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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]

This paper develops a generalized admittance matrix approach in Fortescue coordinate system to solve unbalanced/unsymmetrical distribution networks including different number of phases. This generalized Fortescue \pi equivalent is defined in this paper for solving the heterogeneous phase, and thus Fortescue, network model. The performance of the approach is demonstrated in different model networks with number of nodes ranging between 168 and 14200. It is found that the current iteration method exploiting the decoupling in admittance matrix in Fortescue coordinate is substantially faster than the typical unbalanced three-phase solution in phase domain. The method has a significant potential for application in real time active power network management. [ABSTRACT FROM PUBLISHER]

This paper proposes a new framework in calculating the ex post prices for the spot electricity market. The proposed method finds a set of prices that are as consistent as possible with the actual outputs of resources correctly following their dispatch instructions. Two alternative consistency metrics are proposed in the paper. One measures the difference between the actual performance of an individual resource and its bid-based profit-maximizing response to the ex post prices in a perfectly competitive market. Another measures the difference between the ex post price and the price that supports the actual response of an individual resource. Compared to the existing approaches adopted in the real-time electricity markets in the U.S., the proposed method solves the ex post energy and ancillary service prices directly and simultaneously. It does not require heuristics that are hard to justify, and has a much clear definition for the pricing problem than the existing approaches do. Moreover, the proposed approach is flexible in the price control required by the market operators. Numerical examples are presented to further demonstrate the validity of this approach. [ABSTRACT FROM AUTHOR]

With increasingly large scale of intermittent and non-dispatchable resources being integrated into power systems, the power flow problem presents greater uncertainty. In order to obtain the upper and lower bounds of power flow solutions including voltage magnitudes, voltage angles and line flows, Cartesian coordinates-based power flow is utilized in this paper. A quadratically constrained quadratic programming (QCQP) model is then established to formulate the interval power flow problem. This non-convex QCQP model is relaxed to linear programming problem by introducing convex and concave enclosures of the original feasible region. To improve the solutions bounds while still encompassing the true interval solution, optimality-based bounds tightening (OBBT) method is employed to find a better outer hull of the feasible region. Numerical results on IEEE 9-bus, 30-bus, 57-bus, and 118-bus test systems validate the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

In this paper, a flexible optimization-based framework for intentional islanding is presented. The decision is made of which transmission lines to switch in order to split the network while minimizing disruption, the amount of load shed, or grouping coherent generators. The approach uses a piecewise linear model of AC power flow, which allows the voltage and reactive power to be considered directly when designing the islands. Demonstrations on standard test networks show that solution of the problem provides islands that are balanced in real and reactive power, satisfy AC power flow laws, and have a healthy voltage profile. [ABSTRACT FROM PUBLISHER]

This paper proposes a novel iterative approach to contingency filtering for corrective security-constrained optimal power flow (CSCOPF) problems that include conflicting contingencies. The rescheduling index (the minimum of the maximal controllable rescheduling value in the post-contingency state) becomes the filtering index in a modified CSCOPF (MCSCOPF) model designed to deal with conflicting contingencies. Moreover, a decomposed parallel interior point method (DPIPM) is developed to factorize the primal-dual system into blocks according to contingency scenarios and compute these blocks with a coarse-grained parallelism. The feasibility and effectiveness of the proposed approach is verified by solving for conflicting contingencies in a standard testing system and a real-world system. [ABSTRACT FROM PUBLISHER]

Distribution system state estimation (DSSE) is becoming an essential element of many distribution management systems (DMS), serving as the basis of numerous smart grid applications. In this paper, a new DSSE approach is proposed based on the modified augmented nodal analysis formulation, which is known to have advantageous numerical characteristics. Special consideration is given to the estimation of transformer and regulator tap positions, as they are seldom telemetered on the distribution level. The proposed approach can be easily derived from existing power flow and short-circuit calculation algorithms, thus unifying the major steady-state analysis tools for distribution systems. The proposed DSSE algorithm is tested on the IEEE 8500-Node Test Feeder, and is shown to have good accuracy and efficiency. The proposed DSSE approach is also compared to existing algorithms and shown to have better convergence while yielding a more accurate solution. [ABSTRACT FROM PUBLISHER]

This paper presents an analysis of the evolution of the probability density function of the dynamic trajectories of a single machine infinite bus power system. The probability density function can be used to determine the impact of random (stochastic) load perturbations on system stability. The evolution of the state probability density function over time leads to several interesting observations regarding stability regions as a function of damping parameter. The Fokker-Planck equation (FPE) is used to describe the evolution of the probability density of the states. The FPE is solved numerically using PDE solvers (such as finite difference method). Based on the results, the qualitative changes of the stationary density produce peak-like, ridge-like and other complicated shapes. Lastly, the numerical FPE solution combined with SMIB equivalent techniques lay the framework extended to the multimachine system. [ABSTRACT FROM PUBLISHER]

The influence of wind turbine generators (WTGs) on power system dynamic performance is becoming increasingly important as wind generation grows. The dynamic behavior of WTGs should therefore be thoroughly understood. The paper analyzes dynamic models of type-3 WTGs, and in particular the WECC generic model. The behavior of such models is governed by interactions between the continuous dynamics of state variables, and discrete events associated with limits. It is shown that these interactions can be quite complex, and may lead to switching deadlock that prevents continuation of the trajectory. Switching hysteresis is proposed for eliminating deadlock situations. Various type-3 WTG models include control blocks that duplicate integrators. It is shown that this leads to non-uniqueness in the conditions governing steady-state, and may result in pre- and post-disturbance equilibria not coinciding. It also gives rise to a zero eigenvalue in the linearized WTG model. [ABSTRACT FROM PUBLISHER]

Solution approaches to chance constrained programming (CCP) have been recently developed and applied in many areas for optimization under uncertainty. Due to the nonlinear model with multiple uncertain variables as well as multiple output constraints, CCP has not been directly applied to optimal power flow (OPF) under uncertainty. The objective of this paper is twofold. First, we introduce the CCP approach to OPF under uncertainty and analyze the computational complexity of the chance constrained OPF. Second, the effectiveness of implementing a back-mapping approach and a linear approximation of the nonlinear model equations to solve the formulated CCP problem is investigated. Load power uncertainties are considered as multivariate random variables with correlated normal distribution. Based on both the nonlinear and the linearized model, results of a five-bus system and the IEEE 30-bus test system are presented to demonstrate the scope of chance constrained OPF. [ABSTRACT FROM PUBLISHER]

An accurate estimation of critical load levels (CLLs) is beneficial in evaluating the confidence level for the predicted locational marginal prices (LMPs) in power markets. This paper proposes an efficient algorithm to quickly identify CLLs under the with-loss-DCOPF framework. The proposed method approximates the trajectory of DCOPF solutions with respect to the system load variations. The quadratic coefficients of the trajectory can be efficiently obtained by solving a small-scale nonlinear system of equations formed by the variable substitution method, which does not require additional OPF runs and is thus more computationally efficient than existing methods such as binary search and interpolation. The obtained trajectory can be used for a quick calculation of OPF solutions without re-running OPF. Further, through trajectory extrapolation, new congestions and other binding constraints can be identified simultaneously with the CLL predictions. Particularly, the proposed method is not restricted to a specific DCOPF-based model and can be easily applied to other DCOPF-based variants. Numeric studies on a revised IEEE 30-bus system are presented to illustrate the high computational efficiency and accuracy of the approach. It is further tested on the IEEE 118-bus system using four different DCOPF-based models to illustrate its model adaptability. [ABSTRACT FROM PUBLISHER]

We propose an autonomous state estimation based on robotic concepts and advanced state estimation methods. An autonomous, intelligent monitoring infrastructure is proposed that reliably and automatically detects devices as they are plugged-in or -out; it identifies changes in system state and automatically updates the real-time model of the system. The real-time model is used for control, operation, and optimization of the system via application software that are not addressed in this paper. [ABSTRACT FROM PUBLISHER]

This paper describes inexact two-sided Jacobi- Davidson (ITSJD) method to compute the critical (least damping ratio) eigenvalues and corresponding left and right eigenvectors of power systems. Using approximation correction vectors to expand search spaces of two-sided Jacobi-Davidson method leads to ITSJD, which is used to compute eigenvalues closest to the target. Only one LU factorization is needed in whole iteration to improve the computing efficiency. The critical eigenvalues are mapped to extreme eigenvalues of Cayley transformation matrix which can be calculated by using ITSJD. The proposed method has been tested on systems with orders of 493, 1461, and 3781. The results show that ITSJD is effective and able to compute the critical eigenvalues and eigenvectors. [ABSTRACT FROM PUBLISHER]

The integration of the spot electricity markets in Europe shall lead to multi-area power exchanges that will substitute the local markets. In such scheme, market prices are affected by physical (e.g., network) constraints, yet they should sometimes follow regulatory policy rules, which do not necessarily reflect or depend on physical characteristics. In some cases, complex pricing rules should be implemented, which impose price discrimination for supply and demand entities within the same area. The methodology presented in this paper enables the balancing of supply and demand in a multi-area market considering energy and reserve bids, under complex pricing rules, which mix energy and reserve prices. A demand bid corresponds to the whole cost a demand entity is willing to pay for its participation in the energy market, including the cost for the procurement of the necessary reserves. The approach attains price integration of energy and reserves markets, simultaneous settlement of energy and reserves, and significant decrease of the payments through the uplift accounts. The main principle is the formulation of a mixed complementarity problem for the system equilibrium conditions, in which supply and demand are associated to explicitly or implicitly defined prices, which may be different even in the same zone. [ABSTRACT FROM PUBLISHER]

A so-called voltage-behind-reactance (VBR) machine model has recently been proposed for the electro-magnetic transient programs (EMTP) as an advantageous alternative to the conventional qd and phase-domain models. This paper extends the previous research and proposes a magnetically saturable VBR synchronous machine model for EMTP-type solutions. The proposed saturable VBR model utilizes the saliency factor approach to represent main-flux saturation for the salient-pole synchronous machines with the qd axes static and dynamic cross saturation included. An efficient piecewise-linear method is used for representing the nonlinear saturation characteristic within the discretized EMTP solution. Case studies verify that the new model maintains the improved numerical accuracy in steady state and transients even with large time step. [ABSTRACT FROM PUBLISHER]

In this paper, a receding-horizon multi-step optimization is proposed to correct nonviable transmission voltages and prevent long-term voltage instability. The proposed control scheme is based on real-time control, inspired by model predictive control, and steady state power-flow-based equations. In order to anticipate load behavior and avoid using dynamic equations in the control scheme, explicit formulations are used to model evolution of load with time. The simulation results of the proposed technique are presented on the Nordic32 test system. [ABSTRACT FROM PUBLISHER]

It is difficult to forecast renewable energy resources due to their variability. High uncertainty of the resources increases the concern about the reliable operation of the electric power system. Storage devices have been considered a candidate to control variable energy resources, and most studies on storage devices are performed in the economic dispatch. Therefore, electric power adequacy may be an issue. In this paper, a new approach in the optimal power flow framework is proposed for deploying storage devices, and the feasibility and economic impact analyses are discussed. [ABSTRACT FROM AUTHOR]

System restoration involves status assessment, optimization of generation capability, and load pickup. The optimization problem needs to take complex constraints into consideration, and therefore, it is not practical to formulate the problem as one single optimization problem. The other critical consideration for the development of decision support tools is its generality, i.e., the tools should be portable from a system to another with minimal customization. This paper reports a practical methodology for construction of system restoration strategies. The strategy adopted by each power system differs, depending on system characteristics and policies. A new method based on the concept of “generic restoration milestones (GRMs)” is proposed. A specific restoration strategy can be synthesized by a combination of GRMs based on the actual system conditions. The decision support tool is expected to reduce the restoration time, thereby improving system reliability. The proposed decision support tool has been validated with cases based on a simplified Western Electricity Coordinating Council (WECC) 200-Bus system and Hawaiian Electric Company system. [ABSTRACT FROM PUBLISHER]

This paper presents a method for determining the double outage contingencies that threaten the system without solving the full contingency set. Two methods for contingency screening with complementary properties are presented. The results of the algorithms are compared to the full double outage contingency analysis results for a large North American case. The results show that the screening algorithms are able to detect nearly all of the contingencies that will result in violations, while requiring only a small fraction of the contingencies to be solved. [ABSTRACT FROM PUBLISHER]

Market clearing has always been an issue of great interest and research as liberalized electricity markets evolved over time in many countries. As trading in electricity evolves rapidly, multi-area power exchanges appear to substitute the local markets. The tie-lines constitute a significant parameter in multi-area power exchanges, since congestion leads to price differentiation. Prices are affected by physical (e.g., network) constraints, yet they should sometimes follow regulatory policy rules, which do not necessarily reflect or depend on physical characteristics. Until now, all approaches in clearing a multi-area power dispatch (or a multi-area market) are based on a zonal or nodal pricing model, which is applied uniformly to both production and demand within the same zone (or at each node). These approaches are not able to deal with complex pricing rules, which impose price discrimination for supply or demand entities within the same area. This paper presents a mathematical approach for the solution of a multi-area dispatch, in which production and demand of the same area may be cleared in different prices. The main principle is the formulation of a mixed complementarity problem for the system equilibrium conditions, in which supply and demand are associated to explicitly or implicitly defined prices. Illustrative implementations and test results for a simple five-zone system and the 73-bus IEEE RTS-96 are presented. [ABSTRACT FROM PUBLISHER]

In this paper, we present a new Matlab-based toolbox for power system analysis, called MatDyn. It is open-source software, and available for everyone to download. Its design philosophy is based on the well-known open-source Matlab toolbox MATPOWER , but its focus is transient stability analysis and time-domain simulation of power systems, instead of steady-state calculations. [ABSTRACT FROM AUTHOR]

This paper presents the application of dynamic phasor analysis to understand the effect of passive phase imbalance schemes on the torsional modes of a turbine-generator system. These schemes have been proposed in the previous literature as subsynchronous resonance (SSR) countermeasures. Dynamic phasor analysis of the unbalanced system yields a linearized and time-invariant model which facilitates eigen-analysis. It is seen that large levels of phase imbalance can cause a significant movement in the subsynchronous network modal frequencies. Therefore, in specific cases, SSR can be avoided due to detuning of the torsional and network modes. However, the analysis also shows that damping torque in a series compensated network is negative at subsynchronous frequencies even with phase imbalance. Therefore, phase imbalance cannot be a general countermeasure to the problem of SSR. [ABSTRACT FROM AUTHOR]

An improved approach based on sequential method for the AC-DC power flow calculation is proposed in this paper. This approach solves the convergence problem caused by voltage violations at AC buses during the power flow calculation for the DC subsystems. The convergence property can be significantly improved by adjusting the converter transformer tap position flexibly. In order to adjust the tap position of the converter transformer flexibly, three mainly modifications are proposed. Firstly, the equations for whole DC systems are decoupled into individual DC systems so as to easily figure out which DC system's tap position needs adjustment. Secondly, the tap ratio of a converter transformer is selected as an alternative state variable to replace the cosine of the control angle when necessary. Thirdly, the Newton-Raphson method is utilized to solve DC subsystems instead of the method using the linear equations. Furthermore, a theoretical analysis of the advantages of the proposed approach is also presented. Numerical simulations and practical applications show that the proposed approach meet the requirement of different system operating conditions and has advantages in terms of convergence and speed. The proposed approach has been successfully integrated into the Energy Management System (EMS) for China Southern Power Grid. [ABSTRACT FROM PUBLISHER]

This paper provides a methodology to assist a strategic producer in making informed decisions on generation investment. A single target year is considered with demand variations modeled through blocks. The strategic behavior of the producer is represented through a bilevel model: the upper-level considers both investment decisions and strategic production actions and the lower-level corresponds to market clearing. Prices are obtained as dual variables of power balance equations. Rival uncertainties (on offering and investment) are characterized through scenarios. The resulting model is a large-scale mixed-integer LP problem solvable using currently available branch-and-cut techniques. Results pertaining to an illustrative example and a case study are reported and discussed. [ABSTRACT FROM PUBLISHER]

This paper develops a novel online fast load shedding strategy aimed at shedding the most effective load to mitigate fault-induced delayed voltage recovery (FIDVR). Induction motor kinetic energy deviation has been shown to be identical to the integral of power imbalance. Instead of using voltage as an indicator, the proposed strategy applies a centralized scheme making use of equivalent motor kinetic energy to identify the most effective loads to shed. In order to derive kinetic energy, the equivalent inertia and the speed of the induction motor are needed. A methodology is proposed to obtain these variables through online measurements. Simulations on a sample power system illustrate the novel load shedding strategy and its effectiveness. The proposed strategy is compared with conventional four-stage under-voltage load shedding (UVLS) scheme. The results have validated that the proposed strategy can effectively mitigate fault-induced delayed voltage recovery and require much less load to be shed. [ABSTRACT FROM AUTHOR]

Recent research has shown that the load flow equations describing the steady-state conditions in a radial network can be formulated as a second-order cone program and solved using polynomial-time interior point methods. This paper extends the conic formulation to meshed networks by including a trigonometric functional constraint for the voltage angle spread on each line in the network. In particular, it is shown that the load flow solution of a meshed network can be obtained from a sequence of conic programming solutions. The proposed formulation and iterative procedure are validated by comparing with the Newton-Raphson solution of the standard power flow model. Testing is reported on seven networks. The proposed format of equations opens the door for new implementations of energy management system functions based on efficient and numerically robust conic quadratic optimization methods. [ABSTRACT FROM AUTHOR]