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A good quality stability model is a key factor for accurate power system operations.Inaccurate parameters of the stability models affect the decision making which paves the way for serious consequences. Thus, it is necessary to calibrate the stability model parameters in a regular manner. There are several calibration methods in the literature which are based on simultaneous estimation of the parameters and states. However, not all of the model parameters are well estimable simultaneously. Simultaneous estimation of parameters with high collinearity may result in biased calibration results. In this paper, the trajectory sensitivity method is used to detect the sensitive parameters and construct the sensitivity matrix. Then, parameters with high linear dependency are identified using the sensitivity matrix. It is shown that, despite the high sensitivity of a parameter, its estimability degrades as the collinearity with other parameters increase. In this paper an identifiability analysis that detects the collinearity among the sensitive parameters is proposed. The proposed method is validated using WSCC 9-Bus System. [ABSTRACT FROM AUTHOR]

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

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

The loss of small signal stability under parameter variation (e.g., fluctuation of loads and wind powers) can be ascribed to local bifurcations, i.e., saddle-node, Hopf, singularity-induced, and limit-induced bifurcations. Classic bifurcation calculation methods like the direct method and continuation method can only provide a bifurcation point or two-parameter bifurcation curve. Based on Galerkin method and the implicit function theorem, this paper proposes accurate polynomial approximations of bifurcation hypersurfaces in the multi-dimensional parameter space of interest. The proposed method can ensure high accuracy in this parameter space, and thus is preferable to the existing Taylor expansion-based local approximation method, given the intrinsic large-variation characteristic of wind powers. Acquired bifurcation hypersurfaces are immediately used to construct the small signal stability region of the continuous system, and then compute the stability margin for the operating point subjected to uncertainty of wind generation. Besides, the validity scope of the proposed method is analyzed, and the handling of limit-triggered equation switching as well as its computational difficulty is discussed. Computational results on the two-parameter 11-bus two-area and six-parameter IEEE 145-bus test systems validate the high accuracy and effectiveness of the proposed method. [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]

The paper provides a novel framework to study the accuracy and stability of numerical integration schemes when employed for the time domain simulation of power systems. A matrix pencil-based approach is adopted to evaluate the error between the dynamic modes of the power system and the modes of the approximated discrete-time system arising from the application of the numerical method. The proposed approach can provide meaningful insights on how different methods compare to each other when applied to a power system, while being general enough to be systematically utilized for, in principle, any numerical method. The framework is illustrated for a handful of well-known explicit and implicit methods, while simulation results are presented based on the WSCC 9-bus system, as well as on a 1,479-bus dynamic model of the All-Island Irish Transmission System. [ABSTRACT FROM AUTHOR]

This paper focuses on the issue of network connectedness (NC) in security-constrained optimal transmission switching problems, which is complicated by branch contingencies and corrective line switching. Two criteria are firstly proposed with the principle of preserving NC as much as possible within reasonable limits. By extending the electrical flow based NC constraints, a proposition is derived to associate different cases of NC with the optimum of a linear program, yielding the mathematical formulation of the NC criteria. By Karush-Kuhn-Tucker conditions, this formulation is further transformed into a tractable version which can be incorporated with existing SCOTS models without affecting the applicability of original solution approaches. Finally, case studies on various networks and SCOTS models demonstrate the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

Electric distribution grid operations typically rely on both centralized optimization and local non-optimal control techniques. As an alternative, distribution system operational practices can consider distributed optimization techniques that leverage communications among various neighboring agents to achieve optimal operation. With the rapidly increasing integration of distributed energy resources (DERs), distributed optimization algorithms are growing in importance due to their potential advantages in scalability, flexibility, privacy, and robustness relative to centralized optimization. Implementation of distributed optimization offers multiple challenges and also opportunities. This paper provides a comprehensive review of the recent advancements in distributed optimization for electric distribution systems and classifications using key attributes. Problem formulations and distributed optimization algorithms are provided for example use cases, including volt/var control, market clearing process, loss minimization, and conservation voltage reduction. Finally, this paper also presents future research needs for the applicability of distributed optimization algorithms in the distribution system. [ABSTRACT FROM AUTHOR]

This paper presents a circuit breaker (CB) aging failure model based on condition monitoring. This model is inserted into a basic CB Markov model and applied in substation reliability assessment. The proposed model can accurately incorporate the wearing status and aging process of CBs. The results from applying the proposed method to a utility substation configuration demonstrate that ignoring aging failures of CBs can lead to significant underestimation of substation unreliability. [ABSTRACT FROM PUBLISHER]

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]

This paper presents a new control strategy for enhancing the dc voltage regulation and the transient response in the multi-terminal VSC-HVDC system by ensuring swift power-sharing among converters when encountering large disturbance such as converter loss or ac fault at one of the converter stations. The quick power sharing can be realized using direct power control (DPC) since it has a merit of fast power dynamic response. On the other hand, to limit the converter current during ac fault, a new coordination strategy between DPC and vector current control (VCC) is proposed. Furthermore, a new simplified model of the MTDC system is developed to study the performance of DPC in enhancing the dc voltage dynamics response analytically. The time-domain simulation of the detailed model of the four converter stations MTDC system verify that the proposed control strategy significantly reduces the overshoot in the transient dc voltage response following an outage or ac fault. As a result, together with the droop gain selection for the maximum permissible steady-state dc voltage deviation, the proposed control strategy can help to reduce the size of the dc chopper in the MTDC grid or even avoiding it. Moreover, the comparative analysis based on time-domain simulation depicts that the proposed simplified model has the same dc voltage response compared to the detailed model of the MTDC system except for a steady-state error of 0.47% and a little bit longer settling time (1.5 ms) at transient. [ABSTRACT FROM AUTHOR]

The paper proposes a technique for the on-line estimation of Thévenin equivalent (TE) which only needs the present phasor measurements. The technique is based on the wide-area measurements including voltage and current phasors of the system loads and synchronous generators, so that it can simultaneously estimate TE of the system seen from the interested buses. The technique has two main steps. In the first step, the conventional impedance matrix $\bar{Z}_{\rm bus}$ is modified to be suitable for TE estimation. In the second step, a correction coefficient based on the sensitivity theory calculated by using two consecutive phasor measurements is applied to correct the diagonal terms of the $\bar{Z}_{\rm bus}$ matrix. Simulation results carried on the IEEE 39-bus and 118-bus test systems show that the proposed technique can accurately estimate the TE for both generation and consumption buses under any load-increase scenario. The comparison scenarios verify the superiority of the proposed technique over others. [ABSTRACT FROM AUTHOR]

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

In order to reduce the dependence on accumulated experience that is difficult to replicate for the human dispatchers to make power generation scheduling more automatically, quickly, and intelligently, higher requirements are placed on the level of the auxiliary decision-making system. In this paper, a short-term scheduling problem was treated as a regression task that concentrates on how to learn a reliable statistic model that concludes the intrinsic logic of the dispatching policy from extensive historical dispatching experience. In this way, since Kullback-Leibler distance can better measure the distance between two distributions, we designed a novel GAN-based learning method for the scheduling task. Also, we proposed a feasible framework that combines the stage of learning, decision-making, and deployment to support the practical implementation of the proposed algorithm. In the experiment, a real case that takes short-term scheduling tasks on a regional large-scale power system is considered in our experiments. As a result, the comparison of several methods further shows the superiority of the proposed GAN-based method under our implementations. [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]

State estimation plays a key role in the transition from the passive to the active operation of distribution systems, as it allows to monitor the networks and provides the necessary information to perform control actions. However, designing state estimators for distribution systems is challenging, due to the characteristics of the networks, such as limited measurement availability. Furthermore, the features of the distribution system present significant local variations, e.g., voltage level and number and type of customers, which makes it hard to design a “one-size-fits-all” state estimator. This paper introduces a unifying framework that allows to easily implement and compare diverse unbalanced static state estimation models. This is achieved by formulating state estimation as a general constrained optimization problem. The advantages of this approach are described and supported by numerical illustration on a large set of real distribution feeders. The framework is also implemented in software and made available open-source. [ABSTRACT FROM AUTHOR]

This paper proposes a new deep learning (DL) based model-free robust method for bulk system on-line load restoration with high penetration of wind power. Inspired by the iterative calculation of the two-stage robust load restoration model, the deep neural network (DNN) and deep convolutional neural network (CNN) are respectively designed to find the worst-case system condition of a load pickup decision and evaluate the corresponding security. In order to find the optimal result within a limited number of checks, a load pickup checklist generation (LPCG) algorithm is developed to ensure the optimality. Then, the fast robust load restoration strategy acquisition is achieved based on the designed one-line strategy generation (OSG) algorithm. The proposed method finds the optimal result in a model-free way, holds the robustness to handle uncertainties, and provides real-time computation. It can completely replace conventional robust optimization and supports on-line robust load restoration which better satisfies the changeable restoration process. The effectiveness of the proposed method is validated using the IEEE 30-bus system and the IEEE 118-bus system, showing high computational efficiency and considerable accuracy. [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]

Optimal power flow (OPF) programs must be able to provide sound operating points for power systems under different conditions while meeting a large number of constraints. These constraints, however, either due to the operating conditions at hand or by construction, can have linearly dependent gradients, thus defining ill-behaved feasible sets. This paper analyzes the use of an alternative set of optimality conditions, derived from the Fritz-John (FJ) conditions, to represent OPF solutions in such critical cases. Results are presented for realistic test systems. [ABSTRACT FROM PUBLISHER]

This paper proposes a new decentralized data-driven load restoration (DDLR) scheme for transmission and distribution (TD) systems with high penetration of wind power. Robust DDLR models are constructed in order to handle uncertainties and ensure the feasibility of decentralized schemes. The Wasserstein metric is used to describe the ambiguity sets of probability distributions in order to build the complete DDLR model and realize computationally tractable formulation. A data-driven model-nested analytical target cascading (DATC) algorithm is developed to obtain the final load restoration result by iteratively solving small-scale mathematical models. The proposed DDLR scheme provides load restoration results with adjustable robustness, and performance efficiency is independent from the amount of data. The DDLR scheme makes full use of the available data while respecting information privacy requirements of independent operated systems, and ensures the feasibility of a decentralized load restoration strategy even in the worst-case condition. The effectiveness of the proposed method is validated using a small-scale TD system and a large-scale system with the IEEE 118-bus TS and thirty IEEE-33 DSs, showing high computational efficiency and superior restoration performance. [ABSTRACT FROM AUTHOR]

A new hierarchical multi-area power system state estimation method is proposed in this paper. Instead of exchanging boundary measurements or state estimates, the proposed technique is based on exchanging the sensitivity functions of local state estimators. The main benefit of the proposed scheme is the improved convergence speed, which also reduces the amount of information exchange required. Extensive numerical results involving IEEE standard systems and a utility scale system are presented. [ABSTRACT FROM AUTHOR]

Voltage source converter (VSC)-based high-voltage direct current (HVDC) transmission systems have been employed widely in recent years. However, connecting a VSC-HVDC link to a very weak grid (a high-impedance grid) is challenging. A vector-controlled VSC is incapable of injecting/absorbing its maximum theoretical active power in such grids. A simple yet effective control system for a standard vector-controlled VSC in a very weak grid condition has not been reported in the literature. This paper, benefiting from a comprehensive small-signal model, presents a detailed analysis of the VSC dynamics and shows how the assumptions made for designing VSC regulators in strong grids are no longer valid in very weak grids. The paper then proposes and compares two straightforward solutions: retuning the control parameters and using an artificial bus for converter-grid synchronization. Both methods enable the VSC to operate at the maximum theoretical active power at a very weak grid condition (i.e., at unity short-circuit ratio) by minimal modification in the widely accepted vector control method. The advantages and disadvantages of each method are discussed. The analytical results are verified by detailed nonlinear time-domain simulation results. [ABSTRACT FROM AUTHOR]

Solving nonlinear algebraic equations is a core task in many fields of engineering and the sciences. Iterative methods such as Newton's method have been popular in solving power flow equations. Recently, the non-iterative holomorphic embedding (HE) methods that employ polynomial embedded systems have been proposed to solve power flow equations. It is advantageous for the solution functions obtained by the HE method to possess an algebraic property. The present paper points out that algebraic solution functions can have several desired properties for the HE method to work. This paper also exemplifies that the algebraic property cannot be ensured by the elimination process, which corrects an assertion in the literature. It is hence essential to study required conditions for ensuring the existence of algebraic solution functions. The present paper is devoted to the theoretical foundation of HE methods using a polynomial embedded system and develops a novel general theorem and sufficient conditions to ensure the required algebraic property. Examples and numerical results are presented to better explain the derived theoretical results. [ABSTRACT FROM AUTHOR]

The increasing complexity of modern AC/DC power systems poses a significant challenge to a fast solution of large-scale transient stability simulation problems. This paper proposes the hybrid parallel-in-time-and-space (PiT+PiS) transient simulation on the CPU-GPU platform to thoroughly exploit the parallelism from time and spatial perspectives, thereby fully utilizing parallel processing hardware. The respective electromechanical and electromagnetic aspects of the AC and DC grids demand a combination of transient stability (TS) simulation and electromagnetic transient (EMT) simulation to reflect both system-level and equipment-level transients. The TS simulation is performed on GPUs in the co-simulation, while the Parareal parallel-in-time (PiT) scheduling and EMT simulation are conducted on CPUs. Therefore, the heterogeneous CPU-GPU scheme can utilize asynchronous computing features to offset the data transfer latency between different processors. Higher scalability and extensibility than GPU-only dynamic parallelism design is achieved by utilizing concurrent GPU streams for coarse-grid and fine-grid computation. A synthetic AC/DC grid based on IEEE-118 Bus and CIGRÉ DCS2 systems showed a good accuracy compared to commercial TSAT software, and a speedup of 165 is achieved with 48 IEEE-118 Bus systems and 192 201-Level detail-modeled MMCs. Furthermore, the proposed method is also applicable to multi-GPU implementation where it demonstrates decent efficacy. [ABSTRACT FROM AUTHOR]

With the growing penetration of distributed renewable energy, distributed control approaches are widely utilized in voltage control of active distribution networks (ADNs), suffering from limited applicability for control devices or heavy communication burden. This paper develops an innovative distributed voltage control strategy of ADNs with global sensitivities (DVC-GS), which integrates network information from a global optimization view to coordinate energy storages, PV inverters and the OLTC with little communication and computing time. The global sensitivities of voltage violations across all buses with respect to nodal voltage and active/reactive power injection are formulated to quantify the ability of each controllable resource for alleviating voltage violations in the entire ADN. The back-and-forth communication combined with the modified DistFlow model is newly developed for the real-time update of global sensitivities at each bus with high accuracy and no iteration. Then the coordinated control of various devices is implemented on basis of global sensitivities to effectively ensure voltage security of ADNs. Comprehensive simulations based on modified 11-bus and 123-bus systems demonstrate the significant efficiency and superiority of the global sensitivities and DVC-GS. [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]

Evaluation of conservation voltage reduction (CVR) factor is critical to peak load reduction, 556 energy conservation, and many CVR-related power system control/optimization strategies. This paper proposes a novel robust CVR factor evaluation method using soft constrained gradient analysis based on time-varying load modeling and real utility field measurements. Firstly, the time-varying ZIP parameter identification is formulated as an over-determinant problem composed of first-order gradient with respect to each coefficient and soft constraints representing temporal correlation of loads in each time step, in order to improve the robustness and smoothness of CVR factor evaluation. Then, problems in time series are coordinated with a sliding window approach. A necessary condition for selecting the smallest window size is proposed and strictly proved to guarantee the existence and uniqueness of the solution of time-varying load modeling problem. Finally, time-varying CVR factors are accurately and robustly calculated with field measurements and the identified load model. Case studies are performed using sufficient field measurements obtained from two real utilities. Unlike existing methods that require a large number of measurements to obtain precise estimation of CVR factor, the proposed method is sufficiently accurate even when the measurements are limited or of low time resolution. Further, the accuracy and robustness of the proposed approach are validated under different types of uncertainties and compared with other existing data processing and CVR factor evaluation methods. [ABSTRACT FROM AUTHOR]

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

The paper establishes convergence properties of decentralized and distributed control strategies that use a Steinmetz-based technique for mitigating voltage unbalance on distribution feeders. Reactive power from distributed energy resources (DERs), such as solar photovoltaic (PV), is used to balance voltages at critical nodes in the distribution network. Interactions between controllers are analyzed and a theoretical guarantee is derived for stability of the control algorithms. This is achieved using Banach fixed-point theory. Providing such convergence results ensures robustness of the proposed control algorithms in realistic settings where parameters are uncertain and/or slowly varying, disturbances are prevalent, and control and measurement signals are prone to delays. The convergence results are evaluated on three test distribution networks. [ABSTRACT FROM AUTHOR]

The nonlinear and nonconvex nature of ac power flow challenges the analysis and optimization of unbalanced distribution networks. To tackle this issue, this paper proposes an online feedback-based linearized power flow model for unbalanced distribution networks with both wye-connected and delta-connected loads. The online feedback-based linearized model is grounded on the first-order Taylor expansion of the branch flow model (BFM), and updates the model parameters via online feedback by leveraging the instantaneous measurements of voltages and load consumption. Exploiting the connection structure of unbalanced radial distribution networks, we also provide a unified matrix-vector compact form of the model. The numerical tests on the IEEE 123-bus test system validate its accuracy and superiority compared with other offline BFM methods. Additionally, we apply the proposed model to the optimal power flow for voltage regulation, which further demonstrates its effectiveness. [ABSTRACT FROM AUTHOR]

The modern power grid is undergoing unprecedented levels of transformations due to the rising prevalence of diverse power entities, cyber-enablement of grid components and energy deregulations. In this paper, we focus on distribution networks (DNs) to enable the seamless plug-and-play coordination of actuating cyber-enabled power entities for cost-effective and feasible system operations. The proposed distributed algorithm empowers individual cyber-physical agents residing in active power nodes with the ability to iteratively compute local actuation setpoints by exchanging information with neighbouring entities. The main contribution of this work is the identification of hidden convexities in the original non-convex optimal power flow (OPF) formulation for the DN via strategic decomposition and strong duality principles. These eliminate the need for OPF relaxations/approximations. Strong convergence and feasibility results are presented via theoretical analysis and practical simulation studies conducted on realistic systems. [ABSTRACT FROM AUTHOR]

For nearly 20 years, the Test Feeder Working Group of the Distribution System Analysis Subcommittee has been developing openly available distribution test feeders for use by researchers. The purpose of these test feeders is to provide models of distribution systems that reflect the wide diversity in design and their various analytic challenges. Because of their utility and accessibility, the test feeders have been used for a wide range of research, some of which has been outside the original scope of intended uses. This paper provides an overview of the existing distribution feeder models and clarifies the specific analytic challenges that they were originally designed to examine. Additionally, this paper will provide guidance on which feeders are best suited for various types of analysis. The purpose of this paper is to provide the original intent of the Working Group and to provide the information necessary so that researchers may make an informed decision on which of the test feeders are most appropriate for their work. [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]

With the improvement of traffic electrification, the coupling between power and transportation systems becomes more and more intensified. In this paper, electrified railway is firstly introduced into power system to support frequency regulation under high penetration of renewable energy sources. A novel frequency regulation framework consisting of day-ahead capacity estimation, frequency control parameters dispatch, and real-time response is constructed for electrified railway to provide primary frequency control support. Motion equations of electric trains under regulation are developed in detail. To fulfill the frequency regulation requirement and ensure punctual arrival, a multi-train joint response strategy is proposed to coordinate different electric trains for primary frequency control. The frequency regulation capacity estimation problem and frequency control power dispatch problem are established based on the multi-train joint response strategy. A novel sequential cutting plane algorithm is developed to linearly relax the nonlinear capacity estimation problem and power dispatch problem with ordinary differential equation constraints and iteratively tighten the relaxation area to improve solution optimality with desirable efficiency. Comprehensive numerical studies verify the effectiveness of the proposed primary frequency control framework, indicating the high potential of electrified railway to support frequency regulation of modern power systems. [ABSTRACT FROM AUTHOR]

Power flow (PF) calculation provides the basis for the steady-state power system analysis and is the backbone of many power system applications ranging from operations to planning. The calculated voltage and power values by PF are essential to determining the system condition and ensuring the security and stability of the grid. The emergence of multicore processors provides an opportunity to accelerate the speed of PF computation and, consequently, improve the performance of applications that run PF within their processes. This paper introduces a fast Newton-Raphson power flow implementation on multicore CPUs by combining sparse matrix techniques, mathematical methods, and parallel processing. Experimental results validate the effectiveness of our approach by finding the power flow solution of a synthetic U.S. grid test case with 82,000 buses in just 1.8 seconds. [ABSTRACT FROM AUTHOR]

Power flow analysis is a key tool for planning, operation and control of power systems. With future hybrid Supergrids in mind, a wide variety of power flow algorithms for multi-terminal VSC AC/DC systems have been proposed. However, the nonlinear nature of these formulations represents a challenge for its use in real power systems. Whereas in the study of AC networks linear approximations are frequently utilized to speed up multi-scenario steady-state analysis, an equivalent tool has not been proposed for hybrid AC/DC grids. This paper fills that gap by formulating a linear MW-only power flow algorithm with losses for multi-terminal VSC AC/DC systems. The proposed algorithm provides a consistent estimation of converters' losses and allows modelling of all branches within the converter stations. Moreover, two novel schemes for the inclusion of DC network losses are proposed and a circuit-equivalent model of the linear power flow problem in multi-terminal VSC AC/DC systems is suggested. [ABSTRACT FROM AUTHOR]

The paper presents a methodology for estimation of dynamic response of aggregate load at distribution network buses by taking into account daily variation in demand composition and generic dynamic responses of different types of load. Dynamic load models for different load categories obtained from field or laboratory measurements or through appropriate mathematical modeling are used in combination with hourly load composition at the given bus. The load composition is derived based on past demand surveys, and daily loading curves for different classes of customers. Uncertainties in both dynamic load models/responses of individual loads and load compositions at different times of the day are modeled probabilistically. With established dynamic signatures of different load categories and load compositions at different times of the day, Monte Carlo simulations are used to estimate probabilistic real and reactive power responses, including ranges of variation of these responses, for every hour of the day for a given or anticipated mix of demand. [ABSTRACT FROM PUBLISHER]

This paper presents a new reliability-based incremental phasor measurement unit (PMU) placement method via an enumeration-based integer linear programming optimization approach. By evaluating the proposed reliability indices for node and system observability, incremental PMUs are sequentially placed on the locations where the reliability of entire system's observability can be best improved at each step. As a result, a pre-set desired reliability of the system's observability can be achieved while using the minimal number of PMUs. The proposed method is generic and flexible in a way that different kinds of failures that impact the reliability of system observability can be easily included in the method. The 1st-order and 2nd-order failures of PMUs and lines are considered in this paper. The proposed method is validated using a 4-node system, the IEEE 14-node system and the IEEE RTS 96 test system. Simulation results show that the proposed method is effective and efficient in enhancing the reliability of observability for any system regardless of what the initial PMU placement of the system may be. [ABSTRACT FROM AUTHOR]

Recent research has presented a sufficient condition for the existence of a practical power flow solution in distribution networks, and a fixed-point linear approximation in complex coordinates. By employing Wirtinger calculus, this paper shows that the fixed-point linear approximation can be obtained via a complex-variable first-order Taylor series expansion around the no-load operating point; it then presents new simplified formulas for second- and third-order Taylor series expansions. The high-order power flow solutions are shown to be highly accurate on standard distribution networks available in the literature, and significantly more precise than the existing linear approximation. The proposed power flow approximations are useful in circular arithmetic methods, which extend the modeling of parameter uncertainty from the real line to the complex plane. The application of circular arithmetic is finally illustrated for the solution of power flow based Volt/VAr control under power injection uncertainty. The results show the capacity of the approach in mitigating voltage violations whenever injections deviate from their nominal values. [ABSTRACT FROM AUTHOR]

This paper proposes mathematical models for sequential coordination of transmission expansion planning with strategic generation investments. The proactive and reactive coordinations are modeled and studied. The interaction between transmission company (Transco) and strategic generation companies (Gencos) is modeled using the sequential-move game. This is while the interaction between the strategic Gencos is modeled as a simultaneous-move game. In the proactive coordination, the Transco expands its future transmission capacities taking into account the strategic investments by Gencos. In the reactive coordination, strategic Gencos move first and expand their future generation capacities and then Transco expands the transmission capacity. The proactive coordination is modeled as a mixed-integer bilevel linear program (MIBLP) and the reactive coordination is modeled as a mixed-integer linear program (MILP). The MIBLP has binary variables in both upper and lower levels. The Moore–Bard algorithm is parallelized and used to solve the MIBLP. The mathematical models and the parallelized Moore–Bard algorithm are tested on 3-bus and 6-bus example systems and the modified IEEE-RTS96. Also, the IEEE 118-bus test system is studied using a heuristic version of the Moore–Bard algorithm. [ABSTRACT FROM AUTHOR]

System operators are required to serve the load in the most cost-effective way while maintaining the integrity of the system and heeding reliability requirements. In the day-ahead market, operators acquire reserves in an attempt to guarantee N-1 reliability; yet, reserve deliverability is not guaranteed. Prior research has shown that the use of transmission switching, or topology control, may help improve reserve deliverability. In this paper, transmission switching is used as a corrective mechanism to help the system achieve N-1-1 reliability, where not only has the system lost a single element, but also it experiences the loss of a second major element after an adjustment period. In an attempt to preserve N-1-1 reliability, for this paper, a day-ahead unit commitment model that acquires supplementary reserves is solved. The day-ahead market solution is then tested for N-1-1 reliability using contingency analysis models with and without transmission switching. The methodology can be employed at the day-ahead time stage to ensure the system has acquired sufficient supplemental reserves. The results demonstrate that not only can corrective transmission switching be beneficial post-contingency without inhibiting the ability to return to N-1 reliability, but it can also help obtain an N-1-1 reliable solution. [ABSTRACT FROM AUTHOR]

This paper discusses the modeling and analysis of a carbon capture technology-based resource scheduling/unit commitment (UC) methodology in carbon/emission-constrained environment. In carbon markets, the overall generation from conventional/fossil-fueled thermal plants is constrained over the total cost which is the sum of generation, capture cost/emission avoidance cost. Therefore, in this paper, generalized/uniform performance indices affecting the UC schedule are derived. Also, a commitment/scheduling methodology based on capture and fuel cost is devised rather than the existing penalty cost methodology as in the modernized markets everything was dealt in monetary value. Furthermore, the impact of type of resource used, i.e., coal rank is also considered to evaluate the sensitivity of scheduling decisions and financial influence of carbon capture technology. Along with performance indices, correction factors are also proposed to justify the effect of resource/coal rank in the process of optimal generation allocation. The effect of correction factors and type of coal is observed to be predominant at lower capture efficiencies compared to higher capture efficiency. The effectiveness of the proposed method over the penalty method is reflected in reduced generation cost and emission avoidance cost when compared to the penalty-based methodology. [ABSTRACT FROM AUTHOR]

A framework for performing fast online contingency selection in unbalanced power systems is presented in this paper. Selection methods are typically based on the principle of identifying the effect of contingencies on multiple normalized performance indices and ranking them using the results. Presently used performance indices are highly nonlinear and they are known to mask the effects of single contingencies leading to misclassifications. In this paper, we propose two new methods, one relying on margin-based performance indices and another based on state sensitivity. New performance indices are proposed based on margins of 1) circuit loading, 2) bus voltages, and 3) reactive power. In addition, a state sensitivity method is proposed which estimates a system's post contingency operating state via a single iteration of the quadratized power flow model and provides estimates of post contingency line loading, bus voltages, and reactive power levels. Numerical experiments on a three phase version of the IEEE Reliability Test System show that the proposed performance indices yield more accurate results, at a computational cost comparable to a single power flow iteration. The state sensitivity method is more accurate in identifying critical contingencies but its computational cost is higher. The method has been also demonstrated in the larger PEGASE systems. [ABSTRACT FROM AUTHOR]

One of the most important aspects of time-domain simulations for power system planning studies is load modeling. For a realistic representation of the load, the Western Electricity Coordinating Council (WECC) model validation and working group developed the composite load model. The composite load model represents the aggregation of different types of loads at the substation level. However, there exists some uncertainty in determining the load parameters and the percentage composition of the different components. Trajectory sensitivity (TS) analysis provides a systematic approach to study the impact of parameter uncertainty on power system response to disturbances. The non-smooth nature of the composite load model may present some additional challenges to sensitivity analysis in a realistic power system. This paper presents an application of TS analysis to study the impact of load parameter uncertainty on the system response. The impact of the non-smooth nature of load models on the sensitivity analysis is also addressed. This paper further suggests a method to determine the perturbation size limit for which accurate linear approximations can be made. The study was performed using the WECC system model. [ABSTRACT FROM AUTHOR]

In a recent paper, we proposed a system identification method for constructing reduced-order models for the electro-mechanical dynamics of large power systems, divided into multiple coherent clusters, using Synchrophasors. Every cluster in the actual model was represented as an aggregate generator in the reduced-order model. An aggregate network graph connected one aggregate generator to another. In this paper, we extend this identification approach to differential-algebraic (DAE) models. First, every cluster is associated with a unique terminal bus, referred to as the pilot bus, that couples its internal network to the rest of the system. The proposed algorithm uses Synchrophasor measurements from the pilot buses to identify the dynamic model of the aggregate generator for each cluster using nonlinear least squares while retaining the identity of all the pilot buses. The resulting reduced-order model is in the form of a nonlinear electric circuit described by aggregate differential and algebraic equations. We illustrate our results using two case studies, one for the IEEE 9-bus power system and another for the IEEE 39-bus power system. We also discuss how these reduced-order DAE models may be useful for designing shunt controllers at the pilot buses by using Synchrophasor feedback. [ABSTRACT FROM AUTHOR]

This paper proposes a new approach for power system transient stability simulation, which is based on a semi-analytical solution (SAS) of power system differential-algebraic equations. In this paper, an SAS is derived using the Adomian decomposition method as a closed-form explicit function of symbolic variables such as time, the initial state, and other variables on system conditions and; hence, it can directly give a power system's dynamic trajectory being accurate for a certain time window. Unlike a traditional numerical integration based simulation approach, the proposed new approach offline derives an SAS and online evaluates the SAS by plugging in values of symbolic variables for a series of time windows making up the desired simulation period. This paper further studies the maximum length of the time window for an SAS being accurate and proposes a divergence indicator for simulation using adaptive time windows. Implementation of this new approach on parallel computers is also studied. The new approach is validated through contingency simulation of the IEEE 10-generator 39-bus system with detailed generator models. [ABSTRACT FROM AUTHOR]

This paper addresses the positive sequence modeling of converter-based sources in commercial transient stability analysis software. A simple and computationally economical model of the converter has been developed while ensuring a reliable representation of the detailed converter behavior. This model has been implemented as a user defined model in commercial positive sequence software such as PSLF. The behavior of the proposed model in positive sequence has the same form as the behavior obtained from detailed point on wave simulation. Tests have been carried out on a three-generator nine-bus equivalent system and the 18,205 bus Western Electricity Coordinating Council system to assess the impact and performance of the converters. The behavior of these converter interfaced generation sources for various system contingencies has been investigated. [ABSTRACT FROM AUTHOR]

As part of the day-ahead market clearing process, MISO solves one of the most challenging Security Constrained Unit Commitment (SCUC) models. With footprint expansions and increased activity from financial traders, the day-ahead market unit commitment encounters significant performance challenges from time to time. This paper reviews MISO's day-ahead market clearing process and identifies the factors contributing to these performance challenges. It then shares techniques that have been developed to overcome these challenges. Three alternative backup solving approaches were developed. An incremental solving algorithm is proposed to better handle the iterative market clearing process and to perform solution polishing and commitment reason identification. Numerical results based on MISO data are presented. [ABSTRACT FROM PUBLISHER]

Large-scale blackouts and extreme weather events in recent decades raise the concern for improving the resilience of electric power infrastructures. Distribution service restoration (DSR), a fundamental application in outage management systems, provides restoration solutions for system operators when power outages happen. As distribution generators (DGs) and remotely controllable devices are increasingly installed in distribution systems, an advanced DSR framework is needed to perform optimally coordinated restoration that can achieve maximal restoration performance. This paper introduces a DSR modeling framework, which can generate optimal switching sequences and estimated time of restoration in the presence of remotely controllable switches, manually operated switches, and dispatchable DGs. Two mathematical models, a variable time step model and a fixed time step model, are presented and compared. The proposed models are formulated as a mixed-integer linear programming model, and their effectiveness is evaluated via the IEEE 123 node test feeder. [ABSTRACT FROM AUTHOR]

As Type-3 wind turbine (WT) has already become a typical type of highly penetrated power sources in modern power systems, characterizing its properties during grid fault is a basic requirement for system analysis. However, many significant factors have not been considered in the existing analytical methods and results, such as various switching of internal control and protection circuits in low voltage ride through (LVRT) solutions. In this paper, performance of Type-3 WT during LVRT is first illustrated and summarized as the sequential switching characteristic in multi time scales, viz., instant control, ac control, dc voltage control, and rotor speed control time scales. Thus, for magnitude drops in stator voltage, a mathematical model is proposed to understand this characteristic and fault current analysis's features. Then, an analytical method, based on the operational inductance, is proposed so that fault current components, with the sequential switching considered, can be depicted with a unified and simple analytical expression. By identifying magnitude of symmetrical current, the transient and steady-state equivalent circuits of Type-3 WT are proposed to estimate momentary current and electrical power approximately. Finally, analytical results are verified by comparisons with real-time simulation results of a detailed 1.5 MW WT model in RT-LAB. [ABSTRACT FROM AUTHOR]