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This paper presents a method for controlling the voltage of inverter-based Microgrids by proposing a new scale-free distributed cooperative controller. The main contribution of this paper is that the proposed distributed cooperative controller is scale-free where is independent of any information about the communication system and the number of distributed generators, as such it works for any Microgrids with any size. Moreover, the communication network is modeled by a general time-varying graph which enhances the resilience of the proposed protocol against communication link failure, data packet loss, and arbitrarily fast plug and play operation in the presence of arbitrarily finite communication delays as the protocol does not require the knowledge of the upper bound on the delay. The stability analysis of the proposed protocol is provided. The proposed method is simulated on the CIGRE medium voltage Microgrid test system. The simulation results demonstrate the feasibility of the proposed scale-free distributed nonlinear protocol for regulating voltage of Microgrids in the presence of communication failures, data packet loss, noise, and degradation. [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 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]

Thermostatically controlled loads (TCLs) are regarded as one of the promising resources for suppressing power fluctuations due to renewable energy (RENs). However, due to the great burdens of fully considering each users’ characteristics, it is difficult to achieve unity of the individual optimal decisions and global optimum in demand-side management (DSM). This paper proposes a game-theoretic DSM that can optimize the global power consumption schedule by individual TCL user's optimization. By integrating the prediction of REN outputs into the pricing mechanism, the proposed DSM can guide the users to make their best power consumption schedules along with intermittent REN generations, thus to smooth the tie-line power of microgrids. In this paper, a novel pricing mechanism is firstly developed based on the concave N-person game theory, which is more adaptive and flexible compared with existing game-theoretic DSM. Then, an individual's power consumption optimization and its simplified model are developed considering the constraints of the TCL model and personal preferences. The simplified model can be easily solved and achieve a fast solution in the power consumption game. An implementation framework of the proposed DSM is further developed for practical application. Finally, numerical studies verify the effectiveness of the proposed models and methods. [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]

Ensuring long-term voltage stability is critical for reliable operations of power grids. High share of distributed energy resources (DERs) can create complicated system operation modes that may invalidate the traditional long-term voltage stability analysis based on typical operation modes. To address this challenge, this paper investigates how to compute the shortest path to the voltage stability boundary in the DER aggregated load space with large dispersion. Instead of working in the Euclidean space, we establish the analysis and computations on the algebraic power flow manifold to better capture the curvature change of the shortest path along the direction of losing stability. A modified optimal control framework is presented for obtaining the ground-truth of the smooth shortest path on the manifold. To efficiently and accurately solve for the shortest path, we further leverage the geometric features of the power flow manifold and propose a tri-sectional approximation model that is scalable for large-scale systems. Several numerical examples, up to the 1354-bus system, with different DER penetration levels and high dimensional renewable power injection variations are evaluated. The simulation results demonstrate that the tri-sectional approximation achieves high accuracy and efficiency to approximate the shortest path to the voltage stability boundary. [ABSTRACT FROM AUTHOR]

Achieving the low-carbon transition of power systems requires the coordination of renewable energy generation and other emerging electricity technologies. Their technical indicators are changing rapidly since these technologies are in the initial stages of development. Determining the technical and policy targets for achieving the low-carbon transition is critical for regulators and power system planners. This paper defines this problem as a backcasting problem, whose concept is derived from environmental science research. We introduce it into the power system planning field and innovatively model it as a bi-level optimization problem. According to the characteristics of the backcasting problem, an improved barrier method is proposed to solve it efficiently. The effectiveness of the proposed model and algorithm are verified through case studies on a modified Garver’s 6-bus system and a realistic Northwest China power system, and they are compared with state-of-the-art solution techniques. The results of the backcasting problem provide a new perspective on the economic impacts of the low-carbon transition and are helpful in energy policy formulation for power systems. [ABSTRACT FROM AUTHOR]

The high penetration of renewables has sparked new oscillatory concerns in hybrid AC/DC grids. Knowledge of the oscillation regarding its source and propagation mechanism, is crucial to system operation. In this respect, the frequency-domain modal analysis (FMA) provides a way (e.g., participation factor) to extract these oscillation properties, and has been widely applied in converter-based AC grids. Compared to AC grids, oscillation properties of hybrid AC/DC grids are much more complex. Such complexity mainly originates from the diversity of oscillation propagation behaviors in hybrid AC/DC grids, where a distinctive local-area oscillation will emerge. Therefore, a dedicated oscillation propagation analysis for hybrid AC/DC grids is desired, which is the main focus of this paper. First, the mechanism of the distinctive local-area oscillation is analyzed considering AC/DC coupled dynamics of converters. Then, a systematic method for the oscillation propagation analysis is presented, where indices for characterizing the local-area oscillation and its impact area are established. Finally, some propagation properties are discussed, by which a strategy for the online oscillation source locating is designed. Case studies are carried out in a typical hybrid AC/DC grid to validate the propagation analysis in this paper. [ABSTRACT FROM AUTHOR]

High renewable energy penetration increases the electricity seasonal imbalance in the long-term timescale. Power system planning needs to consider the optimal configuration of various flexibility resources and electricity balance in different timescales. The coupling of multiple timescales largely increases the computation complexity of the power system planning problem. Thus, this paper presents an efficient source-grid-storage co-planning model which incorporates a year-round hourly operation simulation. To improve the computation efficiency of the planning model, from the temporal scale, a self-adaptive compact panorama time series (CPTS) model is applied, which greatly reduces the number of variables related to short-term decisions. From the spatial scale, a network-constrained relaxed clustered unit commitment (NC-RCUC) model is introduced, which significantly reduces the number of variables related to unit commitment decisions. Case studies on the modified Garver’s 6-node system and HRP-38 system prove the validation and efficiency of the proposed model (“HRP” stands for high renewable penetration). The studies on the China power grid in 2035 demonstrate the future planning results of generation, transmission and storage in China power systems based on the proposed model. [ABSTRACT FROM AUTHOR]

The low-frequency oscillations (LFOs) inherent in power systems will be impacted by the increasing penetration of renewable energy sources (RESs). This paper investigates the impact of virtual synchronous machine (VSM) based RESs on the LFOs in power systems. A detailed two-machine test-bed has been developed to analyze the LFOs which exists when VSMs replace synchronous generators. The characteristics of the LFO modes, and the dominant states have been comprehensively analyzed. Furthermore, this study analyzes the LFO modes which exists in an all-VSM grid. The role of the power system stabilizers in the all-VSM grid has been comprehensively evaluated. The IEEE benchmark two-area four-machine system has been employed to corroborate the results of the small-signal analysis, and observe the transient performance. The analysis in this paper have been performed in MATLAB/SIMULINK environment. [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 proposes a market framework to approach economic dispatch as a subproblem in smart distribution systems. Four subproblems are associated with four different submarkets (SMs) in the presented framework. Market participants are eligible to bid in different submarkets based on the type of their distributed generation (DG) unit. To effectively tackle the conflicts among objective functions of different submarkets, the corresponding formulated subproblems are assigned to two different agents, namely distribution system operator (DSO) and a green bank agent (GBA). A communication mechanism is designed within the proposed framework such that DSO and GBA compromise their solutions and find a tradeoff to reasonably address the concerns of the four subproblems within SMs 1-4. The effectiveness of the proposed market framework is validated on a well-known 136-bus distribution system, which is modified to contain wind turbine DG aggregators, photovoltaic DG aggregators, and diesel-engine DG aggregators. [ABSTRACT FROM AUTHOR]

This paper proposes a new uncertainty quantification framework for power flow (PF) and optimal power flow (OPF) considering the nonlinear correlations of uncertain power injections with limited information. The D-Vine copula is leveraged to capture the nonlinear correlations among uncertain power injections from historical data. This is further integrated with the evidence theory and the reformulated quadratic affine form to obtain PF and OPF results. The D-Vine copula and evidence theory allow one to effectively eliminate the explosive-growth joint focal elements of large-scale power system with large numbers of partial known uncertain power injections, leading to significant reduction of computing time. The reformulated quadratic affine form aims at characterizing the PF and OPF outputs with partially known uncertain power injections in a simple form based on Dempster-Shafer structure, yielding further computational efficiency improvement without the loss of accuracy. Comparison results with other alternatives show that the proposed framework leads to more accurate PF and OPF outcomes while achieving high computational efficiency for large-scale power systems with large numbers of nonlinear correlated power injections in presence of limited information. [ABSTRACT FROM AUTHOR]

Penetration of renewable energy resources (RERs) in the power grid continues to increase as we strive toward a greener environment for the future. While they have many advantages, most RERs possess little or no rotational kinetic energy, thereby threatening the frequency stability of future power grids. Energy storage systems (ESSs) can be used to mitigate this problem, as they are capable of providing virtual inertia to the system. This paper proposes a novel analytical approach for sizing ESSs to provide inertial support to the grid and maintain frequency stability in presence of RERs. This method analytically estimates the total inertia of the system using probability distributions of the outage states of conventional generators and RERs. RERs are modeled as multi-state units, considering the variability of their output power due to changes in weather conditions and also the forced outages of their equipment. The ESS is utilized to provide virtual inertia to the grid in the form of active power once the estimated system inertia falls below the minimum required during a disturbance. The efficacy of the proposed approach is tested on the IEEE 39 bus system and the results obtained by the analytical approach are validated using Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

Emergency frequency control is one of the most critical approaches to maintain power system stability after major disturbances. With the increasing number of grid-connected renewable energy sources, existing model-based methods of frequency control are facing up with challenges of computational speed and scalability for large-scale systems. In this paper, the emergency frequency control problem is formulated as a Markov Decision Process and solved through a novel distributional deep reinforcement learning (DRL) method, namely the distributional soft actor critic (DSAC) method. Compared with other reinforcement learning methods that only estimate the mean value, the proposed DSAC model estimates the distribution of value function over returns. This advancement can lead to more insights and knowledge for the agent, with the benefit of a much faster and more stable learning process, and the improved frequency control performance. The simulation results on IEEE 39-bus and IEEE 118-bus systems demonstrate the effectiveness and robustness of proposed models, as well as the advantage compared to other state-of-the-art DRL algorithms. [ABSTRACT FROM AUTHOR]

As an important application in the power system operation and electricity market clearing, the network-constrained unit commitment (NCUC) problem is usually executed by Independent System Operators (ISO) in an open-looped predict-then-optimize (O-PO) process, in which an upstream prediction (e.g., on renewable energy sources (RES) and loads) and a downstream NCUC are executed in a queue. However, in the O-PO framework, a statistically more accurate prediction may not necessarily lead to a higher NCUC economics against actual RES and load realizations. To this end, this paper presents a closed-loop predict-and-optimize (C-PO) framework for improving the NCUC economics. Specifically, the C-PO leverages structures (i.e., constraints and objective) of the NCUC model and relevant feature data to train a cost-oriented RES prediction model, in which the prediction quality is evaluated via the induced NCUC cost instead of the statistical forecast errors. Therefore, the loop between the prediction and the optimization is closed to deliver a cost-oriented RES power prediction for NCUC optimization. Lagrangian relaxation is adopted to accelerate the training process, making the C-PO applicable for real-world systems. Case studies on an IEEE RTS 24-bus system and an ISO-scale 5655-bus system with real-world data show that the proposed C-PO can effectively improve the NCUC economics as compared to the traditional O-PO. [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]

Power systems are undergoing fundamental changes with increasing penetration of renewable energies. A reactive power ancillary service market is of significance to incentivize private providers, such as thermal power units and renewable power plants (RPPs), to participate in maintaining voltage security. Because of the local nature of reactive power, one of the recognized issues is that monopolistic participants may have great market power and strategically manipulate their costs. To pursue economic efficiency, this paper proposes an incentive-compatible mechanism based on Vickery-Clarke-Groves (VCG) auctions for the day-ahead reactive power ancillary service market. The obligations of reactive power ancillary service are quantified in the VCG-based market mechanism. Depending on the expected performance of participants compared with the corresponding obligations, payments are obtained for thermal power units, RPPs, and loads. Hence, providers have the incentive to declare their true costs and undertake obligations. Furthermore, a scarcity price is employed to reward the provision of scarce reactive power resources and ensure reliable market clearing. The proposed mechanism is illustrated using the IEEE 24-bus and 118-bus systems. The results verify the effectiveness of the proposed mechanism. Moreover, high rewards or penalties are observed for voltage weak areas, thereby inducing appropriate investments in reactive power capacities. [ABSTRACT FROM AUTHOR]

The reduced inertia levels in low-carbon power grids necessitate explicit constraints to limit frequency’s nadir and rate of change during scheduling. This can result in significant curtailment of renewable energy due to the minimum generation of thermal plants that are needed to provide frequency response (FR) and inertia. Additional consideration of fast FR, a dynamically reduced largest loss and under frequency load shedding (UFLS) allows frequency security to be achieved more cost effectively. This paper derives a novel constraint from the swing equation to contain the frequency nadir using all of these services. The expected cost of UFLS is found probabilistically to facilitate its comparison to the other frequency services. We demonstrate that this constraint can be accurately and conservatively approximated for moderate UFLS levels with a second order cone (SOC), resulting in highly tractable convex problems. Case studies performed on a Great Britain 2030 system demonstrate that UFLS as an option to contain single plant outages can reduce annual operational costs by up to $\pounds $ 559 m, 52% of frequency security costs. The sensitivity of this value to wind penetration, abundance of alternative frequency services, UFLS amount and cost is explored. [ABSTRACT FROM AUTHOR]

With the increasing penetration of renewable energy, accurate and efficient probabilistic optimal power flow (POPF) calculation becomes more and more important to provide decision support for secure and economic operation of power systems. This paper develops a novel nonparametric probabilistic optimal power flow (N-POPF) model describing the probabilistic information by quantiles, which avoids any parametric probability distribution assumptions of random variables. A novel critical region integral method (CRIM) which combines the multiparametric programming theory and discrete integral is proposed to efficiently solve the N-POPF problem. In the CRIM, the critical region partitioning algorithm is firstly introduced into the POPF model to directly establish the mapping relationship from wind power to optimal solutions of the POPF problem. Besides, a discrete integral method is developed in the CRIM to achieve the probability convolution calculation based on quantiles. Comprehensive numerical experiments verify the superior performance of the proposed CRIM in estimation accuracy and computational efficiency, and demonstrate that N-POPF model significantly improves the accuracy of uncertainty analysis. In general, the proposed N-POPF model and CRIM form a new framework of POPF problem for power system analysis and operation. [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]

The fast development of renewable energies leads to an increase in the power electronics penetration in transmission systems. This is particularly true if one considers a 100% renewable energies power system, where wind and solar photovoltaic energies, which make most of the renewable energies connections today, are connected to the grid through power electronics converters. Because power electronics-based generators and synchronous machines-based generators have very different dynamic behaviours, some approximations usually used to run transient simulations of transmission systems might not be optimal for future grids. The systematic use of the phasor approximation applied to the power lines, implemented in most of the Transient Simulation Programs, is indeed not relevant any more. To avoid the use of Electromagnetic Transient simulations, that are resource-demanding and time-consuming, this paper presents a novel Model Order Reduction technique for large grids with a high penetration of power electronic devices. Compared to the classical phasor approximation, this event-based state residualization approximation allows accurate transient simulations and at the same time an optimal reduction of the number of the system’s state variables depending on the observed variables, the considered events and the tolerated approximation error. [ABSTRACT FROM AUTHOR]

There is a growing need for new optimization methods to facilitate the reliable and cost-effective operation of power systems with intermittent renewable energy resources. In this paper, we formulate the robust AC optimal power flow (RAC-OPF) problem as a two-stage robust optimization problem with recourse. This problem amounts to a nonconvex infinite-dimensional optimization problem that is computationally intractable, in general. Under the assumption that there is adjustable generation or load at every bus in the power transmission network, we develop a technique to approximate RAC-OPF from within by a finite-dimensional semidefinite program by restricting the space of recourse policies to be affine in the uncertain problem data. We establish a sufficient condition under which the semidefinite program returns an affine recourse policy that is guaranteed to be feasible for the original RAC-OPF problem. We illustrate the effectiveness of the proposed optimization method on the WSCC 9-bus and IEEE 14-bus test systems with different levels of renewable resource penetration and uncertainty. [ABSTRACT FROM AUTHOR]

In this paper, a new systematic method is proposed to analyze the system frequency in power systems under uncertain variability (UV). UV gradually increases in power systems, which originates from the renewable energy generation, random loads, frequency measurement, and communication channels, exerting noteworthy impacts on dynamic system frequency. The UV is modeled as a stochastic process in this paper. Then, the stochastic differential equations are used to describe the dynamic system frequency response (SFR) of a power system under UV, which is based on the SFR model. To assess system frequency dynamics under UV, an index of intra-range probability is put forward. Based on stochastic analysis theory, an analytic method is proposed to analyze the system frequency under UV, by which the intra-range probability can be analytically solved. Compared with Monte Carlo simulation in a typical SFR case and the Iceland electricity transmission network, the proposed method shows almost the same results using much less computation resource. Finally, insights for improving the SFR under UV are provided. The proposed method can be used to quickly verify whether the system frequency could withstand the UV and stay in the security range. [ABSTRACT FROM AUTHOR]

The control of reactive power exchange between grids of different voltage levels has always been a concern for system operators. With production moving from the transmission to the distribution level, its importance increases. This paper proposes a novel approach to estimate reactive power capability of the grid as a whole. A linearized analytical model for an estimation of available reactive power exchange at the interface between two grids has been developed. The maximum estimation error for the scenarios we tested was only 2%. The model gives the relation between important grid parameters and the supported reactive power. The conclusions drawn from the model are confirmed on typical Swedish distribution network with scattered wind power and small industry consumers. Common scenarios in development of distribution grids are applied to show relevant parameters influence. One studied scenario is replacement of overhead lines with cables. It is shown that this particular change enhances the reactive power capability of the grid which is directly seen from the analytical analysis without running any optimal power flow. The analytical model proposed in this paper gives fundamental understanding of the reactive power capability of radial distribution grids. [ABSTRACT FROM AUTHOR]

This paper analyzes different models for evaluating investments in energy storage systems (ESS) in power systems with high penetration of renewable energy sources. First of all, two methodologies proposed in the literature are extended to consider ESS investment: a unit commitment model that uses the “system states” (SS) method of representing time; and another one that uses a “representative periods” (RP) method. Besides, this paper proposes two new models that improve the previous ones without a significant increase of computation time. The enhanced models are the “system states reduced frequency matrix” model which addresses short-term energy storage more approximately than the SS method to reduce the number of constraints in the problem, and the “representative periods with transition matrix and cluster indices” (RP-TM&CI) model which guarantees some continuity between representative periods, e.g., days, and introduces long-term storage into a model originally designed only for the short term. All these models are compared using an hourly unit commitment model as benchmark. While both system state models provide an excellent representation of long-term storage, their representation of short-term storage is frequently unrealistic. The RP-TM&CI model, on the other hand, succeeds in approximating both short- and long-term storage, which leads to almost 10 times lower error in storage investment results in comparison to the other models analyzed. [ABSTRACT FROM AUTHOR]

Over the past 20 years, the rapid integration of renewable energy has resulted in electricity markets that are increasingly complex, interconnected, and uncertain. Similar to the banking system's financial crisis in 2008 due to chained reactions, severe financial losses due to uncertainty at a large renewable farm could induce significant financial losses at other market participants. The spread of such financial shocks can be worsened by centralized market clearing, and systemic risks consequently germinate in electricity market operations. Therefore, our previous work has compared systemic risk with systematic risk in the electricity market with uncertainties. However, the scope of our previous work has been limited to risk indices. This paper aims to broaden the study by proposing the theoretical foundation of systemic risk analysis in electricity markets with uncertainties. First, an electricity market financial network is defined to describe the cash inflow/outflow of all participants, and the financial contagion is employed to model the interlinks between different entities. Then, two financial properties, financial resilience and financial reliability, are proposed to evaluate the systemic risk in market settlements with uncertainties. Finally, the proposed theoretical foundation of systemic risk is demonstrated on the Texas synthetic 2000-bus system with 70% renewable penetration. [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]

New resource mix, e.g., renewable resources, are imposing operational complexities to modern power systems by intensifying uncertainty and variability in the system net load. This issue has motivated independent system operators (ISOs), e.g., California ISO (CAISO), to add flexible ramping products (FRPs) to their day-ahead (DA) market models. Such structural changes in the DA market formulation require further analyses and detailed design to ensure adequate operational flexibility, market efficiency, and reliability. This paper conducts a comprehensive study to: (a) augment existing DA market models with enhanced FRP design to schedule ramp capabilities that are more adaptive with respect to the real-time (RT) 15-min net load variability and uncertainty, and (b) design corresponding market payment policies that accurately reflect the value of the added flexibility through enhanced FRP design. The proposed FRP design can be implemented in present-day system operations with minimal disruption to existing DA market models. Performance of the proposed DA market model, which includes the enhanced FRP design, is compared against the DA market model with existing FRP design through a validation methodology based on RT unit commitment model. This validation methodology mimics fifteen-minute markets of CAISO. The proposed method is tested on an IEEE 118-bus test system. [ABSTRACT FROM AUTHOR]

Uncertainties in renewable generation make accurate load forecast essential for reliable power system operation. This paper considers energy imbalance market (EIM), where market players are allowed to procure energy ahead of time and trade the mismatch due to forecast error and strategic behaviors. The ISO sets the trading prices according to the market conditions, and pursues various system-level objectives. We first identify the power-law relationship between data volume and forecast accuracy, which enables the formulation of forecast cost model. Then, we cast the interactions in the EIM in the Stackelberg game framework with the ISO acting as the leader. We offer explicit subgame perfect equilibrium among the players in EIM, and derive the sufficient condition for the existence of unique equilibrium. Then, we show that this equilibrium, if exists, supports the maximal social welfare and under certain conditions, minimizes the total mismatch. We further examine the local and global impacts of the forecast errors under mild conditions, together with robustness analysis. Such analysis provides mechanism design guidelines for the ISO to enable the data sharing and forecast method sharing among market players in the EIM. Numerical studies further examine the effectiveness, robustness and sensitivity of the subgame. [ABSTRACT FROM AUTHOR]

As the crucial interface of renewable energy integration, the grid-tied inverter is a complicated system with a multi-timescale feature, containing both fast dynamics and slow dynamics that determine the system stability. However, previous researches on stability analysis mainly focus on the slow dynamics without considering the impact of fast dynamics, which may bring to inaccurate stability prediction. In this paper, the impact of fast dynamics on stability is investigated for grid-tied inverter from a physical perspective. Considering the dynamics of the current control loop and network, a two degrees-of-freedom oscillator model is firstly established to extract the fast dynamics separately. The damping torque analysis is then applied to analyze the impact of the extracted fast dynamics on the damping and spring coefficients of slow dynamics. Moreover, based on the fast dynamic analysis, a novel reduced-order model is proposed with the consideration of the dominant characteristics of fast dynamics, which improves the model accuracy without increasing the complexity. Eventually, both numerical evaluations and experiments are performed to validate the proposed analysis method. [ABSTRACT FROM AUTHOR]

With the increasing penetration of renewable energy, frequency response and its security are of significant concerns for reliable power system operations. Frequency-constrained unit commitment (FCUC) is proposed to address this challenge. Despite existing efforts in modeling frequency characteristics in unit commitment (UC), current strategies can only handle oversimplified low-order frequency response models and do not consider wide-range operating conditions. This paper presents a generic data-driven framework for FCUC under high renewable penetration. Deep neural networks (DNNs) are trained to predict the frequency response using real data or high-fidelity simulation data. Next, the DNN is reformulated as a set of mixed-integer linear constraints to be incorporated into the ordinary UC formulation. In the data generation phase, all possible power injections are considered, and a region-of-interest active sampling is proposed to include power injection samples with frequency nadirs closer to the UFLC threshold, which enhances the accuracy of frequency constraints in FCUC. The proposed FCUC is investigated on the IEEE 39-bus system. Then, a full-order dynamic model simulation using PSS/E verifies the effectiveness of FCUC in frequency-secure generator commitments. [ABSTRACT FROM AUTHOR]

The high penetration of renewable energy will substantially change the power system operation. Traditionally, the annual operation of a power system can be represented by some typical operation modes and acts as the basis for the power-system-related analysis. The introduction of highly penetrated renewable energy will make the power system operation mode highly diversified and variable. These modes may not follow traditional empirical patterns. In this paper, we propose a data-driven method based on high-dimensional power system operation data (including power flow, unit generation, and load demand) to identify the pattern of the operation modes and analyze the impact of high renewable penetration. Specifically, the proposed data-driven method is composed of simulation, preprocessing, clustering, dimension reduction, and visualization with the aim to provide an intuitive understanding of the operation mode variety under high renewable penetration. In addition, several indices are introduced to quantify the space dispersion, time variation, and seasonal consistency of operation modes. A case study on actual Qinghai provincial power system in China validates the effectiveness of the proposed data-driven method and indicates that the dispersion and time variation of operation mode will significantly increase in the beginning and then saturate with the increase in renewable penetration level. The operation mode is also less correlated with seasons in renewable energy dominated power system. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new methodology to formulate storage behavior in medium- and long-term power system models that use a load duration curve. Traditionally in such models, the chronological information among individual hours is lost; information that is necessary to adequately model the operation of a storage facility. Therefore, these models are not fully capable of optimizing the actual operation of storage units, and often use pre-determined data or some sort of peak-shaving algorithm. In a rapidly changing power system, the proper characterization of storage behavior and its optimization becomes an increasingly important issue. This paper proposes a methodology to tackle the shortcomings of existing models. In particular, we employ the so-called system states framework to recover some of the chronological information within the load duration curve. This allows us to introduce a novel formulation for storage in a system states model. In a case study, we show that our method can lead to computational time reductions of over 90% while accurately replicating hourly behavior of storage levels. [ABSTRACT FROM PUBLISHER]

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 novel method to analyze impacts of uncertain variability on power system dynamics. There is considerable interest in integrating intermittent renewable energy and plug-in electric vehicles into power systems. Therefore, power systems are in an environment with increasing uncertain variability. In this paper, the uncertain variability is described as a continuous-time stochastic process, and thus, the power system under uncertain variability is modeled by stochastic differential equations. To quantify impacts of uncertain variability on power system dynamics, an intra-region probability index is presented. Based on the stochastic averaging method, an analytical method is proposed to calculate the intra-region probability. Compared to Monte Carlo simulation, the proposed method is many orders of magnitude faster without sacrificing the result accuracy. Furthermore, several insights are given to improve the power system dynamics under uncertain variability. [ABSTRACT FROM AUTHOR]

As the installation of electronically interconnected renewable energy resources grows rapidly in power systems, system frequency maintenance and control become challenging problems to maintain the system reliability in bulk power systems. As two of the most important frequency control actions in the control centers of independent system operators (ISOs) and utilities, the interaction between Economic Dispatch (ED) and Automatic Generation Control (AGC) attracts more and more attention. In this paper, we propose a robust optimization based framework to measure the system flexibility by considering the interaction between two hierarchical processes (i.e., ED and AGC). We propose a cutting plane algorithm with the reformulation technique to obtain seven different indices of the system. In addition, we study the impacts of several system factors (i.e., the budget of operational cost, ramping capability, and transmission line capacity) and show numerically how these factors can influence the system flexibility. [ABSTRACT FROM AUTHOR]

Solar energy and bioenergy are two leading renewable forms of energy in the move toward a near-zero-emission electric power industry. Concentrated solar power units coupled with thermal storage and biomass power plant offer dispatchable electricity, raising their ever-growing role in future renewable-dominated networks. This paper proposes a day-ahead and intraday dispatch model for maximizing the profit of an Integrated Biomass-Concentrated Solar (IBCS) system considering the synergies arising from their coupled operation. To sensibly capture uncertainty and decision sequence of real-life electricity markets, a two-stage stochastic structure is proposed, while the solar-related uncertainty is involved using Information Gap Decision Theory (IGDT). The model is complemented with a novel multi-objective architecture based on the compound of IGDT and Conditional Value-at-Risk (CVaR), which allows handling risk exposure to both stochastic and IGDT inputs. The Pareto strategies in the multi-objective model are extracted through an expanded form of the $\epsilon$ -constraint method, whereas a posteriori approach based upon the out-of-sample assessment is applied to derive the optimal dispatch pattern among the generated Pareto strategies. The simulation results demonstrate that: 1) the proposed integrated dispatch model achieves substantial profitability, and 2) the performance of the suggested CVaR-IGDT model is superior to conventional approaches. [ABSTRACT FROM AUTHOR]

As renewable energy penetration increases and system inertia levels drop, primary frequency control is becoming a critical concern in relatively small interconnections such as the Electric Reliability Council of Texas (ERCOT). To address this problem ERCOT is implementing a number of market rule changes including the introduction of a new Fast Frequency Response (FFR) reserve type to the electricity market. This FFR reserve type aims to help the traditional Primary Frequency Response (PFR) reserve type in arresting frequency decline in the event of a large generator outage. This paper derives reserve requirements to ensure sufficient reserve to arrest frequency decline before reaching the critical frequency threshold while coupling PFR reserve, FFR reserve, and system inertia. The general reserve requirement places limits on the amount of PFR reserve that can be provided by each unit based on its ramping capabilities. Two such limits are derived from first principles and another is proposed that is capable of accommodating the equivalency ratio introduced in previous work. These PFR reserve limits also provide first principles insight into equivalency ratios, which have only been studied empirically in the past. High-level insights are provided on a large Texas test case. [ABSTRACT FROM AUTHOR]

The frequency stability of microgrids is of paramount importance due to their low inertia and high share of renewable energy sources. In this paper, a frequency stability-constrained microgrid scheduling (FSC-MS) model is developed based on a time-dependent discretized frequency response model considering seamless unintentional islanding events. The optimal dispatch of controllable units, as well as optimal upward and downward primary reserves, are determined with a minimum operating cost while ensuring frequency stability criteria are maintained in their safe ranges following an unintentional islanding event, such as rate of change of frequency (RoCoF) and frequency nadir and overshoot. The limitation of generators with respect to primary frequency response is formulated in the form of primary reserve capacity and primary ramp rate limits. A cost-based model is presented to describe the available primary reserve of synchronous generators. The proposed FSC-MS model is formulated as a mixed-integer linear programming (MILP) problem using Benders decomposition. Simulation results on a medium voltage microgrid test system demonstrate the effectiveness of the proposed model to meet the frequency stability constraints while minimizing the total operating cost. [ABSTRACT FROM AUTHOR]

As wind power penetration increases and fossil plants are retired, it is feared that there will be insufficient kinetic energy (KE) from the plants to support the system frequency. This paper shows the fear is groundless because the high inertias (H ≅ 4 seconds) of wind turbine-generators (WTGs) can be integrated to provide frequency support during generation outage. [ABSTRACT FROM AUTHOR]

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]

The uncertain nature of renewable energy resources (RERs) and fast demand response lead to recurring voltage violations in the power systems, which causes frequent transformer tap shifting and capacitor switching. Therefore, this paper resorts to the static var compensators (SVCs) to manage the bus voltages based on the multi-agent deep reinforcement learning (MA-DRL) algorithm. The proposed scheme includes several system agents and SVC agents to collaboratively adjust the injected reactive power to restrict the bus voltages within the normal range. All the agents are trained centrally and executed separately, which requires minimum communication cost. The IEEE 14-bus system, IEEE 300-bus system, and China 157-node urban power grid are used to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Due to their fast response ability and high ramping rates, pumped-storage hydropower (PSH) plants are playing an increasingly critical role in mitigating power generation fluctuations induced by the growing proliferation of renewable energy resources. However, because they are energy-limited resources, actual reserve deployment from PSHs would cause the deviation of state-of-charge (SOC) from the scheduled value, which, once accumulated over time, could induce potential violations of SOC limits and cause non-dispatchability of PSHs. In recognizing this potential issue, it can become important to securing the reserve schedule of PSHs and other energy limited resources preventively in the day-ahead market clearing. To ensure reserve dispatchability of PSHs despite SOC deviations, this paper proposes the reserve secure constraints, which are cast as a distributionally robust chance-constrained formulation by judiciously introducing random parameters to describe deployment ratios of scheduled regulation reserve from PSHs. These constraints are converted into tractable second-order cone constraints, and further approximated as linear constraints to be compatible with the current ISO day-ahead market clearing model. A modified IEEE 118-bus system with multiple PSHs is adopted to verify the proposed approach. [ABSTRACT FROM AUTHOR]

Battery-based Energy Storage Transportation (BEST) is the transportation of modular battery storage systems via train cars or trucks representing an innovative solution for a) enhancing Variable Renewable Energy (VRE) utilization and load shifting, and b) providing a potential alternative for managing transmission congestions. This paper focuses on point b) and proposes a long-term transmission-planning model coordinated with both stationary and mobile storage units. The planning-problem objective function minimizes the total system cost, i.e., the sum of i) the investment cost of candidate transmission lines, stationary and mobile storage systems, and ii) the operation cost, including conventional generating units fuel consumption, load shedding penalty and BEST transportation costs. An alternative approach for BEST vehicle scheduling problem is implemented. The contribution lies in the accomplishment of the spatial-temporal scheduling of the mobile storage units by including the Number-of-nonzero mathematical function in the optimization model set of constraints instead of using additional binary variables as generally accomplished. The identification of either storage systems optimal location, or both optimal location and size of storage systems is also allowed. BEST usefulness is analyzed and discussed for a test-system emulating a reals system in China-Northwestern-grid with high VRE penetration divided in five regional areas, of which the most promising one for BEST implementation is identified. [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 objective of this paper is to explore the efficacy of applying risk-based security assessment (RBSA) to define reliability standards for electricity grids with high penetration of converter-interfaced generation. A novel approach to estimate the impact of transient instability is presented in this paper by modeling several important protection systems in the transient stability analysis. In addition, a probabilistic model is developed to capture the uncertainty of increased converter-interfaced renewable penetration. A synthetic test case is derived from a realistic power system to verify the proposed method. The simulation results show that RBSA not only provides significantly relaxed security limits, but also helps in identifying critical aspects of system reliability that are not possible using conventional deterministic methods. [ABSTRACT FROM AUTHOR]

This paper proposes a generalized analytical approach to evaluate the reliability of active distribution networks. The studies are implemented in the context of renewable-based energy hubs. The reliability of energy demands is determined as a function of reliability characteristics of energy hub input resources and converters as well as hub operating strategies. The framework proposed in this paper involves the main attributes of different distributed generation technologies as well as vehicle-to-grid (V2G)-capable vehicles in the reliability studies. Dealing with the uncertainty in energy services provided by the wind turbine output generation and V2G programs, efficient probabilistic methods are presented to attain the reliability models of these energy resources for the studies. The fluctuations in energy demands are also represented through multistate analytical models. Convolving the probabilistic models of energy hub resources by the load profiles’ models, different reliability indices are calculated taking into consideration possible operating strategies of the energy hubs. Effectiveness of the proposed methodology is validated using extensive numerical studies on an energy hub and the obtained results demonstrate its applicability in adequacy studies of active energy networks. [ABSTRACT FROM AUTHOR]

Currently, power system planning practices are undergoing various transformations in an attempt to integrate efficiently significant amounts of low-carbon power generation technologies. At the heart of this efficient integration lies the need to plan for and exploit the available flexibility in power systems. In the past, the emphasis was on planning the capacity (i.e., power) of operating reserve requirements, in the form of categorized reserve types. Such approach was suitable for traditional power systems exhibiting low variability and uncertainty. The concept of power system flexibility is emerging as a way to emphasize the need to also consider the ramping capability of operating reserve needed to accommodate high variability and uncertainty arising from renewable energy integration. Prior considerations of power system flexibility, however, are found to be inadequate to handle energy-limited power system resources like energy storage assets and demand response. Hence, this paper sets to consider systematically energy limitations of operating reserve by proposing energy-based operating reserve definitions. We demonstrate the benefits of the new reserve definitions, using a receding-horizon economic dispatch integrating energy storage. [ABSTRACT FROM PUBLISHER]