problems are essential tools to transmission system operators for long-term and operational planning and real-time operation. The general goal of SCOPF problems is to optimize electricity network operation while ensuring that operational and planning decisions are consistent with technical limits under both pre- and post-contingency states. The solution of SCOPF problems is challenging because of the inherent size and scope of modern grids. As empirical evidence and longstanding operator experience show, relatively few of the constraints of SCOPF problems actually serve to enclose their feasible region. Hence, all those constraints not contributing directly to set up the SCOPF feasible space are superfluous and could be discarded. In light of this observation, this paper proposes an optimization-based approach for identifying so-called umbrella constraints in SCOPF problems where the network operation is approximated by the dc power flow. Umbrella constraints are constraints which are necessary and sufficient to the description of the feasible set of an SCOPF problem. The resulting umbrella constraint discovery problem (UCD) is a convex optimization problem with a linear objective function. For SCOPF problems of practical importance, the UCD is also quite large and requires the use of a decomposition technique. In this paper, we concentrate on an SCOPF formulation for preventive security generation dispatch. We show that by removing superfluous constraints, the resulting sizes of SCOPF problems are much smaller and can be solved significantly faster. [ABSTRACT FROM PUBLISHER]

This paper proposes a flow-based approach for the transmission tariff allocation problem based on the notions of long-run marginal cost (LRMC) and nodal exchange factors (NEFs). A worst-case power flow, expressed in terms of NEFs, is formulated to characterize the system state. Additionally, the NEFs optimal values are determined considering a specific criterion to compute tariffs. The resulting problem is formulated as a bilevel program. The upper level is a worst-case power flow that maximizes line flows taking into account the transmission tariffs computed in the lower level. The criterion considered in the lower level aims to minimize the variation range of transmission tariffs, which is particularly desirable to provide incentives for renewable sources installed far away from load centers. The resulting bilevel problem may have multiple solutions. Here, the uniqueness in tariffs is preserved by solving an alternative problem once both the generation dispatch and the variation range of transmission tariffs are known. Numerical results are provided for a 6-bus system and the IEEE 118-bus system. [ABSTRACT FROM AUTHOR]

Power flow analysis is one of the tools that is required in most of the distribution system studies. An important characteristic of distribution systems is the load unbalance in the phases and a three-phase power flow analysis is needed. In this paper, a three-phase linear power flow (3LPF) formulation is derived based on the fact that in a typical distribution system, voltage angles and magnitudes vary within relatively narrow boundaries. The accuracy of the proposed 3LPF is verified using several test cases. Potential applications of the proposed method are in distribution systems state estimation and volt-VAR optimization. [ABSTRACT FROM PUBLISHER]

The discrete coordinate-descent algorithm is a practical approach that is currently used in centralized Volt/VAr Control (VVC) implementations, mainly due to its good performance and speed for real-time applications. Its viability is however challenged by the increasing number of distributed generation that contribute to the VVC solution, in addition to the conventional transformer taps and switched capacitors. This paper presents the exact computation of sensitivity factors that speed up the discrete coordinate-descent implementation, by significantly reducing the number of forward/backward substitutions in the current injection power flow method; the speed up is achieved without affecting the control setting quality of the original implementation. The optimality of the discrete coordinate-descent solutions is investigated by computing the gaps relative to mixed-integer linear programming set-points, derived from a polyhedral reformulation of the VVC problem. The sensitivity-based discrete coordinate-descent algorithm is tested starting from two initial points, the default one given by the current control set-points, and a continuous solution obtained from a linear approximation of the VVC problem. Numerical results on networks with up to 3145 nodes show that the sensitivity-based approach significantly improves the runtime of the discrete coordinate-descent algorithm, and that the linear programming initialization leads to VVC solutions with gaps relative to the mixed-integer set-points that are less than 0.5%. [ABSTRACT FROM PUBLISHER]

This paper proposes an effective approach based on the particle swarm optimization with integer coded to determine the switch operation schemes for feeder reconfiguration. The proposed approach, enhanced integer coded particle swarm optimization (EICPSO), is able to improve the search efficiency for feeder reconfiguration problems by considering the historical local optimal solutions when generating new particles. The local optimal solutions found during the evolution process are used when new particle are generated. Three different distribution systems are used in this paper to verify and validate the effectiveness of the proposed method. Simulation results show that the proposed method can find the solutions for feeder reconfiguration problems faster than other approaches such as discrete particle swarm optimization, modified binary particle swarm optimization, and genetic algorithm. [ABSTRACT FROM PUBLISHER]

This paper is the second of a two-part paper and describes the application of a multiperiod generalized network flow model that is used to analyze the economic efficiencies of the energy movements from the coal and natural gas suppliers to the electric load centers, providing a simulation tool that captures dynamics of and interdependencies between the coal, natural gas, and electricity networks. The modeling approach, mathematical formulation, and modeling assumptions are presented in part I. This sequel presents and discusses numerical results to illustrate the application of the model. The model enables public and private decision makers to carry out comprehensive analyses of a wide range of issues related to the energy sector, such as strategic planning, economic impact assessment, and different regulatory regimes. [ABSTRACT FROM AUTHOR]

This paper is the first of a two-part paper presenting a multiperiod generalized network flow model of the integrated energy system in the United States. Part I describes the modeling approach used to evaluate the economic efficiencies of the systemwide energy flows, from the coal and natural gas suppliers to the electric load centers. Under the proposed problem formulation, fuel supply and electricity demand nodes are connected via a transportation network, and the model is solved for the most efficient allocation of quantities and corresponding prices. The methodology includes physical, economic, and environmental aspects that characterize the different networks. Part II of this paper provides numerical results that demonstrate the application of the model. [ABSTRACT FROM AUTHOR]

Under the deregulated environment of electric power industry, generation can be installed anywhere in the system resulting in an "imbalance" between the generation and transmission. Shortages of generation in some subregions result in "bottle- necks" within a system raising reliability concerns regarding subregional adequacy. Excess of generation capacity raises the issue of how much capacity in which location is entitled to receive payments for Stalled capacity Therefore, there is a need to determine loactional requirement for both generation and transmission such that assistance to subregions under random generator outages is not restricted. This paper presents optimization procedures for the determination of adequacy and responsibility for locational generation and transmission. The outlined procedures applicable to situations of planning to identify additional needs as well as to situations of market design for installed capacity in subregions. The paper closes by a discussion of forward auctions for the procurement of capacity in subregions. [ABSTRACT FROM AUTHOR]

Increasing penetration of variable loads and renewable generation will cause the conventional operation strategy of the distribution system to become less certain and effective. This paper presents a method of determining the minimum loss network configuration of a distribution system with uncertain load and renewable generation. A robust optimization model is proposed wherein the optimal decisions on network configurations and losses are derived in two subsequent steps. The first step enforces the radiality constraint before knowing the actual system loads and output level of renewable generation. Power flows are computed next to achieve minimum network losses considering the worst operating conditions over the uncertainty sets. A mixed-integer two-stage robust optimization formulation and a decomposition algorithm in a master-slave structure are proposed to solve the problem. Results of an illustrative example and two test systems are presented to demonstrate the proposed method. [ABSTRACT FROM PUBLISHER]

This paper considers future distribution networks featuring inverter-interfaced photovoltaic (PV) systems, and addresses the synthesis of feedback controllers that seek real- and reactive-power inverter setpoints corresponding to AC optimal power flow (OPF) solutions. The objective is to bridge the temporal gap between long-term system optimization and real-time inverter control, and enable seamless PV-owner participation without compromising system efficiency and stability. The design of the controllers is grounded on a dual \epsilon-subgradient method, while semidefinite programming relaxations are advocated to bypass the non-convexity of AC OPF formulations. Global convergence of inverter output powers is analytically established for diminishing stepsize rules for cases where: i) computational limits dictate asynchronous updates of the controller signals, and ii) inverter reference inputs may be updated at a faster rate than the power-output settling time. [ABSTRACT FROM PUBLISHER]

This paper presents a planning framework to find the minimum storage sizes (power and energy) at multiple locations in distribution networks to reduce curtailment from renewable distributed generation (DG), specifically wind farms, while managing congestion and voltages. A two-stage iterative process is adopted in this framework. The first stage uses a multi-period AC optimal power flow (OPF) across the studied horizon to obtain initial storage sizes considering hourly wind and load profiles. The second stage adopts a high granularity minute-by-minute control driven by a mono-period bi-level AC OPF to tune the first-stage storage sizes according to the actual curtailment. Congestion and voltages are managed through the optimal control of storage (active and reactive power), on-load tap changers (OLTCs), DG power factor, and DG curtailment as last resort. The proposed storage planning framework is applied to a real 33-kV network from the North West of England over one week. The results highlight that by embedding high granularity control aspects into planning, it is possible to more accurately size storage facilities. Moreover, intelligent management of further flexibility (i.e., OLTCs, storage, and DG power factor control) can lead to much smaller storage capacities. This, however, depends on the required level of curtailment. [ABSTRACT FROM AUTHOR]

Most existing approaches for distribution network reconfiguration assume that the distribution system is (three-phase) balanced and a single-phase equivalent is used. However, distribution feeders are usually unbalanced due to a large number of single-phase loads, nonsymmetrical conductor spacing, and three-phase line topology. This paper builds on our previous work and studies feeder reconfiguration for unbalanced distribution systems with distributed generation (DG). The three-phase bus locations and sizes of DG units are determined using sensitivity analysis and nonlinear programming, respectively, and distribution feeders are reconfigured every hour based on the status of time-varying loads, output power from DG units and faults on the network while minimizing the energy loss costs and DG operating costs. Simulation results show the effectiveness and computational efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive mathematical model to solve the restoration problem in balanced radial distribution systems. The restoration problem, originally modeled as mixed integer nonlinear programming, is transformed into a mixed integer second-order cone programming problem, which can be solved efficiently using several commercial solvers based on the efficient optimization technique family branch and bound. The proposed mathematical model considers several objectives in a single objective function, using parameters to preserve the hierarchy of the different objectives: 1) maximizing the satisfaction of the demand, 2) minimizing the number of switch operations, 3) prioritizing the automatic switch operation rather than a manual one, and 4) prioritizing especial loads. General and specialized tests were carried out on a 53-node test system, and the results were compared with other previously proposed algorithms. Results show that the mathematical model is robust, efficient, flexible, and presents excellent performance in finding optimal solutions. [ABSTRACT FROM PUBLISHER]

In this paper, a new optimization framework is proposed to coordinate the operation of large, price-maker, and geographically dispersed energy storage/battery systems in a nodal transmission-constrained energy market. The energy storage units are assumed to be investor-owned and independently-operated, seeking to maximize their total profit. Various design factors are taken into consideration such as the location, size, efficiency, and charge and discharge rates of the energy storage units as well as the joint impact of the energy storage operations on the locational marginal prices. While the formulated optimization problem is originally nonlinear and hard to solve, nonlinearities are tackled both in the objective function and in the constraints and the problem is transformed into a tractable mixed-integer linear program, for which the global optimal solutions are found for the charge and discharge schedules of each energy storage unit. Both deterministic and stochastic design scenarios are addressed. Various case studies are presented. It is observed that transmission line congestion is often, but not always, desirable for the coordinated storage systems. Locational diversity, practice of arbitrage, robust design, self-scheduling versus economic bidding, and the overall power system performance are also investigated. [ABSTRACT FROM AUTHOR]

Existing population-based Stochastic Search Algorithms (SSAs) are too time-consuming to solve dynamic optimal power flow (OPF). The solution proposed in this paper is to accelerate SSAs with memory. Two memory schemes, the similarity retrieval scheme and the mean-based immigrants scheme, are proposed and applied together to the Differential Evolution and Particle Swarm Optimizer, which are two representatives of SSAs. Experiments are conducted on modified IEEE 30-bus and IEEE 118-bus systems with changing load buses and the objective of minimizing real power transmission loss. The results show that the proposed schemes significantly improve the performance of the two existing algorithms, and that SSAs could be practical for tracking optima of dynamic OPF. [ABSTRACT FROM AUTHOR]

This paper proposes a computationally efficient technique for estimating the composite load model parameters based on analytical similarity of parameter sensitivity. When the model parameters are updated in the optimization procedure to best fit the actual load dynamics, i.e., measurements, parameters of similar sensitivity representation in the given mathematical model structure are updated in the same manner at every iterative step. This research allows for practically reducing the number of load model parameters to be identified in the estimation process and the overall computational cost while preserving the desired complexity and accuracy of the original model. This approach consequently facilitates the parameter estimation in the optimization process and helps manage increased number of parameters often criticized for adopting the dynamic composite load model via measurement-based approach. Case studies for the real power system demonstrate the computational efficiency and intact accuracy of the proposed method with reference to the existing methods of estimating all the parameters of the given composite load model independently. [ABSTRACT FROM AUTHOR]

In this paper, a new scenario-based stochastic optimization framework is proposed for price-maker economic bidding in day-ahead and real-time markets. The presented methodology is general and can be applied to both demand and supply bids. That is, no restrictive assumptions are made on the characteristics of the pool and its agents. However, our focus is on the operation of time-shiftable loads with deadlines, because they play a central role in creating load flexibility and enhancing demand response and peak-load shaving programs. Both basic and complex time-shiftable load types are addressed, where the latter includes time-shiftable loads that are uninterruptible, have per-time-slot consumption limits or ramp constraints, or comprise several smaller time-shiftable subloads. Four innovative analytical steps are presented in order to transform the originally nonlinear and hard-to-solve price-maker economic bidding optimization problem into a tractable mixed-integer linear program. Accordingly, the global optimal solutions are found for the price and energy bids within a relatively short amount of computational time. A detailed illustrative case study along with multiple case studies based on the California energy market data are presented. It is observed that the proposed optimal price-maker economic bidding approach outperforms optimal price-maker self-scheduling as well as even-load-distribution. [ABSTRACT FROM AUTHOR]

It has been recently proven that the semidefinite programming (SDP) relaxation of the optimal power flow problem over radial networks is exact under technical conditions such as not including generation lower bounds or allowing load over-satisfaction. In this paper, we investigate the situation where generation lower bounds are present. We show that even for a 2-bus 1-generator system, the SDP relaxation can have all possible approximation outcomes, that is 1) SDP relaxation may be exact, 2) SDP relaxation may be inexact, or 3) SDP relaxation may be feasible while the optimal power flow (OPF) instance may be infeasible. We provide a complete characterization of when these three approximation outcomes occur and an analytical expression of the resulting optimality gap for this 2-bus system. In order to facilitate further research, we design a library of instances over radial networks in which the SDP relaxation has positive optimality gap. Finally, we propose valid inequalities and variable bound tightening techniques that significantly improve the computational performance of a global optimization solver. Our work demonstrates the need of developing efficient global optimization methods for the solution of OPF even in the simple but fundamental case of radial networks. [ABSTRACT FROM AUTHOR]

Emerging smart-grid-enabling technologies will allow an unprecedented degree of observability and control at all levels in a power system. Combined with flexible demand and storage, they could allow procuring energy at minimum cost and environmental impact. That however presupposes real-time coordination of demand of individual households and industries down at the distribution level, with generation at the transmission level. This is closely related with the balancing market economic dispatch (ED) problem, which currently does not take into account distribution network constraints and flexible demand characteristics. Still, assuming a suitably modified form of that problem was available, due to both computational and communications requirements, its centralized solution in its full detail would not be tractable. While there is currently a wealth of literature dealing with distributed optimization applications in power systems, it typically focuses on smaller parts of the overall energy management problem (e.g., transmission area synchronization or electric vehicles management) often without considering its full scale or establishing any association with energy market mechanisms. The target of this paper is twofold: 1) identify a flexible demand and distribution network inclusive formulation for ED and 2) propose a solution method. [ABSTRACT FROM AUTHOR]

Increasing penetration of renewable power sources (RESs) is bringing more uncertainties to power systems. Real-time economic dispatch should be able to handle the fluctuations caused by the load as well as RESs, and obtain new optimal operating points after deviating from original generation schedules. This paper proposes a generation adjustment algorithm based on the base point and participation factor method. The objective of the method is to obtain fast adjustments to generators’ real power outputs in real-time economic dispatch. The proposed method achieves significant and consistent improvements comparing to the original participation factor method by using a more precise model of transmission losses in the optimization process. The computational burden and execution time of the proposed method is much less than OPF and heuristic economic dispatch methods. The proposed method and its effectiveness are tested using IEEE 30-bus system, IEEE 118-bus system, and GuangDong 1018-bus system. Simulation results are demonstrated with comparisons and discussions. [ABSTRACT FROM AUTHOR]

Charging schedules of plug-in electric vehicles (PEVs) coordinated by an aggregating agent may increase system efficiency of allocating generation, transmission and distribution resources. Decentralized self-scheduling and local charging control appear to be preferred by vehicle manufacturers and PEV drivers who are simultaneously concerned about the longevity and reliability of their energy storage systems. In such a setting, the aggregator would have to determine energy retail prices as means to indirect load control. This paper proposes a mathematical program with equilibrium constraints optimizing the aggregator’s decisions. It endogenously determines the profit-optimal price level subject to the cost minimizing charging schedule of the final customers, who are reacting to a combination of retail price signals and distribution use-of-system network charges. This active response follows an affine demand-price relationship, which is individually parametrized for each vehicle by local information of vehicle characteristics and mobility pattern. The proposed program is applied to two cases: 1) a small case study with 3 vehicles, which highlights the model functionality with detailed hourly information per vehicle; 2) a large-scale fleet of 1000 vehicles provides insights on computational burden. Numerical results indicate that adequate competition in the retail market is necessary to limit the aggregator’s monopolistic profitability. Finally, sensitivity runs show dependency on the individual’s willingness to pay, the cost of alternative fueling opportunities and minimum state-of-charge requirements. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method to optimally set the tap position of voltage regulation transformers in distribution systems. We cast the problem as a rank-constrained semidefinite program (SDP), in which the transformer tap ratios are captured by 1) introducing a secondary-side “virtual” bus per transformer, and 2) constraining the values that these virtual bus voltages can take according to the limits on the tap positions. Then, by relaxing the non-convex rank-1 constraint in the rank-constrained SDP formulation, one obtains a convex SDP problem. The tap positions are determined as the ratio between the primary-side bus voltage and the secondary-side virtual bus voltage that result from the optimal solution of the relaxed SDP, and then rounded to the nearest discrete tap values. To efficiently solve the relaxed SDP, we propose a distributed algorithm based on the alternating direction method of multipliers (ADMM). We present several case studies with single- and three-phase distribution systems to demonstrate the effectiveness of the distributed ADMM-based algorithm, and compare its results with centralized solution methods. [ABSTRACT FROM AUTHOR]

An optimal supply and demand bidding, scheduling, and deployment design framework is proposed for battery systems. It takes into account various design factors such as the day-ahead and real-time market prices and their statistical dependency, as well as the location, size, efficiency, lifetime, and charge and discharge rates of the batteries. Utilizing second-life/used batteries is also considered. Without loss of generality, our focus is on the California Independent System Operator (ISO) energy market and its two available bidding options, namely self-schedule bidding and economic bidding. While the formulated stochastic optimization problems are originally nonlinear and difficult to solve, we propose a methodology to decompose them into inner and outer subproblems. Accordingly, we find the global optimal solutions within a short amount of computational time. All case studies in this paper are based on real market data. [ABSTRACT FROM AUTHOR]

Spatially distributed energy storage devices can provide additional flexibility to system operators, which is needed to transition from primarily fossil fuel based electricity generation to variable renewable generation. Aggregators in charge of controlling distributed energy storage can take advantage of existing economic incentives for more flexibility. However, controlling large numbers of energy storage devices with individual constraints in accordance with the strict rules of existing energy and reserve markets is challenging. The purpose of this paper is to investigate the design and performance of a system that enables aggregators to bring large numbers of dedicated and fully controllable energy storage devices to multiple markets concurrently. In particular, we propose algorithms and heuristic optimization methods that allow aggregators to control such energy resources in accordance with arbitrary market rules and participation strategies. Our evaluation is based on a realistic dual market (reserve and intra-day energy) use case. We find that effective market-conform control of large numbers of energy storage devices using the proposed algorithms is feasible, even on short time scales. Furthermore, our results also indicate that the scalability of the proposed system design can be further improved via parallelization without limiting the reserve/energy brought to market. [ABSTRACT FROM AUTHOR]

This paper proposes a novel comprehensive operation and self-healing strategy for a distribution system with both dispatchable and nondispatchable distributed generators (DGs). In the normal operation mode, the control objective of the system is to minimize the operation costs and maximize the revenues. A rolling-horizon optimization method is used to schedule the outputs of dispatchable DGs based on forecasts. In the self-healing mode, the on-outage portion of the distribution system will be optimally sectionalized into networked self-supplied microgrids (MGs) so as to provide reliable power supply to the maximum loads continuously. The outputs of the dispatchable DGs will be rescheduled accordingly too. In order to take into account the uncertainties of DG outputs and load consumptions, we formulate the problems as a stochastic program. A scenario reduction method is applied to achieve a tradeoff between the accuracy of the solution and the computational burden. A modified IEEE 123-node distribution system is used as a test system. The results of case studies demonstrate the effectiveness of the proposed methodology. [ABSTRACT FROM PUBLISHER]

This paper proposes a new transmission-constrained unit commitment method that combines the cost-efficient but computationally demanding stochastic optimization and the expensive but tractable interval optimization techniques to manage uncertainty on the expected net load. The proposed hybrid unit commitment approach applies the stochastic formulation to the initial operating hours of the optimization horizon, during which the wind forecasts are more accurate, and then switches to the interval formulation for the remaining hours. The switching time is optimized to balance the cost of unhedged uncertainty from the stochastic unit commitment against the cost of the security premium of the interval unit commitment formulation. These hybrid, stochastic, and interval formulations are compared using Monte Carlo simulations on a modified 24-bus IEEE Reliability Test System. The results demonstrate that the proposed unit commitment formulation results in the least expensive day-ahead schedule among all formulations and can be solved in the same amount of time as a full stochastic unit commitment. However, if the range of the switching time is reduced, the hybrid formulation in the parallel computing implementation outperforms the stochastic formulation in terms of computing time. [ABSTRACT FROM PUBLISHER]