Search

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]

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 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 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]

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]

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]

Although distribution grid customers are obliged to share their consumption data with distribution system operators (DSOs), a possible leakage of this data is often disregarded in operational routines of DSOs. This paper introduces a privacy-preserving optimal power flow (OPF) mechanism for distribution grids that secures customer privacy from unauthorised access to OPF solutions, e.g., current and voltage measurements. The mechanism is based on the framework of differential privacy that allows to control the participation risks of individuals in a dataset by applying a carefully calibrated noise to the output of a computation. Unlike existing private mechanisms, this mechanism does not apply the noise to the optimization parameters or its result. Instead, it optimizes OPF variables as affine functions of the random noise, which weakens the correlation between the grid loads and OPF variables. To ensure feasibility of the randomized OPF solution, the mechanism makes use of chance constraints enforced on the grid limits. The mechanism is further extended to control the optimality loss induced by the random noise, as well as the variance of OPF variables. The paper shows that the differentially private OPF solution does not leak customer loads up to specified parameters. [ABSTRACT FROM AUTHOR]

This paper proposes a Transient Stability Constrained Optimal Power Flow (TSCOPF) formulation that models non-synchronous renewable generation equipped with synthetic inertia. The proposed optimization problem calculates the optimal operating point of the system, accommodating high shares of non-synchronous renewable generation while ensuring transient stability in the event of critical incidents. Synthetic inertia controllers are used to improve the dynamic stability of the system in cases of very high share of renewable generation. The proposed tool is tested in the North-West Spanish system, a network with a high penetration of wind energy that causes a reduction in the total system inertia. The results of the study show that 1) synthetic inertia in renewable power plants can diminish electromechanical oscillations after a severe contingency, reducing the cost of ensuring transient stability; 2) using synthetic inertia the system becomes more stable when conventional generation is decommissioned following de-carbonization and renewable promotion policies; and 3) the proposed model can be used to calculate the parameters of the synthetic inertia control. [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]

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]

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]

Reliable planning of electricity networks is a crucial challenge to maintain the continuous power supply. This can be ensured through careful planning which requires a number of parameters as inputs such as electricity demand, generation capacity, fuel price, renewable intermittent generation, among others. The uncertain behaviors of such parameters have been well studied in literature. Another important parameter which is a vital requirement for reliable planning is the resistance of overhead transmission lines. Traditionally, the current models ignore to consider the resistance variations due to Joule heating and ambient temperature changes in transmission expansion planning (TEP) problem. In this sense, this paper presents an adaptive robust optimization (ARO) framework for TEP to model the uncertain resistance through ellipsoidal uncertainty set. Moreover, a data-driven selection of the ellipsoidal uncertainty set is proposed. In this regard, Khachiyan's algorithm (KA) is used to identify the minimum-volume covering ellipsoid (MVCE) that contains all uncertain parameters. A case study based on IEEE 118-bus power system is presented to demonstrate the effectiveness of the proposed method. Simulation results show that resistance uncertainty is of serious concern in the TEP problem since the solutions are highly sensitive to fluctuations in the line resistances. [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]

Given its physical characteristics and the range of services that it can provide, energy storage raises unique modeling challenges. This paper summarizes capabilities that operational, planning, and resource-adequacy models that include energy storage should have and surveys gaps in extant models. Existing models that represent energy storage differ in fidelity of representing the balance of the power system and energy-storage applications. Modeling results are sensitive to these differences. The importance of capturing chronology can raise challenges in energy-storage modeling. Some models ‘decouple’ individual operating periods from one another, allowing for natural decomposition and rendering the models relatively computationally tractable. Energy storage complicates such a modeling approach. Improving the representation of the balance of the system can have major effects in capturing energy-storage costs and benefits. [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]

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]

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]

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]

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 studies an extended formulation of the security constrained optimal power flow (SCOPF) problem, which explicitly takes into account the probabilities of contingency events and of potential failures in the operation of post-contingency corrective controls. To manage such threats, we express the requirement that the probability of maintaining all system operational limits, under any circumstance, should remain acceptably high by means of a chance constraint. Furthermore, representing power flow as per the full AC model, we propose a heuristic solution approach leveraging state-of-the-art methodologies and tools originally developed to tackle the standard, deterministic-constrained SCOPF statement. We exemplify the properties of our proposal by presenting its application on the three area version of the IEEE-RTS96 benchmark, stressing the interpretability of both the chance-constrained reliability management strategy and of the heuristic algorithm proposed to determine it. This paper serves to showcase that the first step on the transition toward probabilistic reliability management can be achieved by suitably adapting presently available operational practices and tools. [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]

Under transactive (market-based) coordination, a population of distributed energy resources (DERs), such as thermostatically controlled loads (TCLs) and storage devices, bid into an energy market. Consequently, a certain level of demand will be cleared based on the operating conditions of the grid. This paper analyzes the influence of various factors, such as price signals, feeder limits, and user-defined bid functions and preferences, on the aggregate energy usage of DERs. We identify cases that can lead to load synchronization, undesirable power oscillations and highly volatile prices. To address these issues, the paper develops an aggregate model of DERs under transactive coordination. A set of Markov transition equations have been developed over discrete ranges (referred to as “bins”) of price levels and their associated DER operating states. A detailed investigation of the performance of this aggregate model is presented. With reformulation of the transition equations, the bin model has been incorporated into a model predictive control setting using both mixed integer programming and quadratic programming. A case study shows that a population of TCLs can be managed economically while avoiding congestion in a distribution grid. Simulations also demonstrate that power oscillations arising from synchronization of TCLs can be effectively avoided. [ABSTRACT FROM AUTHOR]

The distributed Volt/Var control solution is a promising one for active distribution networks (ADNs), but a critical issue is how to improve the distributed algorithm's convergence with less communication burden. In this paper, we propose a bi-level consensus alternation direction multiplier method-based fully distributed Volt/Var optimization algorithm (B-FADMM) for ADNs by exploiting inverter-based rapid control devices. In the first level, the Volt/Var optimal solution of subpartitions is obtained in parallel, and the second level completes the variable increment of each partition to correct the search direction of the first level. In the algorithm, firstly, an adaptive matrix $\omega $ initialization strategy is proposed to adapt to the different magnitude of variables, which avoids non-convergence or slow convergence of the algorithm. Secondly, the null-space method is used in the second level of the algorithm to obtain the null-space basis matrix on the active constraint of the subpartition, which reduces the dimensions of the problem and the computational complexity. In addition, the conjugate gradient (CG) algorithm is used to update the dual multiplier of each partition only by exchanging coupling information among partitions, which protects information privacy. Experiments showed the proposed approach attains the same result as the centralized, the computational performance of the proposed method is far superior to some popular other distributed methods in terms of accuracy, computational efficiency, and scalability. [ABSTRACT FROM AUTHOR]

Pumped storage hydro units (PSHU) can provide flexibility to power systems. This becomes particularly valuable in recent years with the increasing shares of intermittent renewable resources. However, due to emphasis on thermal generation in the current market practices, the flexibility from PSHUs has not been fully explored and utilized. This paper proposes a configuration based pumped storage hydro (PSH) model for the day-ahead market, in order to enhance the use of PSH resources in the system. A strategic design of incorporating and fully optimizing PSHUs in the day-ahead market is presented. We show the compactness of the proposed model. Numerical studies are presented in an illustrative test system and the Midcontinent Independent System Operator (MISO) system. [ABSTRACT FROM AUTHOR]

In the steady-state contingency analysis, the traditional Newton-Raphson method suffers from non-convergence issues when solving post-outage power flow problems, which hinders the integrity and accuracy of security assessment. In this paper, we propose a novel robust contingency analysis approach based on holomorphic embedding (HE). The HE-based simulator provides theoretical convergence guarantee, which is desirable because it avoids the influence of numerical issues and provides a credible security assessment conclusion. In addition, based on the multi-area characteristics of real-world power systems, a partitioned HE (PHE) method is proposed with an interface-based partitioning of HE formulation. The PHE method does not undermine the numerical robustness of HE and significantly reduces the computation burden in large-scale contingency analysis. The PHE method is further enhanced by parallel or distributed computation to become parallel PHE (P2HE). Tests on a 458-bus system, a synthetic 419-bus system and a large-scale 21 447-bus system demonstrate the advantages of the proposed methods in robustness and efficiency. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to dynamic phasor-based transient stability simulation. The proposed method is based on the modified nodal analysis (MNA) approach to circuit simulation, which is used to construct continuous differential-algebraic equations (DAEs). The proposed method makes use of the stamp technique, which makes it possible to construct a general purpose MNA-based simulator. Stamp-based models for common power system components are derived in this work. A new MNA-based synchronous machine model is presented, which represents machines as nonlinear inductances instead of subtransient equivalents. The resultant continuous DAEs are numerically solved using the general purpose variable step and variable order library IDA. Simulation results from the IEEE 68 bus test system, a real 400 bus power system, and the IEEE 39 bus test system with an embedded HVdc transmission system demonstrate that the proposed method is suitable for large ac networks with power electronic devices. The results demonstrate good agreement between the proposed method and electromagnetic transient (EMT) simulation. The results also demonstrate that the proposed method is fast and scalable with CPU times that are up to 200 times faster than EMT simulation. [ABSTRACT FROM AUTHOR]

This paper develops a grey-box approach to small-signal stability analysis of complex power systems that facilitates root-cause tracing without requiring disclosure of the full details of the internal control structure of apparatus connected to the system. The grey-box enables participation analysis in impedance models, which is popular in power electronics and increasingly accepted in power systems for stability analysis. The Impedance participation factor is proposed and defined in terms of the residue of the whole-system admittance matrix. It is proved that, the so defined impedance participation factor equals the sensitivity of the whole-system eigenvalue with respect to apparatus impedance. The classic state participation factor is related to the impedance participation factor via a chain-rule. Based on the chain-rule, a three-layer grey-box approach, with three degrees of transparency, is proposed for root-cause tracing to different depths, i.e. apparatus, states, and parameters, according to the available information. The association of impedance participation factor with eigenvalue sensitivity points to the re-tuning that would stabilize the system. The impedance participation factor can be measured in the field or calculated from the black-box impedance spectra with little prior knowledge required. [ABSTRACT FROM AUTHOR]

In light of the increasing coupling between electricity and gas networks, this paper introduces two novel iterative methods for efficiently solving the multiperiod optimal electricity and gas flow (MOEGF) problem. The first is an iterative MILP-based method and the second is an iterative LP-based method with an elaborate procedure for ensuring an integral solution. The convergence of the two approaches is founded on two key features. The first is a penalty term with a single, automatically tuned, parameter for controlling the step size of the gas network iterates. The second is a sequence of supporting hyperplanes and halfspaces for controlling the convergence of the electricity network iterates. Moreover, the two proposed algorithms use as a warm start the solution from a novel polyhedral relaxation of the MOEGF problem, for a noticeable improvement in computation time as compared to a cold start. Unlike the first method, which invokes a branch-and-bound algorithm to find an integral solution, the second method implements an elaborate steering procedure that guides the continuous variables to take integral values at the solution. Numerical evaluation demonstrates that the two proposed methods can converge to high-quality feasible solutions in computation times at least two orders of magnitude faster than both a state-of-the-art nonlinear branch-and-bound (NLBB) MINLP solver and a mixed-integer convex programming (MICP) relaxation of the MOEGF problem. The experimental setup consists of five test cases, three of which involve the real electricity and gas transmission networks of the state of Victoria with actual linepack and demand profiles. [ABSTRACT FROM AUTHOR]

This paper studies the communication time-delay issue in islanded microgrids (MGs) with the distributed secondary control architecture. Firstly, a time-delayed MG small-signal model is developed. Then, a new weight-average-prediction (WAP) controller is proposed to compensate the delayed system states. By introducing a time-delayed differential term in the proposed control law, the traditional time-delayed small-signal model is transformed into a neutral time-delayed mathematic model. Based on the developed model, the stability analysis is conducted considering both fixed time delay and time-varying delay. For the fixed time delay, a novel graphic analytical method is proposed to evaluate the time delay margin, which eliminates the conservatism compared with existing time-domain methods. For the time-varying delay, stability condition is established by a Lyapunov-Krasovskii function and linear matrix inequalities. In addition, some non-linear WAP control methods are discussed to guide the parameter tuning with a higher resolution. Lastly, the proposed method and analytical result are verified in the OPAL-RT real-time test platform. The results demonstrate the effectiveness and high performance of the proposed controller. [ABSTRACT FROM AUTHOR]

Distributed optimization algorithms for security-constrained economic dispatch (SCED) problems have been the subject of significant research interest in recent years. However, existing distributed SCED algorithms can be ineffective in the presence of malicious participants and inefficient in the absence of a coordinator. On the other hand, blockchain, an emerging technique known as the trust machine, has not shown its potential to address the above challenges in state-of-the-art literature. This paper proposes a blockchain-based distributed SCED algorithm. Using blockchain to form a coordination committee and enable balance among committee members, the proposed method allows the use of hierarchical SCED algorithms in the absence of a coordinator and can disable malicious participants. Numerical results show the robustness and necessity of the proposed blockchain-based SCED algorithm, by comparing the SCED results with and without blockchain. [ABSTRACT FROM AUTHOR]

The frequency stability of microgrids is of paramount importance due to their low inertia and high share of renewable energy sources. In this paper, a frequency stability-constrained microgrid scheduling (FSC-MS) model is developed based on a time-dependent discretized frequency response model considering seamless unintentional islanding events. The optimal dispatch of controllable units, as well as optimal upward and downward primary reserves, are determined with a minimum operating cost while ensuring frequency stability criteria are maintained in their safe ranges following an unintentional islanding event, such as rate of change of frequency (RoCoF) and frequency nadir and overshoot. The limitation of generators with respect to primary frequency response is formulated in the form of primary reserve capacity and primary ramp rate limits. A cost-based model is presented to describe the available primary reserve of synchronous generators. The proposed FSC-MS model is formulated as a mixed-integer linear programming (MILP) problem using Benders decomposition. Simulation results on a medium voltage microgrid test system demonstrate the effectiveness of the proposed model to meet the frequency stability constraints while minimizing the total operating cost. [ABSTRACT FROM AUTHOR]

Isothermal natural gas flow model with constant gas temperature has been widely used in conventional coordinated operations of integrated electricity and natural gas systems (IEGS). However, as a crucial state variable in IEGS, gas temperature varies significantly among nodes in a natural gas system, which can be calculated along with nodal pressures and mass flow rates. This paper proposes a novel non-isothermal optimal power and gas flow (OPGF) model that avoids the isothermal assumptions involved in traditional natural gas network model and improves the accuracy significantly. In the proposed model, partial differential terms with minimal weights are neglected based on the quantitative analysis of the energy conservation equation to further simplify the energy conservation equation. A non-isothermal model of natural gas networks is developed by introducing the finite difference method and laws of thermodynamics to incorporate the gas temperature change into the coordinated operation of IEGS. A start point initialization scheme is developed based on the Newton-Raphson algorithm to accelerate the interior point method solution convergence and improve its solution quality. Numerical experiments presented for two test systems validate the effectiveness of the proposed OPGF model and solution methodology. [ABSTRACT FROM AUTHOR]

Bulk integrated electricity and gas systems (IEGSs) introduce complex coupling relations and induce synergistic operation challenges. The growing uncertainty arising from the renewable power generation in the IEGS further aggravates the synergistic problems. Considering the availability of historical wind power generation data, this paper adopts a two-stage sample robust optimization (SRO) model, which is equivalent to the two-stage distributionally robust optimization (DRO) model with a ${\text{type}} - \infty $ Wasserstein ambiguity set, to address the wind power penetrated unit commitment optimal energy flow (UC-OEF) problem for the IEGS. Compared to the equivalent DRO model, the two-stage SRO model can be approximately transformed into a computationally efficient form. Specifically, we employ linear decision rules to simplify the proposed UC-OEF model. Moreover, we further enhance the tractability of the simplified model by exploring its structural features and, accordingly, develop a solution method. Simulation results on two IEGSs validate the effectiveness of the proposed model and solution method. [ABSTRACT FROM AUTHOR]

Chance-constrained economic dispatch (CCED) is widely used to cope with uncertainties brought by renewable energy sources. In CCED, security of power system is guaranteed by restricting risks under permitted level. As the penetration rate of renewable energy increases rapidly, the CCED model may be infeasible because of inadequate system reserve and/or transmission congestion under certain circumstances. Therefore, the curtailment of renewable energy is indispensable to guarantee security in some scenarios for power systems with high penetration of renewable energy. To address this crucial issue, this paper proposes a novel CCED model, where generation of conventional units and curtailment strategies of renewable energy are co-optimized to minimize total operational cost and restrict operational risks. An efficient solution method is developed to schedule generation and curtailment sequentially, in which tractable optimization models are formulated for each step. Numerical tests demonstrate that the proposed model can significantly reduce the probability of emergency control of curtailment compared with conventional CCED models. Furthermore, this solution method also outperforms scenario-based method with significantly improved computational efficiency and higher-quality solution. [ABSTRACT FROM AUTHOR]

The penetration of photovoltaics (PVs) has been increasing in active distribution networks (ADN), which leads to severe voltage violation problems. PV inverters can provide fast and flexible reactive power support and are now allowed to participate in the voltage regulation process. This paper proposes a real-time combined central and local Volt/Var control (VVC) strategy to mitigate voltage violation problems while minimizing the network power loss. Based on the historical PV and load data, the load flow and optimal power flow are performed in the centralized controller (CC) to obtain multiple voltage and optimal power settings for each PV system. The local controller (LC) then generates voltage control curves with these optimal scatters. To improve the voltage control effect, a novel 3-Dimension voltage control curve is proposed considering both the measurements of node voltage and PV generation. Moreover, a data-driven deep convolution neural network is designed and trained to generate optimal local voltage control curves without prior knowledge of specific curve functions. The proposed approach is tested on the IEEE 33-bus distribution system and simulation results verify the effectiveness in voltage control compared with the optimal Q(V) and Q(P) method. [ABSTRACT FROM AUTHOR]

The disturbance propagation mechanism is crucial for the preventive, corrective, and in-extremis control of power grids. This paper proposes a novel non-uniform frame structure model for power system disturbance propagation analysis. A general state transition model of the power grid is derived from the electromechanical wave propagation process. This is further used together with the Gaussian function to derive the non-uniform heterogeneous inertial continuum model, where the non-uniform parameters of the inertia are estimated using the state transition model. The proposed non-uniform frame structure model can be integrated with the electromechanical wave equation to study the disturbance propagation process. These novel developments allow us to tackle the inertial loss and uniform homogenous assumption in existing models. Extensive comparison results carried out on both the chain grid and the IEEE 118-bus system demonstrate that the proposed model can achieve 5- and 3-times accuracy improvements of the state-of-the-art SHU-FSM and ISHU-FSM models, respectively. [ABSTRACT FROM AUTHOR]

Increasing penetration of renewable energy sources based on power electronic interfaces in traditional power systems reduces the inertia constant and damping coefficient. It also increases uncertainty and the sensitivity of the system to disturbances. The concept of the virtual synchronous generator (VSG) is used to emulate the inertia constant and damping property like a synchronous generator. It can be shown that all given VSG structures have the same dynamics as the proportional-integral-derivative (PID) controller. In this paper, the quantitative feedback theory (QFT) is used to tune the VSG parameters such that robust system stability and performance are guaranteed. Moreover, the desired disturbance attenuation is also taken into account. Through frequency response analysis and time-domain simulations, it is shown that the proposed strategy can be successfully used to solve the load-frequency control problem in islanded microgrids (MGs). In addition, the proposed QFT-based VSG is compared with another robust VSG designed by the well-known $H_\infty$ technique to illustrate its better performance against disturbances. [ABSTRACT FROM AUTHOR]

Electric power grids regularly experience uncertain fluctuations from load demands and renewables, which poses a risk of violating operational limits designed to safeguard the system. In this paper, we consider the robust AC OPF problem that minimizes the generation cost while requiring a certain level of system security in the presence of uncertainty. The robust AC OPF problem requires that the system satisfy operational limits for all uncertainty realizations within a specified uncertainty set. Guaranteeing robustness is particularly challenging due to the non-convex, nonlinear AC power flow equations, which may not always have a solution. In this work, we extend a previously developed convex restriction to a robust convex restriction, which is a convex inner approximation of the non-convex feasible region of the AC OPF problem that accounts for uncertainty in the power injections. We then use the robust convex restriction in an algorithm that obtains robust solutions to AC OPF problems by solving a sequence of convex optimization problems. We demonstrate our algorithm and its ability to control robustness versus operating cost trade-offs using PGLib test cases. [ABSTRACT FROM AUTHOR]

Time delays are inevitable in load frequency control (LFC) of the power system, especially in a deregulated system where open communication networks are more favorable than the dedicated ones. However, extensive delays may affect the stability of a system. In this paper, an exact frequency-domain method for calculating the delay margin of LFC systems is presented, which is likely to be used to assess a system's stability caused by time-delays and guide the controller design. Firstly, a dynamic model of load frequency control systems is established, described by delay differential and algebraic equations (DDAEs). The Rekasius substitution is then employed to eliminate the transcendental terms in the characteristic equation without making any approximation. Afterward, an eigenvalue perturbation theory is introduced to transform the problem of calculating the delay margin into solving a series of one-dimensional nonlinear equations. Since only equivalent transforms are involved in the whole process, the delay margins obtained by the proposed method are exact. Finally, a two-area and a three-area deregulated LFC systems are applied to verify the correctness and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents an optimal transient-stability control strategy that modulates the real power injected and absorbed by distributed energy-storage devices. These devices are located at the high-voltage bus of several generators in a synchronous power system. The system is broken into areas based upon groupings of generators. The control strategy consists of two parallel feedback loops. One loop focuses on preserving the synchronism of the generator to its own area. The second loop focuses on preserving the synchronism of a given area to the other areas. Each control loop strategy is based upon local and center-of-inertia frequency measurements. The strategy is derived from two perspectives. With the first, the goal is to remove as much kinetic energy gained during a disturbance as quickly as possible before it is converted to potential energy. With the second perspective, an optimal transient control cost-function is minimized. Both perspectives result in the same strategy. The performance of the control strategy is evaluated on a four-machine power system model and on a 34-generator reduced-order model of the western North-American grid. The results show that this control approach significantly improves the transient stability of power systems. [ABSTRACT FROM AUTHOR]

In this paper, a Frequency Stability Constrained Unit Commitment (FSCUC) model is presented. The on/off status of generating units, generation levels and operating reserves are optimized to minimize the operational daily costs. The frequency stability constraints are included in the proposed FSCUC model to guarantee the safety of System Frequency Response (SFR) under sudden generation outages. A new multi-area SFR model is proposed to capture the regional dynamics of system frequency with considering the impacts of transmission network. An SFR model is developed for each electric region and then the resulted regional SFRs are coupled via a set of constraints. In order to enhance the primary SFR and keep the daily operating point at its economic schedule, Flywheel Energy Storage (FES) devices are utilized in the proposed FSCUC model. The proposed multi-area SFR model allows the optimal allocation of operating reserve and the accurate modeling of FESs in FSCUC model. The proposed FSCUC model is formulated as a Mixed Integer Linear Programming (MILP) problem and is applied over the IEEE 118-bus test system to show the accuracy of the proposed multi-region SFR and the impact of FES in frequency support. The developed MILP model is solved using CPLEX in GAMS. [ABSTRACT FROM AUTHOR]