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Microgrids are unique in that they can combine unbalanced three-phase systems with other AC and DC network sections, which may include a range of renewable energy sources, energy storage elements, and controllable AC-DC converters. Existing unbalanced power flow techniques such as the Ladder Iterative Technique and the three-phase Newton-Raphson (NR) method can analyze microgrids in sections but lack a complete system representation. Hence, there is a need for a power flow algorithm that considers the complete system model and solves it. A novel \pi-model of a controllable AC-DC converter and a single set of power balance equations for modeling a grid comprising multiple three-phase AC and DC sections is proposed. The \pi-model of a controllable AC-DC converter enables its inclusion into the network bus admittance matrix (YBUS) along with three-phase AC and DC network sections. Verification of the \pi-model is also described in the paper. The results of power flow studies with three-phase balanced and unbalanced AC and DC network sections are presented. The outcome of the \pi-model verification study and power flow study show that the proposed \pi-model is consistent and accurate. While the proposed model was developed for microgrids, it is applicable for all power system analysis applications. [ABSTRACT FROM PUBLISHER]

This paper applies a known stochastic approximation method to solve a two-phase optimal power dispatch problem under load uncertainty using a novel realistic model for random loads. The stochastic power dispatch problem is solved with the Robbins–Monro method applied with the Kiefer–Wolfowitz procedure with random directions. The constraints of this optimization problem have been investigated and considered by truncated algorithms. Two numerical examples are presented for illustration of the significant improvement obtained with the proposed method. In the first example, the optimizable cost of the system can be reduced by 1.6% under 2.68% load variation. In the second example, the results show that the possibility of voltage violations is reduced from 49.5% to 0.01%. All the improvements are compared with deterministic optimal solutions validated with scenario-based Monte Carlo simulations. The method is 60 times faster than scenario-based Monte Carlo for similar accuracy for the IEEE 30-bus test system. [ABSTRACT FROM PUBLISHER]

This paper introduces a novel idea for adding virtual inertia in power systems by controlling the frequency swing dynamics through voltage channel. The purpose is to develop a frequency-based supplementary VAR modulation to assist governor action during power imbalance events. In this aim, we propose a two-band power system stabilizer, tuned for very low-frequency common swing mode, to adaptively adjust reference voltage of a Synchronous Condenser (SC) and modulate its reactive power on a second-by-second basis. The feasibility of this idea is supported by theoretical and simulation evidences. From theoretical side, we formulate a computational procedure to measure the degree of control impact, accompanied by sensitivity analyses around varying operating points. On the simulation side, we perform extensive studies on four well-known IEEE multi-machine test systems. The results show that VAR modulation by SC has a considerable impact on the minimum post-contingency frequency (frequency nadir), even more than so-called load modulation methods in some cases, which in fact has not been given enough attention in the past. In addition, we show that the proposed method can aid governors to improve primary frequency response particularly in low inertia power systems by reducing post-event frequency settling time and bias. [ABSTRACT FROM PUBLISHER]

The discrete coordinate-descent algorithm is a practical approach that is currently used in centralized Volt/VAr Control (VVC) implementations, mainly due to its good performance and speed for real-time applications. Its viability is however challenged by the increasing number of distributed generation that contribute to the VVC solution, in addition to the conventional transformer taps and switched capacitors. This paper presents the exact computation of sensitivity factors that speed up the discrete coordinate-descent implementation, by significantly reducing the number of forward/backward substitutions in the current injection power flow method; the speed up is achieved without affecting the control setting quality of the original implementation. The optimality of the discrete coordinate-descent solutions is investigated by computing the gaps relative to mixed-integer linear programming set-points, derived from a polyhedral reformulation of the VVC problem. The sensitivity-based discrete coordinate-descent algorithm is tested starting from two initial points, the default one given by the current control set-points, and a continuous solution obtained from a linear approximation of the VVC problem. Numerical results on networks with up to 3145 nodes show that the sensitivity-based approach significantly improves the runtime of the discrete coordinate-descent algorithm, and that the linear programming initialization leads to VVC solutions with gaps relative to the mixed-integer set-points that are less than 0.5%. [ABSTRACT FROM PUBLISHER]

The complex voltage variation is an emerging issue caused by the large-scale distributed energy resources (DERs) integration and the forming prosumers. The prosumers with uncertain photovoltaic (PV) generation will serve as autonomous entities for distributed voltage regulation, which have interaction during the voltage regulation process and have not been fully researched. This paper proposed a stochastic game approach for distributed voltage regulation based on autonomous PV prosumers, where the interactive prosumers’ PV uncertainties are formulated as a dynamic process during the voltage regulation. An economic incentive-based voltage regulation model is built for autonomous prosumers, which takes the reactive power as strategies and considers the PV curtailment, reactive power compensations, and PV uncertainties. The Markov decision process is adopted, and the approach of changing discrete PV uncertainties to continuous probability distribution is proposed to solve the stochastic game model, while dealing with the “curse of dimensionality” issue arising from the PV uncertainties. Finally, the case study is conducted on the IEEE 33 and 118 node system with real data, and the simulation results demonstrate the effectiveness of the proposed voltage regulation method in terms of the nodal voltage, prosumers’ utility, PV uncertainties management, and scalability. [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]

Kinetic energy available from the turbomachinery may boost short-term ramp rates during load shifting between generator and fuel cell that may be exploited to optimize the performance of turbine-fuel cell hybrid systems during load following. The paper starts with modeling a gas turbine, gearbox, and generator sitting on the rigid shafts as a two-mass model primarily for estimating the rotational inertia available from the turbogenerator. The gas turbine and its environment impose constraints of available space allowances, measurements from high-speed rotating parts, lack of accessibility to the shaft of measure, making replacements and/or required installation adjustments of the torque transducer difficult. It is demonstrated that in the absence of torque measurement, the data containing only a slow excursion of the rotor motion in response to a slight load change is sufficient to determine inertia and damping coefficients from the model. Furthermore, the generator's reactive power capability was investigated because it serves as an asset in integrated hybrid systems to meet dynamic reactive power demands, reducing the burden on the fuel cell's power electronics control in generating reactive power. [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]

This paper proposes a multifunctional control strategy and associated control algorithms for distributed wind-turbine (WT) based nano-grids connected to a distorted utility-grid. The contribution is on a new strategy with innovative control algorithms to coordinate multiple converters for a multitasking operation of the nano-grids. The novelty is on a unique control design with feasibilities: maximizing the generated power from WT, maintaining power quality in both ac- and dc-sides under critical conditions of the power grid, and improving power quality against distortion from local nonlinear loads under a reduced switching frequency. A robust fast-dynamic predictive control method is developed for current controllers to fulfil the multifunction. Unconstrained deadbeat control inputs are derived in twofold targets: ensuring fast dynamic response and significantly reducing both the computation and switching frequency for finite predictive control. The control system is applied on a permanent-magnet synchronous generator (PMSG) WT-based nano-grid connected to a distorted utility-grid. An OPAL-RT-based real-time platform is used for comparative studies among the proportional integration (PI) control, finite predictive control (FS-MPC), and proposed control method. The performance verification exhibits the power quality improvement in both the nano- and utility-grids under critical conditions via high-performed regulation of currents, voltages, reactive power, and rotor-speed of the PMSG-WT. [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]

To design a reliable and secure power system, it is necessary to have enough transmission capacity. The solution of transmission expansion planning (TEP) problem determines cost-optimal investment in future transmission equipment. In this paper, we propose a new global solver, named Global-TEP, for the TEP problem with an AC network representation (ACTEP), which is a mixed-integer nonlinear programming problem. The proposed solver is based on second-order cone relaxation, enhanced relaxation tightening constraints, and optimization-based/feasibility-based bound tightening techniques. Multiple enhanced relaxation tightening constraints are incorporated into the mixed-integer second-order cone relaxation of TEP in order to obtain a very strong relaxation as the lower bounding problem. In addition, a novel feasibility-based bound tightening technique is proposed to tighten the bounds of decision variables in a considerably short runtime. Finally, introducing a novel application of optimization-based bound tightening technique, Global-TEP is constructed that can solve the ACTEP problem efficiently with a guaranteed optimality gap. As illustrated by numerical case studies, Global-TEP is more scalable, more flexible, and much faster than the available global solvers. [ABSTRACT FROM AUTHOR]

This paper proposes a multi-option power flow approach for hybrid AC/DC grids. A unified AC-DC unit is introduced which can be used in two different cases: case a) AC grids with embedded VSC-based MTDC grids, and case b) asynchronous AC grids connected via a common VSC-based MTDC grid. In the proposed method for each MTDC grid (regardless of the number of converters), a new state variable is introduced to handle any kind of converter loss models. For the case (b), the AC-DC unit can be used in two different analyses, namely, a1) the separated analysis and a2) the integrated analysis. Both a1) and a2) can be used in the practical analysis of the real-size power systems. However, it is shown that the separated analysis not only offers a shorter computational time but it is also very suitable for the future connection between large existing AC systems and other AC systems or remote renewable energy sources through the DC grids. The proposed methodology is implemented in MATLAB software and verified using commercial software SIMPOW. [ABSTRACT FROM PUBLISHER]

The linear supply function equilibrium (SFE) model can be used to investigate bid-based electricity pool markets. Several studies assume that the market players construct optimal strategic bids by parameterizing the linear marginal cost function of their generating units. Four different types of parameterization are possible, for which the slope and/or the intercept of the marginal cost functions are varied. This paper reviews the existing literature and proposes a primal-dual nonlinear interior point algorithm to solve a bi-level market problem with AC network representation, using any of the parameterization methods. Part II of this paper uses the proposed algorithm to examine the effects of the different parameterizations on the resulting SFE solutions, the role of network complexity and the nature of the equilibrium points. [ABSTRACT FROM PUBLISHER]

This paper presents a multi-stage fuel consumption minimization method in an autonomous voltage source converter (VSC)-based microgrids considering microgrid small signal stability (SSS) margin, frequency and voltage regulation, and the minimum and maximum allowable range of active and reactive output power of VSCs. In VSC-based microgrid, the parameters of each VSC power sharing controller have significant influence on microgrid SSS margin, frequency and voltage regulation, and the ratio of active and reactive power shared between VSCs. Considering all of these effects in fuel consumption minimization method with straightforward technique leads to having a complicated constrained optimization problem, which cannot be solved in a short time. The computation time of solving this optimization problem is very important in practical applications. In order to eliminate this problem, a multi-stage method is developed in this paper. This method can optimize the fuel consumption and consider the output active and reactive power limit, SSS margin, and frequency and voltage regulation in different stages without significant interactions on each other. Hence, the computation time is strongly reduced. The simulation results in a microgrid, which has a wind turbine, two gas turbines, and a micro-turbine with heat load, demonstrate the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

Notable benefit can be brought by combined operation of a coupled electricity and heat system (CEHS), and be enhanced by introducing thermal energy storage (TES). Existing literature researching on this topic either neglects the heat network, or requires TES system being located and operated together with a combined heat and power unit. This paper aims at removing such requirement whilst taking heat network into account. With prevalent constant-flow variable temperature control strategy of heat network, the optimal dispatch model of CEHS considering independent TES (ITES) system with networked electric and heat energy distribution systems is presented. The non-convex parts in the heat network, mainly caused by the MFR reversal when ITES changes its operation state, are exactly reformulated to mixed-integer linear (MIL) constraints, which leads to a mixed-integer second-order programming formulation of the problem. Case studies demonstrate that introducing ITES not only brings reduction in the total operation cost, but also ameliorates the system reliability and its capability in accommodating renewables. [ABSTRACT FROM AUTHOR]

In this paper, we propose a framework for coordinating distributed energy resources (DERs) connected to a power distribution system, the model of which is not completely known, so that they collectively provide a specified amount of active power to the bulk power system, while respecting distribution line capacity limits. The proposed framework consists of a linear time-varying input-output (IO) system model that represents the relation between the DER active power injections (inputs), and the total active power exchanged between the distribution and bulk power systems (output); an estimator that aims to estimate the IO model parameters; and a controller that determines the optimal DER active power injections so that the power exchanged between both systems equals to the specified amount at a minimum generating cost. We formulate the estimation problem as a box-constrained quadratic program and solve it using the projected gradient descent algorithm. To resolve the potential issue of collinearity in the measurements, we introduce random perturbations in the DER active power injections during the estimation process. Using the estimated IO model, the optimal DER coordination problem to be solved by the controller can be formulated as a convex optimization problem, which can be solved easily. The effectiveness of the framework is validated via numerical simulations using the IEEE 123-bus distribution test feeder. [ABSTRACT FROM AUTHOR]

In this paper, a two-stage optimization framework is proposed for optimal placement and centralized real-time control of low-voltage static var compensators (LV-SVCs) in unbalanced distribution circuits to achieve feeder level benefits namely voltage regulation and energy loss minimization. The number, locations, and the optimal real-time reactive power injections from the LV-SVCs are determined from a proposed three-phase unbalanced ac optimal power flow (ACOPF). The ACOPF is formulated as a multi-objective optimization with operating constraints written in rectangular coordinates. The resulting nonlinear nonconvex problem is solved using the predictor-corrector primal-dual interior point method. The proposed approach is scalable for application to large distribution circuits, treats the constraints of physical space limitations effectively, and can take advantage of communication capabilities of LV-SVCs for centralized real-time control. The benefits of the proposed real-time control of LV-SVCs as compared to their operation with local autonomous voltage-based distributed control is demonstrated. The results show that, the proposed approach addresses the LV-SVC placement and control problem effectively to minimize energy losses while maintaining the voltage regulation. [ABSTRACT FROM AUTHOR]

This paper proposes a novel power flow formulation and solution algorithm for a generalized large-scale interconnected transmission system encompassing multi-frequency HVac and HVdc grids having arbitrary numbers of buses, topologies, and operating frequencies. Back-to-back and ac/dc voltage-source converters are employed to interconnect and control the voltage and power interchange between two power grids operating at different frequencies. The power Flow formulation is based on a steady-state model of back-to-back and ac/dc converters operated in centralized and distributed droop control strategies. Each power grid is represented by a set of nonlinear power balance equations. These equations are solved simultaneously using a unified power flow algorithm, taking into account generator and converter limits. It is shown that the solution convergence is achieved rapidly despite the system size, topology, and converter control strategies. The efficacy and accuracy of the proposed steady-state solution algorithm are demonstrated by comparing the numerical solution to the one obtained by time-domain electromagnetic models of multi-frequency HVac and HVdc transmission systems with fully controllable back-to-back and ac/dc converters. The results obtained by using the proposed algorithm and the time-domain simulation are practically identical. [ABSTRACT FROM AUTHOR]

This paper presents a closed-form and non-iterative solution for the long-studied SCADA-based state etimation problem, where unsynchronized traditional measurements from remote terminal units are used. In this regard, a novel reformulation of the problem is introduced, where unknowns are expressed as complex variables in terms of unsynchronized SCADA measurements. To this end, it is assumed that bus voltage amplitudes as well as current amplitudes and active and reactive power flows/injections are available. The resulting system of equations is solved by the classic linear weighted least-squares method. In contrast to the traditional approaches, several drawbacks, such as initialization, and issues with convergence (especially for large-scale systems) are resolved, without using synchrophasors. The method is validated on a 3-bus test network and applied to the IEEE 118-bus test system, as well as 1341-bus and 9241-bus European high-voltage transmission networks. [ABSTRACT FROM AUTHOR]

The new IEEE 1547-2018 standard includes dynamic Volt/VAr control for photovoltaic (PV) smart inverters. While recent research has addressed the problem of optimal inverter dispatch, the interaction between inverters and the classical Volt/VAr control (VVC) regulation system needs further study. This paper proposes an approach that builds on the classical VVC solution with PVs, by computing for each inverter a rule that modulates the smart inverter reactive power in function of its real power. Two approaches are presented for computing the inverter's reactive power equation slope: the first approach is based on the robust minimization of the absolute voltage magnitude deviation via a linear program, whereas the second approach yields closed-form solutions inspired from distributionally robust chance constraints. Numerical results are presented on weakly meshed distribution networks having up to 3146 nodes; they demonstrate that the voltage violations due to intermittent real power variations are significantly reduced by the decision rules as compared to maintaining the last computed VVC set-points, even when the inverters operate at constant power factor or with default Volt/VAr settings proposed in the literature; additionally, the reactive power decision rules maintain a network loss level that is close to the average from a centralized solution. [ABSTRACT FROM AUTHOR]

Optimal power flow (OPF) is an important power systems optimization tool. However, due to the inherent nonlinearity of the solution space, OPF methods may yield a local optimal solution, leading to economic loss. For this reason, an OPF remains a major research topic. Changing power balance equations can change the solution space, alter solution time, and create a chance of reaching a better solution. In this paper, a new simple line-wise optimal power flow (LWOPF) formulation is proposed using line-wise power balance equations and solved using the successive linear programming (SLP) technique. The study results on nine different test systems, up to a 9 241-bus real power system, show that the proposed method is accurate, provides monotonic convergence, scales well for large systems and is consistently faster, up to twice the speed of MATPOWER and other proven bus-wise SLP approaches to solve the OPF. [ABSTRACT FROM AUTHOR]

High penetration of distributed renewable energy introduces significant uncertainties to active distribution networks. Optimal control methods accounting for inherent uncertainties are needed to facilitate economic and reliable operation of active distribution networks. This paper proposes a stochastic receding horizon control method based on modified stochastic model predictive control framework to integrate high penetration of distributed generation. Multiple controllable resources are jointly optimized over a finite prediction horizon while ensuring relevant security restrictions. The simplified Z-bus sensitivity for active distribution networks is developed for computationally efficient estimation of system nonlinearity with high accuracy, and is combined with the sequential linear programming to iteratively derive the linear state space model for compensation of cumulative modeling errors. Furthermore, the voltage limitations are reformulated as chance constraints to indicate the probabilistic reliability index of voltage qualification rate, and achieve tradeoffs between cost reduction and voltage regulation. The affine-disturbance feedback control policy is leveraged here to enforce close-loop control performance and analytically transform intractable chance constraints into second-order cone constraints. Comprehensive case studies based on 33-bus and 123-bus distribution systems are carried out to demonstrate the capability and effectiveness of the proposed approach in terms of modeling accuracy, control performance, cost reduction, and method scalability. The proposed approach can effectively enforce voltage regulation against uncertainties with the prescribed probability level. Control costs and constraint violation can be reduced compared with deterministic model predictive control and open-loop control strategies. [ABSTRACT FROM AUTHOR]

Linear power flow models are widely used in power systems to simplify the nonlinear power flow equations. The DC power flow model is one of the representatives. There are many other linear power flow models that improve the DC power flow model with the inclusion of $\boldsymbol{Q}$ and $\boldsymbol{v}$. However, existing linear models are derived based on empirical mathematical approximation without a general methodology guidance. In this paper, we found that the fundamental difference among different linear power flow models lies in the formulation of “independent variables.” Based on this finding, a general formulation of linear power flow models is proposed. The linearization error is theoretically analyzed. In particular, the case when $\boldsymbol{ \theta }$ and $\boldsymbol{v^{\scriptscriptstyle k}}$ are regarded as independent variables is thoroughly investigated. Method for finding the linear power flow with the minimum error is presented. The formulation of the independent variables associated with the minimum linearization error is determined by the distribution of state variables $\boldsymbol{v}$ and $\boldsymbol{\theta }$. It is shown that the linearization error when $\boldsymbol{v^{\scriptscriptstyle 2}}$ is regarded as an independent variable is normally smaller than that for $\boldsymbol{v}$ because of the special properties of the distribution of $\boldsymbol{v}$ in power grids. [ABSTRACT FROM AUTHOR]

This paper proposes an optimal design algorithm for distributed secondary voltage control in islanded microgrids (MGs), including communication topology and controller gains. First, upon the consensus-based secondary voltage control, the sufficient condition for network connectivity of communication topology is revealed by the reachability matrix. A multi-objective optimization criterion is first proposed for the network design, taking the convergence performance, network-relevant time delays, and communication costs into consideration. After obtaining the Pareto frontier of this multi-objective model, an optimal network is selected to meet the practical requirements. Based on static output feedback, a small-signal dynamic model of an MG installed with a secondary voltage controller is established, where the distributed secondary voltage controller can be converted into an equivalent decentralized controller. Thereby, a linear quadratic regulator is formulated for the near-optimal design of controller parameters. Our approach customizes the optimal design framework of the topology and controller, which have been largely ignored in the existing literatures. Therefore, it promises to improve the performance of distributed secondary control. The effectiveness of the proposed methodology is verified by a simulation study. [ABSTRACT FROM AUTHOR]

Smart inverters provide additional control capability to help optimize the operation of distribution systems. This paper proposes a framework for exact optimal active and reactive power dispatch of distributed photovoltaic (PV) generation, switched capacitors, and voltage regulators in large multi-phase unbalanced distribution systems. The objectives of the optimal dispatch are minimization of the energy loss, PV active power curtailment, and operations of capacitors and voltage regulators, in addition to elimination of voltage violations and reverse power flow. The optimization problem is formulated in rectangular coordinates as a nonlinear, nonconvex problem. Effective computational strategies are proposed to allow the application of predictor-corrector primal-dual interior point method to solve optimization problems in real-time with a large number of constraints and variables, including discrete variables corresponding to switched capacitors and voltage regulators. The accuracy of the numerical solution and the ability to implement the proposed framework are validated using the unbalanced multi-phase IEEE 34-bus and EPRI 2,998-bus distribution systems with 15-minute load and PV data. The results show a significant loss reduction and elimination of both voltage violations and reverse power flow. [ABSTRACT FROM AUTHOR]

Using VSC-MTDC for wind farm integration is considered to be a promising solution. In order to provide a stable ac voltage control and avoid active power control conflicts, the amplitude-phase control strategy, rather than the active/reactive power decoupled control strategy, is generally applied for the VSC connected to wind farms. However, using such a control strategy, the flexibility of power flow control will be partly lost. As the positive and negative pole dc networks in the bipolar VSC-MTDC can operate independently, a novel hybrid control strategy is proposed in this paper. In the proposed hybrid control strategy, the amplitude-phase control and active/reactive power decoupled control can be applied to the positive and negative poles, respectively. Hence, the hybrid strategy combines the advantages of the amplitude-phase control and active/reactive power decoupled control and can be adapted to bipolar VSC-MTDC for large-scale wind farm integration. Simulation results using PSCAD show that the hybrid control strategy can provide the stable ac voltage control and active/reactive power flow control for the integration of wind farms; moreover, such a hybrid control strategy is helpful to avoid the overload of dc lines, stabilize the dc voltage, and enhance the power transfer capability. [ABSTRACT FROM AUTHOR]

Extreme weather events have a significant impact on the aging and outdated power distribution infrastructures. These high-impact low-probability events often result in extended outages and loss of critical services, thus, severely affecting customers’ safety. This calls for the need to ensure the resilience in distribution networks by quickly restoring the critical services during a disaster. This paper presents an advanced feeder restoration method to restore critical loads using distributed energy resources (DERs). A resilient restoration approach is proposed that jointly maximizes the amount of restored critical loads and optimizes the restoration times by optimally allocating grids available DER resources. The restoration problem is modeled as a mixed-integer linear program with the objective of maximizing the resilience to postrestoration failures while simultaneously satisfying grids critical connectivity and operational constraints and ensuring a radial operation for a given open-loop feeder configuration. Simulations are performed to demonstrate the effectiveness of the proposed approach using the IEEE 123-node feeder with five DERs supplying 11 critical loads and the IEEE 906-bus feeder with three DERs supplying 17 critical loads. The impacts of DER availability and fuel reserve on restored networks are assessed and it is shown that the proposed approach is successfully able to restore a maximum number of critical loads using available DERs. [ABSTRACT FROM AUTHOR]

Lack of efficient coordination schemes between photovoltaic (PV) panels may result in voltage stability issues. In this paper, we exploit the power control potential enabled by the PV inverters for voltage regulation. There are considerable obstacles to design a viable coordination scheme. Physically, the power flow equations lead to a highly nonconvex constraint set. With respect to the market implementation, voltage regulation is predominately conducted by the system operator, and voltage regulation related products rarely exist. We cast the voltage regulation as a nonconvex optimization problem, and devise an analytical framework to show that based on a linearized model, one can design a gradient descent-based distributed scheme, which, when implemented in the nonconvex branch flow model, will converge to a local minimum exponentially fast. Additionally, we design a compensation scheme which incentivizes the PV panel owners to provide voltage regulation. The compensation naturally leads to a game between all the PV panel owners. By design, the equilibria coincide with the global minimizers to the social planner problem. Simulation results confirm the convergence rate of the control actions in practice. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel transactive energy trading (TET) framework to deal with the economic issues in energy trading and the technical issues in distribution system operation in a holistic manner. In particular, we innovatively integrate a bilateral energy trading mechanism with the optimal power flow (OPF) technique to increase economic benefits to individual participants, and meanwhile ensure the reliability and security of the system operation. In order to resolve the inherent conflict of interests, Nash bargaining theory is used to model the TET problem, which is further decomposed into a multiperiod OPF problem and a payment bargaining problem. Moreover, we develop an efficient distributed algorithm for solving the TET problem base on alternating direction method of multipliers (ADMM). Instead of directly solving optimization subproblems like most ADMM-based distributed algorithms, we derive closed-form solutions to all subproblems to significantly improve the computational efficiency. Finally, numerical tests on the IEEE 37-bus and 123-bus distribution systems demonstrate the effectiveness of our proposed framework and the efficiency of our distributed algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes a multi-timescale volt/var optimization for the optimal dispatch of battery energy storage system in smart distribution grids. It aims to coordinate the substation on-load tap changer operation on slow-timescale (hourly basis) with the photovoltaic inverters and battery storage operations on fast-timescale (15 min basis). This coordination is achieved by using two-stage stochastic programming and implemented via model predictive control. The power loss and energy purchase cost are reduced while maintaining voltages within limits. The forecasting uncertainties are modeled by generating a large number of random scenarios and then subsequently reducing scenario numbers to establish a tradeoff between computational burden and accuracy of the solution. The mixed-integer second-order cone program (MISOCP) is formulated with reduced scenarios, which achieves global optimum. Simulation results demonstrate the effectiveness of proposed MISOCP model in keeping the voltages within limits under forecasting uncertainties. [ABSTRACT FROM AUTHOR]

Due to growing environmental concerns, wind power has taken a larger share of the generation market. While the increase in wind generation provides diversification of the supply, it also undermines system reliability by introducing uncertainty in power supply and decreasing the maneuverability of the grid in terms of VAR absorbance and provision. To restore the reliability of high wind penetrated systems, this paper proposes hierarchical voltage control (HVC). The proposed pattern generalization methodology is based on principle component analysis and a three-layer feedback architecture utilizing online state estimation. The proposed control includes both steady-state and dynamic constraints. Governed by an optimization trained with cases representing operating snapshots and solved via an active-set algorithm adopting stepwise linearization, the proposed HVC provides efficiency and adaptability. As a result, the proposed control provides adequate system support under a wide range of contingencies and operating conditions to enhance grid reliability. Its capability to regulate yearly round operations in real time is validated using a reduced Western Electricity Coordinating Council power system model. [ABSTRACT FROM AUTHOR]

The work reported in this paper aims at developing an algorithm for identifying the worst contingencies to be used in a security-constrained optimal power flow problem. A bilevel max-min optimization model is proposed to find the worst contingency scenario while solving an ac optimal power flow problem and considering corrective actions. The objective is to minimize the total cost including generation and load shedding cost while satisfying all relevant constraints. The upper-level problem allows representing contingencies using binary variables. We formulate a second-order cone problem in the lower-level to represent the ac power flow equations. Duality is used to merge the upper- and lower-level problems into a single-level one. The resulting mixed-integer second-order conic problem can be efficiently solved. Three case studies are presented as applications of this novel technique. [ABSTRACT FROM AUTHOR]

This paper proposes a resilience-oriented design (ROD) technique to protect distribution grids against high-impact but low-probability extreme weather events. The problem is formulated as a two-stage stochastic mixed integer problem. The first stage is to make ROD decisions, i.e., hardening existing distribution lines and deploying ROD resources such as back-up distributed generators and automatic switches. The second stage evaluates the system operation cost during a realized extreme weather event and repair cost after the event. A novel modeling strategy is proposed to deal with the decision-dependent uncertainty of distribution line damage status, which is affected by the first-stage hardening decisions. As both stages have binary variables, a modified and computationally efficient progressive hedging algorithm with scenario bundling is introduced. The algorithm performance is evaluated by calculating lower bounds of solutions. The proposed model and algorithms are demonstrated on 34-bus and 123-bus test feeders. [ABSTRACT FROM AUTHOR]

Decentralizing energy systems require renewable energy sources to assume a higher degree of system responsibility. Concerning voltage stability and reactive power management, wind and PV parks connected to 110 kV grids are technically capable of providing reactive power. A controllable and situation-dependent feed-in depending on the respective situation could not only reduce grid losses in the distribution grid, but also facilitate a flexible reactive power exchange with the transmission grid in order to support the voltage stability of the system. In this paper, a two-step approach is presented to estimate the nodal reactive power potential and to estimate cost savings arising from a flexible reactive power exchange between transmission and 110 kV grid. Results are deducted for a simple test grid as well as for the German transmission grid. [ABSTRACT FROM AUTHOR]

Chance constrained optimal power flow (OPF) has been recognized as a promising framework to manage the risk from variable renewable energy (VRE). In the presence of VRE uncertainties, this paper discusses a distributionally robust chance constrained approximate ac-OPF. The power flow model employed in the proposed OPF formulation combines an exact ac power flow model at the nominal operation point and an approximate linear power flow model to reflect the system response under uncertainties. The ambiguity set employed in the distributionally robust formulation is the Wasserstein ball centered at the empirical distribution. The proposed OPF model minimizes the expectation of the quadratic cost function w.r.t. the worst-case probability distribution and guarantees the chance constraints satisfied for any distribution in the ambiguity set. The whole method is data-driven in the sense that the ambiguity set is constructed from historical data without any presumption on the type of the probability distribution, and more data leads to smaller ambiguity set and less conservative strategy. Moreover, special problem structures of the proposed problem formulation are exploited to develop an efficient and scalable solution approach. Case studies are carried out on the IEEE 14 and 118 bus systems to show the accuracy and necessity of the approximate ac model and the attractive features of the distributionally robust optimization approach compared with other methods to deal with uncertainties. [ABSTRACT FROM AUTHOR]

The penetration of distributed renewable energy sources in the distribution grid is increasing considerably in the last years. This is one of the main causes that contributed to the growth of technical problems in both transmission and distribution systems. An effective solution to improve system security is to exploit the flexibility that can be provided by distributed energy resources (DER), which are mostly located at the distribution grids. Their location combined with the lack of power flow coordination at the system operators interface creates difficulties in taking advantage of these flexible resources. This paper presents a methodology based on the solution of a set of optimization problems that estimate the flexibility ranges at the distribution and transmission system operators (TSO-DSO) boundary nodes. The estimation is performed while considering the grid technical constraints and a maximum cost that the user is willing to pay. The novelty behind this approach comes from the development of flexibility cost maps, which allow the visualization of the impact of DER flexibility on the operating point at the TSO-DSO interface. The results are compared with a sampling method and suggest that a higher accuracy in the TSO-DSO information exchange process can be achieved through this approach. [ABSTRACT FROM AUTHOR]

The deployment of smart grids has facilitated the integration of a variety of investor assets into power distribution systems, giving rise to the consequent necessity for positive and active interaction between those investors and local distribution companies (LDCs). This paper proposes a novel incentive-based distribution system expansion planning model that enables an LDC and distributed generation (DG) investors to work in a collaborative way for their mutual benefit. Using the proposed model, the LDC would establish a bus-wise incentive program based on long-term contracts, which would encourage DG investors to integrate their projects at specific system buses that would benefit both parties. The model guarantees that the LDC will incur minimum expansion and operation costs while concurrently ensuring the feasibility of DG investors’ projects. To derive appropriate incentives for each project, the model enforces several economic metrics including internal rate of return, profit investment ratio, and discounted payback period. All investment plans committed to by the LDC and the DG investors for the full extent of the planning period are then coordinated accordingly. Several linearization approaches are applied to convert the proposed model into an MILP model. The intermittent nature of both system demand and wind- and PV-based DG output power is handled probabilistically, and a number of DG technologies are taken into account. Case study results have demonstrated the value of the proposed model. [ABSTRACT FROM AUTHOR]

The ever-increasing number of wind farms has brought both challenges and opportunities in the development of wind power forecasting techniques to take advantage of interdependencies between tens or hundreds of spatially distributed wind farms, e.g., over a region. In this paper, a sparsity-controlled vector autoregressive (SC-VAR) model is introduced to obtain sparse model structures in a spatio-temporal wind power forecasting framework by reformulating the original VAR model into a constrained mixed integer nonlinear programming (MINLP) problem. It allows controlling the sparsity of the coefficient matrices in direct manner. However this original SC-VAR is difficult to implement due to its complicated constraints and the lack of guidelines for setting its parameters. To reduce the complexity of this MINLP and to make it possible to incorporate prior expert knowledge to benefit model building and forecasting, the original SC-VAR is modified and a correlation-constrained SC-VAR (CCSC-VAR) is proposed based on spatial correlation information about wind farms. Our approach is evaluated based on a case study of very-short-term forecasting for 25 wind farms in Denmark. Comparison is performed with a set of traditional local methods and spatio-temporal methods. The results obtained show the proposed CCSC-VAR has better overall performance than both the original SC-VAR and other benchmark methods, taking into account all evaluation indicators, including sparsity-control ability, sparsity, accuracy, and efficiency. [ABSTRACT FROM AUTHOR]

The need for a market based approach for reactive power procurement has been recognized by FERC. Due to the localized characteristic of reactive power, regulatory mechanisms are necessary to mitigate the possibility of holding market power by generators. The regulator is responsible for devising the regulatory mechanisms that provide incentives to generators to supply reactive power while preventing the abuse of market power. This paper proposes a mathematical model to simulate the strategic behavior of generators supplying reactive power while considering the system operator's schedule. The proposed method can be used by the regulator to simulate the market behavior in the reactive power supply. We further study how regulatory policies affect the strategic behavior. An alternative price cap method has been proposed and tested in the numerical example to mitigate the effect of strategic behavior of generators in reactive power procurement by the system operator. The numerical examples are tested on the Nordic 32-bus system. [ABSTRACT FROM AUTHOR]

This paper describes the principle and implementation of a new MW+MVAr-Miles charging methodology, which was developed to reflect three key cost drivers in distribution network development: the distance used to support nodal real and reactive power injection/withdrawal; the degree of support offered by the network assets; and the operating condition of the supporting assets in terms of their power factors. The inclusion of the latter driver allows the developed charging methodology to reward network users who are contributing to better power factors and better network utilization, while penalizing customers who worsen power factors and network utilization. As a consequence, the charging model is able to provide forward-looking incentives for network customers to behave in a manner to better the network condition, which will in turn help to reduce the cost of future network development. In addition, the separation of real and reactive power pricing would give network users clear indications of the cost of their reactive power draw from the network, which in turn could help them to evaluate the economics in investing in reactive power compensation devices. The proposed charging methodology is demonstrated on a practical eight-busbar distribution system with a mixed demand and embedded generation (EG). This paper results from work undertaken in a project on distribution charging methodologies for Western Power Distribution. The views in this paper expressed are not those of Western Power Distribution. [ABSTRACT FROM AUTHOR]

This paper investigates the use of the constraint reactive implicit coupling (CRIC) method for the engine of a continuation power flow program. Full Newton continuation power flow methods are robust and accurate but are computationally expensive. Fast decoupled methods provide accurate results and require less computational time, but their performance worsens at heavy loading conditions, where the system active/reactive power decoupling characteristics are lost. This paper makes use of the CRIC method, which preserves the decoupled power flow solution structure but better models the active/reactive coupling. Effective stopping criteria are proposed for the continuation method, which helps to speed up computation. Such stopping criteria are also applied for tracing QV curves for some practical Brazilian power systems, with all operating limits considered. [ABSTRACT FROM AUTHOR]

An advanced high side voltage control (HSVC) that can improve power system stability by adding supplemental con- trol to conventional generator excitation systems has been developed. Since the introduction of this advanced HSVC at the IEEE PES 2000 Summer Meeting, additional development has further improved the advanced HSVC as reported in a companion paper. This paper describes field verification results for the HSVC that were carried out on a hydro power plant of the U.S. Army Corps of Engineers on the Columbia River at The Dalles. The advanced HSVC was temporarily added to the existing digital automatic voltage regulators (AVRs) of two generators in a 22-machine hydro power plant. Various tests, such as confirmation of droop, performance of the cross-current suppression function, switching on and off of a nearby capacitor bank, and others, were successfully carried out. It was confirmed through these field verification tests that the advanced HSVC displayed beneficial impacts on voltage control and system stability as compared to a conventional AVR. [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]

Existing power system resilience enhancement methods, such as proactive generation rescheduling, movable sources dispatch, and network topology reconfiguration, do not explore the capability and flexibility of shunts to maintain voltage stability during and after disrupting events. Besides, existing methods rely on accurate system models that are not easily scalable for large integrated power grids. In this paper, a data-driven multi-agent framework based on a deep-reinforcement-learning algorithm is proposed to overcome the computation and scalability concerns related to precise system models and to plan for the deployment of shunts for power system resilience enhancement. Specifically, voltage violations due to outages of multiple lines during windstorms are taken as an example of a power system resilience improvement problem. Then, a multi-agent based hybrid soft actor critic (HSAC) algorithm is developed for offline siting and sizing as well as online controlling of shunt reactive power compensators to enhance voltage resilience. The HSAC algorithm is derived from the fundamental SAC algorithms that contain both continuous and discrete action spaces. The proposed multi-agent framework learns from previous experiences and eventually gets trained to determine proper locations and sizes for shunts to avoid voltage violations during multiple line failures. The proposed approach is demonstrated on the IEEE 57-bus and IEEE 300-bus systems. The results show that the proposed multi-agent framework is effective for installation planning and controlling of shunts to enhance power system resilience. [ABSTRACT FROM AUTHOR]

Utility-scale battery energy storage system (BESS) technologies have huge potential to support system frequency in low-inertia conditions via fast frequency response (FFR) as well as system voltage via dynamic reactive power response. However, technical challenges may emerge in weak grids where low system strength could cause voltage instability, eventually potentially hindering provision of FFR too. This paper provides a systematic and comprehensive analysis of the challenges, and proposes relevant solutions, for BESS in providing FFR and general dynamic active and reactive responses under low system strength conditions. In particular, first we propose a constraint to describe the negative impact of low system strength on BESS phase-locked loop (PLL) stability and possible mitigation solutions. We then investigate the negative impact of large contingencies on BESS DC-link stability and active power control by introducing d-q current-power sensitivity factors and propose a solution based on reactive power prioritization that prevents converter-level instabilities while providing simultaneous active and reactive dynamic responses. Possible negative active/reactive power interactions due to BESS converter capacity constraints and the impact of the BESS operating point are also addressed. All these issues are investigated, and the proposed solutions tested, through explicit mathematical modelling as well as dynamic simulations of the South Australia's Eyre Peninsula weak grid. [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 considers the co-operation of distributed generators (DGs), battery energy storage systems (BESSs) and voltage regulating devices for integrated peak shaving and voltage regulation in distribution grids through a co-optimization framework, which aims to minimize the operational costs while fulfilling the operational constraints of network and devices. To account for the uncertainties of load demand and generation, we then convert the co-optimization model into a two-stage stochastic program where state-of-charge (SoC) trajectories of BESSs and operation of voltage regulating devices are optimized at the first stage for day-ahead scheduling, while the reactive powers of DGs and BESSs are left at the second stage for potential intra-day scheduling to handle short-term voltage issues. The proposed co-optimization scheme is validated on the IEEE 37-node test feeder and compared with other practices. [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]