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This paper proposes an approach to determine the participation of algebraic variables in power system modes. The approach is based on a new interpretation of the classical participation factors, as well as on the definition of adequate output variables of the system's state-space representation. The paper considers both the linear and generalized eigenvalue problems for the calculation of the participation factors and presents a theorem to cope with eigenvalue multiplicities. An illustrative example on the two-area system, as well as a study on a 1479-bus dynamic model of the all-Irish transmission system are carried out to support the theory and illustrate the features of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper is concerned with a fuzzy analysis of power-flow (PF) involving uncertainties of load demands and network parameters. The crux of this paper is to propose an advanced fuzzy arithmetic. Fuzzy transformation method merges with backward–forward sweep in order to evaluate the contribution and propagation of uncertainty in IEEE 33-bus and 69-bus distribution systems. Results are validated by true intervals and random ranges. To determine true intervals, Global Optimization Problems (GOPs) are defined and solved through derivative-based and free techniques. To estimate random ranges, Monte-Carlo Simulations (MCSs) are employed. Our findings confirm that the sharpness of fuzzy intervals, tractability of computations, and applicability of possibility distributions. Following scenario-based evaluations, this paper discusses new implications of power losses, voltage profiles, optimal re-configuration, feeder extension, and reactive power compensation so that results would be beneficial to system planners and operators. Altogether, this paper provides a blueprint for a new way to handle uncertainties in a wide variety of power system problems without global optimization, linearization, and randomized simulations. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the existence and stability of equilibrium of dc micro-grids under the master-slave control (where some distributed generations (DGs) are under droop control with dual-loop (Droop-DGs) and some DGs are under MPPT control (MPPT-DGs)). Firstly, the power-flow equation of the dc micro-grids under master-slave control with CPLs is obtained. Then, we transform the solvability of the power-flow equation into the existence of a fixed point for a contraction mapping. Based on Banach's fixed point theorem, a sufficient condition to guarantee the existence of the power-flow solution in dc micro-grids is derived. The condition derived in this paper is not only useful for master-slave control but also for droop control. Besides, to calculate the power-flow solution, an iterative algorithm with exponential convergence rate is proposed. Secondly, we use a singular perturbation model to predict the qualitative behavior of the system near the equilibrium point. By analyzing eigenvalues of the boundary layer system and reduced-order system Jacobian matrix, the robust stable analytic conditions of the system are obtained. The effect of the sampling delay on the system stability is analyzed, the robust stability condition is obtained by using linear matrix inequality. The simulation results verify the correctness of the proposed conditions. The obtained conditions provide a reference for establishing a reliable dc micro-grid. [ABSTRACT FROM AUTHOR]

This paper discusses the impact of discrete secondary controllers on the dynamic response of power systems. The idea of the paper originates from the observation that there is a range of values, from few tens of seconds to few minutes, of the execution cycles of conventional automatic generation control (AGC) that leads to a limit cycle. Below and above this range the system is stable. This is certainly not a problem in practice as the AGC updates the power set points of generating units every few seconds. However, this phenomenon has interesting consequences if one considers real-time electricity markets with short dispatch periods (i.e., 5 minutes) as these markets can be modeled as a sort of AGC. The paper first provides a formal analogy between conventional AGC and real-time electricity markets. Then it shows that the discretization-driven instability exists if the system includes a real-time electricity market modeled as secondary frequency controller. Finally, the paper discusses the impact of the combined effect of high wind generation shares and discrete secondary controllers on power system dynamics. [ABSTRACT FROM AUTHOR]

Economic dispatch with valve-point effect (EDVPE) considered is presented as a more accurate model of the real problem compared to the conventional economic dispatch model. It is basically a non-convex, non-differentiable, and multi-modal optimization model with many local minima. Part I of the paper focuses on the local minimum analysis of the EDVPE. The analysis indicates that a local minimum consists of the singular points, the small convex regions, and the output of a slack unit that is dispatched to balance the load demand. Two types of local minima are identified and the second type could be ignored. To verify the rationality of the analyses, a traverse search has been performed to solve the EDVPE with and without considering the transmission loss on different test systems. All the simulation results support the analysis given in the paper. To effectively solve the EDVPE on a large-scale power system, based on the analysis presented in this paper, a new method, dimensional steepest decline method, is proposed in Part II of the paper. [ABSTRACT FROM PUBLISHER]

State estimation (SE) of distribution networks heavily relies on pseudo measurements that introduce significant errors, since real-time measurements are insufficient. Interval SE models are regularly used, where true values of system states are supposed to be within the estimated intervals. However, conventional interval SE algorithms cannot consider the correlations of same interval variables in different terms of constraints, which results in overly conservative estimation results. In this paper, we propose a new interval SE model that is based on the relative distance measure (RDM) arithmetic. In the proposed model, measurement errors are assumed to be bounded in given sets and the state variables are described as RDM variables. Since the SE model is a non-convex, the solution's credibility cannot be guaranteed. Therefore, each nonlinear measurement equation in the model is transformed into dual inequality linear equations using the mean value theorem. The SE model is finally reformulated as a linear programming contractor that iteratively narrows the upper and lower bounds of the estimated state variables. Numerical tests on IEEE three-phase distribution networks show that the proposed method outperforms the conventional interval-constrained propagation, modified Krawczyk-operator and optimization based interval SE methods. [ABSTRACT FROM AUTHOR]

There is an opportunity in modern power systems to explore the demand flexibility by incentivizing consumers with dynamic prices. In this paper, we quantify demand flexibility using an efficient tool called time-varying elasticity, whose value may change depending on the prices and decision dynamics. This tool is particularly useful for evaluating the demand response potential and system reliability. Recent empirical evidences have highlighted some abnormal features when studying demand flexibility, such as delayed responses and vanishing elasticities after price spikes. Existing methods fail to capture these complicated features because they heavily rely on some predefined (often over-simplified) regression expressions. Instead, this paper proposes a model-free methodology to automatically and accurately derive the optimal estimation pattern. We further develop a two-stage estimation process with Siamese long short-term memory (LSTM) networks. Here, a LSTM network encodes the price response, while the other network estimates the time-varying elasticities. In the case study, the proposed framework and models are validated to achieve higher overall estimation accuracy and better description for various abnormal features when compared with the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The paper introduces the concept of complex frequency. The imaginary part of the complex frequency is the variation with respect of a synchronous reference of the local bus frequency as commonly defined in power system studies. The real part is defined based on the variation of the voltage magnitude. The latter term is crucial for the correct interpretation and analysis of the variation of the frequency at each bus of the network. The paper also develops a set of differential equations that describe the link between complex powers and complex frequencies at network buses in transient conditions. No simplifications are assumed except for the usual approximations of the models utilized for the transient stability analysis of power systems. A variety of analytical and numerical examples show the applications and potentials of the proposed concept. [ABSTRACT FROM AUTHOR]

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

A large number of non-linear hardware and control units exists in power electronic system used in grid connected devices. The analytical transient stability analysis of grid-connected converters presents numerous difficulties. A common method to tackle this problem is the stability analysis using Lyapunov’s method. By applying this method, difficulties arise not only from finding a suitable Lyapunov function, but also from checking the constraint of Lyapunov stability. If the appropriate Lyapunov function is a high-order polynomial, it is very challenging to test if it meets the constraints of Lyapunov stability in certain regions. In this paper, the sum-of-squares programming method is used to obtain the estimation of a converter’s domain of attraction with a relatively small number of iterations compared to classically applied methods, such as the Monte Carlo method. The estimation of the domain of attraction are verified by time-domain simulations and StarSim’s controller hardware-in-the-loop tests in this paper. [ABSTRACT FROM AUTHOR]

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

Moving towards regional Supergrids, an increasing number of interconnections are formed by High Voltage Direct Current (HVDC) lines. Currently, in most regions, HVDC losses are not considered in market operations, resulting in additional costs for Transmission System Operators (TSOs). Nordic TSOs have proposed the introduction of HVDC loss factors in the market clearing algorithm, to account for the cost of losses and avoid HVDC flows between zones with zero price difference. In this paper, we introduce a rigorous framework to assess the introduction of loss factors, in particular HVDC loss factors, in nodal and zonal pricing markets. First, we focus on the identification of an appropriate loss factor. We propose and compare three different models: constant, linear, and piecewise linear. Second, we introduce formulations to include losses in market clearing algorithms. Carrying numerical tests for a whole year, we find that accounting only for HVDC or AC losses may lead to lower social welfare for a non-negligible amount of time. To counter this, this paper introduces a framework for including both AC and HVDC losses in a zonal or nodal pricing environment. We show both theoretically and through simulations that such a framework is guaranteed to increase social welfare. [ABSTRACT FROM AUTHOR]

This paper presents a market-based resource adequacy assessment framework to analyze the system generation portfolio that results in a competitive market environment. In particular, we apply the modeling framework to investigate the impact of high penetration levels of variable renewable energy resources and different market designs on achieving resource adequacy. The model captures the strategic capacity investment and retirement decision-making of profit-maximizing generation companies. In contrast to many previous studies, this paper considers markets for capacity, energy, and reserve products in detail; thus, the modeling framework allows improved analysis of generation expansion and revenue sufficiency in a competitive market environment. The modeling framework is based on Stackelberg leader–follower games and is formulated as a bi-level optimization problem, which is then transformed into a mathematical program with equilibrium constraints. Furthermore, we employ a Lagrangian decomposition algorithm to enhance computational performance. In a case study of the electric reliability council of texas (ERCOT) system, we compare the results from the proposed model with those obtained from a traditional centralized least-cost planning model. The results demonstrate the effectiveness of the proposed modeling framework and highlight the importance of considering strategic behavior in a competitive market framework when assessing resource adequacy. [ABSTRACT FROM AUTHOR]

The primary goal of this paper is to develop an optimization framework for studying the efficacy of transmission line reactance tweaking as a mechanism for post-disturbance control in a transmission network. We start by developing a mixed-integer linear programming (MILP) formulation for tracking the redistribution of direct current (DC) flows and the graph-theoretic evolution of a network topology over the course of cascading failures. Next, we propose a min–max setup for studying the impact of post-disturbance reactance tweaking on the resilience of the system to a worst-case disturbance. We devise a MILP reformulation scheme for the underlying bilevel non-convex mixed-integer nonlinear program to facilitate the computation of its globally optimal solution. We then develop a MILP framework for computing a tight upper bound (best-case scenario) on the efficacy of post-disturbance reactance tweaking for a given set of bus loads. Our numerical case study suggests that post-disturbance reactance tweaking, even on only a small number of lines, can be effective in reducing the amount of load shed in some scenarios in the tested system. [ABSTRACT FROM AUTHOR]

As the share of renewables in the grid increases, the operation of power systems becomes more challenging. The present paper proposes a method to formulate and solve chance-constrained optimal power flow while explicitly considering the full nonlinear ac power flow equations and stochastic uncertainties. We use polynomial chaos expansion to model the effects of arbitrary uncertainties of finite variance, which enables to predict and optimize the system state for a range of operating conditions. We apply chance constraints to limit the probability of violations of inequality constraints. Our method incorporates a more detailed and a more flexible description of both the controllable variables and the resulting system state than previous methods. Two case studies highlight the efficacy of the method, with a focus on satisfaction of the ac power flow equations and on the accurate computation of moments of all random variables. [ABSTRACT FROM AUTHOR]

In this paper, a simplified model of a 2 × 25 kV bi-level traction power system for feeding high-speed trains is presented. A modified nodal analysis (MNA) based algorithm for solving the system with and adaptive damping factor is also explained. The main novelties of this paper are the inclusion of train protections (over-current and over-voltage) in the model and the development of the MNA solving procedure that increases the stability and robustness of the iterative solving process. Another important feature of the model is that it can be easily adapted to a single voltage feeding systems by deactivation of specific parameters. The accuracy and performance of the proposed simulator is compared and verified relative to the derivative based solvers. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach for power system dynamic simulation based on the differential transformation (DT). The DT is introduced to study power systems as high-dimensional nonlinear dynamical systems for the first time, and is able to avoid computations of high-order derivatives with nonlinear differential equations by its transform rules. This paper, first, proposes and proves several new transform rules for generic nonlinear functions that often appear in power system models, and then uses these rules to transform representative power system models such as the synchronous machine model with trigonometric functions and the exciter model with exponential and square root functions. This paper also designs a DT-based simulation scheme that allows significantly prolonged time steps to reduce simulation time compared to a traditional numerical approach. The numerical stability, accuracy, and time performance of the proposed new DT-based simulation approach are compared with widely used numerical methods on the IEEE 39-bus system and Polish 2383-bus system. [ABSTRACT FROM AUTHOR]

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

Aging asset management requires careful consideration of end-of-life of any asset. This is particularly serious with aging infrastructure which may require complete replacement of a large asset which has a long lead time. In many current End-of-Life analysis approaches to calculate unavailability, the period of interest is sub-divided into yearly cycles with the assumption that the asset is available at the start of the year. Although this assumption is adequate if the replacement time for the asset occurs within the year, with longer lead times this can create excessively optimistic availabilities. This paper presents an improved probabilistic tool for risk assessment due to End-of-Life failure unavailability which overcomes this deficiency. The End-of-Life methodology proposed in this paper is required when aging assets have long lead times to replacement and so the capital investment decision must be made several years ahead. The method is applied to evaluate the End-of-Life unavailability of Manitoba Hydro Bipole II HVdc converters. The results are corroborated using Monte Carlo simulation. Finally, the risk of End-of-Life is incorporated into an economic cost-benefit analysis corresponding to the presented unavailability evaluation method. [ABSTRACT FROM AUTHOR]

This paper presents some results on the accuracy of normal form analysis for large deviations from the stable equilibrium point (SEP) in a power system. The results of studies on the region of convergence of Neumann series, which is required for normal form analysis, are presented. A polynomial function approximation is proposed to model the generator exciter limiter. Studies on the accuracy of higher order normal form analysis for large deviations from SEP are presented. Use of Prony analysis in addition to simulation is proposed for the verification of accuracy. [ABSTRACT FROM AUTHOR]

This paper proposes a systematic and general approach to model correlated stochastic processes in power systems by means of stochastic differential-algebraic equations. The paper discusses the theoretical background of stochastic differential-algebraic equations and provides a variety of examples of correlated stochastic models for power system applications. With this aim, stochastic processes with Normal and Weibull distributions are considered. The case study utilizes the well-known two-area system to demonstrate that the presence of correlation between the stochastic processes can cause instability, despite the fact that the same system is stable if the same processes are uncorrelated. The case study also considers a 1479-bus dynamic model of the all-island Irish transmission system to show the scalability of the proposed technique, and to compare scenarios with different levels of correlation among stochastic processes. Results indicate that correlation has a non-negligible impact on short-term dynamics. A high level of correlation among the processes, in fact, can give raise to instability. [ABSTRACT FROM AUTHOR]

A semi-analytical formulation is presented in this paper for the probability computation of branch current in multiphase systems. The developed formula is derived based on the linear power flow model in rectangular coordinates. The system uncertainty injections can be renewable energy resources or loads and are modeled using a Gaussian mixture model (GMM). The developed formula can be used to compute the line current violation probability as well as integrate into optimal power flow problem as chance-constraint relaxation. The proposed formula is first compared with the Matlab embedded numerical integration function to show its performance. Besides, the semi-analytical formula is validated and compared with the Monte Carlo simulation method using the IEEE 123-bus system, EPRI Ckt5, and Ckt7 systems. [ABSTRACT FROM AUTHOR]

This paper investigates a procedure of coordinated tuning of power system decentralized damping controllers based on reduced-order model (ROM). In the paper, the cross-gramian technique is applied to obtain an equivalent ROM for power systems. Once the controllers' locations are selected appropriately, the critical modes are approximated well in the reduced model. The controllers are designed on ROM using search algorithm and then tested on the unreduced system to demonstrate their availability. The benefit of adopting ROM is to decrease the complexity of objective function computation. The proposed method is tested on power systems with 4-machine and 156-machine to validate its efficiency. [ABSTRACT FROM AUTHOR]

This paper proposes a framework for online monitoring of subsynchronous oscillations using ambient sensor data from high speed sampling devices such as digital fault recorders (DFRs). Ambient data is continuously available in the form of routine system responses to random load fluctuations. This paper shows the usefulness of ambient data for tracking the frequency, damping ratio and mode shape of torsional modes related to subsynchronous resonance (SSR). Frequency domain decomposition (FDD) and recursive least square (RLS) algorithms are tested for ambient monitoring of SSR modes. IEEE second SSR benchmark model is used as the study system. Nonlinear and linearized equations of this system are analyzed for testing the performance of measurement based methods and to compare their results with respective linearized system modes. It is shown that both electrical and mechanical signals can be used for the SSR monitoring while the torsional modes are more observable in mechanical signals such as generator speeds. In addition to estimating the frequency and damping ratio, torsional mode shapes can be identified by implementing FDD as a multi-dimensional method on the speeds of the masses of the turbine shaft. The algorithms are tested on an archived real system data set from a DFR. [ABSTRACT FROM AUTHOR]

The fast development of renewable energies leads to an increase in the power electronics penetration in transmission systems. This is particularly true if one considers a 100% renewable energies power system, where wind and solar photovoltaic energies, which make most of the renewable energies connections today, are connected to the grid through power electronics converters. Because power electronics-based generators and synchronous machines-based generators have very different dynamic behaviours, some approximations usually used to run transient simulations of transmission systems might not be optimal for future grids. The systematic use of the phasor approximation applied to the power lines, implemented in most of the Transient Simulation Programs, is indeed not relevant any more. To avoid the use of Electromagnetic Transient simulations, that are resource-demanding and time-consuming, this paper presents a novel Model Order Reduction technique for large grids with a high penetration of power electronic devices. Compared to the classical phasor approximation, this event-based state residualization approximation allows accurate transient simulations and at the same time an optimal reduction of the number of the system’s state variables depending on the observed variables, the considered events and the tolerated approximation error. [ABSTRACT FROM AUTHOR]

Time-domain simulation is the basis of dynamic security assessment for power systems. Traditionally, numerical integration methods are adopted by simulation software to solve nonlinear power system dynamics for any given contingency under a specific operating condition. An alternative simulation approach promising for online applications is to offline derive a semi-analytical solution (SAS) for power system differential equations and then online evaluate the SAS over consecutive time windows regarding the operating condition and contingency until the simulation result over a desired period is obtained. This paper proposes a general semi-analytical approach that derives and evaluates an SAS in the form of a power series in time to approximate the true solution. This paper provides an error-rate upper bound of the SAS for reliable use of adaptive time windows in evaluation of the SAS. To extend the semi-analytical approach for solving general power system differential-algebraic equations, this paper also proposes a dynamic bus method to efficiently link the SAS for dynamic components with the numerical solution of the network algebraic equations. Case studies on the New England 39-bus system and the Polish 2383-bus system test the performance of the proposed approach, compare it with other methods, and show the potentials of the proposed semi-analytical approach for online simulation. [ABSTRACT FROM AUTHOR]

This paper studies the impact of realistic wide-area measurement system (WAMS) time-varying delays on the dynamic behavior of power systems. A detailed model of WAMS delays including quasi-periodic, stochastic, and constant components is presented. Then, this paper discusses numerical methods to evaluate the small-signal stability as well as the time-domain simulation of power systems with inclusion of such delays. The small-signal stability analysis is shown to be able to capture the dominant modes through the combination of a characteristic matrix approximation and a Newton correction technique. A case study based on the IEEE 14-bus system compares the accuracy of the small-signal stability analysis with Monte Carlo time-domain simulations. Finally, the numerical efficiency of the proposed technique is tested through a real-world dynamic model of the all-island Irish system. [ABSTRACT FROM AUTHOR]

A phasor measurement unit (PMU) only state estimator is intrinsically superior to its SCADA analogue with respect to speed, performance, and reliability. However, ensuring the quality of the data stream which enters the linear estimator is crucial before establishing it as the front end of an EMS or other network applications. One approach is to pre-process the phasor data before it arrives at the linear estimator. This paper presents an algorithm for synchrophasor data conditioning and repair that fits neatly as a prefix into the existing linear state estimation formulation. The methodology has been tested using field data obtained from PMUs installed in Dominion Virginia Power's (DVP's) EHV network. The results indicate that the proposed technique provides a computationally simple, elegant solution to the synchrophasor data quality problem. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the optimal power flow (OPF) problem. We have recently shown that a convex relaxation based on semidefinite programming (SDP) is able to find a global solution of OPF for IEEE benchmark systems, and moreover this technique is guaranteed to work over acyclic (distribution) networks. The present work studies the potential of the SDP relaxation for OPF over mesh (transmission) networks. First, we consider a simple class of cyclic systems, namely weakly-cyclic networks with cycles of size 3. We show that the success of the SDP relaxation depends on how the line capacities are modeled mathematically. More precisely, the SDP relaxation is proven to succeed if the capacity of each line is modeled in terms of bus voltage difference, as opposed to line active power, apparent power or angle difference. This result elucidates the role of the problem formulation. Our second contribution is to relate the rank of the minimum-rank solution of the SDP relaxation to the network topology. The goal is to understand how the computational complexity of OPF is related to the underlying topology of the power network. To this end, an upper bound is derived on the rank of the SDP solution, which is expected to be small in practice. A penalization method is then applied to the SDP relaxation to enforce the rank of its solution to become 1, leading to a near-optimal solution for OPF with a guaranteed optimality degree. The remarkable performance of this technique is demonstrated on IEEE systems with more than 7000 different cost functions. [ABSTRACT FROM PUBLISHER]

This paper presents a nonlinear dynamic model of grid-connected combined heat and power (CHP) system that can effectively simulate the thermoelectric interactions and examine the impact of the CHP on the power grid. Based on the theorems of mass balance and energy balance, this paper studies and analyses the principles and dynamic characteristics of the main CHP components, including gas internal combustion engine, synchronous generator, waste heat exchanger, water storage tank, exhaust-heat boiler, and gas fired boiler. Then, the nonlinear time-domain models for each component are built against input and output parameters in order to facilitate the study of CHP operation under various conditions. Subsequently, a simulation method that can deal with the coupling of all models with different time constants is proposed. Finally, dynamic simulation analysis of the developed CHP model is carried out on the MATLAB/Simulink. Extensive demonstration results show that the developed models are accurate to represent the thermoelectric interactions in the gird-connected CHP and capture the impact of these gird-connected CHPs on the power grid. This study is particularly beneficial to the design of new control strategies for CHPs to maximise its efficiency and stability value to the grid. [ABSTRACT FROM AUTHOR]

This paper proposes a novel comprehensive model of a rectifier-controlled induction motor drive for use in positive-sequence transient stability simulation (PSTSS) programs. The model is implemented to approximately capture the behavior of the point-on-wave drive model, and applied to investigate the dynamic performance of the advanced drive loads in system-level simulations. This positive-sequence drive model is systematically developed by reducing the detailed three-phase electrical and control representations into $dq$ axes positive-sequence formulations. For the positive-sequence model, the line-side rectifier is interfaced to the grid through a voltage source with separate $dq$ axes controls to regulate the active and reactive power of the drive. The machine-side inverter control system is represented based on rotor flux oriented control. The dc-link of the drive converter is implemented by employing the average model of the pulse width modulated converter, and is utilized to integrate the line-side rectifier and machine-side inverter. The proposed motor drive model is validated by comparing the performance with the electromagnetic transient point-on-wave drive model. The VAr support capability of the drive load model is investigated by incorporating the developed model into a composite load structure in PSTSS programs. Multiple units of the developed drive models are represented in large-scale transmission systems to examine the system-level responses of drive loads. [ABSTRACT FROM AUTHOR]

This paper presents a new method for studying electromechanical transients in power systems using three phase, combined transmission and distribution models (hybrid models). The methodology models individual phases of an electric network and associated unbalance in load and generation. Therefore, the impacts of load unbalance, single phase distributed generation and line impedance unbalance on electromechanical transients can be studied without using electromagnetic transient simulation (EMTP) programs. The implementation of this methodology in software is called the Three Phase Dynamics Analyzer (TPDA). Case studies included in the paper demonstrate the accuracy of TPDA and its ability to simulate electromechanical transients in hybrid models. TPDA has the potential for providing electric utilities and power system planners with more accurate assessment of system stability than traditional dynamic simulation software that assume balanced network topology. [ABSTRACT FROM PUBLISHER]

The method of symmetrical components is not effective for fault location in the case of untransposed lines, due to potential couplings between the sequence circuits. This paper proposes a non-iterative algorithm in the phase-coordinates for wide-area fault location on untransposed transmission networks. In doing so, first, an improved two-terminal method is suggested to accurately locate faults on untransposed lines. Next, an algorithm is proposed to infer voltage and current phasors at the faulted line ends without direct measurements, by taking advantage of the data provided by phasor measurement units (PMUs). Accordingly, the adverse effect of close instrument transformers transients on the estimation accuracy is minimized. Being highly nonlinear in terms of fault distance and impedance, the fault equations are derived and made linear in this paper by defining six suitable auxiliary variables. The resulting system of equations is solved using the least-squares method to obtain three-phase voltages and currents at the faulted line ends. A main feature of the proposed algorithm is that it only requires a limited number of current and voltage synchrophasors. An additional advantage of the proposed algorithm is that the faulted line is not required to be known a-priori. The proposed algorithm is validated using extensive simulation studies on the New England 39-bus test system, accounting for different fault locations, types and resistances. [ABSTRACT FROM PUBLISHER]

This paper presents a general framework for the doubly fed induction generator connected to a complex power system in order to facilitate the dynamic estimation of its states using noisy PMU measurements. State estimation considering the whole power system with the occurrence of electric faults is performed using the Unscented Kalman Filter (UKF) with a bad data detection scheme. Such a state estimation scheme for a DFIG is important because not all dynamic states of a DFIG are easily measurable. Furthermore, the proposed state estimation technique is decentralized and the network topology of the entire power system is taken into consideration in the estimation process. In order to enhance the error tolerance and self-correction of the power system, bad data detection technique is implemented. A performance comparison with Extended Kalman Filter (EKF) is also discussed. [ABSTRACT FROM PUBLISHER]

The paper proposes a semi-implicit formulation of the differential-algebraic equations (DAEs) describing power system models for transient stability analysis. This formulation, if coupled to an implicit integration scheme, shows two relevant advantages with respect to the conventional explicit formulation: (i) reduce the computational burden; and (ii) increase the sparsity of the Jacobian matrix of the system. The proposed model also allows using null time constants and thus simplifies the computer implementation of the DAEs. The properties and the performance of the proposed semi-implicit formulation and the conventional explicit one are compared through a dynamic 21,177-bus model of the European transmission system. [ABSTRACT FROM PUBLISHER]

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

DC grid has become an important application in power transmission. However, the exist works only have the method to obtain the droop coefficient in a radial topology. Also, this droop coefficient is for V-I droop control. There is no such like method to obtain the droop coefficient for the P-V droop control. This paper proposed a new method for a complex dc grid to obtain the droop coefficients. Firstly, based on the converter control strategies, the types of converter were classified. It will help to find out which kinds of converter can be participated into the dc-side voltage control. Secondly, a virtual node was defined, and the matrix of the dc grid was reshaped to fit the new added virtual node by using the proposed simplification method. An example was shown how this method worked. After that a new method of calculating the P-V droop coefficient was proposed. Finally, a simulation model was investigated to verify if the proposed method can operate in a real system. The results showed that the simplification method can ensure the mathematical relationships of the dc system. And simulations show good performances of the droop coefficient calculation method. [ABSTRACT FROM AUTHOR]

Accurate models of power plants play an important role in maintaining the reliable and secure grid operations. In this paper, we propose a synchrophasor measurement-based generator parameter calibration method by a novel deep learning method with high computational efficiency. An elementary effects-based approach is developed to identify the critical parameters from a nonlinear system with much better performance than the widely used trajectory sensitivity-based method. Then, synchrophasor measurement-based conditional variational autoencoder is developed to estimate the parameters’ posterior distributions even in the presence of a high-dimensional case with eighteen critical parameters to be calibrated. The effectiveness of the proposed method is validated for a hydro generator with a very detailed model. The results show that the proposed approach can accurately and efficiently estimate the generator parameters’ posterior distributions even when the parameters true values are not in support of the prior distribution. [ABSTRACT FROM AUTHOR]

Addressing non-convexity plays a fundamental role in solving the optimal electricity-gas flow models. In this paper, an improved spatial branch-and-bound algorithm is proposed to solve the non-convex problem, which is formulated as a mixed-integer bilinear programming, for its exact solution. The core of the algorithm is to divide the non-convex model into convex and small sub-models by branching on specific continuous variables, so that the non-convex problem can be equivalent to a rooted tree for exploration. The exactness of the algorithm is guaranteed by the same criterion as the classical branch-and-bound algorithm. To alleviate the computational burden, a novel two-stage spatial branching strategy is developed to improve the effectiveness and efficiency of the branching operations. The performance of the proposed algorithm is verified on two integrated electricity-gas systems with different sizes. Numerical results demonstrate that our method achieves a balance among feasibility, optimality, and efficiency. The comparison with another 6 convexification-based methods, 3 state-of-the-art non-convex optimization solvers, and 2 spatial branch-and-bound algorithms with classical branching rules further shows the superiority of our algorithm. [ABSTRACT FROM AUTHOR]

Accurate load modeling is critical for credible power system stability analysis. Because of the increasing complexity in modern system load, establishing a more comprehensive load model and performing accurate parameter estimation are the two biggest challenges in composite load modeling. In this paper, an induction motor with variable frequency drive (IM-VFD) together with the traditional ZIP+IM model is utilized to describe the dynamic characteristics of the system load. We estimate the time-varying probabilistic distributions of all states and parameters to describe their stochastic characteristics, thereby representing the real-time varying features of an actual load. The Fokker-Planck operator is applied to linearize the updated load model in tensor format. We then use tensor decomposition to reduce the computational and storage costs for calculating load model parameters. A sensitivity indicator is used to analyze the sensitivities of the estimated parameter distributions for subsequent model reduction. Simulations demonstrate that the updated load model has better performance than the traditional ZIP+IM model. [ABSTRACT FROM AUTHOR]

Wide-area time-synchronized measurements have recently revealed troublesome forced oscillations (FOs) within modern synchronized power grids. In some cases, these FOs represent a dangerous hazard to the system. Recent research has focused on locating the source of FOs to provide operators with knowledge for mitigating their impact locally. This paper presents a complementary mitigation strategy, which is to purposely induce a second oscillation into the grid which cancels the impact of the FO. Such a strategy is complementary in that it may provide valuable time to operators attempting to locate the FOs source and to determine how to rectify it. This paper presents a suppression control strategy which modulates controllable devices to automatically cancel the impact of the FO without the need for locating the source of the original FO. The strategy is based upon tuned feedback control. The approach is demonstrated on a simulation system via modulation of inverter-based generation. [ABSTRACT FROM AUTHOR]

The conductor temperature is a critical state variable that should be considered in power flow calculations to improve the calculation accuracy and reveal the potential thermal loadability of transmission components. This paper proposes a calculation method for time-process power flow considering the thermal behavior (TPPFCTB) of transmission components to calculate the temperature dynamics of overhead lines, power cables, and transformers under anticipated system operation scenarios. The TPPFCTB model is represented by differential-algebraic equations, which can be solved as a sequence of extended power flow problems at discretization time intervals. Based on the Newton method, incomplete and complete decoupling methods are proposed to decouple the correction equations into several independent groups with constant coefficient matrices, thus improving computational efficiency. The work presented in this paper provides an effective method for the detection of potential power transfer capability problems associated with transmission components, thus guiding operators to make more economical decisions. Numerical simulations were conducted to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a new coordinated method for preventive generation rescheduling and corrective load shedding to maintain power system transient stability under uncertain wind power variation. A two-step bi-level optimization model is proposed where generation rescheduling and load shedding are coordinated by a risk coordination parameter, which adjusts the total coordination cost in the upper level. Then, based on Extended Equal Area Criterion (EEAC) and trajectory sensitivities, the non-linear risk and stability constraints are converted into the linear form for generation rescheduling cost and load shedding cost optimization in the lower level, respectively. Uncertain wind power output is modeled as a small number of robust test scenarios. Finally, the golden section search is applied to solve the bi-level problem. The proposed method is validated on the New-England 39-bus system by using commercial grade software. The computational efficiency, economic optimality, and stability robustness under random wind power of the method are demonstrated. [ABSTRACT FROM AUTHOR]

In this paper, we propose a distributed voltage control in power distribution networks through reactive power compensation. The proposed control can operate in a distributed fashion where each bus makes its decision based on local voltage measurements and communication with neighboring buses, always satisfy the reactive power capacity constraint, drive the voltage magnitude into an acceptable range, and minimize an operational cost. We also perform various numerical case studies to demonstrate the effectiveness and robustness of the controller using the nonlinear power flow model. [ABSTRACT FROM AUTHOR]

This paper focuses on developing an appropriate combinatorial optimization technique for solving the optimal sizing problem of hybrid ac–dc microgrids. A novel two-stage iterative approach is proposed. In the first stage, a meta-heuristic technique based on a tailor-made genetic algorithm is used to tackle the optimal sizing problem, while, in the second, a non-linear solver is deployed to solve the operational problem subject to the obtained design/investment decisions. The proposed approach, being able to capture technical characteristics such as voltage and frequency through a detailed power flow algorithm, provides accurate solutions and, therefore, can address operational challenges of microgrids. Its capability to additionally capture contingencies ensures that the proposed sizing solutions are suitable both during normal operation and transient states. Finally, the genetic algorithm provides convergence of the model with relative computational simplicity. The proposed model is applied to a generalizable microgrid comprising of ac and dc generators and loads, as well as various types of storage technologies in order to demonstrate the benefits. The load and natural resources data correspond to real data. [ABSTRACT FROM AUTHOR]

The integration of the dynamic line rating (DLR) of overhead transmission lines (OTLs) in power systems security constrained unit commitment (SCUC) potentially enhances the overall system security as well as its technical/economic performances. This paper proposes a scalable and computationally efficient approach aimed at integrating the DLR in SCUC problem. The paper analyzes the case of the SCUC with AC load flow constraints. The AC-optimal power flow (AC-OPF) is linearized and incorporated into the problem. The proposed multi-period formulation takes into account a realistic model to represent the different terms appearing in the Heat-Balance Equation (HBE) of the OTL conductors. In order to include the HBE in the OPF, a relaxation is proposed for the heat gain associated to resistive losses while the inclusion of linear approximations are investigated for both convection and radiation heat losses. A decomposition process relying on the Benders decomposition is used in order to breakdown the problem and incorporate a set of contingencies representing both generators and line outages. The effects of different linearization, as well as time step discretization of HBE, are investigated. The scalability of the proposed method is verified using IEEE 118-bus test system. [ABSTRACT FROM AUTHOR]

This paper presents an improved corrective security constrained optimal power flow (CSCOPF) for a meshed AC/DC power transmission network with voltage source converter based multi-terminal HVDC (VSC-MTDC) grids. The security constrains of N-1 contingencies for both AC and DC networks are fully considered in the CSCOPF problem. The corrective actions employed in this paper include not only the traditional long-term rescheduling control actions of the AC system, but also the short term post-contingency fast corrective control of multi-terminal VSC-HVDC. A hybrid method is developed to solve the improved CSCOPF problem and the effectiveness of the proposed method is evaluated and demonstrated in this paper by two example meshed AC/DC power systems. [ABSTRACT FROM AUTHOR]

There currently exists a mature literature on modeling the aggregate load of a distribution feeder by making use of measurements at its feeder-head at substation. The primary application of such feeder-aggregated load models is in sub-transmission or transmission system analysis. However, there is a growing need in practice also to model each individual load across the feeder. If available, such individual load models have applications in power distribution system analysis, e.g., to better integrate distributed energy resources or to improve power quality and reliability. Motivated by this observation, in this paper, we propose a new method for individual load modeling in power distribution systems. It works by using the measurements only at the feeder-head. It takes an innovative approach to analyzing the load switching events across the distribution feeder itself, instead of or in addition to relying on upstream voltage events that are commonly used in feeder-aggregated load modeling. By tracking the downstream load switching events, the proposed method can make a robust estimation of the ZIP load model parameters for all individual loads. The proposed method is examined on small illustrative test-feeders as well as the IEEE 33-bus test system under various operating scenarios. The adverse impact of errors in measurements and system parameters are also investigated on the performance of the developed load modeling method. [ABSTRACT FROM AUTHOR]

Assembly of power-flow equations has traditionally begun from a nodal analysis formulation of the underlying transmission circuit's behavior. Most power-flow formulations encapsulate network constraints in the bus admittance matrix, $Y_{\text{bus}}$. From a circuit perspective, this admittance representation restricts the network elements to be voltage controlled; resulting drawbacks treating zero-impedance branches in such applications as state estimation have long been recognized. This paper explores the advantages of the alternatives to $Y_{\text{bus}}$ -based formulations in power flow. It proposes a sparse tableau formulation (STF), and it demonstrates its computational efficiency, robustness, and generality in detailed comparison to traditional $Y_{\text{bus}}$ -based solution algorithms. In the examples of power networks ranging from 1888 to 82 000 buses, computational case studies indicate that STF provides comparable computational speed, while allowing simple treatment of zero-impedance branches and more reliably converging to solutions in many cases for which $Y_{\text{bus}}$ -based Newton algorithms diverge. [ABSTRACT FROM AUTHOR]

Static security assessment (SSA) has been regularly performed using the power flow (PF) model for decades. It plays an important role in ensuring power system security. This paper numerically shows that, as the loading condition of a power system increases, the differences between the PF solution and the steady state of the corresponding time-domain (TD) solution also increase. The striking differences raise serious concern regarding the accuracy of PF-based SSA under heavy loading conditions. Physical explanations for misclassifications by PF-based SSA are provided. We then evaluate the accuracy of performing SSA with the quasi steady state (QSS) model, especially during heavy loading conditions. By using the steady states of post-contingency TD trajectories as the benchmark, this paper presents analytical results verifying the accuracy of the QSS-based SSA. In this paper, numerical evaluations are presented on the IEEE 6-bus, 14-bus, 30-bus, and 145-bus systems. [ABSTRACT FROM AUTHOR]