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Time-of-use (TOU) is an effective price-based demand response strategy. A reasonable design of TOU strategy can effectively reduce the peak-valley difference, and then produce a lot of benefits (such as delaying power grid investment, reducing interruption cost, and improving reliability). However, changing peak-valley period has a great influence on the peak-valley difference and power supply reliability of power system. Therefore, this paper aims to investigate the optimal modification of peak-valley period considering reliability loss under multiple TOU schemes. Firstly, this paper presents a clustering model and algorithm of optimal load curve based on a minimum error iteration method. Secondly, an optimal modification of peak-valley period based on a dynamic load point method is proposed, and the traditional peak-valley difference is replaced by the global peak-valley difference to calculate the objective function. Thirdly, this paper establishes a load–reliability relation fitting model based on the back propagation neural network. Finally, the effectiveness and correctness of the proposed method are investigated by the Roy Billinton test system and reliability test system. [ABSTRACT FROM AUTHOR]

In interconnected power systems, operated by several system operators, the participating areas are strongly dependent on their neighbors. In order to identify the economically efficient generation dispatch in each area, a distributed multi-area optimal power flow (OPF) must be solved. Additionally, installation of an increasing number of HVDC lines to deal with increased power flows from renewable generation is expected to change the power system operation paradigm. The controllability introduced by the HVDC lines should be considered and incorporated in the OPF algorithm. In this paper we introduce a formulation for the distributed solution of the OPF problem in multi-area systems consisting of both HVAC and HVDC lines. We show the applicability of this formulation on two different operating schemes for HVDC grids and we compare their performance with a central solution for the mixed HVAC/HVDC grid. The proposed formulations are based on a linearized solution of the OPF problem. The only data to be exchanged between the areas pertains to the border nodes. [ABSTRACT FROM AUTHOR]

This paper is concerned with a fuzzy analysis of power-flow (PF) involving uncertainties of load demands and network parameters. The crux of this paper is to propose an advanced fuzzy arithmetic. Fuzzy transformation method merges with backward–forward sweep in order to evaluate the contribution and propagation of uncertainty in IEEE 33-bus and 69-bus distribution systems. Results are validated by true intervals and random ranges. To determine true intervals, Global Optimization Problems (GOPs) are defined and solved through derivative-based and free techniques. To estimate random ranges, Monte-Carlo Simulations (MCSs) are employed. Our findings confirm that the sharpness of fuzzy intervals, tractability of computations, and applicability of possibility distributions. Following scenario-based evaluations, this paper discusses new implications of power losses, voltage profiles, optimal re-configuration, feeder extension, and reactive power compensation so that results would be beneficial to system planners and operators. Altogether, this paper provides a blueprint for a new way to handle uncertainties in a wide variety of power system problems without global optimization, linearization, and randomized simulations. [ABSTRACT FROM AUTHOR]

Following Part I of this paper that reveals two distinct interpretations of demand curves and the corresponding different forms of the market clearing formulation, Part II of this paper analyzes the sequential and the iterative market clearing algorithms currently implemented in some markets. It is shown that these algorithms lead to socially sub-optimal solutions. The root cause of the problem is the lack of a clear representation of the demand benefit. The social surplus optimization based on the proper interpretation of demand curves is then proposed. A small numerical example is used to demonstrate the significant optimality gap between the socially optimal solution and the sequential/iterative solution. The potentially large impacts of the gap on the societal benefit and the individual resource revenues entail a close examination of these algorithms. [ABSTRACT FROM AUTHOR]

The dawn of quantum computing brings on a revolution in the way combinatorially complex power system problems such as Unit Commitment are solved. The Unit Commitment problem complexity is expected to increase in the future because of the trend toward the increase of penetration of intermittent renewables. Even though quantum computing has proven effective for solving a host of problems, its applications for power systems’ problems have been rather limited. In this paper, a quantum unit commitment is innovatively formulated and the quantum version of the decomposition and coordination alternate direction method of multipliers (ADMM) is established. The above is achieved by devising quantum algorithms and by exploiting the superposition and entanglement of quantum bits (qubits) for solving subproblems, which are then coordinated through ADMM to obtain feasible solutions. The main contributions of this paper include: 1) the innovative development of a quantum model for Unit Commitment; 2) development of decomposition and coordination-supported framework which paves the way for the utilization of limited quantum resources to potentially solve the large-scale discrete optimization problems; 3) devising the novel quantum distributed unit commitment (QDUC) to solve the problem in a larger scale than currently available quantum computers are capable of solving. The QDUC results are compared with those from its classical counterpart, which validate the efficacy of quantum computing. [ABSTRACT FROM AUTHOR]

This paper investigates the potential contribution that interconnectors can provide to efficiently support the security of interconnected power systems. The proposed modelling setup introduces a radical paradigm shift in the operation of the interconnectors and in their interactions with multiple markets. To the best of our knowledge, this is the first paper that models a simultaneous allocation of the interconnector capacity for the exchange of energy and of inertia-dependent primary frequency response. The benefits and impact of this new methodology are evaluated with typical market indicators (e.g., social welfare and interconnector revenues) under two different paradigms: a centralized approach where the interconnectors are operated to minimize the system operational cost and a market-based framework where the interconnectors are privately-owned assets with self-interested objectives. By modelling the interconnectors as “price-maker”, the proposed work quantifies the potential inefficiencies of market solutions while considering key elements such as capacity withdrawing. A case study of the GB-France systems assesses the value of interconnectors on system efficiency and security under the considered paradigms. [ABSTRACT FROM AUTHOR]

This paper proposes an optimization approach for day-ahead reactive power planning to improve voltage security in transmission networks. The problem is formulated as a voltage-secure multi-period optimal reactive power dispatch (MP-ORPD) problem. The optimization approach searches for optimal set-points of dynamic and static reactive power (var) resources. Specifically, the output includes set-points for switching shunts, transformer taps, and voltage magnitudes at the regulated buses. The primary goal is to maximize the dynamic reactive power reserve of the system, by minimizing the reactive power supplied by synchronous generators. As the size of the MP-ORPD problem increases significantly with increasing number of contingencies and time periods, efficiency is crucial for practical applications. In this paper, a decomposition technique based on consensus and alternating optimization, where integer variable targets are obtained via MILP, is used to partition the MP-ORPD problem into a set of subproblems, which can be solved in parallel to reduce the computation time. The proposed MP-ORPD problem and its solution algorithm are integrated into the EPRI-VCA software. The results of various power networks of large electric utilities in the Eastern interconnection demonstrate the effectiveness of the proposed algorithm in providing preventive control schedules. [ABSTRACT FROM AUTHOR]

Volt-VAR optimization (VVO) has been investigated extensively in power systems. However, under the era of integrated energy systems (IES), the growing interdependencies between different energy systems complicate traditional VVO. This is further hardened by incurred gas quality problems due to the hydrogen injection in IES, produced by widely applied power-to-gas (P2G) facilitates that couple between power and gas systems. This paper develops a two-stage volt-VAR-pressure optimization (VVPO) model for PV-penetrated IES to manage the variation of system voltages while managing gas quality indices. In addition to the traditional voltage regulating devices, P2G facilities, which can mitigate fluctuating PV output via converting the surplus generation into hydrogen, are also used for voltage management. A two-stage distributionally robust optimization (DRO) based on moment information is utilized to model PV uncertainty. A semidefinite programming model is formulated and finally solved by the constraint generation algorithm. A 33-bus-20-node IES is used to verify the effectiveness of the proposed VVPO on voltage management, ensured gas quality with high economic efficiency. The proposed VVPO is applicable to injecting other green gases into gas systems while ensuring power quality and enable system operators to provide low-cost but high-quality multi-energy to customers. [ABSTRACT FROM AUTHOR]

In this paper, we investigate whether and under which conditions jointly owning a variable renewable source of electricity (VRES) and an electricity storage generates economies of scope in competitive electricity markets. Using a simple stochastic optimization model that assumes frictionless markets, we analytically show that no economic benefit arises from combining the two assets. This finding is in contradiction to large parts of the literature, which claim that it is in the economic interest of owners of VRES to additionally own electricity storage. We also identify circumstances where our argument does not hold and the combination of storage and VRES could theoretically make economic sense on the level of individual agents. In the last part of the paper, we demonstrate in a numerical case study of the German market that even in cases where our theoretical results do not hold, tying together storage and VRES may produce suboptimal results. [ABSTRACT FROM AUTHOR]

This paper addresses the transmission network expansion planning problem under uncertain demand and generation capacity. A two-stage adaptive robust optimization framework is adopted whereby the worst-case operating cost is accounted for under a given user-defined uncertainty set. This paper differs from previously reported robust solutions in two respects. First, the typically disregarded correlation of uncertainty sources is explicitly considered through an ellipsoidal uncertainty set relying on their variance-covariance matrix. In addition, we describe the analogy between the corresponding second-stage problem and a certain class of mathematical programs arising in structural reliability. This analogy gives rise to a relevant probabilistic interpretation of the second stage, thereby revealing an undisclosed feature of the worst-case setting characterizing robust optimization with ellipsoidal uncertainty sets. More importantly, a novel nested decomposition approach based on results from structural reliability is devised to solve the proposed robust counterpart, which is cast as an instance of mixed-integer trilevel programming. Numerical results from several case studies demonstrate that the effect of correlated uncertainty can be captured by the proposed robust approach. [ABSTRACT FROM AUTHOR]

In the absence of demand-side bids for certain reliability products in the wholesale electricity markets, Independent System Operators (ISOs) traditionally use fixed demand requirements with penalty factors to clear the market. This approach does not allow proper tradeoffs between cost and reliability due to the inelasticity of the fixed requirements. Therefore, ISOs have been replacing the fixed requirements with sloped demand curves. However, the economic interpretation of demand curves, especially for multiple coupled products, is largely missing in both theory and practice. This could lead to the misrepresentation of the demand benefit in the market clearing objective. Using a two-product market model, Part I of this paper reveals two distinct interpretations of demand curves, each associated with a specific form of the market clearing problem. This implies that the construction of demand curves and the use of them in market clearing must be consistent with their economic interpretation. In Part II of this paper, we analyze the sequential and iterative market clearing processes currently implemented in some markets to demonstrate their solution sub-optimality. The root cause of the problem is the lack of a clear representation of the demand benefit. The social surplus optimization based on the proper interpretation of demand curves is proposed. [ABSTRACT FROM AUTHOR]

Renewables, such as solar and wind generation, combined with storage are becoming a key part of modern grid. This paper develops probabilistic tools for analysis of grid reliability with such variable generation resources. The developed tools improve speed and accuracy of the reliability analysis compared to usual Monte Carlo methods. This is achieved by using an extension of well known convolution method applicable to interdependent variables. The interdependent distributions are obtained from historical data using Machine Learning of quantile models. The paper presents a novel approach to the analysis of reliability contribution of storage based on these models and related to Information Theory. The developed tools are demonstrated in several example scenarios for ISO-New England service area. [ABSTRACT FROM AUTHOR]

Moving towards regional Supergrids, an increasing number of interconnections are formed by High Voltage Direct Current (HVDC) lines. Currently, in most regions, HVDC losses are not considered in market operations, resulting in additional costs for Transmission System Operators (TSOs). Nordic TSOs have proposed the introduction of HVDC loss factors in the market clearing algorithm, to account for the cost of losses and avoid HVDC flows between zones with zero price difference. In this paper, we introduce a rigorous framework to assess the introduction of loss factors, in particular HVDC loss factors, in nodal and zonal pricing markets. First, we focus on the identification of an appropriate loss factor. We propose and compare three different models: constant, linear, and piecewise linear. Second, we introduce formulations to include losses in market clearing algorithms. Carrying numerical tests for a whole year, we find that accounting only for HVDC or AC losses may lead to lower social welfare for a non-negligible amount of time. To counter this, this paper introduces a framework for including both AC and HVDC losses in a zonal or nodal pricing environment. We show both theoretically and through simulations that such a framework is guaranteed to increase social welfare. [ABSTRACT FROM AUTHOR]

This paper presents a market-based resource adequacy assessment framework to analyze the system generation portfolio that results in a competitive market environment. In particular, we apply the modeling framework to investigate the impact of high penetration levels of variable renewable energy resources and different market designs on achieving resource adequacy. The model captures the strategic capacity investment and retirement decision-making of profit-maximizing generation companies. In contrast to many previous studies, this paper considers markets for capacity, energy, and reserve products in detail; thus, the modeling framework allows improved analysis of generation expansion and revenue sufficiency in a competitive market environment. The modeling framework is based on Stackelberg leader–follower games and is formulated as a bi-level optimization problem, which is then transformed into a mathematical program with equilibrium constraints. Furthermore, we employ a Lagrangian decomposition algorithm to enhance computational performance. In a case study of the electric reliability council of texas (ERCOT) system, we compare the results from the proposed model with those obtained from a traditional centralized least-cost planning model. The results demonstrate the effectiveness of the proposed modeling framework and highlight the importance of considering strategic behavior in a competitive market framework when assessing resource adequacy. [ABSTRACT FROM AUTHOR]

The primary goal of this paper is to develop an optimization framework for studying the efficacy of transmission line reactance tweaking as a mechanism for post-disturbance control in a transmission network. We start by developing a mixed-integer linear programming (MILP) formulation for tracking the redistribution of direct current (DC) flows and the graph-theoretic evolution of a network topology over the course of cascading failures. Next, we propose a min–max setup for studying the impact of post-disturbance reactance tweaking on the resilience of the system to a worst-case disturbance. We devise a MILP reformulation scheme for the underlying bilevel non-convex mixed-integer nonlinear program to facilitate the computation of its globally optimal solution. We then develop a MILP framework for computing a tight upper bound (best-case scenario) on the efficacy of post-disturbance reactance tweaking for a given set of bus loads. Our numerical case study suggests that post-disturbance reactance tweaking, even on only a small number of lines, can be effective in reducing the amount of load shed in some scenarios in the tested system. [ABSTRACT FROM AUTHOR]

As the share of renewables in the grid increases, the operation of power systems becomes more challenging. The present paper proposes a method to formulate and solve chance-constrained optimal power flow while explicitly considering the full nonlinear ac power flow equations and stochastic uncertainties. We use polynomial chaos expansion to model the effects of arbitrary uncertainties of finite variance, which enables to predict and optimize the system state for a range of operating conditions. We apply chance constraints to limit the probability of violations of inequality constraints. Our method incorporates a more detailed and a more flexible description of both the controllable variables and the resulting system state than previous methods. Two case studies highlight the efficacy of the method, with a focus on satisfaction of the ac power flow equations and on the accurate computation of moments of all random variables. [ABSTRACT FROM AUTHOR]

Droop control is a viable method for the operation of island DC microgrids in a decentralized architecture. This paper presents a mixed-integer conic optimization formulation for the design of generator droop control, comprising the parameters of a piecewise linear droop curve. The mixed-integer formulation originates from a stochastic optimization framework that considers several operating scenarios for finding the optimal design. The convexity of the mixed-integer problem continuous relaxation gives global optimality guarantees for the design problem. The paper presents computational results using a tight polyhedral approximation of the conic program, leading to a mixed-integer linear programming (MILP) problem that is solved using a state-of-the-art commercial solver. The results from the proposed approach are contrasted with both a classic linear droop control design and a recent piecewise linear formulation. The Monte-Carlo simulation results quantify the extent to which the MILP solution is superior in reducing voltage violations and power loss, and the degree to which the loss is close to that from a conic optimal power flow solution. [ABSTRACT FROM AUTHOR]

The increasing penetration of renewable energy, such as wind power, has brought great challenges to the power system operation due to its uncertainty. Flexibility, which measures the ability of power system to deal with the uncertainties, is critical for power system to adapt to the new era of renewable energy. The rising electrical demand of the water distribution system (WDS) creates opportunities for power system to leverage the flexibility provided by WDS. This paper investigates the water-energy relationship between these two systems and makes full use of the water pumps and tanks in the WDS to enhance the power system flexibility. Current WDS designs did not consider well the role WDS plays in the power system. This hinders the WDS from being fully used by power system to provide flexibility. An optimization model is proposed to determine the optimal tank size of WDS, which may provide the maximum available flexibility of power system. The effect of tank size on water quality is also investigated to ensure that the supplied water quality is not compromised. Moreover, a Benders-based heuristic algorithm is proposed to find the optimization solution more efficiently and to protect the data of each energy system. Results of case study highlight the merit of the proposed optimization design and the advantage of using WDS to provide flexibility for power system. [ABSTRACT FROM AUTHOR]

A semi-analytical formulation is presented in this paper for the probability computation of branch current in multiphase systems. The developed formula is derived based on the linear power flow model in rectangular coordinates. The system uncertainty injections can be renewable energy resources or loads and are modeled using a Gaussian mixture model (GMM). The developed formula can be used to compute the line current violation probability as well as integrate into optimal power flow problem as chance-constraint relaxation. The proposed formula is first compared with the Matlab embedded numerical integration function to show its performance. Besides, the semi-analytical formula is validated and compared with the Monte Carlo simulation method using the IEEE 123-bus system, EPRI Ckt5, and Ckt7 systems. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive scheduling framework for residential demand response (DR) programs considering both the day-ahead and real-time electricity markets. In the first stage, residential customers determine the operating status of their responsive devices such as heating, ventilation, and air conditioning (HVAC) systems and electric water heaters (EWHs), while the distribution system operator (DSO) computes the amount of electricity to be purchased in the day-ahead electricity market. In the second stage, the DSO purchases insufficient (or sells surplus) electricity in the real-time electricity market to maintain the supply-demand balance. Due to its computational complexity and data privacy issues, the proposed model cannot be directly solved in a centralized manner, especially with a large number of uncertain scenarios. Therefore, this paper proposes a combination of stochastic programming (SP) and the alternating direction method of multipliers (ADMM) algorithm, called SP-ADMM, to decompose the original model and then solve each sub-problem in a distributed manner while considering multiple uncertain scenarios. The simulation study is performed on the IEEE 33-bus system including 121 residential houses. The results demonstrate the effectiveness of the proposed approach for large-scale residential DR applications under weather and consumer uncertainties. [ABSTRACT FROM AUTHOR]

The wide implementation of information and communication technologies (ICT) cause power system operations exposed to cyber-attacks. Meanwhile, the tendency of integrated multi energy vectors has worsened this issue with multiple energy coupled. This paper proposes a two-stage risk-averse mitigation strategy for water-energy systems (WESs), incorporating power, natural gas and water systems against false data injection attacks (FDIA) under water-energy nexus. The FDIA on individual sub-systems is modelled through hampering false data integrity to the systems. An innovative two-stage risk-averse distributionally robust optimization (RA-DRO) is proposed to mitigate uneconomic operation and provides a coordinated optimal load shedding scheme for the nexus system security. A coherent risk measure, Conditional Value-at-Risk is incorporated into the RA-DRO to model risk. A Benders decomposition method is used to solve the original NP-hard RA-DRO problem. Case studies are demonstrated on a WES under water-energy nexus and results show that the effectiveness of the method to mitigate risks from potential FDIA and renewable uncertainties. This research provides WES operators an economic system operation tool by optimally coordinating energy infrastructures and implementing reasonable load shedding to enhance cybersecurity. [ABSTRACT FROM AUTHOR]

Due to the diversity of power consumption patterns, the false positive rate (FPR) of data-driven electricity theft detection (ETD) methods is too high to meet practical needs, which severely restricts the engineering application of data-based methods. To reduce FPR of ETD methods based on advanced metering infrastructure (AMI), a deep neural network with low FPR (LFPR-DNN) is proposed in this paper. First, a deep model is constructed based on one-dimensional convolution and residual network, which can automatically extract features from consumption data. Then, a two-stage training scheme is used to train the network. In the first stage, the conventional gradient descent algorithm is used to update the network weights. To minimize the impact of data imbalance on detection performance, focal loss is used. Besides, grid search is used to optimize the hyper-parameters of the model. In the second stage, with FPR as the optimization objective, the particle swarm optimization (PSO) algorithm is used to train the network. Finally, the proposed LFPR-DNN is verified by using the open Irish data set. Compared to other state-of-the-art classifiers, LFPR-DNN has the lowest FPR with 0.29% and the highest AUC with 99.42%. The FPR is reduced by an order of magnitude, which verifies the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a novel stochastic robust real-time power dispatch model considering wind uncertainty. In this dispatch model that incorporates automatic power generation control, system constraints are constructed with affinely adjustable robust optimization to enhance the system security, while the objective concerning the expected value of generation cost is optimized to improve the cost efficiency. The optimized objective is consistent with stochastic optimization, while the formulation for the objective is different. A Nataf conversion-based three-point estimate (NC-TPE) is adopted, which uses an approximating function to formulate the expected generation cost with deterministic estimate points. Compared to traditional stochastic sampling methods, the deterministic assessment method NC-TPE achieves an accurate formulation with more stable and efficient computation performance. The dispatch model is derived as a problem with nonconvex objective and bilinear constraints using the dual theory. To address the highly nonconvex problem, the objective and bilinear constraints are first converted to difference-of-convexity functions, and then a tailored difference-of-convexity optimization is employed to convexify the nonconvex functions, such that the original problem can be solved with an iterative quadratically constrained program. Numerical simulations demonstrate the economic superiority and robustness of the proposed model, as well as the effectiveness of the convexified solution. [ABSTRACT FROM AUTHOR]

The wide variety of inverter control settings for solar photovoltaics (PV) causes the accurate knowledge of these settings to be difficult to obtain in practice. This paper addresses the problem of determining inverter reactive power control settings from net load advanced metering infrastructure (AMI) data. The estimation is first cast as fitting parameterized control curves. We argue for an intuitive and practical approach to preprocess the AMI data, which exposes the setting to be extracted. We then develop a more general approach with a data-driven reactive power disaggregation algorithm, reframing the problem as a maximum likelihood estimation for the native load reactive power. These methods form the first approach for reconstructing reactive power control settings of solar PV inverters from net load data. The constrained curve fitting algorithm is tested on 701 loads with behind-the-meter (BTM) PV systems with identical control settings. The settings are accurately reconstructed with mean absolute percentage errors between 0.425% and 2.870%. The disaggregation-based approach is then tested on 451 loads with variable BTM PV control settings. Different configurations of this algorithm reconstruct the PV inverter reactive power timeseries with root mean squared errors between 0.173 and 0.198 kVAR. [ABSTRACT FROM AUTHOR]

The increasing of electric vehicles (EVs) alleviates the faced environmental problems but brings challenges to the optimal operation of transportation network (TN) and distribution network (DN). However, the most of existing research works consider EV charging station assignment and navigation services in the TN separately from charging station power scheduling services in the DN. To overcome this research gap, this paper proposes a collaborative optimal routing and scheduling (CORS) method, providing optimal route to charging stations and designing optimized charging scheduling schemes for each EV. In the order of reporting, whenever an EV reports its charging demand, a CORS optimization model is built and solved so that a specific charging scheme is designed for that EV. Then, the TN and DN status is updated to guide the subsequent EVs operating. The proposed CORS integrates the real-time state of the TN and DN, and effects positive benefits in helping EVs to avoid traffic congestion, improving the utilization level of charging facilities and enhancing charging economy. The combined distributed biased min consensus algorithm and generalized benders decomposition algorithm are adopted to solve the complex nonlinear optimization problem. Through comparing with the existing methods, better effectiveness is verified by simulation results. [ABSTRACT FROM AUTHOR]

Electric distribution grid operations typically rely on both centralized optimization and local non-optimal control techniques. As an alternative, distribution system operational practices can consider distributed optimization techniques that leverage communications among various neighboring agents to achieve optimal operation. With the rapidly increasing integration of distributed energy resources (DERs), distributed optimization algorithms are growing in importance due to their potential advantages in scalability, flexibility, privacy, and robustness relative to centralized optimization. Implementation of distributed optimization offers multiple challenges and also opportunities. This paper provides a comprehensive review of the recent advancements in distributed optimization for electric distribution systems and classifications using key attributes. Problem formulations and distributed optimization algorithms are provided for example use cases, including volt/var control, market clearing process, loss minimization, and conservation voltage reduction. Finally, this paper also presents future research needs for the applicability of distributed optimization algorithms in the distribution system. [ABSTRACT FROM AUTHOR]

The modern photovoltaic inverter has an active power-reactive power (Watt-VAr) control curve that is part of its management modes. The Watt-VAr curve, whose settings can be remotely modified, regulates the inverter reactive power output in function of its active power. This paper proposes the optimization of inverter segregated linear decision rules (LDRs), starting from the legacy Volt-VAr optimization in distribution networks. As opposed to classical LDRs that are interfaced with Volt-VAr optimization, the segregated LDRs are piecewise linear continuous curves that directly satisfy the reactive power capability of inverters, and their multiple segments can capture the correlation in solar power variability. The paper presents linear programming formulations for optimizing the segregated linear decision rules using stochastic optimization, robust optimization, and distributionally robust optimization. The optimization schemes are demonstrated on both meshed and radial networks, and their performance is validated via Monte-Carlo simulation. [ABSTRACT FROM AUTHOR]

The ever-increasing integration of variable wind energy requests for a power system with high flexibility. In this paper, we formulate the real-time economic dispatch problem as a multi-stage robust program to leverage flexible resources, especially energy storage systems, in a broader timescale, and also to avoid the risk of high costs in critical scenarios. The multi-stage robust program is decomposed to the dynamic programming form and the fast robust dual dynamic programming (FRDDP) algorithm is developed to solve it efficiently. To tackle the nonconvexities caused by the inter-temporal constraints of ESSs, an estimation-correction method is developed, and measures of the approximation accuracy are presented. Comprehensive case studies comprising units up to 1371 are carried out to verify the effectiveness of the proposed model. Numerical results show that compared with the existing ones, the proposed multi-stage robust model achieves lower cost under the worst-case scenario and shows better scalability in large-scale systems. [ABSTRACT FROM AUTHOR]

This paper develops a novel two-stage coordinated volt-pressure optimization (VPO) for integrated energy systems (IES) networked with energy hubs considering renewable energy sources. The promising power-to-gas (P2G) facilities are used for improving the interdependency of the IES. The proposed VPO contains the traditional volt-VAR optimization functionality to mitigate the voltage deviation while ensuring a satisfying gas quality due to the hydrogen mixture. In addition to the conventional voltage regulating devices, i.e., on-load tap changers and capacitor banks, P2G converter and gas storage are used to address the voltage fluctuation problem caused by renewable penetration. Moreover, an effective two-stage distributionally robust optimization (DRO) based on Wasserstein metric is utilized to capture the renewable uncertainty with tractable robust counterpart reformulations. The Wasserstein-metric based ambiguity set enables to provide additional flexibility hedging against renewable uncertainty. Extensive case studies are conducted in a modified IEEE 33-bus system connected with a 20-node gas system. The proposed VPO provides a voltage-regulated economic operation scheme with gas quality ensured that contributes to high-quality but low-cost multi-energy supply to customers. [ABSTRACT FROM AUTHOR]

In this paper, we present a two-stage model of zonal electricity markets with day-ahead market clearing, and real-time re-dispatch and balancing that accounts for transmission line switching at both stages. We show how the day-ahead problem with switching can be formulated as an adaptive robust optimization problem with mixed integer recourse, and present a new algorithm for solving the adversarial max-min problem that obeys the structure of an interdiction game. We apply the model on a realistic instance of the Central Western European system, and comment on the impacts of both proactive, and reactive transmission switching on the operating costs of the system. Part I presents day-ahead models of a short-term zonal electricity market with switching, and describes our algorithmic approach for solving these models efficiently. Part II describes variants of the real-time model, and presents the results of our case study on the Central Western European market. [ABSTRACT FROM AUTHOR]

In this paper, a dual-solver framework based on model predictive control (MPC) is proposed, $E-$ solver and $L-$ solver. The economic scheduling problem is formulated using mixed-integer linear programming (MILP), which can be solved in an efficient way by using commercial solver ($E-$ solver). While the transmission loss problem is formulated using non-linear programming (NLP), which can be solved in the interior point method, namely $L-$ solver. The $E-$ solver provides an economic priority power scheduling plan for the $L-$ solver, and the $L-$ solver solves the entire microgrid accurate power flow scheduling plan. The proposed planning model decomposition technique aims to solve the planning model in a time-sharing manner and combines the characteristics of the two optimizers with a reasonable matching algorithm to achieve economic, efficient, and fast real-time control. A case study of a DC microgrid is employed to assess the performance of the online optimization-based control strategy. Simulations based on eight-node DC microgrid show that the method reduces the operating cost by $12.10\%$ and increases the calculation speed by $80.18\%$ compared with the traditional interior point method. With a shorter delay, the proposed optimization method will facilitate the implementation of real-time control and optimization. [ABSTRACT FROM AUTHOR]

Natural disasters, such as extreme weather events (EWEs), can cause significant damage to power systems. In fact, it is expected that the intensity and frequency of EWEs will increase the next years due to climate change, making power system resilience enhancement necessary. This paper proposes a transmission resilience planning solution by determining the lines to be placed underground in order to minimize load shedding in the most cost-efficient way taking into account historical EWEs (HEWEs). The problem is formulated as a stochastic robust optimization problem and is decomposed into a master problem determining the lines to be placed underground and a number of subproblems, where each subproblem corresponds to a HEWE and provides the worst damage scenario that leads to the maximization of load shedding. The problem is solved using a decomposition-based algorithm. The proposed method is illustrated on a modified IEEE Reliability Test System and IEEE 118-bus System and it is evaluated by applying a Sequential Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

Renewable Energy Sources (RESs) integration strengthens the need for a power network that can robustly handle the system’s uncertain scenarios. This paper proposes the first nonlinear novel dual-based bi-level approach for robust AC Transmission Expansion Planning (TEP) with uncertainties in RES generations and loads. It utilizes a convex relaxation and is solved by Benders Decomposition (BD), where the master determines the robust AC expansion plan. The novel dual slave for the second level of BD circumvents the issues in using conventional conic dual theory and aids in the worst-case realization of uncertainties using additional novel constraints. The proposed slave is solved using Interior Point Method (IPM), as it is not a mixed-integer problem. The proposed work includes additional linear constraints to speed up BD’s convergence and direct the master towards optimality. The approach is tested on several transmission systems, including the Indian Northern Regional Power Grid (NRPG) system. The robustness of the obtained plans is verified by Monte-Carlo Simulation (MCS) of the actual nonlinear and nonconvex AC Optimal Power Flow (OPF). The effect of the budget of uncertainty on the AC expansion plan is also investigated. A comparison with two previous works reveals the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, a novel distributed control strategy addressing a (feasible) psycho-social-physical welfare problem in islanded Direct Current (DC) smart grids is proposed. Firstly, we formulate a (convex) optimization problem that allows prosumers to share current with each other, taking into account the technical and physical aspects and constraints of the grid (e.g., stability, safety), as well as psycho-social factors (i.e., prosumers’ personal values). Secondly, we design a controller whose (unforced) dynamics represent the continuous time primal-dual dynamics of the considered optimization problem. Thirdly, a passive interconnection between the physical grid and the controller is presented. Global asymptotic convergence of the closed-loop system to the desired steady-state is proved and simulations based on collected data on psycho-social aspects illustrate and confirm the theoretical results. [ABSTRACT FROM AUTHOR]

In order to reduce the dependence on accumulated experience that is difficult to replicate for the human dispatchers to make power generation scheduling more automatically, quickly, and intelligently, higher requirements are placed on the level of the auxiliary decision-making system. In this paper, a short-term scheduling problem was treated as a regression task that concentrates on how to learn a reliable statistic model that concludes the intrinsic logic of the dispatching policy from extensive historical dispatching experience. In this way, since Kullback-Leibler distance can better measure the distance between two distributions, we designed a novel GAN-based learning method for the scheduling task. Also, we proposed a feasible framework that combines the stage of learning, decision-making, and deployment to support the practical implementation of the proposed algorithm. In the experiment, a real case that takes short-term scheduling tasks on a regional large-scale power system is considered in our experiments. As a result, the comparison of several methods further shows the superiority of the proposed GAN-based method under our implementations. [ABSTRACT FROM AUTHOR]

This paper presents a new security-constrained multiobjective optimal dispatch (SC-MOOD) framework for an economic and reliable operation of microgrids. The framework is developed based on a computationally effective multiobjective optimization technique, Pareto concavity elimination transformation (PaCcET). The new method considers grid steady-state and dynamic constraints while solving the optimal dispatch in both grid-connected and islanded modes. The constraints consist of power balance, voltage magnitude, line flows, power generation, frequency, and voltage transients. The proposed framework finds the most economic operating solutions to not only minimize the generation cost but also minimize the reliability cost. In this paper, the PaCcET is utilized to solve the SC-MOOD. The PaCcET uses an extraordinary transformation to first transfer all the points from a multiobjective space to a transformed objective space. It then solves a linear combination of transformed objectives using a single-objective optimizer to find all the nondominated points of the original multiobjective space. The performance of the new framework is verified using the simulation results in a microgrid with several distributed energy resources in both grid-connected and islanded modes. The results are then compared with two multiobjective optimization techniques, nondominated sorting genetic algorithm II and multiobjective particle swarm optimization, as two well-known benchmarks. [ABSTRACT FROM AUTHOR]

This paper presents an optimization approach for the placement of geomagnetically induced current (GIC) blocking devices (BDs) on power system transformers to mitigate the adverse effects of a geomagnetic disturbance (GMD). Solar storms lead to GMDs which, in turn, drive GICs along transmission lines and through transformer windings. GICs cause half-cycle saturation in power transformers, increase their shunt reactive power loss, lead to a significant lack of power system reactive power support, and, as a result, create voltage instability and, potentially, large-scale voltage collapse. To mitigate these detrimental effects, a long-term remedy is to install GIC BDs at the neutral point of transformers. Since these devices are fairly costly, their placement should be performed in an optimal manner. The optimization problem proposed in this paper minimizes the cost of BD placement while satisfying power system voltage and generator maximum reactive power limits. The numerical results demonstrate the effectiveness of the proposed method in maintaining an acceptable voltage profile for the power system in case of GMDs with any degree of severity. [ABSTRACT FROM AUTHOR]

Optimal power flow (OPF) programs must be able to provide sound operating points for power systems under different conditions while meeting a large number of constraints. These constraints, however, either due to the operating conditions at hand or by construction, can have linearly dependent gradients, thus defining ill-behaved feasible sets. This paper analyzes the use of an alternative set of optimality conditions, derived from the Fritz-John (FJ) conditions, to represent OPF solutions in such critical cases. Results are presented for realistic test systems. [ABSTRACT FROM PUBLISHER]

Volt/VAr Optimization (VVO) is becoming increasingly crucial in distribution management systems with renewable sources that require setting their reactive power in coordination with legacy voltage and reactive power control devices. This paper presents a VVO method that operates in complex variables based on the Wirtinger calculus; it employs a penalty method that keeps voltage magnitudes and controller parameters within limits together with a probabilistic rounding technique for handling switched device variables. The complex variable implementation permits using the compensation technique when solving the Karush-Kuhn Tucker (KKT) system, thus achieving a significant speedup due to limiting the number of linear system factorizations. The proposed method is contrasted with a classical VVO implementation employing discrete coordinate search from the current operating point and an enhanced version that uses sensitivity information. Numerical results on distribution networks having up to 3147 nodes show that the proposed method is significantly faster than classical methods and gives operating points free of voltage magnitude violations and lower power loss. [ABSTRACT FROM AUTHOR]

The foreseen development of large-scale Offshore Windfarms (OWFs) further from the shore dictates that the OWF transmission system must be optimally designed based on Dynamic Thermal Rating (DTR) in order to fully utilize the intermittent nature of the wind and to keep the offshore wind cost-competitive. In this paper, a comprehensive, DTR-based, two-stage stochastic model is presented, which has been developed for investment decision support for OWF size and HVAC transmission systems. Complex DTR models for all the critical HV components are made fit for the mixed-integer linear programming problem, while accounting for the stochasticity in wind generation and component availability. The main decisions incorporate the discrete size of OWFs, HV subsea export cable cross-sections and ratings for transformers and shunt reactors. For validation, an actual testcase OWF off the east coast of U.K. has been used. Results indicate that DTR-based iterative design of OWF and its transmission components can significantly improve the business case, even though transmission efficiency and energy delivered are not maximum for the optimal design [ABSTRACT FROM AUTHOR]

Due to the increasing penetration of large-scale renewable energy generation at transmission level, hybrid AC/DC transmission expansion is becoming more relevant by the day, especially if the considered renewable generation is far away from existing AC grid infrastructure. This paper presents a multi-period hybrid AC/DC network expansion planning model that incorporates node voltages, reactive power and network losses. Since the operation of a high voltage DC link is influenced considerably by the converter stations, converter transformer, filter, and phase reactor are modeled in each converter station. Since the AC power flow equations render a non-convex problem whose solution algorithms do not always guarantee convergence or optimality, a second-order conic relaxation is utilized. The resulting model is a mixed-integer convex problem with a convergence guarantee that embodies a better approximation of system operation than its DC linear counterpart. Three case studies are considered to illustrate the proposed model. [ABSTRACT FROM AUTHOR]

State estimation plays a key role in the transition from the passive to the active operation of distribution systems, as it allows to monitor the networks and provides the necessary information to perform control actions. However, designing state estimators for distribution systems is challenging, due to the characteristics of the networks, such as limited measurement availability. Furthermore, the features of the distribution system present significant local variations, e.g., voltage level and number and type of customers, which makes it hard to design a “one-size-fits-all” state estimator. This paper introduces a unifying framework that allows to easily implement and compare diverse unbalanced static state estimation models. This is achieved by formulating state estimation as a general constrained optimization problem. The advantages of this approach are described and supported by numerical illustration on a large set of real distribution feeders. The framework is also implemented in software and made available open-source. [ABSTRACT FROM AUTHOR]

This paper proposes a dynamic valuation framework to determine the opportunity value of battery capacity degradation in grid applications based on the internal degradation mechanism and utilization scenarios. The proposed framework follows a dynamic programming approach and includes a piecewise linear value function approximation solution that solves the optimization problem over a long planning horizon. The paper provides two case studies on price arbitrage and frequency regulation using real market and system data to demonstrate the broad applicability of the proposed framework. Results show that the battery lifetime value is critically dependent on both the external market environment and its internal state of health. On the grid service side, results show that second-life batteries can provide more than 50% of the value compared to new batteries, and frequency regulation provides two times more revenue than price arbitrage throughout the battery lifetime. [ABSTRACT FROM AUTHOR]

This paper proposes a new deep learning (DL) based model-free robust method for bulk system on-line load restoration with high penetration of wind power. Inspired by the iterative calculation of the two-stage robust load restoration model, the deep neural network (DNN) and deep convolutional neural network (CNN) are respectively designed to find the worst-case system condition of a load pickup decision and evaluate the corresponding security. In order to find the optimal result within a limited number of checks, a load pickup checklist generation (LPCG) algorithm is developed to ensure the optimality. Then, the fast robust load restoration strategy acquisition is achieved based on the designed one-line strategy generation (OSG) algorithm. The proposed method finds the optimal result in a model-free way, holds the robustness to handle uncertainties, and provides real-time computation. It can completely replace conventional robust optimization and supports on-line robust load restoration which better satisfies the changeable restoration process. The effectiveness of the proposed method is validated using the IEEE 30-bus system and the IEEE 118-bus system, showing high computational efficiency and considerable accuracy. [ABSTRACT FROM AUTHOR]

Addressing non-convexity plays a fundamental role in solving the optimal electricity-gas flow models. In this paper, an improved spatial branch-and-bound algorithm is proposed to solve the non-convex problem, which is formulated as a mixed-integer bilinear programming, for its exact solution. The core of the algorithm is to divide the non-convex model into convex and small sub-models by branching on specific continuous variables, so that the non-convex problem can be equivalent to a rooted tree for exploration. The exactness of the algorithm is guaranteed by the same criterion as the classical branch-and-bound algorithm. To alleviate the computational burden, a novel two-stage spatial branching strategy is developed to improve the effectiveness and efficiency of the branching operations. The performance of the proposed algorithm is verified on two integrated electricity-gas systems with different sizes. Numerical results demonstrate that our method achieves a balance among feasibility, optimality, and efficiency. The comparison with another 6 convexification-based methods, 3 state-of-the-art non-convex optimization solvers, and 2 spatial branch-and-bound algorithms with classical branching rules further shows the superiority of our algorithm. [ABSTRACT FROM AUTHOR]

A reduced level of system inertia due to renewable integration increases the need for cost-effective provision of ancillary services, such as Frequency Response (FR). In this paper a closed-form solution to the differential equation describing frequency dynamics is proposed, which allows to obtain frequency-security algebraic constraints to be implemented in optimization routines. This is done while considering any finite number of FR services with distinguished characteristics, such as different delivery times and activation delays. The problem defined by these frequency-security constraints can be formulated as a Mixed-Integer Second-Order Cone Program (MISOCP), which can be efficiently handled by off-the-shelf conic optimization solvers. This paper also takes into account the uncertainty in inertia contribution from the demand side by formulating the frequency-security conditions as chance constraints, for which an exact convex reformulation is provided. Finally, case studies highlighting the effectiveness of this frequency-secured formulation are presented. [ABSTRACT FROM AUTHOR]

Stochastic optimization can be used to model predictable but uncertain element failures, in an attempt to enhance system reliability in power system operation and planning. In practical applications, such as preventive operation during severe weather, the uncertainty set is often very large. This will lead to two challenges: (i) every possible scenario cannot be practically identified; and (ii) the computational demands of stochastic optimization with a large scenario set cannot be met. To address these challenges, this paper develops a multidimensional scenario selection method, which creates a rather small but representative set of scenarios. The developed method makes use of failure features as well as network features of the elements that may fail, to achieve a superior performance. The simulations studies on a synthetic large-scale Texas system, show the dominant performance of the method compared to existing algorithms in the literature, as well as common industry practices. Due to its effectiveness, the method presented in this paper enables computationally efficient implementation of stochastic power system operation and planning software tools. Such stochastic tools will improve system reliability and efficiency through enhanced use of the existing resources, without requiring any expensive system upgrade. [ABSTRACT FROM AUTHOR]

This paper proposes a methodology for advanced demand side management (DSM) in the distribution network (DN), catering at the same time for the requirements of the network operator, transmission or distribution, the available flexibility of the demand side, and the preservation of network performance. The basic premise of the study is that the distribution network operator is providing flexibility to the transmission system operator through load shaping. Different, one or more, indicators can be chosen to assess preservation of network performance. In this paper, for illustrative purposes of the methodology, the steady state voltage stability index, namely the load margin, is chosen as the network performance indicator. This is evaluated before and after a DSM action, in order to analyse the possible effect of DSM on network loadability. Load at each DN bus is represented using a realistic composite load model comprising controllable and uncontrollable loads. The DSM is initially performed based on optimal power flow calculation to ensure that the distribution system load profile at the grid supply point follows the required (pre-specified) load profile during a 24 hour period. Following this, a particle swarm optimisation is used to modify DSM program in those time steps of the planning horizon where load margin is reduced. The methodology is illustrated on a number of case studies using modified IEEE 33 bus distribution network model. The results illustrate the extent to which the available flexibility of demand can be used in support of transmission network operation when the preservation of network performance and appropriate load modeling are considered. [ABSTRACT FROM AUTHOR]

The paper focuses on the day-ahead operational planning of a grid-connected local energy community (LEC) consisting of an internal low-voltage network and several prosumers including generation units, battery storage systems, and local loads. In order to preserve, as much as possible, the confidentiality of the features of prosumers’ equipment and the production and load forecasts, the problem is addressed by designing a specific distributed procedure based on the alternating direction method of multipliers (ADMM). The distributed procedure calculates the scheduling of the available energy resources to limit the balancing action of the external grid and allocates the internal network losses to the various power transactions. Results obtained for various case studies are compared with those obtained by a centralized optimization approach. The results confirm that, in the considered LEC framework, each of the prosumers achieves a reduction in costs or increases revenues in case it participates to the LEC with respect to the case in which it can only transact with an external energy provider. [ABSTRACT FROM AUTHOR]

This paper considers the problem of releasing optimal power flow (OPF) test cases that preserve the privacy of customers (loads) using the notion of Differential Privacy. It is motivated by the observation that traditional differential privacy algorithms are not suitable for releasing privacy preserving OPF test cases: The added noise fundamentally changes the nature of the underlying optimization and often leads to test cases with no solutions. To remedy this limitation, the paper introduces the OPF Load Indistinguishability (OLI) problem, which guarantees load privacy while satisfying the OPF constraints and remaining close to the optimal dispatch cost. The paper introduces an exact mechanism, based on bilevel optimization, as well as three mechanisms that approximate the OLI problem accurately. These mechanisms enjoy desirable theoretical properties, and the computational experiments show that they produce orders of magnitude improvements over standard approaches on an extensive collection of test cases. [ABSTRACT FROM AUTHOR]