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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 jointly addresses two major challenges in power system operations: 1) dealing with non-convexity in the power flow equations, and 2) systematically capturing uncertainty in renewable power availability and in active and reactive power consumption at load buses. To overcome these challenges, this paper proposes a two-stage adaptive robust optimization model for the multi-period AC optimal power flow problem (AC-OPF) with detailed modeling considerations, such as reactive capability curves of conventional and renewable generators and transmission constraints. This paper then applies strong second-order cone programming (SOCP)-based convex relaxations of AC-OPF combined with the use of an alternating direction method to identify worst-case uncertainty realizations, and also presents a speed-up technique based on screening transmission line constraints. Extensive computational experiments show that the solution method is efficient and that the robust AC OPF model has significant advantages both from the economic and reliability standpoints as compared to a deterministic AC-OPF model. [ABSTRACT FROM PUBLISHER]

Linear droop control is a standard approach for the decentralized operation of AC microgrids. While the traditional design of the real and reactive power droop functions does not consider economic aspects, recent approaches present modifications to enable least-cost operation. This paper proposes mixed-integer conic programming (MICP) for computing the real and reactive power droop parameters from a stochastic optimization framework that captures several snapshots of the microgrid’s operation. The model permits distributed generation to switch between grid-forming and grid-feeding modes. Unlike previous works, MICP provides droop parameters that are globally optimal for the design scenarios. Numerical results show that using traditional linear cost-based droop design methods may result in voltage magnitude violations. In contrast, the proposed method gives a solution free of violations and is yet more economical. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm to be implemented in a distribution management system (DMS) that is capable of managing an active distribution network (ADN). This goal is achieved by minimizing the cost of system operation, which is expressed in terms of cost of energy losses, cost of curtailed energy, cost of reactive support, and cost of shed energy. Furthermore, the exploitation of network reconfiguration in ADNs is investigated. This paper shows that the coordination of flexible network topology with the continuous active management of energy resources allows improving the efficiency of power delivery. The proposed DMS algorithm allows reducing the risk of energy loss rise, caused by the bigger generation capacity and the deferment of network upgrade that may be a follow-up of ADNs. The proposed method has been applied on a test network to verify the validity of the approach. [ABSTRACT FROM AUTHOR]

The work reported in this paper aims at developing an algorithm for identifying the worst contingencies to be used in a security-constrained optimal power flow problem. A bilevel max-min optimization model is proposed to find the worst contingency scenario while solving an ac optimal power flow problem and considering corrective actions. The objective is to minimize the total cost including generation and load shedding cost while satisfying all relevant constraints. The upper-level problem allows representing contingencies using binary variables. We formulate a second-order cone problem in the lower-level to represent the ac power flow equations. Duality is used to merge the upper- and lower-level problems into a single-level one. The resulting mixed-integer second-order conic problem can be efficiently solved. Three case studies are presented as applications of this novel technique. [ABSTRACT FROM AUTHOR]

Chance constrained optimal power flow (OPF) has been recognized as a promising framework to manage the risk from variable renewable energy (VRE). In the presence of VRE uncertainties, this paper discusses a distributionally robust chance constrained approximate ac-OPF. The power flow model employed in the proposed OPF formulation combines an exact ac power flow model at the nominal operation point and an approximate linear power flow model to reflect the system response under uncertainties. The ambiguity set employed in the distributionally robust formulation is the Wasserstein ball centered at the empirical distribution. The proposed OPF model minimizes the expectation of the quadratic cost function w.r.t. the worst-case probability distribution and guarantees the chance constraints satisfied for any distribution in the ambiguity set. The whole method is data-driven in the sense that the ambiguity set is constructed from historical data without any presumption on the type of the probability distribution, and more data leads to smaller ambiguity set and less conservative strategy. Moreover, special problem structures of the proposed problem formulation are exploited to develop an efficient and scalable solution approach. Case studies are carried out on the IEEE 14 and 118 bus systems to show the accuracy and necessity of the approximate ac model and the attractive features of the distributionally robust optimization approach compared with other methods to deal with uncertainties. [ABSTRACT FROM AUTHOR]

With the large-scale integration of distributed generators (DGs), the coupling relations between transmission network (TN) and distribution networks (DNs) are getting closer. Coordinating the black-start processes of TN and DNs is beneficial to improving restoration efficiency. Therefore, a distributed black-start optimization method for global transmission and distribution (T&D) network is proposed in this paper. Firstly, a black-start optimization model of global T&D network is established to minimize the outage costs. Then, it is decomposed into the TN black-start optimization sub-problem and several DN black-start optimization sub-problems based on the analytical target cascading (ATC). The mixed integer quadratic programming (MIQP) is used for sub-problem modeling. The models take into account the restoration operations of different grid components at each black-start time step. The transmission control center (TCC) and distribution control centers (DCCs) only need to exchange partial information including the boundary power at each time step for distributed coordination, to obtain the coordinated black-start scheme for T&D network. Finally, the effectiveness of the proposed model and method is validated using a global T&D network case. [ABSTRACT FROM AUTHOR]

Modern mixed-integer quadratic solvers generally handle binary variables more efficiently than nonlinear mixed-integer solvers. This is relevant to the power system operation models as the unit commitment formulations typically contain a large number of binary variables. This paper investigates how to achieve the accuracy level close to the one of the exact nonlinear models, but by utilising convex models and solvers. The presented unit commitment model is based on a Taylor-series expansion where both the voltage magnitude and angle are quadratically constrained. To achieve high accuracy, the model takes advantage of the meshed transmission network structure that enables replacement of the quadratic inequality constraints that cause constraint relaxation errors with the linear equality constraints. Quadratic constraints to be replaced as well as the operating point parameters are determined based on the presolve. The first presented case study validates the model's accuracy and the convergence of the iterative algorithm, while the second is a non-iterative full unit commitment problem. Unit commitment results show superior accuracy and similar computation times to the existing quadratic formulations on one hand and faster computation times than the exact nonlinear polar formulation on the other. [ABSTRACT FROM AUTHOR]

Within an alternating current (AC) optimal power flow (OPF) market clearing framework, market-settlement surplus (MS) is inevitable due to network losses, congestion, and reactive power. For a general AC-OPF model, decomposition of MS into its constituents is a challenge. Therefore, this paper proposes a solution for decomposing MS into its constituents, i.e., network losses, congestion, and reactive support services, by deriving analytical expressions for each of the components. An optimization problem, named pseudo-IV-OPF, is set up around the existing AC-OPF solution to derive expressions. The central idea involved in current and voltage OPF, that the current flow at sending end is exactly equal and opposite at receiving end, is exploited to derive the elements of MS by using Karush–Kuhn–Tucker conditions of optimality. It is important to note that a converged OPF solution, obtained from the standard AC-OPF model used by the utility, is an input to the proposed model. The efficacy of the proposed expressions is illustrated on various benchmark systems. [ABSTRACT FROM AUTHOR]

Renewable generation and energy storage are playing an ever increasing role in power systems. Hence, there is a growing need for integrating these resources into the optimal power flow (OPF) problem. While storage devices are important for mitigating renewable variability, they introduce temporal coupling in the OPF constraints, resulting in a multiperiod OPF formulation. This paper explores a solution method for multiperiod AC OPF that combines a successive quadratic programming approach (AC-QP) with a second-order cone programming (SOCP) relaxation of the OPF problem. The SOCP relaxation's solution is used to initialize the AC-QP OPF algorithm. Additionally, the lower bound on the objective value obtained from the SOCP relaxation provides a measure of solution quality. This combined method is demonstrated on several test cases with up to 4259 nodes and a time horizon of eight time steps. A comparison of initialization schemes indicates that the SOCP-based approach offers improved convergence rate, execution time, and solution quality. [ABSTRACT FROM PUBLISHER]

This paper applies recently developed mixed-integer programming (MIP) tools to the problem of optimal siting and sizing of distributed generators in a distribution network. We investigate the merits of three MIP approaches for finding good installation plans: a full AC power flow approach, a linear DC power flow approximation, and a nonlinear DC power flow approximation with quadratic loss terms, each augmented with integer generator placement variables. A genetic algorithm-based approach serves as a baseline for the comparison. A simple knapsack problem method involving generator selection is presented for determining lower bounds on the optimal design objective. Solution methods are outlined, and computational results show that the MIP methods, while lacking the speed of the genetic algorithm, can find improved solutions within conservative time requirements and provide useful information on optimality. [ABSTRACT FROM AUTHOR]

The existence of locally optimal solutions to the AC optimal power flow problem (OPF) has been a question of interest for decades. This paper presents examples of local optima on a variety of test networks including modified versions of common networks. We show that local optima can occur because the feasible region is disconnected and/or because of nonlinearities in the constraints. Standard local optimization techniques are shown to converge to these local optima. The voltage bounds of all the examples in this paper are between \pm5% and \pm10% off-nominal. The examples with local optima are available in an online archive (http://www.maths.ed.ac.uk/optenergy/LocalOpt/) and can be used to test local or global optimization techniques for OPF. Finally we use our test examples to illustrate the behavior of a recent semi-definite programming approach that aims to find the global solution of OPF. [ABSTRACT FROM PUBLISHER]

A semidefinite programming (SDP) relaxation globally solves many optimal power flow (OPF) problems. For other OPF problems where the SDP relaxation only provides a lower bound on the objective value rather than the globally optimal decision variables, recent literature has proposed a penalization approach to find feasible points that are often nearly globally optimal. A disadvantage of this penalization approach is the need to specify penalty parameters. This paper presents an alternative approach that algorithmically determines a penalization appropriate for many OPF problems. The proposed approach constrains the generation cost to be close to the lower bound from the SDP relaxation. The objective function is specified using iteratively determined weights for a Laplacian matrix. This approach yields feasible points to the OPF problem that are guaranteed to have objective values near the global optimum due to the constraint on generation cost. The proposed approach is demonstrated on both small OPF problems and a variety of large test cases representing portions of European power systems. [ABSTRACT FROM AUTHOR]

Smart energy management system (SEMS) is a core part of a smart grid system, which can make this system more intelligent. The final goal of SEMS is to lay a groundwork which would allow efficient management of the smart grid by minimizing the operating costs and by reducing the emission level while meeting the load demand. In this paper, a new technique called as the jump and shift method is developed to handle the multi-objective optimization in SEMS. A 14-bus microgrid (MG) and a 112-bus power system are used to verify the multi-objective optimization algorithm based on the jump and shift method. The results show that the proposed technique performs very well, and it can be used to solve the multi-objective optimization in SEMS for smart grids. [ABSTRACT FROM AUTHOR]

This paper proposes an innovative system for Smart Grid (SG) management aiming at minimizing the total costs supported for carrying out the delivery of energy to consumers. These costs include the production costs of distributed generators, the cost of the power provided by the primary substation, and the cost associated with grid power losses. After a brief overview on the main SG aspects, this paper describes the proposed approach that makes use of an optimal power flow algorithm and the active management schemes. The efficiency of the method is verified on a distribution system comprising wind turbines and diesel generators, considering the time-varying characteristics of the load demand and wind power generation. [ABSTRACT FROM AUTHOR]

Reserve services are an essential part of a standard market design and are under development in major electricity markets. This paper presents the development of differential evolution algorithm for optimal allocation of energy and spinning reserve. The optimization is performed in an integrated market with biddable spinning reserve and sectional price offer curves while considering all security and power systems constraints in steady state and system credible contingencies. The effectiveness of the proposed method is examined by application of the proposed algorithm on the IEEE 30-bus test system. Some comparisons are made with analytical and evolutionary methods in various cases. [ABSTRACT FROM PUBLISHER]

This paper proposes a new decentralized restoration scheme in order to realize efficient coordinated restoration of the coupled transmission and distribution (TS-DS) system. First, considering the separated operation of the TS operator (TSO) and DS operators (DSOs) and to avoid the TSO data processing burden, the TS-DS system is divided into several subsystems according to their physical connection. Then, in order to implement the independent but coordinated decision-making of the subsystems, a decentralized decision-making framework is constructed by model decoupling and iterative interaction between TS and DS. Furthermore, for the sake of the convergence of the iterative process with non-convex models, a new decentralized optimization method is developed to obtain the optimal coordinated restoration strategy of the TS-DS system. The proposed decentralized restoration scheme achieves independent decision-making of the TSO and DSOs in the coupled TS-DS system, and solves the non-convergence problem of the decentralized optimization method. The effectiveness of the proposed method is validated using two IEEE standard test systems and a real-world power system. [ABSTRACT FROM AUTHOR]

Isolated microgrid power systems are prone to large frequency and voltage deviations, since they have limited generation and finite inertia and may include pulse power loads and large proportion of dynamic loads. Thus, they require effective power management methods to operate optimally, while satisfying operating and security constraints. In this paper, a novel integrated security-constrained model-based power management approach is proposed for isolated microgrids in all-electric ships during the normal/alert operating state. The new power management method was formulated as a multi-objective optimal control problem. A method based on the Nondominated Sorting Genetic Algorithm II was developed to solve the problem. The developed integrated security-constrained power management approach was applied to a notional all-electric ship computer model. The simulation results, conducted in PSCAD, showed the effectiveness of the new power management method. [ABSTRACT FROM PUBLISHER]

In this paper, we formulate and solve the ac optimal power flow (AC-OPF) as an equivalent circuit problem in terms of current, voltage, and admittance state variables. The generator models are represented using conductance and susceptance state variables, and the operational and network constraints are translated to corresponding current/voltage constraints without loss of accuracy or generality. To understand the physics behind the optimality conditions of the optimization problem, we extend the linear adjoint circuit theory to translate them to equivalent circuit domain. It is shown that the operating point that defines the equivalent circuit solution precisely represents an AC-OPF solution. We then further exploit the equivalent circuit representation to use power flow simulation techniques to robustly solve the optimization problem. The efficiency of our approach is demonstrated for several AC-OPF benchmark test cases (up to 70 k buses) under nominal and congested operating conditions, and the runtime and scalability properties are presented. [ABSTRACT FROM AUTHOR]

In this paper, we establish a mathematical model of the multi-objective reactive power optimization (MORPO) problem in an ac–dc hybrid power system. To get an evenly distributed set of Pareto solutions of this MORPO problem throughout a whole day, we propose a piecewise normalized normal constraint (PNNC) method. Based on this method, the Pareto frontier is divided into four arcs so that the fluctuation of angle between the tangent line at each Pareto point and its sub-Utopia line is reduced. By doing so, the original MORPO problem is transformed into four sets of single objective optimization problems, which can be solved efficiently by a nonlinear primal-dual interior-point method. Performance of the PNNC method is tested on a real ac–dc interconnection system. The results demonstrate that it has the capability to generate a more evenly distributed set of Pareto solutions when compared with the normalized normal constraint (NNC) and weighted sum (WS) methods. In addition, a fuzzy-based membership value assignment method is employed to derive 96 optimal compromise solutions corresponding to 96 time periods in a whole day; the numerical outcomes show that a saving in active power loss and an improvement in the voltage profile can be gained simultaneously. [ABSTRACT FROM PUBLISHER]

This paper presents an efficient and fast-converging optimization technique based on a modification of the traditional big bang-big crunch method for optimal placement and sizing of voltage controlled distributed generators. The proposed algorithm deals with the optimization problems incorporating multiple distributed generators for the sake of power as well as energy loss minimization in balanced/unbalanced distribution systems. The proposed algorithm is implemented in MATLAB environment and tested on the 33-bus feeder system and the IEEE 37-node feeder. Validation of the proposed method is done via comparing the results with published results obtained from other competitive methods. [ABSTRACT FROM PUBLISHER]

Power system static voltage stability region boundary (SVSRB) is a complicated hypersurface in parameter space. Due to inequality constraints such as generator reactive power limits, different critical points on the SVSRB may be related to different groups of active constraints and can be associated with different types of loadability limit, which makes it difficult to approximate the whole SVSRB at once or assemble many local approximations of the SVSRB. To overcome the difficulty, this paper proposes an approach for globally approximating the whole SVSRB considering generator reactive power limits at one go. First, a parametric optimization model incorporating all inequality constraints is formulated to describe the SVSRB, where the optimal solutions are the critical points on the SVSRB. The optimality condition, i.e., parametric Karush–Kuhn–Tucker conditions (KKT conditions), is also derived. Then, by applying the Galerkin method to the parametric KKT conditions in an interior-point-method-like manner, the whole SVSRB is approximated and represented using a single polynomial expression. Case studies in a 10-bus system and IEEE 300-bus system verify the effectiveness and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proves the practicality of an iterative algorithm for solving realistic large-scale security-constrained optimal power flow (SCOPF) problems. This algorithm is based on the combination of a contingency filtering scheme, used to identify the binding contingencies at the optimum, and a network compression method, used to reduce the complexity of the post-contingency models included in the SCOPF formulation. We show that by combining these two complementary ideas, it is possible to solve in a reasonable time SCOPF problems on large power system models with a large number of contingencies. Unlike most results reported for large-scale SCOPF problems, our algorithm uses a nonlinear AC network model in both pre-contingency and post-contingency states, optimizes both active/reactive powers flows jointly, and treats the discrete variables. The proposed algorithm is implemented with state-of-the-art solvers and applied to two systems: a national grid with 2563 buses and 1297 contingencies, and a model of the European transmission network with 9241 buses and 12\thinspace000 contingencies. [ABSTRACT FROM PUBLISHER]

For large power systems with huge proportions of industrial loads, dynamic var sources (DVSs) such as STATCOMs and generators provide significant protection against short-term voltage instability. Simultaneously optimizing the locations and capacities of STATCOMs and the settings for adjustment coefficients of generator excitation systems is a goal of this paper; thus, we formulate a multi-objective, mixed-integer dynamic optimization (MOMIDO) model subject to short-term voltage security and rotor-angle stability under multiple contingencies. We also present a reduced convex relaxation (RCR) method to handle STATCOM locations (which are integer variables) and to avoid their combinatorial explosion, and convert the MOMIDO model into a multi-objective nonlinear programming problem via Radau collocation. To obtain complete Pareto optimal solutions for the MOMIDO model, we propose a reduced wide normalized normal constraint (RWNNC) method by enlarging the Utopia plane so that the Pareto optimal solutions are covered completely by its vertical projection, while pruning redundant sections on the Utopia plane to reduce the amount of calculations. Moreover, the simulation results on an IEEE standard 39-bus system and a real provincial power system demonstrate that the proposed method can handle integer variables effectively and obtain complete Pareto optimal solutions. [ABSTRACT FROM PUBLISHER]

Power distribution systems are transitioning from a traditional single distribution system operator (DSO) to a more integrated flexible network that incorporates multiple microgrids (MGs). This paper presents a novel stochastic framework to investigate the impact of correlated wind generators on energy management of DSO and MGs. In order to decouple the problem formulation in DSO and MGs, a linear approximation is proposed which enables parallel processing of the optimization problems. Further, a stochastic framework based on improved point estimate method is proposed to model the uncertainties in load and wind generation, and account for the statistical correlations among wind generators. The proposed method is applied to a modified IEEE 69 bus test feeder and the results are validated in terms of efficiency and accuracy. [ABSTRACT FROM PUBLISHER]

This paper presents a novel framework based on range arithmetic for solving power flow problems whose input data are specified within real compact intervals. Reliable interval bounds are computed for the power flow problem, which is represented as an optimization model with complementary constraints to properly represent generator bus voltage controls, including reactive power limits and voltage recovery processes. It is demonstrated that the lower and upper bounds of the power flow solutions can be obtained by solving two determinate optimization problems. Several numerical results are presented and discussed, demonstrating the effectiveness of the proposed methodology and comparing it to a previously proposed affine arithmetic based solution approach. [ABSTRACT FROM PUBLISHER]

This paper presents an optimal power flow function for aiding restoration studies of subsystems having long transmission segments. The method simultaneously computes an optimal set of variables which are critical for the subsystem restoration: the generation power plant high-side voltage, the minimum shunt reactor configuration and the maximum load to be safely energized. A set of overvoltage restoration scenarios following load rejection is constructed in such a way that the computed shunt reactor compensation becomes distributed along the transmission corridor. The whole problem is formulated as a single optimization problem whose solution is obtained by an optimal power flow, based on the Primal-Dual Interior Point Method. The described results for a restoration study on a system from practice confirm the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

This paper presents an optimization procedure that enables the optimal dispatching of distributed generators and storage systems in a medium-voltage islanded microgrid. The network is assumed to be supplied by programmable (dispatchable) and nonprogrammable generators (i.e. nondispatchable, such as renewable energy sources—based units). The optimization goal is to minimize the overall microgrid operating cost and the pollutants emission of the programmable generators, assuming that all of the power made available by the renewable generators (photovoltaic and wind systems) is either directly injected into the network or stored in order to be subsequently delivered according to the proposed storage units' management strategy. The optimization is carried out by a niching evolutionary algorithm (NEA) that is able to find multiple optima and the variation of the objective function in their neighborhood. NEAs allow overcoming the performance of standard algorithms used for optimal power-flow calculations in power systems by avoiding falling into local optima. The optimization procedure is performed on a test microgrid and verified by computer simulations. The numerical results show that the solutions can always improve the microgrid performances irrespective of the network operating conditions in all of the considered cases. [ABSTRACT FROM AUTHOR]

This paper proposes an active-reactive power dispatch procedure that is expressed via a bilevel optimization problem whose upper and lower level criteria are, respectively, the minimum opportunity cost and minimum offered price of active power. It analyzes the impact of minimizing such criteria on system operation, and it investigates the behavior of marginal prices and opportunity costs and their use in mechanisms to compensate generators for power provision. The bilevel problem is solved using a version of interior point methods derived for mathematical programs with complementarity constraints. Results obtained with three test systems are analyzed. [ABSTRACT FROM PUBLISHER]

In this paper, a receding-horizon multi-step optimization is proposed to correct nonviable transmission voltages and prevent long-term voltage instability. The proposed control scheme is based on real-time control, inspired by model predictive control, and steady state power-flow-based equations. In order to anticipate load behavior and avoid using dynamic equations in the control scheme, explicit formulations are used to model evolution of load with time. The simulation results of the proposed technique are presented on the Nordic32 test system. [ABSTRACT FROM PUBLISHER]

This paper deals with some essential open questions in the field of optimal power flow (OPF) computations, namely: the limitation of the number of controls allowed to move, the trade-off between the objective function and the number of controls allowed to move, the computation of the minimum number of control actions needed to satisfy constraints, and the determination of the sequence of control actions to be taken by the system operator in order to achieve its operation goal. To address these questions, we propose approaches which rely on the computation of sensitivities of the objective function and inequality constraints with respect to control actions. We thus determine a subset of controls allowed to move in the OPF, by solving a sensitivity-based mixed integer linear programming (MILP) problem. We study the performances of these approaches on three test systems (of 60, 118, and 618 buses) and by considering three different OPF problems important for a system operator in emergency and/or in normal states, namely the removal of thermal congestions, the removal of bus voltage limits violation, and the reduction of the active power losses. [ABSTRACT FROM PUBLISHER]

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]

Active Network Management is a philosophy for the operation of distribution networks with high penetrations of renewable distributed generation. Technologies such as energy storage and flexible demand are now beginning to be included in Active Network Management (ANM) schemes. Optimizing the operation of these schemes requires consideration of inter-temporal linkages as well as network power flow effects. Network effects are included in optimal power flow (OPF) solutions but this only optimizes for a single point in time. Dynamic optimal power flow (DOPF) is an extension of OPF to cover multiple time periods. This paper reviews the generic formulation of DOPF before developing a framework for modeling energy technologies with inter-temporal characteristics in an ANM context. The framework includes the optimization of nonfirm connected generation, principles of access for nonfirm generators, energy storage, and flexible demand. Two objectives based on maximizing export and revenue are developed and a case study is used to illustrate the technique. Results show that DOPF is able to successfully schedule these energy technologies. DOPF schedules energy storage and flexible demand to reduce generator curtailment significantly in the case study. Finally, the role of DOPF in analyzing ANM schemes is discussed with reference to extending the optimization framework to include other technologies and objectives. [ABSTRACT FROM PUBLISHER]

In power system operation, transmission congestion can drastically limit more economical generation units from being dispatched. In this paper, optimal transmission switching as a congestion management tool is utilized to change network topology which, in turn, would lead to higher electricity market efficiency. Transmission switching (TS) is formulated as an optimization problem to determine the most influential lines as candidates for disconnection. In order to relieve congestion without violating voltage security, TS is embedded in an optimal power flow (OPF) problem with AC constraints and binary variables, i.e., a mixed-integer nonlinear programming (MINLP) problem, solved using Benders decomposition. Also, a methodology is presented which provides a guideline to the system operator showing the order of switching manoeuvres that have to be followed in order to relieve congestion. It is also shown that TS based on DC optimal power flow (DCOPF) formulation as used in the literature may jeopardize system security and in some cases result in voltage collapse due to the shortcomings in its simplified models. In order to evaluate the applicability and effectiveness of the proposed method, the IEEE 57-bus and IEEE 300-bus test systems are used. [ABSTRACT FROM PUBLISHER]

Increasing wind capacity integration results in displacement of active power from conventional generators and a reduction in reactive power sources available. As such, voltage stability may become a concern in certain periods for power system operation particularly in weaker areas of the network. Thus, it is of importance to consider the AC constraints for optimal wind generation planning (long term) in order to decrease the possibility of a wind capacity allocation that requires costly remedies from the power system operation perspective (short term). In this work, a procedure is proposed for wind capacity allocation with the aim of benefiting from the potential of an optimal wind capacity allocation for enhancing the voltage stability margin. The procedure is based on a multi operating conditions voltage stability constrained optimal power flow. The wind capacity target is set and the loadability margin is tracked. The results will show the applicability of the proposed procedure and will emphasize the effects of the pattern of wind capacity allocation on the loadability margin. This will result in a wind capacity allocation that enhances the minimum loadability margin among the possible future operating conditions considered for planning. The procedure uses the Maximin concept for this purpose. [ABSTRACT FROM AUTHOR]

Power system voltage control has traditionally been the responsibility of transmission-connected reactive power resources. Accordingly, high penetration levels of distributed generation present new challenges for reactive power management. Simply stipulating voltage control operation for distributed generators will not generally deliver voltage-responsive reactive power flows at the transmission system level, due mainly to the voltage-isolating effects of tap-changing bulk supply transformers. Additionally, the resistance of distribution system conductors establishes an unhelpful interaction between active power flows and voltage magnitudes. This work uses optimal power flow techniques to explore two ways to overcome these challenges. Most innovatively, a methodology is presented to optimally select static voltage control settings for distributed generators and transformers, such that they will provide an autonomous voltage-responsive behavior without supervisory control systems. In this scheme, distributed generators are exposed to transmission voltage fluctuations as far as is feasible, by blocking the tapping of the bulk supply transformer when operating within an optimally-determined range of transmission voltages. Comparatively, an active control scheme is presented, where reactive power and tap positions are dispatched period-to-period to support the transmission system voltage. Comparing these approaches suggests the level of smart-grids investment required to effectively harness the reactive power available from distributed generation. [ABSTRACT FROM AUTHOR]

Transmission system operators (TSOs) are increasingly requesting frequency support, reactive power compensation, and grid-forming capability to power plants interfaced by power converters. In these plants, a large number of converters is operated in parallel and all of them should be adequately coordinated to provide these services. For that purpose, the virtual synchronous machine (VSM) control technique is commonly adopted. However, the dynamic characteristics of the whole plant depend on the number of converters connected, their size, control parameters, and electrical interconnections. This makes it difficult to know the aggregated dynamic characteristic of the plant and how each VSM contributes to the plant response. In this article, the operation of VSMs in parallel configuration for island and grid-connected applications is studied. The developments make it possible to adapt the VSMs parameters so that the grid sees the power plant as an equivalent generator whose low-frequency characteristics do not vary with the number of converters in operation. The developments were validated in a laboratory consisting of four 15 kVA converters operating as VSMs, and a grid emulator. [ABSTRACT FROM AUTHOR]

With the introduction of high voltage direct current (HVDC)-system, especially the voltage source converter (VSC)-based implementation, new degrees of freedom have been made accessible for system operation and for ensuring system security where they can be utilized either in the form of preventive or curative actions. This work presents an optimization model meant to determine a set of preventive and curative relief measures. Thereby, both methods are not calculated in a successive approach, but the optimization of the curative actions is nested into the preventive optimization. By doing so, a feedback can be given in cases the preventive optimization is evolving in regions where no feasible curative actions can be provided. A numerical case study is conducted, where the calculation of the curative set-points is performed with a linearized power flow model. Thereby, an effect is shown, where preventive insecure contingencies appear as curative feasible as the linearized model does not show any violated constraints. [ABSTRACT FROM AUTHOR]

The optimal reactive power dispatch (ORPD) problem is an alternating current optimal power flow (ACOPF) problem where discrete control devices for regulating the reactive power, such as shunt elements and tap changers, are considered. The ORPD problem is modeled as a mixed-integer nonlinear optimization problem and its complexity is increased compared to the ACOPF problem, which is highly nonconvex and generally hard to solve. Recently, convex relaxations of the ACOPF problem have attracted a significant interest since they can lead to global optimality. We propose a tight conic relaxation of the ORPD problem and show that a round-off technique applied with this relaxation leads to near-global optimal solutions with very small guaranteed optimality gaps, unlike with the nonconvex continuous relaxation. We report computational results on selected MATPOWER test cases with up to 3375 buses. [ABSTRACT FROM AUTHOR]

Distributed or multi-area optimal power flow (OPF) in alternating current (AC) grids is currently a subject undergoing intense study to cope with computational burdens in large-scale grids and to maintain self-control of a regional system operator. However, future power grids will most likely be hybrid grids consisting of the conventional AC transmission system combined with high voltage direct current (DC) technology. Thus, we reformulate the full AC–DC OPF problem such that it becomes separable and, therefore, accessible to distributed algorithms. Then, we show in detail two different approaches on the decomposition of a hybrid AC–DC grid. Finally, we implement an improved alternating direction of multipliers method (ADMM) as well as the most recently proposed augmented Lagrangian based alternating direction inexact Newton (ALADIN) method. Simulation results show that optimality gaps below 0.01% are reached with both decomposition approaches and algorithms for two different test systems (5-bus and 66-bus). Furthermore, convergence rates and wall clock times are reduced by around one order of magnitude from ADMM to ALADIN. [ABSTRACT FROM AUTHOR]

We propose a novel global solution algorithm for the network-constrained unit commitment problem that incorporates a nonlinear alternating current (ac) model of the transmission network, which is a nonconvex mixed-integer nonlinear programming problem. Our algorithm is based on the multi-tree global optimization methodology, which iterates between a mixed-integer lower-bounding problem and a nonlinear upper-bounding problem. We exploit the mathematical structure of the unit commitment problem with ac power flow constraints and leverage second-order cone relaxations, piecewise outer approximations, and optimization-based bounds tightening to provide a globally optimal solution at convergence. Numerical results on four benchmark problems illustrate the effectiveness of our algorithm, both in terms of convergence rate and solution quality. [ABSTRACT FROM AUTHOR]

Equipment failures, operator errors, natural disasters and cyber-attacks can and have caused extended blackouts of the electric grid. Even though such events are rare, preparedness for them is critical because extended power outages endanger human lives, compromise national security, or result in economic losses of billions of dollars. Since most of the generating units cannot restart without connecting to an energized grid, the system operator relies on a few units with the ability to start autonomously, called Black Start (BS) units, to restore the power system. Allocating and maintaining these units is costly and can severely impact the restoration security and time. We formulate an optimization problem to optimally allocate BS units in the grid, while simultaneously optimizing over the restoration sequence. We extend existing optimal allocation models by including grid considerations such as active power nodal balance, transmission switching, nodal reactive power support and voltage limits. In order to aid the branch and bound tree that solves the resulting large scale mixed integer program, we propose a randomized heuristic that is executed multiple times in parallel on a high-performance computing environment to find feasible solutions. We proceed to solve the IEEE-39, the IEEE-118, and a simplified WECC system with 225 nodes and 136 generators to near optimality. [ABSTRACT FROM AUTHOR]

The ubiquity of synchronous generation should not be assumed in highly renewable power systems. Various problems may consequently arise, not least of which are the difficulties entailed in maintaining regional reactive power balance. Offering a potential solution to such problems, modern renewable generator technologies offer controllable reactive power resources. As many of these generators will be embedded in distribution networks, their incorporation into transmission system operational and planning activities appears challenging. An extension of the capability chart concept offers insight here: for a given active power exchange between the transmission system and a distribution network section, the range of controllable reactive power typically available is of interest. This aggregate capability depends on the innate machine capabilities of the distributed generators and on the prevailing conditions within the distribution network. Novel optimisation techniques are useful in addressing the latter point, offering a means to identify the combination of power flow profiles within the distribution system most restrictive to reactive power provision. The capability chart thus derived gives the dependable range of reactive power available, under the assumption that each generator is operated to locally maximize its own reactive power contribution. Such a description can be applied in transmission system planning or to quantify the effects of modifications to the distribution system. [ABSTRACT FROM PUBLISHER]

For the nonlinear power flow problem specified with standard PQ, PV, and slack bus equality constraints, we present a sufficient condition under which the specified set of nonlinear algebraic equations has no solution. This sufficient condition is constructed in a framework of an associated feasible, convex optimization problem. The objective employed in this optimization problem yields a measure of distance (in a parameter set) to the power flow solution boundary. In practical terms, this distance is closely related to quantities that previous authors have proposed as voltage stability margins. A typical margin is expressed in terms of the parameters of system loading (injected powers); here we additionally introduce a new margin in terms of the parameters of regulated bus voltages. [ABSTRACT FROM PUBLISHER]

This letter proposes a methodology for finding the equilibrium point of a microgrid operating in a wide range of loading levels, which includes the possible exhaustion of the power reserve of some of the generating units. The search of the equilibrium would require the use of two different models when using Newton-Raphson-like methods. It is shown herein that the problem can be reformulated instead within the nonlinear constrained minimization framework by employing a complementarity condition. [ABSTRACT FROM PUBLISHER]