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As one of the most widely installed utility-scale storage facilities, pumped storage hydro (PSH) plays an essential role in providing flexibility for power systems worldwide. Thus, to accurately quantify the flexibility of PSH units in operational optimization problems is important. The conventional PSH models in the literature rarely consider detailed state transitions due to their hourly-based settings. However, it becomes imperative for operational optimization on short-term intervals, especially with increasing shares of renewable energy in power systems. To this end, this paper presents a novel deterministic PSH model that considers the transition time and trajectory between three states of PSH units in look-ahead dispatch. Moreover, to better characterize the varying efficiency of PSH units with water head and flow rate, this paper proposes to model detailed head-dependent efficiency curves (hereafter called input-output curves) in look-ahead dispatch, which encounters heavy computational burdens when short time intervals are applied. In this work, a zig-zag piece-wise linear approximation method is used for input-output curve modeling. This can enable an accurate quantification for variable efficiency and head dependence in a computationally effective manner. Numerical results are presented to show performances of the proposed PSH model in both flexibility quantification and computation time. [ABSTRACT FROM AUTHOR]

The integration of the variable renewable energies makes the operation conditions of the power system ever-changeable. Consequently, the power system operational reliability evaluation is increasingly important. This paper introduces the concept of decision-dependent uncertainty (DDU) in the operational reliability evaluation. Unlike the exogenous uncertainties, DDU reveals that the decisions of the system operation could significantly affect the resolution of the uncertainties which influence the reliability metrics. In this paper, the proposed DDU modeling method links the device reliability indices, i.e., the forced outage rate, and the operational-decision variables. The impacts of DDU on operational reliability are analyzed based on a reliability-constrained stochastic unit commitment (UC) model. An adaptive reliability improvement UC (ARIUC) algorithm is proposed to efficiently solve the problem. Case studies underline the necessity of considering DDU in power system operational reliability evaluations. [ABSTRACT FROM AUTHOR]

Renewable generation has grown rapidly these years due to its advantages in low environmental impacts. Stand-alone microgrid with renewable generation and energy storage is a promising option in remote areas beyond the reach of an existing power grid. This paper proposes a multiobjective optimization model to co-optimize the sizes of renewable generation and energy storage in stand-alone microgrids, which minimizes the load shedding risk and the total investment cost. The load shedding degree is obtained by an optimal operation problem and measured by shortfall risk, considering the uncertainties of demand and renewable resources. To deal with the inaccurate empirical distribution, distributionally robust shortfall risk is further established under a Wasserstein-metric-based ambiguity set, and an equivalent distributionally robust formulation is obtained. Then a conservative approximation is developed, and the resulting problem appears to be a bi-objective linear program. The Pareto frontier is proven to be piecewise linear, and the analytical expression of the Pareto frontier is derived. Case studies demonstrate the effectiveness and performance of the proposed method. [ABSTRACT FROM AUTHOR]

Optimal Volt/VAR control (VVC) in distribution networks relies on an effective coordination between the conventional utility-owned mechanical devices and the smart residential photovoltaic (PV) inverters. Typically, a central controller carries out a periodic optimization and sends setpoints to the local controller of each device. However, instead of tracking centrally dispatched setpoints, smart PV inverters can cooperate on a much faster timescale to reach optimality within a PV inverter group. To accommodate such PV inverter groups in the VVC architecture, this paper proposes a bi-level optimization framework. The upper-level determines the setpoints of the mechanical devices to minimize the network active power losses, while the lower-level represents the coordinated actions that the inverters take for their own objectives. The interactions between these two levels are captured in the bi-level optimization, which is solved using the Karush-Kuhn-Tucker (KKT) conditions. This framework fully exploits the capabilities of the different types of voltage regulation devices and enables them to cooperatively optimize their goals. Case studies on typical distribution networks with field-recorded data demonstrate the effectiveness and advantages of the proposed approach. [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]

Distribution systems are becoming more active and provide more power support for transmission systems via their connection points at the transmission-distribution (T-D) interfaces. This paper proposes a chance constrained optimization model to estimate the flexibility area at a T-D interface. In this model, network flexibility is for the first time involved and facilitated by introducing power flow routers (PFRs) into the distribution system. The chance-constrained flexibility area (CCFA) given by the proposed model provides a description of the aggregated power dispatchability of distribution system with the guarantee of low risks of voltage violations under renewable uncertainties. We exploit the mechanism of network flexibility and reveal that it significantly reduces the voltage standard deviations, which cannot be achieved by node power flexibility. To evaluate the CCFA, an efficient two-layer iteration algorithm is designed. The inner layer finds the boundary point of CCFA along a given direction for active and reactive power. The outer layer determines those key directions to be included in the estimation as the corresponding points capture the features of the CCFA boundary. Case studies show that PFRs significantly enlarge the CCFA, which reveals that network flexibility is an important supplement to node power flexibility in T-D interaction. [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]

Uncertainty arising from renewable energy results in considerable challenges in optimal power flow (OPF) analysis. Various chance-constrained approaches are proposed to address the uncertainty within OPF models. However, most existing approaches either assume that the uncertainty distributions are known a priori or consider individual chance constraint modeling. This paper proposes a distributionally robust (DR) joint chance-constrained OPF model, which ensures that the operational constraints are simultaneously satisfied with a given probability and does not require an assumption of specific probability distributions. An ambiguity set built on the first two moments is used to model the uncertainty. An optimized Bonferroni approximation (OBA) is first introduced to decompose the DR joint chance constraint into DR individual chance constraints. The resulting OBA formulation is strongly nonconvex. Different convex approximations are then proposed to formulate the OBA formulation as tractable forms. The proposed convex approximations can be easily extended to incorporate the structural information associated with uncertainty, and correlations among reserve chance constraints. Case studies demonstrate the effectiveness of the proposed convex approximation methods and their extensions. [ABSTRACT FROM AUTHOR]

With theincreased penetration of renewable sources, power gridsare becoming stressed due to fluctuating generation. To alleviate stress from inconsistent sources, utilities employ energy storage systems alongside renewable sources and rely on dispatching synchronous generators. However, optimal dispatch of such devices is limited by traditional AC optimal power flow methods that do not account for time-dependent constraints, such as the state of charge of energy storage systems and generator ramping constraints. Multi-period optimal power flow is proposed as a large non-convex non-linear problem to optimally dispatch and control generators and energy storage elements across multiple time periods. In this paper, we introduce a scalable, robust framework to solve multi-period optimal power flow using a differential dynamic programming scheme that makes it capable of scaling to large systems containing energy storage devices. We demonstrate the efficacy of this solution by optimizing the SyntheticUSA testcase over a set of time periods. A robust homotopy method is applied to achieve fast simulation times that can be parallelized for further improvements. [ABSTRACT FROM AUTHOR]

The output of renewable generation depends on the real-time weather conditions and changes rapidly; so the economic operating point of the power system varies over time. This paper aims to find the explicit mapping from variable renewable power to optimal power flow solutions. To this end, we propose a parametric distribution optimal power flow (P-DOPF) method, which gives the optimal dispatch strategy and power flow status as analytical functions of the renewable output. With the established distribution optimal power flow problem based on the relaxed Distflow model, the first step is to perform a global polyhedral approximation on the second-order cone constraints to develop a linearized formulation. The second step is to obtain the P-DOPF model by treating renewable power output as parameters; then, the P-DOPF problem gives rise to a multi-parametric linear program (mp-LP). Third, we prove that the optimal solution and optimal value of the P-DOPF are piecewise linear functions of the parameters and we design an adaptive-sampling algorithm to construct the optimal value and optimal solution functions, as well as the partition of the parameter set, subject to a given error tolerance; this algorithm is not influenced by model degeneracy, a common difficulty of existing mp-LP algorithms. The P-DOPF framework provides an explicit real-time control policy of generators in response to the renewable output. Case studies on the IEEE 33 and 69-bus systems verify the effectiveness and performance of the proposed method; by comparison, the proposed method outperforms the established affine policy method in computational efficiency and optimality by 24.5% and 4.62%, respectively. [ABSTRACT FROM AUTHOR]

The utilization of aggregated demand-side flexibility via demand response (DR) has become a promising pathway for the integration of renewable energy resources in power systems. Nowadays, there are several management strategies for DR such as the price-based transactive control strategies. However, many of such existing price-based control strategies neglect the physics and operational constraints of the underlying distribution networks when computing the price, raising concerns regarding their theoretical and practical values. This paper studies this issue and investigates optimal DR (ODR) by incorporating the distribution locational marginal price (DLMP). In particular, we discuss DR in connection with DLMPs and propose a multi-period bilevel optimization problem to find the ODR strategy. The objective is to minimize the peak load, load fluctuation, and payments of load aggregators. In addition, a robust bilevel ODR model is formulated to provide a robust ODR strategy while minimizing operating costs under the worst-case realization of uncertainties; this mitigates the impact of forecasting errors on renewable energy resources. Then, we propose an efficient solution approach by employing the Karush-Kuhn-Tucker conditions and strong duality. Simulation results are presented to illustrate the mutual impacts of the interaction between DR and DLMP and the benefits of the robust ODR strategy. [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]

This paper presents a two-timescale multi-objective coordinated volt/var optimization system for active distribution networks with renewable energy resources (RESs). In the hourly timescale, power loss and the number of control actions of on-load tap changers and (switchable) shunt capacitors for 24 h are minimized by coordinating on-load tap changers, (switchable) shunt capacitors, and reactive power outputs of RESs. A three-step method consisting of global search, user preference, and local search is adopted to solve the corresponding multi-objective mixed-integer nonlinear optimization problem. A rolling volt/var optimization is executed every 6 h, considering the day-ahead RES forecast errors. In the 15-min timescale, the RES reactive powers are optimized with RES uncertainties explicitly taken into consideration to minimize the pilot-bus voltage deviation under all representative scenarios. The pilot buses are those buses whose voltage magnitudes capture the network voltage profile. In this paper, a linear method is applied to quickly identify a set of pilot buses, and the impact of the identified pilot bus on the entire network voltage profile is evaluated. The IEEE 33-bus distribution network is used to evaluate the proposed two-timescale volt/var optimization formulations and methods with promising results. [ABSTRACT FROM AUTHOR]

This paper proposes a holistic framework of data-driven distributionally robust joint chance constrained economic dispatch (ED) optimization, which seamlessly incorporates deep learning-based optimization for effective utilization of renewable energy in power systems. By leveraging a deep generative adversarial network (GAN), an f-divergence-based ambiguity set of wind power distributions is constructed as a ball centered around the probability distribution induced by a generator neural network. In particular, the GAN is well suited for capturing complicated spatial and temporal correlations of wind power. Based upon this ambiguity set, a distributionally robust joint chance constrained ED model is developed to hedge against distributional uncertainty present in multiple constraints, without assuming a perfectly known probability distribution. The proposed deep learning based ED optimization framework greatly mitigates the conservatism inflicting on distributionally robust individual chance constrained optimization. Theoretical a priori bound on the required number of synthetic wind power data generated by GAN is explicitly derived for the multi-period ED problem to guarantee a predefined risk level. The effectiveness and scalability of the proposed approach are demonstrated in the six-bus and IEEE 118-bus systems by comparing with the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Virtual power plant (VPP) has gradually become a key technology to the increasing penetration of renewable energy. The uncertainty and variability of renewable energy and load demand pose significant challenges to the efficiency and stability of VPP's operation. In this paper, a data-driven two-stage stochastic robust optimization (SRO) scheduling model is proposed for a VPP considering wind power, solar power, load demand, and market price uncertainties. The objective is to maximize the profit of the VPP in the energy market and minimize the total system cost of the VPP in the reserve market under the worst-case realization of the uncertainties. The Dirichlet process mixture model (DPMM) and variational inference algorithm are employed for constructing the data-driven uncertainty ambiguity set considering the correlations among multiple uncertainties. The tailored column-and-constraint generation algorithm is developed to solve the SRO model iteratively by reformulating the second stage with the application of the Karush-Kuhn-Tucker conditions. Results from a case study illustrate the effectiveness and superiority of the proposed model. [ABSTRACT FROM AUTHOR]

With Europe dedicated to limiting climate change and greenhouse gas emissions, large shares of Renewable Energy Sources (RES) are being integrated in the national grids, phasing out conventional generation. The new challenges arising from the energy transition will require a better coordination between neighboring system operators to maintain system security. To this end, this paper studies the benefit of exchanging primary frequency reserves between asynchronous areas using the Supplementary Power Control (SPC) functionality of High-Voltage Direct-Current (HVDC) lines. First, we focus on the derivation of frequency metrics for asynchronous AC systems coupled by HVDC interconnectors. We compare two different control schemes for HVDC converters, which allow for unilateral or bilateral exchanges of reserves between neighboring systems. Second, we formulate frequency constraints and include them in a unit commitment problem to ensure the N-1 security criterion. A data-driven approach is proposed to better represent the frequency nadir constraint by means of cutting hyperplanes. Our results suggest that the exchange of primary reserves through HVDC can reduce up to 10% the cost of reserve procurement while maintaining the system N-1 secure. [ABSTRACT FROM AUTHOR]

Chance-constrained economic dispatch (CCED) is widely used to cope with uncertainties brought by renewable energy sources. In CCED, security of power system is guaranteed by restricting risks under permitted level. As the penetration rate of renewable energy increases rapidly, the CCED model may be infeasible because of inadequate system reserve and/or transmission congestion under certain circumstances. Therefore, the curtailment of renewable energy is indispensable to guarantee security in some scenarios for power systems with high penetration of renewable energy. To address this crucial issue, this paper proposes a novel CCED model, where generation of conventional units and curtailment strategies of renewable energy are co-optimized to minimize total operational cost and restrict operational risks. An efficient solution method is developed to schedule generation and curtailment sequentially, in which tractable optimization models are formulated for each step. Numerical tests demonstrate that the proposed model can significantly reduce the probability of emergency control of curtailment compared with conventional CCED models. Furthermore, this solution method also outperforms scenario-based method with significantly improved computational efficiency and higher-quality 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]

Appropriately designed renewable support policies can play a leading role in promoting renewable expansions and contribute to low emission goals. Meanwhile, ill-designed policies may distort electricity markets, put power utilities and generation companies on an unlevel playing field and, in turn, cause inefficiencies. This paper proposes a framework to optimize policymaking for renewable energy sources, while incorporating conflicting interests and objectives of different stakeholders. We formulate a tri-level optimization problem where each level represents a different entity: a state regulator, a power utility and a wholesale electricity market. To solve this tri-level problem, we exploit optimality conditions and develop a modification of the Column-and-Cut Generation (C&CG) algorithm that generates cuts for bilinear terms. The case study based on the ISO New England 8-zone test system reveals different policy trade-offs that policymakers face under different decarbonization goals and implementation scenarios. [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 proposes a new scheme for bulk system restoration considering the available black-start resources (BSRs) in the distribution system (DS). The DS assisted generator start-up sequence (D-GSS) scheme is realized in a decentralized way, so that it does not only benefit the bulk system GSS by utilizing available BSRs in the DS, but also respects the independent operation of the transmission system operator (TSO) and distribution system operators (DSOs). First, the decentralized D-GSS scheme is presented including the interaction of the TSO and DSOs and the corresponding compact models. The models of the decentralized D-GSS scheme are built with the bulk system GSS modeled as a mixed-integer quadratic program (MIQP), the DS multi-step operation modeled as mixed-integer second-order conic programs (MISOCPs) and reliable power supply assessments of renewable energy sources as linear programs (LPs). Finally, a projection function based analytical target cascading (P-ATC) method is developed to iteratively solve the decentralized models with model complexity reduction. The P-ATC algorithm can handle integer variables and improve the computational efficiency of the iterative calculation process. The effectiveness of the proposed method is validated using the small-scale T6D2 system and large-scale T118D5 system, showing good GSS performance and computation efficiency. [ABSTRACT FROM AUTHOR]

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]

This paper deals with the impact of linear approximations for the unknown nonconvex confidence region of chance-constrained ac optimal power flow problems. Such approximations are required for the formulation of tractable chance constraints. In this context, we introduce the first formulation of a chance-constrained second-order cone (SOC) OPF. The proposed formulation provides convergence guarantees due to its convexity, while it demonstrates high computational efficiency. Combined with an ac feasibility recovery, it is able to identify better solutions than chance-constrained nonconvex ac-OPF formulations. To the best of our knowledge, this paper is the first to perform a rigorous analysis of the ac feasibility recovery procedures for robust SOC-OPF problems. We identify the issues that arise from the linear approximations, and by using a reformulation of the quadratic chance constraints, we introduce new parameters able to reshape the approximation of the confidence region. We demonstrate our method on the IEEE 118-bus system. [ABSTRACT FROM AUTHOR]

As the level of uncertain renewable capacity increases on power systems worldwide, industrial and academic researchers alike are seeking a scalable, transparent, and effective approach to unit commitment under uncertainty. This paper presents a statistical ranking methodology that allows adaptive robust stochastic unit commitment using a modular structure, with much-needed flexibility. Specifically, this paper describes a bus ranking methodology that identifies the most critical buses based on a worst-case metric. An important innovation is the ability to identify alternative metrics on which to rank the uncertainty set—for example, to minimize economic dispatch cost or ramping needs, to provide a customized robust unit commitment solution. Compared to traditional robust unit commitment models, the proposed model combines statistical tools with analytical framework of power system networks. The resulting formulation is easily implementable and customizable to the needs of the system operator. The method and its applications are validated against other established approaches, showing equivalent solution to the state-of-the-art approach. Case studies were conducted on the IEEE-30, IEEE-118, and the pegase-1354 networks. In addition, the flexibility of bus ranking formulation is illustrated through implementation of alternative definitions of worst-case metrics. Results show that the bus ranking method performs as well as the best of these methods, with the provision of additional flexibility and potential for parallelization. [ABSTRACT FROM AUTHOR]

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

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

Increasing the penetration of variable generation has a substantial effect on the operational reliability of power systems. The higher level of uncertainty that stems from this variability makes it more difficult to determine whether a given operating condition will be secure or insecure. Data-driven techniques provide a promising way to identify security rules that can be embedded in economic dispatch model to keep power system operating states secure. This paper proposes using a sparse weighted oblique decision tree to learn accurate, understandable, and embeddable security rules that are linear and can be extracted as sparse matrices using a recursive algorithm. These matrix rules can then be easily embedded as security constraints in power system economic dispatch calculations using the Big-M method. Tests on several large datasets with high renewable energy penetration demonstrate the effectiveness of the proposed method. In particular, the sparse weighted oblique decision tree outperforms the state-of-art weighted oblique decision tree while keeping the security rules simple. When embedded in the economic dispatch, these rules significantly increase the percentage of secure states and reduce the average solution time. [ABSTRACT FROM AUTHOR]

High shares of renewable energy resources are increasing the value of using demand response (DR) mechanisms to enhance the resiliency and efficiency of power system operation. In this context, residential DR is expected to become an increasingly important asset. In order to exploit this resource, DR aggregators are expected to combine the capabilities of a large group of householders and participate, as a single provider, in the electricity market. In doing so, it is imperative for aggregators to consider the operational constraints of the local network. Otherwise, the quality of the electricity service can be jeopardized and the true DR potential overestimated. This paper presents a novel methodology that integrates DR aggregators with distribution network operators for a secure and efficient scheduling and real-time operation of DR in residential radial feeders. The method is evaluated on a real unbalanced feeder where DR provision (from a mix of technologies) is coordinated with the network steady-state thermal and voltage limits. In this study, with the corresponding data seasonality and controllable devices, it is shown that complying with network operational constraints can impose, at certain times, a significant limit to the allocation of DR. [ABSTRACT FROM AUTHOR]

As significant amounts of renewable distributed generation (RDG) are installed in the power grid, it becomes increasingly important to plan RDG integration to maximize the utilization of renewable energy and mitigate unintended consequences, such as phase unbalance. One of the biggest challenges in RDG integration planning is the lack of sufficient information to characterize uncertainty (e.g., load and renewable output). In this paper, we propose a two-stage data-driven distributionally robust optimization model (O-DDSP) for the optimal placement of RDG resources, with both load and generation uncertainties described by a data-driven ambiguity set that both enables more flexibility than stochastic optimization (SO) and allows less conservative solutions than robust optimization (RO). The objective is to minimize the total cost of RDG installation plus the total operational cost on the planning horizon. Furthermore, we introduce a tight approximation of O-DDSP based on principal component analysis (leading to a model called P-DDSP), which reduces the original problem size by keeping the most valuable data in the ambiguity set. The performance of O-DDSP and P-DDSP is compared with SO and RO on the IEEE 33-bus radial network with a real data set, where we show that P-DDSP significantly speeds up the solution procedure, especially when the problem size increases. Indeed, as compared to SO and RO, which become computationally impractical for solving problems with large sample sizes, our proposed P-DDSP can use large samples to increase solution accuracy without increasing the solution time. Finally, extensive numerical experiments demonstrate that optimal RDG planning decisions lead to significant savings as well as increased renewable penetration. [ABSTRACT FROM AUTHOR]

The uncertainty has been one of the main obstacles in the operation of distribution systems with renewable energy resources whose power generation is, by nature, highly intermittent, often resulting in the unbalanced conditions of distributed networks. This unbalance degrades voltage profiles and, thus, aggravates power loss consumed in distributed networks. In this sense, the pragmatic coordination scheme between day-ahead and real-time optimization to achieve economic and stable operation is presented in this paper. At the day-ahead optimization stage, the objective aims to minimize operation costs by controlling the energy storage system such as battery systems. This stage is based primarily on historical data about the daily profiles of power demands or renewable distributed generations, so uncertain elements are always inevitable in operational procedures. The real-time monitoring system plays a pivotal role in computing present operating conditions on a real-time basis sufficient to address these uncertainties of renewable energy resources. The operating conditions are, then, utilized to formulate the objective function and relevant constraints to calibrate control orders once decided at the day-ahead optimization stage. This paper explains the proposed coordination scheme with real-time monitoring capability and, then, presents the test results of numerical experiments with a 15-bus test distribution system. [ABSTRACT FROM AUTHOR]

This paper examines optimal energy market bidding behavior for stochastic resources when energy imbalance payments are determined endogenously from market clearing conditions. Some electricity markets require wind producers to settle day-ahead offers based on their real-time energy production. This is usually justified by economic and cost-causation principles, without considering the effects of these policies on curtailment and system balancing costs. Under these real-time settlement requirements, demand and wind forecast errors impact the effective penalty price, so strategic behavior affects the penalty price paid by producers. This paper formulates a two-stage game where producers place energy bids in the day-ahead market and then choose a curtailment level in real-time, and it derives the symmetric subgame perfect equilibrium strategy for producers. It details how supply curve convexity and resource correlation can lead wind producers to bid conservatively even when they are not risk averse. The results show that market-based pricing mechanisms improve tradeoffs between system efficiency and mean squared bid error as compared to the case where penalty levels are determined by alternative policies, suggesting additional benefits of market-based penalty prices beyond those previously studied. [ABSTRACT FROM AUTHOR]

Inspired from recent insights into the common ground of machine learning, optimization and decision-making, this paper proposes an easy-to-implement, but effective procedure to enhance both the quality of renewable energy forecasts and the competitive edge of renewable energy producers in electricity markets with a dual-price settlement of imbalances. The quality and economic gains brought by the proposed procedure essentially stem from the utilization of valuable predictors (also known as features) in a data-driven newsvendor model that renders a computationally inexpensive linear program. We illustrate the proposed procedure and numerically assess its benefits on a realistic case study that considers the aggregate wind power production in the Danish DK1 bidding zone as the variable to be predicted and traded. Within this context, our procedure leverages, among others, spatial information in the form of wind power forecasts issued by transmission system operators (TSO) in surrounding bidding zones and publicly available in online platforms. We show that our method is able to improve the quality of the wind power forecast issued by the Danish TSO by several percentage points (when measured in terms of the mean absolute or the root mean square error) and to significantly reduce the balancing costs incurred by the wind power producer. [ABSTRACT FROM AUTHOR]

Recent research on optimal power flow (OPF) in networks with renewable power involves optimizing both first and second stage variables that adjust the decision once the uncertainty is revealed. In general, only partial information on the underlying probability distribution of renewable power production is available. This paper considers a distributionally robust framework for solving the OPF problem. The formulation stipulates a probability mass function of wind power production, whose probabilities and scenario locations vary in a box of ambiguity with bounds that can be tuned based on historical data. Distributionally robust optimization (DRO) is used to derive new conditional value-at-risk (CVaR) constraints that limit the frequency and severity of branch flow limit violations whenever the renewable power generation deviates from its forecast. Numerical results are reported on networks with up to 2736 nodes and contrasted with classical robust optimization (RO) and stochastic optimization (SO) solutions. The results show an advantage to adopting the proposed DRO for load flow control. In particular, the solution benefits from the observed correlation amongst the uncertain parameters to mitigate branch flow limit violations, and yet maintain an acceptable worst-case expected operational cost as compared to RO and SO solutions. [ABSTRACT FROM AUTHOR]

Coordinated operations of electricity and district heating networks offer a potential for mitigating inherent variability of renewable energy sources (RES) in the ongoing transition to smart grids. This paper proposes a two-stage distributionally robust optimization (DRO) approach to determine the optimal day-ahead unit commitment in coordinated electricity and district heating networks with variable RES power output. The proposed formulation is to minimize the worst-case expected total cost over an ambiguity set comprising a family of probability distributions with given support and moments of RES power output. As such, the proposed DRO approach can overcome the limitations of stochastic programming in its inherent dependence of exact probability distributions along with a huge computational burden, but also becomes less conservative than classical robust optimization. The pertinent DRO model is eventually reformulated as a tractable mixed-integer second-order cone (SOC) programming after employing linear decision rules and the SOC duality. Simplified affine policies are utilized to further improve computational tractability and performance. Finally, case studies are conducted based on Barry Island electricity and district heating networks. The numerical results demonstrate the decision-making superiority of the proposed method as compared with deterministic, stochastic programming, and robust optimization approaches. They also validate the computational improvement of the proposed approach by employing simplified affine policies. [ABSTRACT FROM AUTHOR]

AC–DC hybrid distribution network is viewed as a featured system to efficiently connect to all kinds of power sources and loads. In order to improve the system robustness, adapting to random fluctuations of renewable energy sources, this paper proposed a robust optimal coordinated control method for multiple voltage source converters (VSCs) in AC–DC distribution network. A robust optimization model was established to co-optimize the slopes of active and reactive power droop control of VSCs with the aim to minimize the total network loss, while ensuring the system security. VSC capacity coupling and power flow constraints were both considered. Then, to enhance the computational tractability of the problem, based on the column-and-constraint generation algorithm, ${V^2} - P$ and ${V^2} - Q$ were implemented in the droop control schemes holding the linear feedback characteristic so that the non-convex max–min sub-problem can be transformed into a mixed integer second-order cone (SOC) programming problem. Furthermore, to increase the accuracy of SOC relaxation in the sub-problem, a current limit strategy was designed where the maximum possible network loss was pre-identified to restrain the feasible range of branch current. Numerical experiments suggest that the proposed coordinated control method can improve the system security with little extra economic cost, and the reliability of the results is enhanced by the proposed current limit strategy. [ABSTRACT FROM AUTHOR]

To deal with the difficulties caused by uncertainty of renewable energy sources in solving transmission constrained unit commitment (TCUC), robust optimization (RO) and scenario-based stochastic optimization (SO) methods have gained popularity in recent years. However, RO formulations have a multilevel (min-max-min or min-max) structure and the solution methods are usually complicated. On the other hand, when SO-based formulation is adopted, a careful balance is often required between accuracy and scale of the formulation, since they are conflicting with each other when determining the number of scenarios. Moreover, nonanticipative constraints on economic dispatch (ED) decisions are sometimes not considered in two-stage stochastic UC formulation. An example is given in this paper to show that this may have a serious consequence. The motivation of this paper is to establish a TCUC formulation that can address the above concerns. In summary, the proposed formulation has three features including: it is single-level rather than multilevel, it is established based on very limited scenarios while the solution is feasible to all scenarios, and finally, nonanticipativity of both UC and ED decisions is guaranteed by the formulation. Numerical testing is also performed and the results show that the proposed formulation is effective. [ABSTRACT FROM AUTHOR]

The concept of energy hub (EH) was proposed to facilitate the synergies among different forms of energy carriers. Under the new electricity market environment, it is of great significance to build a win–win situation for prosumers and the hub manager (HM) at the community level without bringing extra burden to the utility grid. This paper proposes a cooperative trading mode for a community-level energy system (CES), which consists of the energy hub and PV prosumers with the automatic demand response (DR) capability. In the cooperative trading framework, a real-time rolling horizon energy management model is proposed based on cooperative game theory considering the stochastic characteristics of PV prosumers and the conditional value at risk (CVaR). The validity of the proposed model is analyzed through optimality proof of the grand coalition. A contribution-based profit distribution scheme and its stability proof are also provided. Moreover, in order to solve the optimization model, it is further transformed into a more easily resolved mixed integer linear programming (MILP) model by adding auxiliary variables. Finally, via a practical example, the effectiveness of the model is verified in terms of promoting local consumption of PV energy, increasing HM's profits, and reducing prosumers’ costs, etc. [ABSTRACT FROM AUTHOR]

This paper develops a tractable formulation for optimal placement and sizing of inverter-based renewable systems in multi-phase distribution networks. The goal of the formulation is to minimize the cost of inverter installation, average power import, and average distributed generation curtailment. Three-phase and single-phase inverter models are presented that preserve the underlying mappings between renewable uncertainty to power injection. The uncertainty of distributed generators (DGs) and loads are characterized by a finite set of scenarios. Linear multi-phase power flow approximations are used in conjunction with scenario reduction techniques to arrive at a tractable two-stage stochastic formulation for optimal DG placement and sizing. First-stage decisions are locations for DG deployment and capacity sizes, and second-stage decisions include DG real power curtailment, reactive power support, as well as feeder voltage profile. The resulting formulation is a mixed-integer second-order cone program and can be solved efficiently either by existing optimization solvers or by relaxing the binary variables to the [0,1] interval. Simulation studies on standard multi-phase IEEE test feeders promise that optimal stochastic planning of DGs reduces costs during validation, compared to a scheme where uncertainty is only represented by its average value. [ABSTRACT FROM AUTHOR]

This paper studies key aspects of preventive and corrective security strategies to coordinate flexible transmission network infrastructure. To do so, we propose a two-stage stochastic optimization model that can efficiently coordinate available preventive and corrective control actions (pre- and post-contingency) from flexible network technologies, generation, and demand, while explicitly considering the likelihood of postcontingency events and wind/solar uncertainty. This stochastic/probabilistic model constitutes the counterfactual against which current deterministic, preventive operational practices are compared. Flexible network equipment such as HVDC and FACTS devices are efficiently modeled through a tight MILP representation and network losses are also included through a linear representation. Through several case studies, we demonstrate the advantages of probabilistic, corrective security to improve coordination of HVDC and FACTS setpoints and thus reduce network congestion and reserve holding levels, improving the overall efficiency of the system operation. We also quantify the value loss associated with current deterministic, preventive control operational practices when coordinating setpoints of flexible network equipment, demonstrating that adding flexible network technology could even increase system costs under a preventive security approach. [ABSTRACT FROM AUTHOR]

Distributed generation (DG) has been rapidly integrated into microgrids. However, uncertain power generation of intermittent DG such as wind turbines brings challenges to the DG planning problem. This paper proposes a novel probability-weighted robust optimization (PRO) method to allocate DG units including microturbines and wind turbines in microgrids, aiming to maximize the total profit over a long-term planning horizon. First, probability-weighted uncertainty sets are proposed to model uncertainties including wind turbine output and load demand during a long-term planning horizon which can fully cover the uncertainty spectrum and accurately represent the uncertainty probability distribution. Then, the PRO method optimizes DG sizing and locating under the worst uncertainty cases considering their occurrence probabilities. Therefore, the planning decision is robust against any possible uncertainty realization. Besides, a modified column-and-constraint generation algorithm is developed to solve the PRO problem. Simulation results show that the DG planning obtained by the proposed method can achieve full operating robustness. [ABSTRACT FROM AUTHOR]

The ever-growing insertion of intermittent energy sources requires to account for this uncertainty by precise models. Probabilistic constraints are an interesting technique to deal with the high fluctuations of such energy resources, while accounting for power flow and unit generating constraints. In the context of hydrothermal unit commitment problems, with a significant share of wind power generation, this paper suggests a novel mixed integer optimization model with joint probability constraints and continuous distributions that handles the probability constraints exactly. Thus, extending classical cutting plane methods, the approach provides at each iteration a feasible solution and a certificate on its gap to optimality. The efficiency of the algorithm is tested by numerical experiments when compared to two popular probability constrained approaches: individual and a sample-based method. A set of out-of-sample Monte-Carlo evaluations confirms that the solutions provided by the algorithm do indeed satisfy the a priori defined probability level with optimal costs, contrary to the solution given by individual probability constraints. The simulations also intend to highlight the advantages of the proposed optimization model since it does not depend on the set of sampled scenarios. The proposed method is also evaluated on a 46-bus based system, showing its capabilities on larger systems. [ABSTRACT FROM AUTHOR]

The rapid development of microgrid (MG) has made it ready to connect multiple MGs for providing regional power supply. The energy management of a multi-MG (MMG) system is the key to the reliable, economic operation of the interconnected power system. The MMG system is rich in distributed generation sources. The intermittence and volatility of renewable energy sources (RESs), such as wind and solar, cannot be ignored in a large-scale hybrid power system. Therefore, the energy management of a MMG system is a complex problem that coordinates distributed generation units within individual MGs, the power exchange among MGs, and the power trading between the grid and MGs. System of systems (SoS) has been identified as an effective way of forming a MMG system and coordinating the participating MGs for energy management. This paper proposes a hierarchical decentralized SoS architecture for the energy management of a MMG system and, accordingly, formulates it as a bilevel optimization problem. Energy management at the level of individual MGs is modeled as a multiple-stage robust optimization to handle the issue of RES uncertainty. Energy management at the level of MMG system further addresses the problem of spatially unbalanced demand and generation in the area. The proposed MMG energy management is further verified through a case study. [ABSTRACT FROM AUTHOR]

Uncertainties from generation sources and loads have introduced tremendous challenges to the optimal dispatch of microgrids. This paper presents a novel two-stage min–max–min robust optimal dispatch model for a representative islanded ac/dc hybrid microgrid that faces uncertainties in renewable energy generation and customer loads. The first stage of the model determines the startup/shutdown state of the diesel engine generator and the operating state of the bidirectional converter of the microgrid. Then, the second stage optimizes the power dispatch of individual units in the microgrid. A new linearized equipment cost model is developed, counting for the degradation of energy storage. The use of this linear model helps maintain the linearity of the objective function without compromising solution accuracy. The column-and-constraint generation algorithm is implemented to efficiently obtain a robust dispatching plan for the microgrid, which minimizes the daily operating cost in the worst-case scenario. A case study and sensitivity analyses further demonstrate the rationale and the unique capability of the proposed model for the operation scheduling of ac/dc hybrid microgrids. [ABSTRACT FROM AUTHOR]

In this paper, an online multiperiod power dispatch with renewable uncertainty and storage is presented. The ac power flow equations, voltage limits, and thermal limits are respected to ensure the obtained solution causes no static violation while ensuring network transfer capability. A scenario reduction technique using affinity propagation clustering is developed to reduce the number of scenarios and relieve the computational burden. A three-stage solution methodology is developed to solve the nonconvex constrained optimization problem, in which a two-parameter homotopy-enhanced methodology with a decomposition scheme is developed to reliably and quickly solve the online multiperiod power dispatch problem. The proposed three-stage solution methodology has been evaluated on several testing systems, ranging from a 30-bus system to a 3012-bus system with four time periods, and the numerical results are promising. [ABSTRACT FROM AUTHOR]

The distribution system asset (DSA) planning process for a new or existing subdivision involves a comparison of several feasible plans and selection of the least costly plan. The costs comprise the cost of new assets and their replacements, operation and maintenance costs, as well as reliability costs. DSA planning tools have been used for distribution utilities for decades, so that mature methods are available for traditional distribution systems. However, most of the DSA planning tools fail to include battery energy storage systems (BESS) as an asset solution for systems with high penetration of renewable energy sources. In addition, minimizing the investment cost and maximizing the reliability performance, which can be measured by the system average interruption duration index (SAIDI), are contradicting objectives. With a large investment, the system will have a small SAIDI, and vice versa. In this paper, a multi-objective algorithm that uses fuzzy optimization technique to handle these contradicting objectives is proposed. The algorithm includes traditional types of assets as well as BESS. One of the main advantages of the proposed method is that the customer interruption costs are not explicitly necessary, as these values cannot be precisely determined for all loads. In the tool, the annual investment cost and SAIDI are minimized, and the optimal size of BESS is obtained. Its performance is demonstrated on a 33-bus distribution system and the results are compared with other methods available in the literature. [ABSTRACT FROM AUTHOR]

Increasing penetration of distributed generators (DGs) and intelligent loads necessitates a transactive system, where a distribution system operator (DSO) is required to submit bidding curves for its net demand. This paper proposes a price-maker bidding approach for a DSO that captures distribution power flows, constraints, and uncertainties arising from DGs and loads. A neurodynamic algorithm is proposed to ensure that the bidding curve can be derived in real time. Simulation results justify the need for considering constraints and uncertainties in the bidding model and explain how these factors impact the bidding curve. [ABSTRACT FROM AUTHOR]

Recent revolution of the electricity distribution sector, especially a deeper penetration of gas-fired distributed generations (DGs), intensifies the interdependence of electricity on natural gas distribution systems. Such integrated electricity and natural gas distribution systems (IENDS) are facing with significant threats from frequent natural disasters that cause enormous economic losses. Network hardening is regarded as an effective technique for enhancing resilience of IENDSs against natural disasters. This paper presents a trilevel robust optimization-based network hardening model for minimizing worst-case total weighted electricity and gas load shedding of IENDSs with respect to hardening budget limits and random damages caused by disasters of different severity levels. Specifically, distinct failure probabilities of overhead power lines and underground gas pipelines are considered, while DGs and gas storages are modeled as effective emergency response resources for supplying high-priority electricity/gas loads during disasters. The proposed model is solved by a column-and-constraint generation approach, in which nonlinear gas network constraints are linearized via Taylor series expansion. Numerical case studies evaluate the proposed robust hardening strategy against natural disasters. [ABSTRACT FROM AUTHOR]

With integration of more and more renewable energy resources, it is becoming increasingly difficult to maintain adequate primary frequency control (PFC) capability for a future power grid, especially under low system inertia conditions. Load resources (LRs) equipped with under-frequency relays can participate in PFC supplementing to the governor responses from synchronous units. In this paper, we propose an energy, inertia and frequency response reserve (FRR) co-optimization formulation in the day-ahead market where both primary frequency reserve (PFR) from synchronous generators and fast frequency response reserve (FFR) from LRs are procured in a cooperative way to meet the desired FRR need tied to the system inertia condition. Since FFR is more effective than PFR in arresting the frequency decline, the proposed approach will yield different marginal prices for FFR and its PFR counterpart to award the speed of response. As the formulation proposed involves bilinear terms in optimization problem, a linear reformulation techniques with big M is proposed to transform the problem into a mixed integer linear programming which can be solved by the commercial solver CPLEX. The case study shows the effectiveness of the proposed approach and the correctness of the quantities and prices of the cleared reserve. [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]