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Since modern smart grids have various and deeply coupled cyber-physical components, they are vulnerable to malicious cyber attacks. Although regular defenses including firewall and IDS are deployed, they may be weakened by zero-day vulnerabilities and sophisticated attack schemes. Therefore, defense strategies to mitigate the risk of blackouts during cyber attacks are necessary. This paper proposes a cyber-physical coordinated defense strategy to overcome the disruption and minimize the risk as much as possible. At the cyber layer, a zero-sum multilevel Markovian Stackelberg game is proposed to model sequential actions of the attacker and the defender. The defender distributes defensive resources to protect lines in a real-time manner, according to the attacker's action. If cyber attacks should result in physical outages, defense at the physical layer is then employed. A security-constrained optimal power flow reserving security margin of critical components will be performed to minimize the blackout scale and potential future risk. To solve the corresponding optimization problem and further get the optimal defense strategy, this paper devises a novel “water-pouring” algorithm. Lastly, test results show that the proposed dynamic defense strategy mitigates risk significantly and outperforms existing methods. [ABSTRACT FROM AUTHOR]

Analogous to the way a good driver is aware of neighboring cars, electrical loads can coordinate with other loads within a building or section of a distribution grid. This paper develops methods that enable groups of cyclic loads (devices that turn on and off periodically to maintain setpoints) to reduce their peak aggregate power demand. The methods accommodate a wide variety of cyclic loads, including those with nonlinear or unknown dynamics, and can be implemented in a fully distributed fashion. This paper targets settings with a few hundred cyclic loads or fewer, where the methods developed here could reduce demand peaks significantly while maintaining or improving quality of service. This could save ratepayers money on monthly demand charges, decrease fuel use in microgrids, or extend the life of power delivery equipment. [ABSTRACT FROM AUTHOR]

DC-DC converters are needed for the future development of high voltage direct current (HVDC) grids, as they allow to interconnect lines with different voltages and topologies. The dc-dc converters can increase the grid controllability adding power flow control, voltage regulation and/or fault blocking capability. The dc modular multilevel converter (dc-MMC) is a non-isolated solution proposed to interconnect HVDC systems with the same line topology. This paper proposes a new dc-MMC with a control strategy, which allows the converter to interconnect different line topologies (e.g., rigid bipole connected to a symmetric monopole). The paper presents the different line topologies in HVDC installations. Then, a mathematical model with a variable transformation is proposed for the new dc-dc converter. A control structure is proposed and implemented in Matlab/Simulink using an average arm model and simplified dc grids. The results validate the control in normal operation, fault blocking capability and post-fault scenario (degraded mode). [ABSTRACT FROM AUTHOR]

In this paper, we propose a new mathematical model for power flow problem based on the linear and nonlinear matrix inequality theory. We start with rectangular model of power flow (PF) problem and then reformulate it as a Bilinear Matrix Inequality (BMI) model. A Theorem is proved which is able to convert this BMI model to a Linear Matrix Inequality (LMI) model along with One Nonconvex Quadratic Constraint (ONQC). Our proposed LMI-ONQC model for PF problem has only one single nonconvex quadratic constraint irrespective of the network size, while in the rectangular and BMI models the number of nonconvex constraints grows as the network size grows. This interesting property leads to reduced complexity level in our LMI-ONQC model which in turn makes it easier to solve for finding a PF solution. The non-conservativeness, iterative LMI solvability, well-defined and easy-to-understand geometry and pathwise connectivity of feasibility region are other important properties of proposed LMI-ONQC model which are discussed in this paper. An illustrative two-bus example is carefully studied to show different properties of our LMI-ONQC model. We have also tested our LMI-ONQC model on 30 different power-system cases including four ill-conditioned systems and compared it with a group of existing approaches. The numerical results show the promising performance of our LMI-ONQC model and its solution algorithm to find a PF solution. [ABSTRACT FROM AUTHOR]

The dual-active bridge (DAB) topology is commonly preferred in bidirectional applications due to several attractive features, including auto-adjust of power flow, galvanic insulation, wide voltage gain, and zero voltage switching (ZVS) capability over some power ranges. However, the efficiency of the converter drops at light loads because the ZVS range is directly dependent on the circulating current. Assuming that the processed power is variable, the DAB converter's design must find a compromise between extending ZVS ranges and reducing the reactive power processing to ensure higher efficiency. Aiming this compromise, many papers propose hybrid approaches in which the modulation strategy is selected according to the processed power. However, this is not a simple solution because it demands multivariable control and offline optimizations. This paper proposes a modulation strategy to ensure ZVS and reduce the circulating current for the DAB converters. While the usual phase-shift modulation provides ZVS operation in a range of 40% to 100% of rated power, the proposed asymmetrical pulse-width modulation can obtain ZVS operation in a range of 2% to 100% of rated power. Experimental results demonstrated that the proposed strategy improves the converter efficiency for all power ranges, especially at light loads. [ABSTRACT FROM AUTHOR]

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

This paper presents a distributionally robust network-constrained unit commitment (DR-NCUC) model considering AC network modeling and uncertainties of demands and renewable productions. The proposed model characterizes uncertain parameters using a data-driven ambiguity set constructed by training samples. The non-convex AC power flow equations are approximated by convex quadratic and McCormick relaxations. Since the proposed min-max-min DR-NCUC problem cannot be solved directly by available solvers, a new decomposition algorithm with proof of convergence is reported in this paper. The master problem of this algorithm is solved using both primal and dual cuts, while the max-min sub-problem is solved using the primal-dual hybrid gradient method, obviating the need for using duality theory. Also, an active set strategy is proposed to enhance the tractability of the decomposition algorithm by ignoring the subset of inactive constraints. The proposed model is applied to a 6-bus test system and the IEEE 118-bus test system under different conditions. These case studies illustrate the performance of the proposed DR-NCUC model to characterize uncertainties and the superiority of the proposed decomposition algorithm over other decomposition approaches using either primal or dual cuts. [ABSTRACT FROM AUTHOR]

Transformers are the most expensive element of a power system, and so transformer monitoring systems are becoming more important as loads increase. Under heavy loading conditions, the hot-spot temperature of a transformer is the most critical parameter to determine the limit of loading. Therefore, to make an accurate estimation of hot-spot temperature and maintain the reliability of a power system, dynamic thermal models or methods must be employed. Due to the complexity of thermal phenomena, the methods presented so far needs to be improved to reduce computational errors. This is particularly the case for variable loading conditions and power utilities are still in need of good techniques. This paper describes two methods to determine temperature in single-phase, oil-immersed transformers. The first method calculates average windings temperature (AWT) using the voltage and current from primary and secondary windings. The second method, which uses data from the first method, determines the hot-spot temperature of the transformer. The methods have been investigated by experiments on a 30 kVA single-phase transformer and verified the results using COMSOL ™ software. Our methods have proven more accurate than the IEEE Annex G method. [ABSTRACT FROM AUTHOR]

Power flow (PF) flexibility in the multi-terminal HVDC (MT-HVDC) grids is a thought-provoking issue. It leads to employing the active DC power flow controller (DC-PFC)s. Hence, this paper examines the static average model (AM) and power injection model (PIM) of an interline DC-PFC (IDC-PFC). It is to provide a suitable base for DC PF studies and easy embedding of the DC-PFCs into MT-HVDC grids’ PF equations. In this regard, this paper proposes a new DC PF solver (DC-PFS) for the IDC-PFC compensated MT-HVDC grids within the well-accepted Newton-Raphson (NR) framework. It requires a few modifications in the main structure of the system's Jacobin (J) matrix compared to the uncompensated MT-HVDC grid. Also, the system's admittance matrix and its symmetry are preserved. In the proposed concept, the IDC-PFC cooperates with other MT-HVDC grid's state variables to satisfy the predetermined control objective(s). Furthermore, this paper proposes a new solution procedure (SP) to handle various system's limitations during the processes of solving the DC PF problem. Meanwhile, there is no need to modify the related J matrix. The effective and accurate performance of the IDC-PFC's models, as well as presented NR-based DC-PFS and SP, are verified by performing several simulations on the 8-bus CIGRE MT-HVDC grid. [ABSTRACT FROM AUTHOR]

Urban power grids are facing many operational and expansion challenges to meet further demand growth and increased reliability requirements. Advanced transmission technologies have been considered by the electric utilities to effectively increase the utilization of existing infrastructure and operational flexibility. The focus of this paper is on VSC-HVDC technologies for urban power grid enhancement and modernization. First, a potential technical scheme is proposed for converting an existing AC circuit to DC operation, which could boost the power transfer capability of the critical transmission corridor and increase network operational flexibility. Second, this paper proposes three operation modes for the VSC-HVDC interties in urban power grids corresponding to normal, emergency and island operating conditions, respectively. An integrated, adaptive emergency control strategy (AEC) is proposed that can enable adaptive power flow responses of the VSC-HVDC intertie under varying system operating conditions and critical contingencies. The flexibility and effectiveness of the proposed operational principles of urban VSC-HVDC intertie and the corresponding control strategies are verified in PSCAD/EMTDC using a realistic urban power grid in China. [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]

Unified power flow controller (UPFC) gains growing application in power systems due to its power flow regulation ability. However, there is still a dilemma in the incorporation of UPFC into security-constrained economic dispatch (SCED). The modeling of UPFC involves nonlinear and nonconvex operational constraints, which is difficult to solve efficiently and accurately. Conventional methods adopted Taylor expansion or sensitivity analysis to realize the convexification of UPFC models, which leads to a loop structure and is subject to initial point choice. In this paper, a novel three-terminal injected UPFC model is proposed. In the proposed model, the voltage source variables are eliminated completely. Instead, only power injection variables are introduced to equivalently describe physical characteristics and constraints of UPFC. The nonlinear and nonconvex operational constraints of UPFC are transformed into mixed integer second-order cone form. Moreover, compared with conventional UPFC models, the control characteristic of UPFC is considered in a more accurate and practical manner in the proposed SCED, which helps to prevent potential risks of power flow over-limit under N-1 contingencies. Simulation results show the effectiveness and efficiency of the established solution. [ABSTRACT FROM AUTHOR]

This paper proposes a hybrid data-driven method for fast solutions of preventive security-constrained optimal power flow (SCOPF) of power systems. The proposed method formulates the SCOPF problem as constraints-satisfying training of a deep reinforcement learning (DRL) agent, where the action-value function of DRL is augmented by contingency security constraints. In the training process, the proposed method hybridizes the primal-dual deep deterministic policy gradient (PD-DDPG) and the classic SCOPF model. Instead of building reward critic networks and cost critic networks via interacting with the environment (i.e., power flow equations), the actor gradients are approximated by solving KKT conditions of the Lagrangian. Finally, with the formulated sparse Jacobians of constraints and sparse Hessians of Lagrangians, the interior point method is incorporated in PD-DDPG to derive the parameters updating rule of the DRL agent. Numerical tests are carried out on a modified IEEE 57-bus system and a modified IEEE 300-bus system for critical contingencies. The results show that the well-trained DRL agent can rapidly (real-time) obtain high-quality SCOPF solutions that satisfy the security constraints. [ABSTRACT FROM AUTHOR]

Severe geomagnetic disturbances (GMDs) increase the magnitude of the electric field on the Earth’s surface (E-field) and drive geomagnetically-induced currents (GICs) along the transmission lines in electric grids. These additional currents can pose severe risks, such as current distortions, transformer saturation and increased reactive power losses, each of which can lead to system unreliability. Several mitigation actions (e.g., changing grid topology) exist that can reduce the harmful GIC effects on the grids. Making such decisions can be challenging, however, because the magnitude and direction of the E-field are uncertain and non-stationary. In this paper, we model uncertain E-fields using the distributionally robust optimization (DRO) approach that determines optimal transmission grid operations such that the worst-case expectation of the system cost is minimized. We also capture the effect of GICs on the nonlinear AC power flow equations. For solution approaches, we develop an accelerated column-and-constraint generation (CCG) algorithm by exploiting a special structure of the support set of uncertain parameters representing the E-field. Extensive numerical experiments based on “epri-21” and “uiuc-150” systems, designed for GMD studies, demonstrate (i) the computational performance of the accelerated CCG algorithm, (ii) the superior performance of distributionally robust grid operations that satisfy nonlinear, nonconvex AC power flow equations and GIC constraints, in comparison with standard stochastic programming-based methods during the out-of-sample testing. [ABSTRACT FROM AUTHOR]

Networked microgrids that integrate the hydrogen fueling stations (HFSs) with the on-site renewable energy sources (RES), power-to-hydrogen (P2H) facilities, and hydrogen storage could help decarbonize the energy and transportation sectors. In this paper, to support the hydrogen-based networked microgrids planning subject to multiple uncertainties (e.g., RES generation, electric loads, and the refueling demands of hydrogen vehicles), we propose a two-stage stochastic formulation with mixed integer conic program (MICP) recourse decisions. Our formulation involves the holistic investment and operation modeling to optimally site and configure the microgrids with HFSs. The MICP problems appearing in the second-stage capture the nonlinear power flow of networked microgrids system with binary decisions on storage charging/discharging status and energy transactions (including the trading of electricity, hydrogen, and carbon credits to recover the capital expenditures). To handle the computational challenges associated with the stochastic program with MICP recourse, an augmented Benders decomposition algorithm (ABD) is developed. Numerical studies on 33- and 47-bus exemplary networks demonstrate the economics viability of electricity-hydrogen coordination on microgrids level, as well as the benefits of stochastic modeling. Also, our augmented algorithm significantly outperforms existing methods, e.g., the progressive hedging algorithm (PHA) and the direct use of a professional MIP solver, which has largely improved the solution quality and reduced the computation time by orders of magnitude. Note to Practitioners—This paper proposes an optimal planning model for electricity-hydrogen microgrids with the renewable hydrogen production, storage, and refueling infrastructures. Our planning model is extended under a two-stage stochastic framework to address the multi-energy-sector uncertainties, e.g., RES generation, electric loads, and the refueling demands of hydrogen vehicles. The first-stage problem is to optimize the siting and sizing plan of microgrids. Then, in the second-stage problem, the coordinated scheduling of electricity and hydrogen supply systems is modeled as second-order conic programs (SOCPs) to accurately capture the power flow representation under stochastic scenarios. Also, the logical constraints with binary variables are introduced to describe the energy transactions and storage operations, which results in an MICP recourse structure. Note that the stochastic MICP formulation could be very challenging to compute even with a moderate number of scenarios. One challenge certainly comes from integer variables that cause the problem nonconvex. Another challenge follows from the fact that the strong duality of SOCPs might not hold in general. To mitigate those two challenges, we prove that the continuous relaxation of our recourse problem has strong duality, and make use of that continuous relaxation and other enhancements to design an augmented decomposition algorithm. As revealed by our numerical tests, the proposed decomposition method outperforms PHA in both the solution quality and computational efficiency. Comparing to the PHA, our ABD method often achieves tighter bounds with trivial optimality gaps. Also, it could reduce the computation time by orders of magnitude. With the help of advanced analytical tool, the proposed planning framework can be readily implemented in real-world applications. [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]

This paper proposes a data-driven small-signal stability constrained optimal power flow (SSSC-OPF) method with high computational efficiency. Instead of repeating the computational expense small-signal stability analysis via differential and algebraic equations during the iterative OPF process, a computationally cheap surrogate constraint for small-signal stability is developed. To reduce the learning difficulty for small-signal stability boundaries, an efficient sample generation strategy is proposed with sampling space compression. This allows us to use the support vector machine (SVM) with a kernel function to derive the explicit data-driven surrogate constraint for small-signal stability. Penalty factor optimization is proposed to compensate for the error caused by SVM. The learned small-signal stability constraint is embedded into the OPF model for generator control. An examination strategy is also developed to avoid the small-signal instability of re-dispatch caused by the error of the data-driven surrogate model. Comparison results with other model-based and data-driven methods on the IEEE 39-bus and 118-bus systems demonstrate the high computational efficiency and economic benefits of the proposed method. [ABSTRACT FROM AUTHOR]

Distribution power systems (DPSs) are generally unbalanced, and their loads may have notable static voltage characteristics (ZIP loads). Hence, although many papers have focused on linear single-phase power flow models, it is still necessary to study linear three-phase distribution power flow models. This paper proposes a data-driven-aided linear three-phase power flow model for DPSs. We first formulate how to amalgamate data-driven techniques into a linear power flow equation to establish our linear model. This amalgamation makes our linear model independent of the assumptions commonly used in the literature (e.g., nodal voltages are nearly 1.0 p.u.); therefore, our model is characterized by relatively high accuracy, even when the assumptions become invalid. We then demonstrate how to apply our model to DPSs with ZIP loads. We also show that with the Huber penalty function employed, the adverse impact of bad data on our model's accuracy is significantly reduced, rendering our model robust to poor data quality. Case studies demonstrate that our model is generally more accurate, with 2- to 100-fold smaller errors, than most existing linear models, and remains fairly accurate even under poor data conditions. Our model also contributes to a rapid solution to DPS analyses and optimization problems. [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]

This paper proposes a novel machine-learning approach for predicting AC-OPF solutions that features a fast and scalable training. It is motivated by the significant training time needed by existing machine-learning approaches for predicting AC-OPF. The proposed approach is a 2-stage methodology that exploits a spatial decomposition of the power network that is viewed as a set of regions. The first stage learns to predict the flows and voltages on the buses and lines coupling the regions, and the second stage trains, in parallel, the machine-learning models for each region. The predictions can then seed a power flow to eliminate the physical constraint violations, resulting in minor violations only for the operational bound constraints. Experimental results on the French transmission system (up to 6,700 buses) and large test cases from the pglib library (up to 9,000 buses) demonstrate the potential of the approach. Within a short training time, the approach predicts AC-OPF solutions with very high fidelity, producing significant improvements over the state-of-the-art. The proposed approach thus opens the possibility of training machine-learning models quickly to respond to changes in operating conditions. [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]

Cascading failure models are important for understanding the mechanism of blackouts and evaluating the control strategies to prevent the failure propagation. The evolution of cascading failure in actual power grid is a continuous dynamic process triggered by discrete events, such as initial disturbances and physical responses. In this paper, we develop an event-triggered hybrid system model to describe the dynamic process of cascading failure. In the model, the evolution of continuous states of power grid is described by differential algebraic equations and the discrete events are defined as transitions between discrete states of power grid. The model also integrates multiple physical responses including relay protection, frequency regulation and dispatching action. Based on the developed model, we propose an event-triggered simulation method of cascading failure to accelerate the simulation process. Compared with the DC power flow model, hidden failure model and topological model, the simulation results of our model are more accurate because the statistical distribution of demand loss in our model is closer to historical blackouts data. The efficiency of the proposed event-triggered method is demonstrated by comparing our model with the time-driven model and three existing models. The experimental results show that our model can trade off the simulation accuracy and time consumption. Note to Practitioners—This paper focuses on modeling the dynamic process of cascading failure with multiple physical responses in power grid. We develop an event-triggered hybrid system model for cascading failure. In the model, the continuous dynamics of power grid and discrete events triggering the evolution of cascading failure are all described by the framework of hybrid system, which is a good example of modeling the hybrid system for automation researchers and engineers. By this way, the model is more accurate in describing the actual characteristics of cascading failure in power grid, and thus supporting the design and evaluation of control strategies for improving the stability of power grid. Based on the developed model, we propose an event-triggered simulation method of cascading failure, which aims to improve simulation accuracy while potentially reducing time consumption. In practice, the model can make fast control strategies to prevent the failure propagation. [ABSTRACT FROM AUTHOR]

This paper develops a computationally efficient algorithm which speeds up the probabilistic power flow (PPF) problem by exploiting the inherently low-rank nature of the voltage profile in electrical power distribution networks. The algorithm is accordingly termed the Accelerated-PPF (APPF), since it can accelerate “any” sampling-based PPF solver. As the APPF runs, it concurrently generates a low-dimensional subspace of orthonormalized solution vectors. This subspace is used to construct and update a reduced order model (ROM) of the full nonlinear system, resulting in a highly efficient simulation for future voltage profiles. When constructing and updating the subspace, the power flow problem must still be solved on the full nonlinear system. In order to accelerate the computation of these solutions, a Neumann expansion of a modified power flow Jacobian is implemented. Applicable when load bus injections are small, this Neumann expansion allows for a considerable speed up of Jacobian system solves during the standard Newton iterations. APPF test results, from experiments run on the full IEEE 8500-node test feeder, are finally presented. [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]

The high-precision parameters in distribution networks are difficult to obtain, which brings difficulties to the model-based methods and analysis. With the widespread deployment of high-precision measurement units, data-driven methods have greater advantages in practice. In addition, with massive integration of distributed renewable generation and fast electric vehicle chargers, the fluctuations of net load increase significantly. The data-driven power flow calculation method based on the linear model becomes difficult to obtain accurate results for the low nonlinear adaptability. To improve the data-driven power flow calculation accuracy under high penetration of renewable distribution generation, this paper proposed an approach with high adaptability to the nonlinearity of power flow. Based on the thought of Koopman operator theory, the nonlinear relationship in power flow calculation is converted into a linear mapping in a higher dimension state space, which can significantly improve the calculation accuracy. Case studies on different IEEE cases have demonstrated that the proposed method can realize higher accuracy in power flow calculation with large-scale power fluctuations, compared to the existing data-driven method, in both mesh and radial networks. Finally, measurement data of a practical 10kV distribution network has been further used to verify the effectiveness of the proposed method in practical applications. [ABSTRACT FROM AUTHOR]

The advantages of operating selected transmission lines at frequencies other than the standard 50 or 60 Hz are numerous, encompassing increased power transfer capacity and better utilization of existing infrastructure. While high voltage DC (HVDC) is by far the most well-established example, there has been an emerging interest low frequency AC (LFAC) transmission in applications ranging from offshore wind to railway systems and mining. In this paper, we investigate the use of LFAC as a transmission upgrade and propose models and analysis methods to determine the optimal choice of frequency. The paper first presents an optimal power flow model with frequency as a variable, assuming modular multilevel converters for frequency conversion. Using this model, we analyze LFAC as an embedded upgrade in a transmission system using existing lines. We quantify the system-wide advantages from improved power flow control and frequency reduction and find that an LFAC upgrade achieves similar and sometimes better results compared with HVDC upgrades. Finally, we analyze the factors which determine the optimal frequency for these upgraded transmission lines, and we demonstrate the benefits of changing the frequency in response to different system topologies and operating conditions. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for solving the AC basic power flow based on some enrichments provided in the bus admittance matrix methods findable in the literature. In particular, the interpretation of the slack bus generator as a current source rather than a voltage one and its inclusion inside an “all-inclusive” admittance matrix allows obtaining strong performances of the algorithm. In fact, this method gives both a well conditioning of the admittance matrix and the reduction of matrix partitioning for each iteration. As a result, a greater precision of the solution, a shorter execution time compared to classical commercial methods, a decreasing number of iterations and optimal convergence properties are obtained. Eventually, in order to show the efficiency of the method, real and fictious networks are tested, by comparing its results and performances with robust open source/commercial software packages that use well-known methods (i.e., Newton-Raphson and Fast Decoupled Load Flow methods). [ABSTRACT FROM AUTHOR]

The proliferation of distributed energy resources (DERs), located at the Distribution System Operator (DSO) level, bring new opportunities as well as new challenges to the operations within the grid, specifically, when it comes to the interaction with the Transmission System Operator (TSO). To enable interoperability, while ensuring higher flexibility and cost-efficiency, DSOs and the TSO need to be efficiently coordinated. Difficulties behind creating such TSO-DSO coordination include the combinatorial nature of the operational planning problem involved at the transmission level as well as the nonlinearity of AC power flow within both systems. These considerations significantly increase the complexity even under the deterministic setting. In this paper, a deterministic TSO-DSO operational planning coordination problem is considered and a novel decomposition and coordination approach is developed. Within the new method, the problem is decomposed into TSO and DSO subproblems, which are efficiently coordinated by updating Lagrangian multipliers. The nonlinearities at the TSO level caused by AC power flow constraints are resolved through a dynamic linearization while guaranteeing feasibility through “ $l_1-$ proximal” terms. Numerical results based on the coordination of the 118-bus TSO system with up to 32 DSO 34-bus systems indicate that the method efficiently overcomes the computational difficulties of the problem. [ABSTRACT FROM AUTHOR]

Multi-inverter microgrid systems, particularly those with loop topology, offer higher power supply reliability and robustness compared to conventional radial distribution systems. In meshed systems, communication-less protection schemes have proved to be ineffective for multi-inverter microgrids due to bidirectional power flow, and limited and controlled fault currents generated by the voltage source converters interfacing the energy source to the network. This makes communication-assisted line protection schemes preferable for such systems despite the necessity for communication means. While these protection schemes are effective, their reliability depends much on the communication availability. This requires a back-up communication path in case the main one fails bringing up the cost issue that hinders their uptake. This paper proposes a novel and low-cost line protection based on directional blocking strategy that can operate as a main as well as a back-up protection to any protection scheme using communication means between the line terminals. As the main, it requires low-bandwidth communication system. As a back-up, it would share the same communication means with the main one and use those of the healthy lines when the faulted line's fails. Thus saving the cost of back-up communication system. [ABSTRACT FROM AUTHOR]

Voltage source converter (VSC) based devices have become widely accepted by the power industry in recent years as a result of renewable energy initiatives and other developments. Due to their nonlinear v∼i characteristics, it is essential to understand and model the harmonic impact of VSC devices in a power system. In response to such a need, this paper proposes a rigorous harmonic model of VSC devices suitable for harmonic power flow studies of large-scale power systems. Through detailed mathematical derivations, this research has shown that the model takes the form of a coupled frequency-dependent impedance matrix. Formulas to compute the impedance elements have been established. The results show that the impedance is independent of the harmonic voltages experienced by the VSC device, and thus it can be easily integrated into existing harmonic power flow tools. The accuracy of the model, as well as its usefulness for harmonic power flow studies, have been verified using EMT simulations. [ABSTRACT FROM AUTHOR]

The penetration of photovoltaics (PVs) has been increasing in active distribution networks (ADN), which leads to severe voltage violation problems. PV inverters can provide fast and flexible reactive power support and are now allowed to participate in the voltage regulation process. This paper proposes a real-time combined central and local Volt/Var control (VVC) strategy to mitigate voltage violation problems while minimizing the network power loss. Based on the historical PV and load data, the load flow and optimal power flow are performed in the centralized controller (CC) to obtain multiple voltage and optimal power settings for each PV system. The local controller (LC) then generates voltage control curves with these optimal scatters. To improve the voltage control effect, a novel 3-Dimension voltage control curve is proposed considering both the measurements of node voltage and PV generation. Moreover, a data-driven deep convolution neural network is designed and trained to generate optimal local voltage control curves without prior knowledge of specific curve functions. The proposed approach is tested on the IEEE 33-bus distribution system and simulation results verify the effectiveness in voltage control compared with the optimal Q(V) and Q(P) method. [ABSTRACT FROM AUTHOR]

Distributed Series Reactances are devices that dynamically increase the impedance of a line to reduce the power flow it carries. This work explores whether widely deploying these devices enhances a power system's robustness against line overload cascading failures. The presence of Distributed Series Reactances may make it less likely that equipped lines would become overloaded by contingencies elsewhere, and so their presence may arrest the propagation of line overloads through a system. However, the efficacy of these devices in this role has not been widely investigated. Likewise, there are few extant methodologies for siting dynamic reactances within the grid to mitigate the propagation of cascades. In this paper, the ability of these devices to arrest the propagation of cascading failures within power grids is investigated. First, a novel dc power flow is formulated, which models dynamic line impedances. A novel methodology is proposed for siting the devices on lines spread throughout the network. With these innovations in hand, the devices’ effects on cascade propagation are simulated using a sizeable database consisting of multiple load & generation snapshots across eight test networks. No major beneficial effect is found, even when 25% of lines are equipped. [ABSTRACT FROM AUTHOR]

Transmission line failure in power systems prop-agate non-locally, making the control of the resulting outages extremely difficult. In Part II of this paper, we continue the study of line failure localizability in transmission networks and characterize the impact of cut set outages. We establish a Simple Path Criterion, showing that the propagation pattern due to bridge outages, a special case of cut set failures, are fully determined by the positions in the network of the buses that participate in load balancing. We then extend our results to general cut set outages. In contrast to non-cut outages discussed in Part I whose subsequent line failures are contained within the original blocks, cut set outages typically impact the whole network, affecting the power flows on all remaining lines. We corroborate our analytical results in both parts using the IEEE 118-bus test system, in which the failure propagation patterns exhibit a clear block-diagonal structure predicted by our theory, even when using full AC power flow equations. [ABSTRACT FROM AUTHOR]

Large blackouts in power grids are often the consequence of uncontrolled failure cascades. The ability to predict the failure cascade process in an efficient and accurate manner is important for power system contingency analysis. In this paper, we propose to apply the influence model for the prediction and screening of failure cascades in large scale DC and AC power networks. Then, the trained influence model is applied to some large power grids with thousands of buses and transmission lines. The prediction performance is evaluated in four different aspects, from the global perspective of the overall failure size to the individual information regarding the link failure time. The results show that under limited training samples, the proposed framework is capable of predicting the failure cascade size with a 7% error rate, the final state of links with a 10% error rate, and the failure time within 1 time unit for both the DC and AC model. One major advantage of the proposed method is that it can reduce the computational time of the failure cascade prediction by a few orders of magnitude with limited compromise in accuracy, as compared to the power flow based contingency analysis. Another important feature of the proposed method is that the trained influence parameters can reveal the critical initial contingencies. This information is very helpful for identifying the worst contingency scenarios for system operators. [ABSTRACT FROM AUTHOR]

Though the convex optimization has been widely used in power systems, it still cannot guarantee to yield a tight (accurate) solution to some problems. To mitigate this issue, this paper proposes an ensemble learning based convex approximation for alternating current (AC) power flow equations that differs from the existing convex relaxations. The proposed approach is based on three-phase quadratic power flow equations in rectangular coordinates. To develop this data-driven convex approximation of power flows, the polynomial regression (PR) is first deployed as a basic learner to fit convex relationships between the independent and dependent variables. Then, ensemble learning algorithms such as gradient boosting (GB) and bagging are introduced to combine learners to boost model performance. Based on the learned convex approximation of power flow, optimal power flow (OPF) is formulated as a convex quadratic programming problem. The simulation results on IEEE standard cases of both balanced and unbalanced systems show that, in the context of solving OPF, the proposed data-driven convex approximation outperforms the conventional semi-definite programming (SDP) relaxation in both accuracy and computational efficiency, especially in the cases that the conventional SDP relaxation fails. [ABSTRACT FROM AUTHOR]

With the introduction of massive renewable energy sources and storage devices, the traditional process of grid operation must be improved in order to be safe, reliable, fast responsive and cost efficient, and in this regard power flow solvers are indispensable. In this paper, we introduce an Interior Point-based (IP) Multi-Period AC Optimal Power Flow (MPOPF) solver for the integration of Stationary Energy Storage Systems (SESS) and Electric Vehicles (EV). The primary methodology is based on: 1) analytic and exact calculation of partial differential equations of the Lagrangian sub-problem, and 2) exploiting the sparse structure and pattern of the coefficient matrix of Newton-Raphson approach in the IP algorithm. Extensive results of the application of proposed methods on several benchmark test systems are presented and elaborated, where the advantages and disadvantages of different existing algorithms for the solution of MPOPF, from the standpoint of computational efficiency, are brought forward. We compare the computational performance of the proposed Schur-Complement algorithm with a direct sparse LU solver. The comparison is performed for two different applicational purposes: SESS and EV. The results suggest the substantial computational performance of Schur-Complement algorithm in comparison with that of a direct LU solver when the number of storage devices and optimisation horizon increase for both cases of SESS and EV. Also, some situations where computational performance is inferior are discussed. [ABSTRACT FROM AUTHOR]

Pricing multi-interval economic dispatch of electric power under operational uncertainty is considered in this two-part paper. Part I investigates dispatch-following incentives for generators under the locational marginal pricing (LMP) and temporal locational marginal pricing (TLMP) policies. Extending the theoretical results developed in Part I, Part II evaluates a broader set of performance measures under a general network model. For networks with power flow constraints, TLMP is shown to have an energy-congestion-ramping price decomposition. Under the one-shot dispatch and pricing model, this decomposition leads to a nonnegative merchandising surplus equal to the sum of congestion and ramping surpluses. It is also shown that, comparing with LMP, TLMP imposes a penalty on generators with limited ramping capabilities, thus giving incentives for generators to reveal their ramping limits truthfully and improve their ramping capacities. Several benchmark pricing mechanisms are evaluated under the rolling-window dispatch and pricing models. The performance measures considered are the level of out-of-the-market uplifts, the revenue adequacy of the system operator, consumer payment, generator profit, level of discriminative payment, and price volatility. [ABSTRACT FROM AUTHOR]

With the advancements of the battery energy storage systems (BESSs), reduction of their manufacturing costs and government subsidies, the BESS uptake is likely to increase rapidly in power distribution networks. This paper investigates the effects of residential BESSs on low-voltage (LV) networks using the actual household load profiles equipped with BESS and solar-photovoltaic (PV) systems. The electricity consumption data collected via smart meters (2200 households with PV/BESS, 1950 households with PV only and 1000 households without a PV or a BESS) at different solar-PV penetration levels and network types are used to simulate real network operating scenarios. A real LV distribution network in Australia is analysed in DIgSILENT PowerFactory under different scenarios, such as, customers with and without a solar-PV/BESS, with a solar-PV but without a BESS, and without a solar-PV, by using both the power flow and quasi-dynamic simulation studies under balanced and the unbalanced network loading conditions. According to the study, customers experience large voltage excursions from solar-PV power exports, which could be resolved by the household BESS, provided that the BESS charging is coordinated with the solar-PV production. Moreover, quasi-dynamic simulation shows that the BESS could reduce the violation of the over-voltage limit during the solar peak hours (midday) by lowering the worst-case feeder voltage by 3%. Finally, extreme-event (high solar PV generation scenario) simulation shows that the implementation of the BESS controller to facilitate charging BESS during afternoon solar-PV export may reduce the negative grid impact and will assist to avoid network upgrades. [ABSTRACT FROM AUTHOR]

The voltage rise problem due to the reverse power flow is one of the main obstacles to expanding the photovoltaic systems (PVSs) in distribution networks. In this paper, a decentralized control method for coordinated control of on-load tap changer (OLTC) transformers and PV inverters, is proposed for the voltage regulation of radial distribution networks. In this method, the allowable voltage range is divided into several zones, and appropriate corrective actions are adaptively taken according to each zone. To reduce the tension on the OLTC, first, the reactive power capability of the PV inverters is employed for the voltage regulation, and if it is insufficient, OLTC is used as the last solution. In this regard, the unused capacity of PV inverters is utilized for the reactive power compensation, considering the grid codes reactive power requirements. Furthermore, decentralized control based on a signaling method is used for coordination between OLTC and PVSs, which eliminates the need for communication links. Finally, the effectiveness of the proposed method is validated by the simulation results for the IEEE 33-bus distribution network, and the impact of different reactive power control methods on the number of OLTC operation is investigated. [ABSTRACT FROM AUTHOR]

The unified power flow controller (UPFC) helps to control the power flow, but its outage due to the abnormal state is a threat to power systems. In this paper, based on the proportion of the random failure, the transition rates of the abnormal state are newly derived. The impact of the routine test (RT) on the transition rates is quantified. The state space models of the UPFC based on voltage-source converter (VSC) and modular multilevel converter (MMC) are extended with the states introduced by the RT. The frequency and duration method is used to aggregate the states. The sensitivities of the availability and outage frequency of the UPFC with respect to the failure rates of the components are newly derived to find the vulnerable component and the optimal RT interval. The numerical results show that the RT reduces the probability of the abnormal state, reduces the failure duration, and improves the availability of the UPFC. [ABSTRACT FROM AUTHOR]

The increasing application of voltage source converter (VSC) based high voltage direct current (VSC-HVDC) technology in power grids has raised the importance of incorporating DC grids and converters into the existing transmission network. This poses significant challenges in dealing with the resulting optimal power flow (OPF) problem. In this paper, a recently proposed nonconvex distributed optimization algorithm—Augmented Lagrangian based Alternating Direction Inexact Newton method (aladin), is tailored to solve the nonconvex AC/DC OPF problem for emerging voltage source converter (VSC) based multiterminal high voltage direct current (VSC-MTDC) meshed AC/DC hybrid systems. The proposed scheme decomposes this AC/DC hybrid OPF problem and handles it in a fully distributed way. Compared to the existing state-of-art Alternating Direction Method of Multipliers (admm), which is in general, not applicable for nonconvex problems, aladin has a theoretical convergence guarantee. Applying these two approaches to VSC-MTDC coupled with an IEEE benchmark AC power system illustrates that the tailored aladin outperforms admm in convergence speed and numerical robustness. [ABSTRACT FROM AUTHOR]

Voltage source converter (VSC) based multi -terminal HVDC (VSC-MTDC) systems have emerged as flexible collector systems for multi-area interconnected AC/DC hybrid grids with high share of volatile renewables energy. However, it remains an open question as how to exploit the flexible and cooperative regulation of multiple VSC stations and enhance secure operation on the premise of information privacy protection of multiple independent dispatch areas. This paper proposed an Analytical Target Cascading (ATC)-based three-layer decentralized optimization approach on flexible operation of VSC-MTDC hybrid systems. The low layer is a chance-constrained stochastic optimal power flow (SOPF) problem for AC grids. To guard against the secure operation risk by a VSC's random unipolar atresia fault, a modified loss of load probability index (MLOLP) is proposed to improve the day-ahead generation-reserve scheme. The middle layer and the high layer are a multiperiod OPF problem for VSC stations and the MTDC grid, respectively, where a detailed power regulation model is built to fully exert the flexible cooperation of multiple VSC stations. Two case systems are tested to verify the effectiveness and superiority of the proposed flexible operation hierarchy. [ABSTRACT FROM AUTHOR]

Moving target defense (MTD) is becoming promising in thwarting the false data injection attacks (FDIAs) on power system state estimation (SE). However, due to the nonlinear dynamics of AC power systems, the investigation of the general evaluation metrics of MTD, namely the effectiveness in terms of attack detection and the hiddenness, is still challenging. To this end, in this paper, we attempt to conduct an explicit analysis on the MTD performance in AC power systems. First, we derive explicit approximations of measurement residuals to quantify the two metrics. Then, based on the projection matrix, maximizing the effectiveness is transformed to maximizing the lower bound of the approximated residual, under which the matrix inverse issue is addressed. Moreover, the maximization of hiddenness is achieved by the minimization of the approximated power flow difference caused by reactance perturbation. To balance the trade-off between effectiveness and hiddenness, the design of explicit residual-based MTD (EXR-MTD) is accomplished by aggregating the two sub-problems with an appropriate weight. Finally, extensive simulations are conducted to validate the performance of EXR-MTD. Numerical results indicate that EXR-MTD performs better than existing MTD strategies in terms of hiddenness, while the effectiveness of EXR-MTD is comparable to those of existing MTD strategies. [ABSTRACT FROM AUTHOR]

Being important information of both network conditions and energy trading, distribution locational marginal prices (DLMPs) are greatly useful for distribution network (DN) management. The goal of this paper is to develop a market mechanism that motivates price-making agents to trade active and reactive power at DLMPs. According to the optimal power flow problem based on second-order cone (SOC) relaxation, we first design the market rules that allow agents to strategically submit proposals of price and power generation/consumption. The market rules induce a noncooperative game between the DN operator and distributed generators. We prove that DLMP pricing can be implemented at any generalized Nash equilibrium (GNE) of the game. We also show that economic properties of strong budget balance, individual rationality, and system cost minimization can be achieved at any GNE. A decentralized algorithm is developed to reach a GNE of the game. Further, based on the convex-concave procedure, an extension of the market mechanism is proposed to cope with the situations that SOC relaxation is inexact. In simulation, the proposed market mechanism is compared with other game-theoretic models, and the economic properties are verified. [ABSTRACT FROM AUTHOR]

Despite cascading failures being the central cause of blackouts in power transmission systems, existing operational and planning decisions are made largely by ignoring their underlying cascade potential. This paper posits a reliability-aware AC Optimal Power Flow formulation that seeks to design a dispatch point which has a low operator-specified likelihood of triggering a cascade starting from any single component outage. By exploiting a recently developed analytical model of the probability of component failure, our Failure Probability-constrained ACOPF (FP-ACOPF) utilizes the system’s expected first failure time as a smoothly tunable and interpretable signature of cascade risk. We use techniques from bilevel optimization and numerical linear algebra to efficiently formulate and solve the FP-ACOPF using off-the-shelf solvers. Extensive simulations on the IEEE 118-bus case show that, when compared to the unconstrained and N-1 security-constrained ACOPF, our probability-constrained dispatch points can significantly lower the probabilities of long severe cascades and of large demand losses, while incurring only minor increases in total generation costs. [ABSTRACT FROM AUTHOR]

A new smooth model is proposed in this paper to eliminate the non-differentiability of several types of limits in power flow models. The proposed smooth model accurately represents power system static models with limits as a continuously differentiable function. Analytic results are developed to show that each solution of the proposed smooth model is arbitrarily close to a solution of the corresponding original power flow model with limits. The proposed smooth model includes a wide range of devices with physical limits, such as generators, transformers, HVDCs, phase shifters, and shunts. In addition, it is shown that every generic static bifurcation in the original model is transformed into a saddle-node bifurcation in the smoothed model. Hence, the search for bifurcations in voltage stability assessment can be greatly simplified. Several numerical studies of the proposed smooth model on a 9241-bus power system and on a 13659-bus power system have shown promising results. [ABSTRACT FROM AUTHOR]

The bidirectional CLLC resonant converter has distinguished potential in battery chargers and energy storage systems for its advantages in soft switching and bidirectional power flow capability. However, traditional CLLC converters generally adopt symmetrical design to maintain bidirectional symmetrical characteristics, which means the secondary LC network is designed to be equal to the primary LC network after reflection. The symmetrical design is only suitable for voltage grade matching scenarios where a wide voltage range is not required, such as CLLC-type dc transformers. Whereas in the field of bidirectional chargers, due to the wide voltage range of battery, there are significant differences in the characteristics required between charging and discharging mode, which makes symmetrical design no longer applicable. To cope with this issue, this paper proposes a novel design methodology of CLLC based on parameter equivalent and time domain model. With the parameter equivalent principle, the CLLC resonant tank with arbitrary parameters is investigated to satisfy the requirements of wide voltage range for bidirectional charger application. Compared with the symmetrical design, the proposed method can meet the requirements of bidirectional gain within preset frequency range and guarantee the achievement of zero-voltage switching under required load conditions with the minimum reactive power. In addition, the area product capacity of the magnetic part of the CLLC resonant tank is minimized based on the parameter equivalent principle. Finally, experiments have been performed on a 1 kW prototype to confirm the validity and feasibility of the proposed design methodology. [ABSTRACT FROM AUTHOR]

It is found from actual data that due to generation dispatch and uncertain renewable generations and loads with complicated correlations, inferring the probabilistic distributions for uncertain inputs is challenging. Many probabilistic power flow approaches have been developed in the literature but their validations using realistic systems and data are lacking. This paper proposes a data-driven probabilistic analysis approach for system risk assessment of the miniWECC system using actual data. The sparse Gaussian process (SGP) is advocated to quantify the impacts of uncertain inputs on voltage security. SGP does not need the probability distribution function of uncertain inputs, can handle correlations and is highly computationally efficient. Results on the miniWECC system using realistic data show that SGP outperforms existing approaches and is able to quantify the voltage violation risks. [ABSTRACT FROM AUTHOR]