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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]

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]

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]

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]

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]

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]

This paper elucidates a new real time energy management framework for radial active unbalance distribution networks (UDNs) by integrating load shedding and conservation voltage reduction (CVR) techniques. In contrast with the shortsighted real time optimization strategies, the proposed technique accounts offline beneficial aspects in real time optimization platform as time coupled stochastic expressions. Those are further simplified to a mixed integer non-convex programming (MINCP) using merger of Queueing theory and Lyapunov optimization process. To solve the complex MINCP portfolio, a consecutive mixed integer linear programming (c-MILP) based solution method is proposed after adopting necessary linear approximations. After demonstrating on modified IEEE 123 bus test network, it is showed that the proposed real time strategy can provide most energy efficient, secure and reliable operation to the UDNs and can accommodate offline advantageous attributes successfully along with the real time load shedding and CVR constraints. Validating the power flow solutions at OpenDSS platform, it is proved that the proposed c-MILP approach possess fast convergence and provide near optimal power flow solutions. Further investigations certify that presence of residential consumers are more beneficial for the networks as they are more sensitive to voltage. [ABSTRACT FROM AUTHOR]

Flexible transmission line impedances on one hand are a promising control resource for facilitating grid flexibility, but on the other hand add much complexity to the concerned optimization problems. This paper develops a convexification method for the AC optimal power flow with flexible line impedances. First, it is discovered that a flexible-impedance line is equivalent to a constant-impedance line linking a pair of transformers with correlated and continuously adjustable tap ratios. Then, with this circuit equivalent, the original optimization problem is reformulated into a semi-definite program under the existing convex relaxation framework, which improves the solution tractability and optimality in an easy-to-implement manner. The proposed method is verified by numerical tests on the IEEE 118-bus system. [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]

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

We consider a distributed optimal power flow formulated as an optimization problem that maximizes a nondifferentiable concave function. Solving such a problem by the existing distributed algorithms can lead to data privacy issues because the solution information exchanged within the algorithms can be utilized by an adversary to infer the data. To preserve data privacy, in this paper we propose a differentially private projected subgradient (DP-PS) algorithm that includes a solution encryption step. We show that a sequence generated by DP-PS converges in expectation, in probability, and with probability 1. Moreover, we show that the rate of convergence in expectation is affected by a target privacy level of DP-PS chosen by the user. We conduct numerical experiments that demonstrate the convergence and data privacy preservation of DP-PS. [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]

Harnessing flexibility from distributed energy resources (DER) to participate in various markets while accounting for relevant technical and commercial constraints is essential for the development of low-carbon grids. However, there is no clear definition or even description of the salient features of aggregated DER flexibility, including its steady-state and dynamic features and how these are impacted by network constraints and market requirements. This paper proposes a comprehensive DER flexibility modelling and characterisation framework that is based on the concept of nodal operating envelope (NOE). In particular, capacity, ramp, duration and cost are identified as key flexibility metrics and associated with different but consistent NOEs describing capability, feasibility, ramp, duration, economic, technical and commercial flexibility features. These NOEs, which conceptually arise from a Venn diagram, can be built via optimal power flow (OPF) analysis, visualised in the active-reactive power space, and used by different stakeholders. Results from a canonical test system and a real distribution system illustrate the value and applicability of the proposed framework to model and characterise provision of flexibility and market services from DER for different use cases. [ABSTRACT FROM AUTHOR]

Despite major advancements in nonlinear programming (NLP) and convex relaxations, most system operators around the world still predominantly use some form of linear programming (LP) approximation of the AC power flow equations. This is largely due to LP technology's superior reliability and computational efficiency, especially in real-time market applications, security-constrained applications, and extensions involving integer variables, in addition to its ability to readily generate locational marginal prices (LMP) for market applications. In the aim of leveraging the advantages of LP while retaining the accuracy of NLP interior-point methods (IPMs), this paper proposes a sequential linear programming (SLP) approach consisting of a sequence of carefully constructed supporting hyperplanes and halfspaces. The algorithm is numerically demonstrated to converge on 138 test cases with up the 3375 buses to feasible high-quality solutions (i) without AC feasibility restoration (i.e., using LP solvers exclusively), (ii) in computation times generally within the same order of magnitude as those from a state-of-the-art NLP solver, and (iii) with robustness against the choice of starting point. In particular, the (relative) optimality gaps and the mean constraint violations are on average around $10^{-3}$ % and $10^{-7}$ , respectively, under a single parameter setting for all the 138 test cases. To the best of our knowledge, the proposed SLP approach is the first to use LP exclusively to reach feasible and high-quality solutions to the nonconvex AC OPF in a reliable way, which paves the way for system and market operators to keep using their LP solvers but now with the ability to accurately capture transmission losses, price reactive power (Q-LMP), and obtain more accurate LMP. [ABSTRACT FROM AUTHOR]

In the face of increasing natural disasters and an aging grid, utilities need to optimally choose investments to the existing infrastructure to promote resiliency. This paper presents a new investment decision optimization model to minimize unserved load over the recovery time and improve grid resilience to extreme weather event scenarios. Our optimization model includes a network power flow model which decides generator status and generator dispatch, optimal transmission switching (OTS) during the multi-time period recovery process, and an investment decision model subject to a given budget. Investment decisions include the hardening of transmission lines, generators, and substations. Our model uses a second order cone programming (SOCP) relaxation of the AC power flow model and is compared to the classic DC power flow approximation. A case study is provided on the 73-bus RTS-GMLC test system for various investment budgets and multiple hurricane scenarios to highlight the difference in optimal investment decisions between the SOCP model and the DC model, and demonstrate the advantages of OTS in resiliency settings. Results indicate that the network models yield different optimal investments, unit commitment, and OTS decisions, and an AC feasibility study indicates our SOCP resiliency model is more accurate than the DC model. [ABSTRACT FROM AUTHOR]

For the popular second-order conic program (SOCP) formulation of AC optimal power flow (OPF) in a radial network, this paper first shows that it does not have the strong duality property in general. Then, through a series of restrictive reformulations, we derive a set of closed-form sufficient conditions on network parameters that ensure its strong duality. Numerical studies on IEEE 33-bus, 69-bus test networks and two real-world distribution systems confirm that non-negligible duality gaps do exist in this SOCP formulation, and also demonstrate the validity of the proposed sufficient conditions on closing the duality gap. Our results provide an analytical tool to ensure the strong duality of the SOCP power flow formulation and to support algorithm developments for its complex extensions. [ABSTRACT FROM AUTHOR]

Hybrid ac-dc grids can gain the benefits of both ac and dc grids. The Ac-Dc circuit analysis can be performed using sequential methods that decouple ac and dc systems or unified (simultaneous) methods that solve the ac and dc mismatch equations simultaneously. This paper introduces a unified ac–dc analysis via an improved model for the ac–dc coupling through which the ac and dc load flow analyses can be simultaneously conducted. The ac–dc coupling is modeled by an admittance building block, and thus, the dc grid is converted to an ac-equivalent circuit within the hybrid network. However, unlike past literature, state variables beyond nodal voltages and angles are avoided, leading to a simpler algorithm, and reactive power injection of the coupling mechanism, a requirement for the IEEE 1547 Std, is explicitly modeled. Furthermore, the proposed model can be applied to both voltage-source and line-commuted converters. Accordingly, the conventional ac power flow algorithms can be applied to the hybrid circuit paving the path for seamless adoption of hybrid circuits and significantly saving time and effort in programming, troubleshooting, and upgrading techniques currently used in research and industry as well as a high-level analysis tool regarding the hybrid ac-dc grid is achieved. [ABSTRACT FROM AUTHOR]

In this paper, we present a data-driven secondary controller for regulating to some desired values several state variables of interest in an inverter-based power system, namely, electrical frequency, voltage magnitudes at critical buses, and active power flows through critical lines. The secondary controller is based on online feedback optimization, leveraging the learned sensitivities of changes in the state variables to changes in inverter active and reactive power setpoints. To learn the sensitivities accurately from data, the feedback optimization has a built-in mechanism for keeping the secondary control inputs persistently exciting without degrading its performance or compromising system operational reliability. To ensure safe and reliable operation, we present an approach based on Gaussian process regression that, by making an inference about the modeling uncertainties not accounted for in the sensitivity-based prediction model, allows the controller to correct the predictions and find safe control actions, for which the prediction errors are more likely to be small. The feedback optimization also utilizes the learned power-voltage characteristics of photovoltaic (PV) arrays to compute DC-link voltage setpoints so as to allow the PV arrays to track the power setpoints. To learn the power-voltage characteristics, we separately execute a data-driven approach that fits a concave polynomial to the collected power-voltage measurements by solving a sum-of-squares (SoS) optimization. We showcase the secondary controller using the modified IEEE-14 bus test system, in which conventional energy sources are replaced with inverter-interfaced DERs. [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]

This paper proposes a two-level distributed algorithmic framework for solving the AC optimal power flow (OPF) problem with convergence guarantees. The presence of highly nonconvex constraints in OPF poses significant challenges to distributed algorithms based on the alternating direction method of multipliers (ADMM). In particular, convergence is not provably guaranteed for nonconvex network optimization problems like AC OPF. In order to overcome this difficulty, we propose a new distributed reformulation for AC OPF and a two-level ADMM algorithm that goes beyond the standard framework of ADMM. We establish the global convergence and iteration complexity of the proposed algorithm under mild assumptions. Extensive numerical experiments over some largest test cases from NESTA and PGLib-OPF (up to 30 000-bus systems) demonstrate advantages of the proposed algorithm over existing ADMM variants in terms of convergence, scalability, and robustness. Moreover, under appropriate parallel implementation, the proposed algorithm exhibits fast convergence comparable to or even better than the state-of-the-art centralized solver. [ABSTRACT FROM AUTHOR]

Soft open points (SOPs) are power electronic devices which provide interconnection between two feeders in place of normally open points in electricity distribution networks. SOPs can continuously control active power flow between feeders and inject reactive power controllably at both nodes, which can be used to provide substantial capacity support to the system. This paper provides a reliability-based method to quantify the capacity value (the additional load which can be accommodated without reducing reliability) of SOPs using the Effective Load Carrying Capability method within a Monte Carlo Simulation (MCS). Optimization of post-fault active/reactive power injections by SOPs to minimize energy not supplied is formulated (directly in matrix form) as a second-order cone programming problem. This results in very low computational times which enables embedding of the optimization problem within the MCS. The proposed methodology is applied to a modified real-world distribution network considering three different SOP sizes (5 SOPs totalling 2.5, 5, 10 MVA) across three redundancy levels (N-1, N-0.75, N-0.5), and on an unbalanced network with distributed generation. Results demonstrate capacity values ranging from 2.4–12.84 MVA. When operating under a relaxed redundancy level, the capacity value of a given SOP capacity can more than double relative to N-1. [ABSTRACT FROM AUTHOR]

This paper proposes a potential distributed reactive power compensation method in dc traction power systems with reversible substations. It utilizes the entire capacity of reversible substations during night hours and the reminding capacity except for regenerative braking energy feedback during day hours. A unified dispatch scheme is developed to allocate reactive power compensation capacity for each reversible substation. During night hours the entire capacity is used to accomplish the optimal power flow objective. During day hours the excess capacity after active power production is used to improve the system reactive power factor dynamically. The different objectives throughout the day are implemented in a unified formula which avoids manually change. In addition the outage of reversible substations and the low dc voltage conditions are considered and an over-modulation suppression strategy is included in the unified dispatch scheme to adjust the reactive power allocation among reversible substations. This novel utilization method of reversible substations is able to provide significant improvements in the power factor of dc traction power systems which would otherwise require expensive additional equipment such as static synchronous compensator. Finally the effectiveness of the proposed method is verified with MATLAB/SIMULINK. [ABSTRACT FROM AUTHOR]

Topology identification and parameter estimation form the basis for the operation and control of the distribution network with little or no observability. This paper proposes a method to estimate the admittance matrix for open-loop distribution networks based only on active/reactive power injection and voltage magnitude data. We derive the linear relationship between the admittance matrix and the measurements based on decoupled linear power flow (DLPF) equations. A total least squares regression method is proposed based on analysis of the characteristics of the open-loop grid admittance matrix. Case studies on the IEEE 33-bus system demonstrate the proposed method's effectiveness, accuracy, and efficiency. [ABSTRACT FROM AUTHOR]

Market and network integration of distributed energy resources can be facilitated by their coordination within a virtual power plant (VPP). However, VPP operation subject to network limits and different market and physical uncertainties is a challenging task. This paper introduces a framework that co-optimizes the VPP provision of multiple market (e.g., energy, reserve), system (e.g., fast frequency response, inertia, upstream reactive power), and local network (e.g., voltage support) services with the aim of maximizing its revenue. To ensure problem tractability, while accommodating the uncertain nature of market prices, local demand, and renewable output and while operating within local network constraints, the framework is broken down into three sequentially coordinated optimization problems. Specifically, a scenario-based robust optimization for day-ahead resource scheduling, with linearized power flows, and two receding horizon optimizations for close-to-real-time dispatch, with a more accurate second-order cone relaxation of the power flows. The results from a real Australian case study demonstrate how the framework enables effective deployment of VPP flexibility to maximize its multi-service value stack, within an uncertain operating environment, and within technical limits. [ABSTRACT FROM AUTHOR]

This paper presents a novel model of voltage source converter (VSC) based energy routers (ERs) in microgrids. The proposed model explicitly describes the circuit laws within the ERs and captures the coupling of control variables among the AC/DC, DC/DC, DC/AC links. Therefore, the proposed model possesses unparalleled control capabilities in the operational parameters of both the AC and DC sides of ERs. By incorporating such a model into the AC-DC optimal power flow formulation, we not only optimize the power flows between the AC and DC sides of ERs, but also strategically schedule the flexible resources. To solve the ERs based AC-DC optimal power flow (ER-OPF) in a distributed fashion, we propose a hierarchical distributed optimization method that decouples the power grids into a master region and several sub-regions. In the master region, we propose a sequence of strong relaxations to transform the problem into a semidefinite program (SDP). We further show that this SDP relaxation is exact. For the sub-regions, we utilize sequential quadratic programming (SQP) to solve multiple small-scale subproblems with non-convex constraints in parallel. Case studies on the IEEE benchmark system show that fuel costs and power losses are reduced dramatically by utilizing ERs in microgrids. In addition, the proposed distributed algorithm can converge faster than alternating direction method of multipliers (ADMM). [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]

The conservative power theory (CPT) is a time-domain theory applicable to any periodic signal single- or polyphase system with or without a neutral conductor. The principle operation is the orthogonal decomposition of electrical variables, resulting in electrical quantities with physical meaning. An important feature of the CPT is the current decomposition. It consists of decomposing any current into five parts. The label of these parts is active current, reactive current, scattered active current, scattered reactive current, and generated current. This paper proposes the application of the current decomposition of the CPT in distributed energy resources (DERs). A supervisory controller (SC) uses the current decomposition in a load power-sharing strategy. The combination of these two issues is the main contribution of this paper. Moreover, the proposal of this paper is more attractive than the conventional droop strategy since the DERs follow their current reference in a current-controlled mode, making the load sharing faster, more reliable, and more accurate. A clear understanding of how the CPT decomposes load currents into its parts is presented, as well as the drawback found in droop strategy when dealing with load power sharing. Later, the SC load power-sharing strategy is described, indicating that the proposal of this paper makes an SC to have a broad option when managing a smart grid with dispatchable DERs. A case study with experimental results shows the efficacy of applying current decomposition of the CPT in load power-sharing strategies. [ABSTRACT FROM AUTHOR]

This paper proposes a hybrid method for probabilistic load flow (PLF) study to analyze the influence of uncertain photovoltaic generations and load demands on transmission system performance. Besides, the paper focuses on accurate approximation of multimodal distributions of result variables in a temperature-augmented PLF model without using any series expansion methods. The effect of uncertain ambient temperature on result variables is discussed. Multiple correlation cases between the input bus powers are considered. The performance of the proposed method is investigated on modified New England 39-bus power system. The results are compared with four well-established analytical methods and Monte Carlo simulation. The effect of multiple input correlations on probability distributions of result variables is analyzed. [ABSTRACT FROM AUTHOR]

The growing interest in optimizing the generation, distribution, and delivery of electric power have motivated the implementation of several smart grid functions in many power systems around the globe. Among such functions are the peak-load management, demand response, direct load control, and integration of distributed power generation. Nowadays, smart grid functions are being implemented for industrial, residential, and/or commercial loads. One of the key requirements for implementing smart grid functions is the accurate and reliable load aggregation. The bottom-up, coordinated, and bus-split aggregation methods have been found applicable for different load types that are included in smart grid functions. This paper reviews the methods and approaches for performing the load aggregation, and provides a discussion for the critical role of load aggregation in power systems operating and smart grid functions. In addition, this paper discusses the applicability of the load aggregation methods in smart grid functions for residential loads. [ABSTRACT FROM PUBLISHER]

This paper proposes a control strategy for a three-phase three-wire thyristor-controlled LC -coupling hybrid active power filter (TCLC-HAPF), which can balance active power and compensate reactive power and harmonic currents under unbalanced loading. Compared with TCLC-HAPF with conventional control strategy, active power filters and hybrid active power filters which either fail to perform satisfactory compensation or require high-rating active inverter part for unbalanced compensation, a control strategy was proposed for TCLC-HAPF to operate with a small rating active inverter part for a variety of loads with satisfactory performance. The control idea is to provide different firing angles for each phase of the thyristor-controlled LC-coupling part (TCLC) to balance active power and compensate reactive power, while the active inverter part aims to compensate harmonic currents. First, the required different TCLC impedances are deduced. Then, independent firing angles referenced to the phase angle of voltage across TCLC are calculated. After angle transformations, final firing angles referenced to phase angle of load voltages are obtained. In this paper, a novel controller for TCLC-HAPF under unbalanced loading is proposed. Simulation and experimental results are provided to verify the effectiveness of the proposed controller in comparison with a state-of-the-art controller. [ABSTRACT FROM PUBLISHER]

This paper deals with the distribution network reconfiguration problem in a multi-objective scope, aiming to determine the optimal radial configuration by means of minimizing the active power losses and a set of commonly used reliability indices formulated with reference to the number of customers. The indices are developed in a way consistent with a mixed-integer linear programming (MILP) approach. A key contribution of the paper is the efficient implementation of the \mmb\varepsilon-constraint method using lexicographic optimization in order to solve the multi-objective optimization problem. After the Pareto efficient solution set is generated, the resulting configurations are evaluated using a backward/forward sweep load-flow algorithm to verify that the solutions obtained are both non-dominated and feasible. Since the \mmb\varepsilon-constraint method generates the Pareto front but does not incorporate decision maker (DM) preferences, a multi-attribute decision making procedure, namely, the technique for order preference by similarity to ideal solution (TOPSIS) method, is used in order to rank the obtained solutions according to the DM preferences, facilitating the final selection. The applicability of the proposed method is assessed on a classical test system and on a practical distribution system. [ABSTRACT FROM AUTHOR]

Passive or active current balancing circuits are usually used to mitigate current imbalance in driving multiple light-emitting-diode (LED) strings. Passive current balancing schemes adopting capacitors with high reliability, small size and low cost are very popular in many applications. However, the high reactive power of the capacitive balancing scheme with variable frequency control will bring high power stress on the VA rating of the main switches which drive this passive current balancing circuit and decrease the overall efficiency. Fixed frequency control does not permit zero-voltage switching (ZVS) under load variations. Hence, this paper proposes a current-source-output LED driver based on LCLC resonant circuit to provide a constant output current regardless of variations in LED parameters. In the LCLC circuit, the number of additional capacitors is scalable with the number of LED strings for current balancing. Moreover, the input impedance of the improved LCLC circuit is designed to be resistive at the operating frequency to minimize reactive power. The conventional duty cycle control can easily incorporate ZVS. The analysis, implementation and verification are detailed in this paper. [ABSTRACT FROM AUTHOR]

Facing the challenges of power quality problems and excessive neutral sections of conventional two-phase electric railway supply system, the way of adopting railway static power conditioner (RPC)-based single-phase supply system is a feasible solution. To enhance the cost-efficiency and reliability of RPC, a novel compensating system named asymmetric double LC-coupled railway power flow conditioner (ALC-RPFC) is proposed in this paper. The study indicates that compared with the conventional RPC, the proposed ALC-RPFC has an effective heavy-load compensating ability with lower power rating, which is benefit to enhance converter's operating efficiency and reliability. Besides, a design method for LC coupling branches mentioned in this paper is suitable for fluctuated railway loads, and is useful for designers of industrial applications as well. Finally, the good heavy-load compensating performance and power capacity decreasing ability of the ALC-RPFC are validated based on simulation and experiment results. [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]

Vernier permanent-magnet (VPM) machines are well known for high torque density but low power factor. This paper deals with the low power factor of VPM machines. The goal is not obtained by reducing the electrical loading or adjusting current advance angle but by proposing a novel vernier topology, i.e., a dual-stator spoke-array (DSSA) VPM topology. In this paper, the characteristics of the DSSA VPM topology, such as active part, auxiliary mechanical structure, and rotor anisotropy, are analyzed in detail. Performances are evaluated based on finite-element analysis, including power factor, torque density, and cogging torque. The results show that the DSSA VPM topology exhibits high power factor, viz., $\sim$0.9, and significantly high torque capability. The verification of the mechanical structure scheme is also done in this paper. Finally, theoretical analyses are validated by the experimental results by a 44-rotor pole 24-slot DSSA VPM prototype. [ABSTRACT FROM AUTHOR]

Frequency control in autonomous microgrids (MG) with high penetration of renewable energy sources represents a great concern to ensure the system stability. In this regard, this paper presents an enhanced control method for battery energy storage systems (BESS) to support the frequency of MG and with the ability of disconnecting from the MG to supplying in the island mode a local consumer. A frequency controller, combining a conventional droop control with an inertia emulation function, governs the BESS active power transfer during the primary frequency control level. The BESS may also provide voltage support in the point of common coupling with the MG. Moreover, the proposed BESS may compensate, partially or totally, the power absorbed by the local loads in order to improve the MG frequency response. When the MG power quality worsens below a certain level, in terms of voltage and frequency, the BESS detaches from the MG and continues to operate islanded. The reconnection is accomplished following a smoothly resynchronization of the local voltage with the MG, without disturbing the local loads supply. Additionally, this paper also discusses about the aspects related to the BESS management and its integration within the proposed system. The simulation and experimental results assess the feasibility of the proposed control solutions. [ABSTRACT FROM AUTHOR]

In this paper, the structure, modeling, parameter design, and control method are proposed for a new hybrid structure of a static var compensator in parallel with a hybrid active power filter (SVC//HAPF). The SVC part of the SVC//HAPF is used to dynamically compensate the reactive power. And, the HAPF part is used to provide harmonic power and small amount of reactive power compensation. Due to the large fundamental voltage drop on coupling the LC part, the active inverter part of the SVC//HAPF has low voltage rating. Meanwhile, the parallel-connected SVC acts as a current divider to reduce the active inverter current. Therefore, the proposed SVC//HAPF shows the great promise in compensating harmonic current and wide-range reactive power with a low (both) voltage and current rating active inverter part. To show the advantages of the proposed SVC//HAPF, simulation comparisons among the active power filter (APF), HAPF, SVC in series with HAPF (SVC−HAPF), and the proposed SVC//HAPF are provided. Finally, experimental results based on the laboratory-scaled hardware prototype are given to show the validity of the SVC//HAPF. [ABSTRACT FROM PUBLISHER]

In this paper, a comprehensive control scheme for a delta-connected cascaded H-bridge (CHB) converter-based static synchronous compensator (STATCOM) is presented, especially focusing on improving dynamic performance by novel feedforward control method. The method can conspicuously improve the dynamics of zero-sequence circulating current regulation of delta-connected CHB STATCOM especially under grid fault condition as well as load unbalance without excessive dc cell capacitor voltage fluctuation. The validity of the proposed method is demonstrated by mathematical proof. Finally, the full-scaled simulation results and the down-scaled experimental results verify that stable operation is guaranteed for both emulated grid and load unbalance conditions. [ABSTRACT FROM AUTHOR]

Back-to-back voltage-source converters enable Type 3 wind turbines (WTs) to operate with zero-power transfer, and this allows them to restore the system both in black-starting and stand-alone loaded stages. Therefore, this paper first identifies the prerequisites for Type 3 WTs to act as voltage-source interfaces in the case of bulk system outage and reveals their inherent deficiency for system restoration from the voltage/frequency and output power ( P–f and Q–V) relationships. These analyses provide the basic guidance for subsequent control updating. Afterwards, to allow Type 3 WTs to provide black-starting capacity, a concomitant control strategy and a restoration sequence are proposed. The uncovered P–f relationship is reinforced by self-maintained frequency control for the subsequent stand-alone loaded stage. The mechanism of frequency matching among multiple WTs is also discussed. Furthermore, a mathematical analysis for the impacts of controller parameters on the frequency characteristics of a Type 3 WTs-based stand-alone system is developed, thereby providing the guidance for control design. Eventually, a specific islanded system, merely consisting of Type 3 WTs and some passive local loads, is constructed to verify the feasibility of Type 3 WTs for system restoration and to validate the analytical results. [ABSTRACT FROM PUBLISHER]

High penetration of renewable energy sources and the increasing share of stochastic loads require the explicit representation of uncertainty in tools such as the optimal power flow (OPF). Current approaches follow either a linearized approach or an iterative approximation of nonlinearities. This paper proposes a semidefinite relaxation of a chance-constrained AC-OPF, which is able to provide guarantees for global optimality. Using a piecewise affine policy, we can ensure tractability, accurately model large power deviations, and determine suitable corrective control policies for active power, reactive power, and voltage. We state a tractable formulation for two types of uncertainty sets. Using a scenario-based approach and making no prior assumptions about the probability distribution of the forecast errors, we obtain a robust formulation for a rectangular uncertainty set. Alternatively, assuming a Gaussian distribution of the forecast errors, we propose an analytical reformulation of the chance constraints suitable for semidefinite programming. We demonstrate the performance of our approach on the IEEE 24 and 118 bus system using realistic day-ahead forecast data and obtain tight near-global optimality guarantees. [ABSTRACT FROM PUBLISHER]

Conventional VAR compensation devices such as capacitor banks and synchronous condensers, after long periods of service, have become aged and less effective to satisfy stringent requirement of short-term voltage stability in high-level wind power penetrated power systems. STATCOMs with a rapid and dynamic reactive power support capability can be an ideal alternative, when combined with a proper equipment retirement and upgrades scheme. This paper proposes a systematic approach for optimal dynamic VAR resource planning and upgrading for a power system with increased wind power penetration and equipment retirement. The problem is constituted by two parts that are aged equipment retirement and new equipment placement. A multiobjective optimization model is proposed to minimize three objectives: the cost of retirement and upgrades, the index of proximity to steady-state voltage collapse, and the index of transient voltage unaccepted performance. To simulate real-world operating situation, multiple contingencies and uncertain dynamic load models are taken into account. Furthermore, low- and high-voltage ride through abilities for wind farms are modeled. The proposed model is tested on the New England 39-bus test system. [ABSTRACT FROM PUBLISHER]

This paper proposes a unified load flow (LF) model for AC–DC hybrid distribution systems (DSs). The proposed model can be applied in hybrid DSs with mixed configurations for AC/DC buses and AC/DC lines. A new classification of DS buses is also introduced for LF analysis. A set of generic LF equations has been derived based on comprehensive analysis of the possible AC–DC hybrid system configurations. Three binary matrices, which are used as a means of describing the configuration of the AC and DC buses and lines, have been employed in the construction of the unified power equations. These matrices enable a single configuration at a time to be activated in the power equations. The proposed LF model is generic and can be used for both grid-connected and isolated hybrid DSs. The new model has been tested using several case studies of hybrid DSs that include different operational modes for the AC and DC distributed generators. As a means of evaluating the effectiveness and accuracy of the proposed model, the LF solution was compared to the solution produced by PSCAD/EMTDC. A comparison of the results reveals the efficacy of the proposed model. [ABSTRACT FROM AUTHOR]

A “one-and-a-half stage” forward-flyback converter for electrolytic capacitor-less light-emitting diode (LED) driver with high power factor (PF), high efficiency, low output ripple current, and long lifetime has been proposed and studied in this paper. The basic topology of the proposed topology is a single-switch forward-flyback converter for achieving high PF. In addition, a buck converter is inserted between the forward subconverter and the load for creating two paralleled power transfer paths. The most of input energy directly reaches the load through flyback subconverter, and only about 1/4 of total energy is transferred to the load through forward subconverter and buck converter. Therefore, the proposed topology is a “one-and-a-half stage” converter and can achieve higher efficiency than the traditional two-stage topologies. At the same time, power decoupling can be realized and the electrolytic capacitor can be eliminated. Optimal control scheme, detailed analysis, and design considerations for this improved converter are presented. Finally, an experimental prototype for 28 V/700 mA LED driver was built up to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper introduces a series compensation philosophy to improve the voltage property of loads using three-phase voltage ellipse parameters intended for optimal utilization of a dynamic voltage restorer. The proposed approach relies on the instantaneous magnitude of voltage signals and functions by inserting a virtual equivalent impedance in series with the distribution feeder during voltage sags, compensating for the difference between faulty and nominal voltages. In addition, the definite mathematical derivations using iterative processes are properly used as an identification mark of the resultant rotating vector tracing an ellipse. The ellipse parameters including major axis, minor axis, and inclination angle are utilized to develop the proposed algorithm and hence, a set of generalized VA loading formulations calculating an optimal sizing with the minimum possible rating are presented. The uniqueness of dual VSCs connected with common dc-side is an attempt to formalize the topological structure keeping a higher level of compensation accuracy. A novel design and the corresponding algorithm are proposed and all possible scenarios concerning sag depth and phase jump are taken into consideration. MATLAB-based simulation results are discussed in detail to support the concept and the test is also performed to verify the effectiveness through real-time experimental laboratory. [ABSTRACT FROM AUTHOR]

This paper describes a technique to model a vector-controlled induction motor drive in large-scale phasor-level dynamic simulation programs. The performance-based load model is implemented by obtaining the linearized power-voltage and power-frequency transfer functions from test data or from detailed electro-magnetic transient simulation used as a surrogate for test data. Voltage and frequency modulations are performed to obtain the amplitude and phase responses of the detailed vector-controlled drive model for a range of discrete frequencies. The prediction error minimization technique is utilized to generate best-fit analytical transfer function expressions. The electrical interface of the performance-based drive load model is developed to interact with the external system in positive-sequence dynamic simulation programs. The drive model is used to investigate the relative damping effects of drive-connected and direct-connected motors on system voltage and frequency oscillations. [ABSTRACT FROM PUBLISHER]

Inverters and loads can freely connect to any node in a meshed parallel inverters system, leading to variations of line impedance between two nodes and the structure of the electric network. More challenges exist for proportional load-sharing control in such a system. An improved proportional load-sharing strategy for a meshed parallel inverters system with complex impedances is proposed in this paper. The RL-type droop method is modified through injecting the power droop information of all other inverters, which can improve the load-sharing accuracy to some extent and completely compensate the voltage amplitude and frequency deviations caused by droop equations under accurate load-sharing conditions. Besides, an adaptive virtual resistance tuned by the integral of the linear combination of output active and reactive powers, is added to eliminate load-sharing errors. In addition, the central controller broadcasts the control variables to all inverters. This improves the simultaneity of control data and minimizes the mismatch of control delay. Three modified droop methods are compared with the small-signal analysis and simulation. Experimental results are presented to investigate the performance of the proposed control strategy. [ABSTRACT FROM PUBLISHER]

An interline dynamic voltage restorer (IDVR) is invariably employed in distribution systems to mitigate voltage sag/swell problems. An IDVR merely consists of several dynamic voltage restorers (DVRs) sharing a common dc link connecting independent feeders to secure electric power to critical loads. While one of the DVRs compensates for the local voltage sag in its feeder, the other DVRs replenish the common dc-link voltage. For normal voltage levels, the DVRs should be bypassed. Instead of bypassing the DVRs in normal conditions, this paper proposes operating the DVRs, if needed, to improve the displacement factor (DF) of one of the involved feeders. DF improvement can be achieved via active and reactive power exchange (PQ sharing) between different feeders. To successfully apply this concept, several constraints are addressed throughout the paper. Simulation and experimental results elucidate and substantiate the proposed concept. [ABSTRACT FROM AUTHOR]