Dynamic Security Region Research Articles

Transient Operation Risk Assessment of Power System with Wind Farm Integration Based on Dynamic Security Region

With continuous expansion of the grid, the power system structure is becoming more complicated, leading to more and more uncertainty of the system. Especially, the massive integration of wind power and other renewable energy to the grid brings more challenges. In this paper, by taking use of DSR (dynamic security region) and risk assessment theory, it proposed the transient risk index calculation and integrated analysis method for wind power integration system, which was able to give quantitative indicators of the system day-ahead scheduling plan. The efficiency and practicality of theories mentioned herein were verified by standard numerical examples.

A Rapid Method to Calculate the Hyper-Plane of DSR Based on EEAC

The existing algorithms to calculate Dynamic Security Region (DSR) have been well developed, but the heavy calculation and large time-consuming hinder their applications. Based on Extend Equal Area Criterion (EEAC), this paper proposes a rapid method to calculate hyper-plane of DSR. Under a given fault, the critical clearing time can be calculated rapidly by using EEAC, then the corresponding critical operating point can be obtained. When enough critical operating points in different search directions are acquired, the hyper-plane of DSR can be obtained by least squares fitting method. Simulation on IEEE 4-11 system shows that the suggested method is fast, reasonable, and practical.

A Directional Rapid Search Method in PDSR Based on the Fitting Method

The fitting method is a basic method of computing power system dynamic security region (DSR) which uses orthogonal point-election method to determine directions when searching for critical points. It has high accuracy while its calculation speed is not fast enough for online application. In this paper, a directional rapid search (directional method for short) method is proposed. The directional method considers the approximate parallel property of different DSRs. It effectively reduces the computation time, since it only searches critical points in effective directions of the given DSR when searching for new DSRs. Through a case of IEEE 10-39 system, the results verify that the maximum distance and angle between the hyper-planes calculated by fitting method and directional method are 0.06341 and 1.8447°.

Optimal Comprehensive Control of Prevention and Emergency Based on DSR and Probabilistic Insecurity Measurement

Transient stability control of power system is a non-linear optimization problem which contains many constraints. Considering the cost of preventive control, emergency control and the following restorative control synthetically, a model of preventive control and emergency control based on DSR(Dynamic Security Region) and probabilistic insecurity measurement is proposed in the paper, and the optimal operating point of the system was obtained by using the improved genetic algorithm. In the end, the feasibility of the model and optimization strategy are verified by the case of the IEEE 4-generators 11-nodes system. Simulation show that the cost of comprehensive control of prevention and emergency is 13.2% less than the case that without the consideration of the random factors of the fault.

Security Region Based Dynamic Security Risk Assessment of Power Transmission System

The paper presents a framework of security region based dynamic security risk assessment of power transmission system. The application of practical dynamic security region (PDSR) in dynamic security risk assessment and the calculation steps of the dynamic security risk assessment are given in this paper. A model of risk assessment optimization which takes account of optimizing preventive and emergency control cost and contingency set decomposition is introduced. The effectiveness of this model has been proved by test results on the New England 10-generator 39-bus system.

Security region based real and reactive power pricing of power system

This paper develops a novel model and an algorithm of security region based real and reactive power pricing of power systems. In the proposed model, the reactive power production cost is represented as the opportunity cost. The static voltage stability region in the cut set power space (CVSR) and the practical dynamic security region (PDSR) in the injection power space are used to represent the constraints of voltage stability and transient stability, so that the consideration of this kind of constraints in the optimization becomes very easy. In the proposed algorithm, a decoupled optimization and iteration method of active power production cost and reactive power production cost is suggested. According to the K-T optimality conditions, the prices of active power and reactive power, and the different components corresponding to the concerned security constraints are derived. The components of spot prices can reflect the influence of different node power injections on each kind of security constraints, so that through the node price all of the participants in power market can be stimulated to take an active part in maintaining the system security. An illustrative example on the New England 10-genetator 39-bus System is used to demonstrate the proposed method.

Security constrained distributed optimal power flow of interconnected power systems

The security constrained distributed optimal power flow (DOPF) of interconnected power systems is presented. The centralized OPF problem of the multi-area power systems is decomposed into independent DOPF subproblems, one for each area. The dynamic security region (DSR) to guarantee the transient stability constraints and static voltage stability region (SVSR) constraints, and line current limits are included as constraints. The solutions to the DOPF subproblems of the different areas are coordinated through a pricing mechanism until they converge to the centralized OPF solution. The nonlinear DOPF subproblem is solved by predictor-corrector interior point method (PCIPM). The IEEE three-area RTS-96 system is worked out in order to demonstrate the effectiveness of the proposed method.

A new transient stability margin based on dynamic security region and its applications

A new transient stability margin is proposed based on a new expression of dynamic security region (DSR) which is developed from the existing expression of DSR. Applications of the DSR based transient stability margin to contingency ranking and screening are discussed. Simulations in the 10-machine 39-bus New England system are performed to show the effectiveness of the proposed DSR based transient stability margin.

Dynamic security risk assessment and optimization of power transmission system

The paper presents a practical dynamic security region (PDSR) based dynamic security risk assessment and optimization model for power transmission system. The cost of comprehensive security control and the influence of uncertainties of power injections are considered in the model of dynamic security risk assessment. The transient stability constraints and uncertainties of power injections can be considered easily by PDSR in form of hyper-box. A method to define and classify contingency set is presented, and a risk control optimization model is given which takes total dynamic insecurity risk as the objective function for a dominant contingency set. An optimal solution of dynamic insecurity risk is obtained by optimizing preventive and emergency control cost and contingency set decomposition. The effectiveness of this model has been proved by test results on the New England 10-generator 39-bus system.

Power System Dynamic Security Region and Its Approximations

Dynamic security region (DSR) for security assessment and preventive control is defined in terms of variables that are under the control of the dispatcher prior to a fault. The boundary of DSR can be expressed using the function describing the stable manifold of the controlling unstable equilibrium point. The function is shown to be the solution of a partial differential equation. Quadratic and linear approximations to the function characterizing the boundary of DSR are derived. Numerical tests of the approximations are conducted. Potential applications of the method are discussed

A novel optimization method of transient stability emergency control based on practical dynamic security region (PDSR) of power systems

This paper proposes a novel optimization method of transient stability emergency control based on a new concept of the so-called extended practical dynamic security region (EPDSR) defined in this paper and four experiential laws about the EPDSRs found from a number of studies in real power systems. In this method, the effect of a control action is represented by the displacement of EPDSR’s critical hyper-plane boundary in the direction of its outer normal vector. If an unstable contingency occurs, appropriate emergency control actions are triggered so that the enlarged EPDSR can cover the current operating point. Based on these ideas, a mathematics model of emergency control strategy is developed for minimizing its total cost and guaranteeing power system transient stability. The simulation results on the 10-generator, 39-bus New-England Test System as well as other real power systems have shown the validity of this method.

A probabilistic approach to dynamic power system security

The problem of dynamic power system security is investigated. A probabilistic approach is chosen, and an appropriate power system model is developed for analyzing the dynamic behavior of the different operational modes of the system. The model includes the transients induced by primary and secondary disturbance events. They are modeled by switches in the model whose states depend on the instantaneous values of certain system variables. The model characterizes the interaction between the dynamic state of the system and the network topology as defined by the status of the various protective relays in the system. A dynamic security region is defined as a subset of the state-structure space of the power system such that at any moment in time an operating point within the region satisfies all the constraints required for secure power system operation. The probabilistic evolution of the state and structure is computed as the solution of a system of linear partial differential equations with matching conditions at the switching boundaries. A dynamic security measure is defined as the integral of the joint probability density of the state and structure of the system over the dynamic security region for all possible structural variations. This computation yields the probability that the power system remains secure for the range of primary events considered. Computer simulations for an example power system illustrate the utility of the approach. >

Probabilistic steady-state and dynamic security assessment

A comprehensive framework for probabilistic steady-state and dynamic security assessment is presented. The time to insecurity is used as the measure of system security. Its probability distribution is obtained from the solution of a linear vector differential equation having coefficients that are expressed in terms of steady-state and dynamic security regions. An illustrative example for a simple system is given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Probabilistic dynamic security assessment of power systems-I: Basic model

A comprehensive framework for power system security assessment which incorporates probabilistic aspects of disturbances and system dynamic responses to disturbances is presented. Standard mathematical models for power system (steady-state) power flow analysis and transient stability (dynamic) analysis are used. A linear vector differential equation is derived whose solution gives the probability distribution of the time to insecurity. The coefficients of the differential equation contain the transition rates of system structural changes and a set of transition probabilities defined in terms of the steady-state and the dynamic security regions. These regions are defined in the space of power injections. Upper and lower bounds on the time to insecurity distribution are obtained.

Dynamic security regions of power systems

A method for deriving dynamic security regions of power systems is developed. A power system operating state is defined to be dynamically secure with respect to a given disturbance if the system, starting in that state maintains transient stability after experiencing the disturbance. Specifically, these are regions of prefault angles such that the post-fault system is asymptotically stable. The proposed approach is to construct affine approximations to the nonlinearities in the transient stability model and then derive quadratic bounds on the errors between the nonlinearities and their approximation. These are then used to derive sufficient conditions for a polytope of operating states to be dynamically secure.