Estimating Critical Clearing Time of Grid Faults Using DA of State-Reduction Model of Power Systems

This paper proposes a critical clearing time (CCT) estimation method by the domain of attraction (DA) of a state-reduction model of power systems using sum of squares (SOS) programming. By exploiting the property of the Jacobian matrix and the structure of the boundary of the DA, it is found the DA of the state-reduction model and that of the full model of a power system are topological isomorphism. There are one-to-one correspondence relationships between the number of equilibrium points, the type of equilibrium points, and solutions of the two system models. Based on these findings, an expanding interior algorithm is proposed with SOS programming to estimate the DA of the state-reduction model. State trajectories of the full model can be transformed to those of the state-reduction model by orthogonal or equiradius projection. In this way, CCT of a grid fault is estimated with the DA of the state-reduction model. The calculational burden of SOS programming in the DA estimation using the state-reduction model is rather small compared with using the full model. Simulation results show the proposed expanding interior algorithm is able to provide a tight estimation of DA of power systems with higher accuracy and lower time costs.

Application of Wind Generation on Weak Networks Considering Potential System Limitations Due to Transients and Faults

Limited resources are available on the application of wind generation systems interconnected to weak powemetworks. With the need to further interface DG （distributed generation） including WG （wind generation） to weak networks, it is necessary to establish a means of determining what is the most efficient quantity of WG that can be applied in order to maintain stability in the network. This paper establishes a concept that can be applied to weak networks. The aim is to estimate how much WG can be installed on weak networks as well as establishing characteristic responses to generation loss without and with faulted conditions. The main contribution is a thorough understanding of weak network limitation proved to be the most critical parameter in these calculations.

A Practical Approach Based on Equal Area Criteria for Stability Analysis of Weak Networks with Wind Generation Penetration

The performance of DFIG-based wind generation systems that interconnected to solid networks is well understood and prevalent in Europe and North America. However, the application of these renewable generating stations to weak network has been examined in very limited occasions. Weak networks have a range of limitations from system capacities to CFCT restrictions which would need to be well understood prior to wind energy integration. Of particular interest would be how much wind generation could be integrated into a weak network prior to increasing voltage and frequency stability issues brought about by penetration issues. This paper introduces a simple and practical approach based on the equal area criteria to investigate the stability of weak networks. Simulation results that are presented to show the proposed approach is a viable preliminary assessment tool to determine system stability on weak networks with wind power penetration.

Utilization of DFIG on an Islanded Power Generation and Distribution System

The utilization of wind generation equipment, such as DFIGs （double fed induction generators）, interconnected to islanded power generation and distribution systems is investigated in order to determine their effects on the overall system operating characteristics and stability. The use of a stable power station （with high speed machines） will be critical in achieving fast and reliable transient response to network events, in particular, when large transient loads are expected on a continuous basis, i.e., industrial mining and mineral processing equipment. Simulation results of this paper assist in understanding how small power stations and wind generation equipment respond to large transients in an islanded network. In particular, detailed simulations and analyses will be presented on impacts of distributed wind generation units （1.5 MW DF1G） on the stability of a small weak network. The novelty of this paper is on detailed analyses and simulation of weak networks with interconnects DFIG＇s including their impacts on system stability under various transient operating conditions.

Hybrid Analytical and Data-Driven Model Based Instance-Transfer Method for Power System Online Transient Stability Assessment

Data-driven methods are widely recognized and generate conducive results for online transient stability assessment.However,the tedious and time-consuming process of sample collection is often overlooked.The functioning of power systems involves repetitive sample collection due to the constant variations occurring in the operation mode,thereby highlighting the importance of collection efficiency.As a means to achieve high sample collection efficiency following the operation mode change,we propose a novel instance-transfer method based on compression and matching strategy,which facilitates the direct acquisition of useful previous samples,used for creating the new sample base.Additionally,we present a hybrid model to ensure rationality in the process of sample similarity comparison and selection,where features of analytical modeling with special significance are introduced into data-driven methods.At the same time,a data-driven method can also be integrated in the hybrid model to achieve rapid error correction of analytical models,enabling fast and accurate post-disturbance transient stability assessment.As a paradigm,we consider a scheme for online critical clearing time estimation,where integrated extended equal area criterion and extreme learning machine are employed as analytical model part and data-driven error correction model part,respectively.Derived results validate the credible efficacy of the proposed method.

Data-driven Transient Stability Assessment Model Considering Network Topology Changes via Mahalanobis Kernel Regression and Ensemble Learning

Transient stability assessment(TSA)is of great importance in power system operation and control.One of the usual tasks in TSA is to estimate the critical clearing time(CCT)of a given fault under the given network topology and pre-fault power flow.Data-driven methods try to obtain models describing the mapping between these factors and the CCT from a large number of samples.However,the influence of network topology on CCT is hard to be analyzed and is often ignored,which makes the models inaccurate and unpractical.In this paper,a novel data-driven TSA model combining Mahalanobis kernel regression and ensemble learning is proposed to deal with the problem.The model is a weighted sum of several sub-models.Each sub-model only uses the data of one topology to construct a kernel regressor.The weights are determined by both the topological similarity and numerical similarity between the samples.The similarities are decided by the parameters in Mahalanobis distance,and the parameters are to be trained.To reduce the model complexity,sub-models within the same topology category share the same parameters.When estimating CCT,the model uses not only the sub-model which the sample topology belongs to,but also other sub-models.Thus,it avoids the problem that there may be too few data under some topologies.It also efficiently utilizes information of data under all the topologies.Moreover,its decision-making process is clear and understandable,and an effective training algorithm is also designed.Test results on both the IEEE 10-machine 39-bus and a real system verify the effectiveness of the proposed model.

Data-driven Transient Stability Assessment Based on Kernel Regression and Distance Metric Learning

Transient stability assessment(TSA) is of great importance in power systems. For a given contingency, one of the most widely-used transient stability indices is the critical clearing time(CCT), which is a function of the pre-fault power flow.TSA can be regarded as the fitting of this function with the prefault power flow as the input and the CCT as the output. In this paper, a data-driven TSA model is proposed to estimate the CCT. The model is based on Mahalanobis-kernel regression,which employs the Mahalanobis distance in the kernel regression method to formulate a better regressor. A distance metric learning approach is developed to determine the problem-specific distance for TSA, which describes the dissimilarity between two power flow scenarios. The proposed model is more accurate compared to other data-driven methods, and its accuracy can be further improved by supplementing more training samples.Moreover, the model provides the probability density function of the CCT, and different estimations of CCT at different conservativeness levels. Test results verify the validity and the merits of the method.

Analytical Representation of Data-driven Transient Stability Constraint and Its Application in Preventive Control

Accurate transient stability assessment(TSA) and effective preventive control are important for the stable operation of power systems. With the superiorities in precision and efficiency, data-driven methods are widely used in TSA nowadays. Data-driven TSA model can be adopted in the stability constraints of preventive control optimization, but existing methods are mostly iteration-based ones, which may result in low efficiency, sometimes even non-convergence. In this paper,an analytical representation method of data-driven transient stability constraint is proposed based on a non-parametric regression model built for TSA. Key feature extraction and dominant sample selection are proposed to reduce the scale of the TSA model, and bi-level linearization is applied to further modify it.Optimal preventive control model is then formulated as a mixed-integer linear program(MILP) problem with the linearized analytical data-driven transient stability constraint, which can be solved without iterations. An overall procedure of datadriven TSA and preventive control is finally developed. Case studies show that the proposed method has high accuracy in TSA and can achieve effective preventive control of power system with high efficiency.