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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]

This two-part paper considers the coordination of a population of thermostatically controlled loads (TCLs) with unknown parameters to achieve group objectives. The problem involves designing the bidding and market clearing strategy to motivate self-interested users to realize efficient energy allocation subject to a peak energy constraint. The companion paper (Part I) formulates the problem and proposes a load coordination framework using the mechanism design approach. To address the unknown parameters, Part II of this paper presents a joint state and parameter estimation framework based on the expectation maximization algorithm. The overall framework is then validated using real-world weather data and price data, and is compared with other approaches in terms of aggregated load response. Simulation results indicate that our coordination framework can effectively improve the operational efficiency of the distribution system and reduce power congestion at key times. [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]

The increasing prevalence of technologies such as advanced metering and controls and continuously variable power electronic devices are enabling a radical shift in the way frequency regulation is performed in the bulk power system. This is a welcome development in light of the increase of unpredictable and variable generation. The idea of active participation of loads in frequency markets is not new, but the rapidly changing landscape of the power grid requires new techniques for successful integration of new types of resources; this paper works towards that end. Previously, it has been shown that residential HVAC systems can be aggregated and used to provide frequency regulation by utilizing their thermal energy capacity and flexibility of energy consumption. The virtual battery model—a first-order linear dynamical model—was analytically shown to be an accurate and simple model to capture the flexibility of residential HVAC systems. This paper presents a technique for creating the same battery-type models for many other types of systems, which can be much more complex. Our technique is based on stress testing detailed software models of physical systems. A realistic case study involving the terminal building of a small airport is presented as evidence of the effectiveness of the proposed techniques. [ABSTRACT FROM PUBLISHER]

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]

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]

This paper presents a new non-deterministic approach for multiyear distribution network reinforcement planning (DNRP) considering the uncertainty sources pertaining to loads, electricity prices, investment costs, and operation costs. Accordingly, the underlying idea of the information-gap decision theory (IGDT) is used to obtain a robust solution protected against different realizations of each uncertain variable lying in its robust region. The proposed model is capable of adjusting the robustness of the optimal solution in terms of a specific parameter designated as the budget of uncertainty. As the uncertain loads, investment and operation costs competitively tend to maximize their robust regions for a particular value of the budget of uncertainty, the normalized normal constraint (NNC) method as a proficient multi-objective optimization method is exploited in this paper to solve the proposed multiobjective IGDT-based DNRP (IGDT-DNRP) model. Mainly, the NNC method presents a set of Pareto optimal solutions rather than a single optimal solution. Accordingly, a posteriori out-of-sample analysis is introduced in this paper to find the best solution among the set of Pareto optimal solutions. The proposed IGDT-DNRP model is implemented on the IEEE 33-bus distribution network under different circumstances. Simulation results illustrate the effectiveness of the proposed nondeterministic approach. [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]

An analytical approach and a control strategy are proposed in Part I of this two-part paper for leveraging the aggregate demand of a population of thermostatically-controlled loads (TCLs) to deliver contingency-type reserve capacity. Further, a metric is introduced to quantify the TCL users' comfort satisfaction in response to a control signal. In Part II, we address the validation of the concepts put forth in the first part of the paper. To do so, we develop an extensive set of case studies based upon a population of 10\thinspace000 electric water heaters (EWH). Here, a physically-based model is first derived for the calculation of EWHs on-time statistics. The model is then extended to calculate the probability of EWH users' comfort satisfaction. The analytical approach and control strategy presented in Part I are validated using the EWH model against Monte Carlo simulations. Further, the trade-off between demand response capacity and EWH users' comfort satisfaction is investigated. [ABSTRACT FROM AUTHOR]

Powers of three-phase aggregates of single-phase static linear loads supplied with a nonsinusoidal voltage are the subject of this paper. It is demonstrated in this paper that the supply current of such systems with a nonsinusoidal voltage can be decomposed into six mutually orthogonal components associated with distinctive physical phenomena in the load, two of which do not exist at a sinusoidal voltage. Such decomposition enables evaluation of contribution of these phenomena to the supply-current rms value increase and the power factor decline. A power equation and definitions of powers in such systems in the presence of voltage harmonics are proposed. This paper shows that all powers can be expressed in terms of load parameters, which can be identified by a measurement at the load terminals. [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]

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

The delta-connected cascaded H-bridge converter has been applied to compensate flicker and unbalance load to meet power quality requirement. Based on the detailed power analysis, this paper presents a dc capacitor voltage-balancing technique for the converter. This paper also proposes a current limit control technique to avoid overstressing the power semiconductor devices of the converter. The control techniques in this paper are verified in a 220-V, 1-kVA laboratory test bench. [ABSTRACT FROM PUBLISHER]

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]

A hierarchical model predictive control (MPC) approach is developed for energy management of aircraft electro-thermal systems. High-power electrical systems on board modern and future aircraft perform a variety of mission- and flight-critical tasks, while thermal management systems actively cool these electronics to satisfy component-specific temperature constraints, ensuring safe and reliable operation. In this paper, coordination of these electrical and thermal systems is performed using a hierarchical control approach that decomposes the multi-energy domain, constrained optimization problem into smaller, more computationally efficient problems that can be solved in real-time. A hardware-in-the-loop (HIL) experimental testbed is used to evaluate the proposed hierarchical MPC in comparison to a baseline controller for a scaled, laboratory representation of an aircraft electro-thermal system. Experimental results demonstrate that the proposed approach outperforms the baseline controller across a range of electrical loading in terms of both efficient energy management and constraint satisfaction. [ABSTRACT FROM AUTHOR]

The stator winding acts as a carrier for the electrical load, and its loss accounts for about 50% of the total loss in AC machines. So how to design the stator winding for reducing winding loss is extremely crucial. Some traditional transposition methods are adopted in the winding design for large AC machines. Although they have a certain effect on reducing winding loss, there is still room for the improvement in the winding design and manufacturing technology. In this paper, a new global transposition method of stator winding is proposed. Then a megawatt driving motor is taken as the research object, and the eddy current losses, circulating current losses and total losses of winding strands are calculated by the three dimensional (3-D) finite element method (FEM) which has been validated by the experiment. In addition, by comparison with the two original transposition methods, it is proved that the proposed global transposition method is more effective in further reducing the winding loss, and the winding loss distribution is more uniform. This global transposition method proposed in this paper provides a reference for the optimal deign of the stator winding in AC machines. [ABSTRACT FROM AUTHOR]

This two-part paper is intended to inform power system engineers, electrical engineering academicians, and suppliers of electrical apparatus of the threat of wildfires initiated from mal-operation of electrical grids and the unexploited opportunity to develop proper solutions and preventive means to such lethal events. This part (Part I) reviews and categorizes research in different fields of science and industrial projects that attempt to address wildfire issues. The topics include prediction and prevention means, detection methods, monitoring and surveillance techniques, suppression methods, allocation and mapping algorithms, and a summary of research and educational efforts. Subsequently, this paper highlights the damages and negative effects that a wildfire can cause to the electric grid and the interruptions to its continuous operation. Finally, this paper analyzes and categorizes the various scenarios of faulty electrical networks that may lead to wildfires. Part I of this paper provides the ground work and information for the solutions and discussions presented in Part II. [ABSTRACT FROM AUTHOR]

In order to provide the ancillary service for smart grid, this paper proposes a modelling and control protocol design approach for the aggregation of heterogeneous thermostatically controlled loads (TCLs). A 2-D state bin is proposed to model the second-order TCL dynamics in a population model. Detailed procedure of calculating the transition probability in the system matrix is provided. In the controller design, a model predictive control (MPC) scheme is proposed to obtain the optimal control actions along the prediction horizon. In addition, implementation of the control signal for adjusting TCLs' statuses are also investigated with practical situations considered. Simulation results reveal the feasibility and efficacy of the proposed modelling and control approach when applied on a large population of TCLs. Some factors that may affect the service performance are also discussed in this paper. [ABSTRACT FROM AUTHOR]

Load-damping characteristic models the load response to the frequency deviation, which has important impact on system frequency response. The load-damping coefficient is normally considered as a constant, obtained from operational experiences in large-scale power systems or from detailed load models in isolated power systems. An industrial isolated power system for aluminum production driven by coal-fired power and large scale wind power is studied in this paper. Since the electrolytic aluminum load is driven by direct current, it is one type of voltage-sensitive load and does not respond to the frequency deviation. This paper proposes a load-damping characteristic control method for such isolated industrial power system with voltage-sensitive load. To decrease the maximum frequency deviation during transient process, a time-varying load-damping coefficient control scheme is presented. Simulation is done on real-time digital simulator (RTDS) and the results verify the effectiveness of the proposed control method. [ABSTRACT FROM PUBLISHER]

The optimal sizing of an energy storage system (ESS) in a power generation system that incorporates photovoltaic (PV) generation is crucial in a power grid for which the reduction of CO2 emissions is important. This problem is particularly challenging when it relates to the power system of a ship because it involves uncertain meteorological and load data along a navigation route. This paper proposes a novel method for multi-objective minimization of investment/replacement cost, fuel cost, and CO2 emissions, to find the optimal size of the ESS considering life-span of the ESS. The generation of power by PV modules on a ship is affected by temporal and geographical variations of irradiation along the navigation route. In particular, operating load conditions and irradiation are uncertain. This paper proposes a novel algorithm for partitioning high-dimensional uncertain data into tractable clusters solved by deterministic optimization method. Case studies of an all-electric ship along a route from Dalian in China to Aden in Yemen are shown to demonstrate the applicability of the proposed clustering-based stochastic optimization method. [ABSTRACT FROM PUBLISHER]

One of the perspective directions in high-energy-density physics is the creation of powerful electro physical facilities capable to form megampere current pulses with short front. This paper presents test results of the device based on five-element disk magnetocumulative generator DMCG480 and an explosive current opening switch. The current pulse of 15 MA with characteristic rise time of \sim 0.8~\mu \texts was obtained in the equivalent multiwire array load of 17 nH at circuit breaking with the current of 32 MA. [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]