Practical Dynamic Security Region Research Articles

Space Division and WGAN-GP Based Fast Generation Method of Practical Dynamic Security Region Boundary

Fast and accurate transient stability analysis is crucial to power system operation. With high penetration level of wind power resources, practical dynamic security region (PDSR) with hyper plane expression has outstanding advantages in situational awareness and series of optimization problems. The precondition of obtaining accurate PDSR boundary is to locate sufficient points around the boundary (critical points). Therefore, this paper proposes a space division and Wasserstein generative adversarial network with gradient penalty (WGAN-GP) based fast generation method of PDSR boundary. First, the typical differential topological characterizations of dynamic security region (DSR) provide strong theoretical foundation that the interior of DSR is hole-free and the boundaries of DSR are tight and knot-free. Then, the space division method is proposed to calculate critical operation area where the PDSR boundary is located, tremendously compressing the search space to locate critical points and improving the confidence level of boundary fitting result. Furthermore, the WGAN-GP model is utilized to fast obtain large number of critical points based on learning the data distribution of the small training set aforementioned. Finally, the PDSR boundary with hyperplanes is fitted by the least square method. The case study is tested on the Institute of Electrical and Electronics Engineers (IEEE) 39-bus system and the results verify the accuracy and efficiency of the proposed method.

A Double‐Layer Optimization Method for Cascading Failure Prevention Considering Transient Stability

In recent years, in order to reduce the damage from the blackout accident, the demand of the power system for its basic resistance ability has gradually increased. Therefore, this paper proposes a double‐layer optimization method for the prevention of cascading failure of the power system that takes into account the transient stability constraint for cascading trips that directly lead to the accident. In terms of models, the paper reconstructs an outer model for optimizing the safety margin based on the inner model that solves the safety margin of cascading failure prevention. In terms of algorithms, the paper uses the Extended Particle Swarm Optimization (EPSO) algorithm with higher precision and accuracy to solve the inner model and innovatively introduced the Practical Dynamic Security Region (PDSR), which uses PSASP software for offline calculation and online application, as a dynamic analysis method to quickly realize transient stability constraint to solve the outer model. Three evaluation indexes of the preventive optimization effect can be obtained by this method; dispatchers can plan more flexible and reliable optimal dispatching schemes through these indexes, to comprehensively improve the safety margin of cascading failure prevention in the current operating state and enhance the risk resistance ability of the power grid. This paper has used MATLAB and PSASP to perform simulation analysis using the IEEE39 node system as a test example to verify the effectiveness and superiority of the proposed model and algorithm.

Improved Multi-point estimation method based probabilistic transient stability assessment for power system with wind power

With the increasing penetration of wind power, probabilistic transient stability assessment becomes critical to deal with the uncertainties and correlations of wind power, thus improving the reliability of power system. This paper proposes an improved multi-point estimation based probabilistic transient stability assessment method. Extreme learning machine (ELM) is introduced to describe the uncertainty of practical wind power output. Gauss-Hermite integral based multi-point estimation method is proposed to calculate transient stability criterion derived through practical dynamic security region (PDSR). Optimal number of the sampling points is determined based on PDSR hyperplanes and an improved particle swarm optimization algorithm (IPSO). Test results on the New England 10-generators 39-buses system and a practical provincial power system in China show that the calculation accuracy of the proposed method is higher than that of other commonly-used point-estimation methods without much loss of computational efficiency under different wind power penetration and correlation levels.

A hybrid data-driven method for fast approximation of practical dynamic security region boundary of power systems

In the context of high-level integration of stochastic renewable energy resources such as wind and solar power, the practical dynamic security region (PDSR) with hyper-plane expression is a powerful tool for power system situational awareness and stability-constrained operation. In this paper, a hybrid data-driven method is proposed to fast approximating the PDSR boundary with hyper-plane expression. Firstly, the operating point data in the high-dimension nodal injection space is analyzed by the RELIEF algorithm to identify the key generators, active output of which has relatively great effect on transient angle stability. Then, based on the orthogonal point selection method and key generators, the equivalent search space and critical points inside it are determined with high accuracy and high speed. The hyper-plane expression of the PDSR boundary, which matches the critical points best, is finally fitted by the least square approach. Test results obtained using the IEEE 39-bus test system show the efficiency of the proposed method.

An Analytical Approach to Probabilistic Dynamic Security Assessment of Power Systems Incorporating Wind Farms

An analytical approach to probabilistic dynamic security assessment of power systems incorporating wind farms is proposed. As the most important and complex step of the evaluation process, the probability of transient stability given a specific fault and uncertainties of output power of wind farm and load is calculated analytically based on the practical dynamic security region of power system with double fed induction generator and Cornish-Fisher expansion. The proposed method can provide meaningful and reliable evaluation results with high accuracy and much less computing time compared with Monte Carlo simulation.

Practical Dynamic Security Region Based on Phase Trajectory

A fast method based on the phase trajectory to compute DSR is developed. Firstly, the phase trajectory sensitivity has more linear effect than power angle sensitivity. According to the phase trajectory boundary function, controlling unstable equilibrium generators could be identified. The PDSR is finally obtained by the sensitivity analysis between the phase and generators’ active power. Test results on the New England 10-genrator 39-bus system are presented and prove the effectiveness of this approach.

Transient stability probability of a power system incorporating a wind farm

An analytical approach for probabilistic evaluation of transient stability of a power system incorporating a wind farm is presented in this study. Based on the fact that the boundary of practical dynamic security region (PDSR) of a power system with double fed induction generators (DFIG) can be approximated by one or few hyper-planes in nodal power injection space, transient stability criterion for given configurations of pre-fault, fault-on and post-fault of a power system is to be expressed by certain expressions of linear combination of nodal injection vector and the transient stability probability (TSP) is further obtained with a much more simplified expression than the complex integral. Furthermore, considering uncertainties of nodal injection power including wind power and load, TSP is calculated analytically by Cornish-Fisher expansion, which can provide reliable evaluation results with high accuracy and much less computing time compared with Monte Carlo simulation. TSP and its visualization can further help operators and planners be aware of the degree of stability or instability and find critical components to monitor and reinforce. Test results on the New England 10-generators and 39-buses power system show the method’s effectiveness and significance for probabilistic security assessment.

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.

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.

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.