Lei Ding

Two-Step Spectral Clustering Controlled Islanding Algorithm

Controlled islanding is an active and effective way of avoiding catastrophic wide area blackouts. It is usually considered as a constrained combinatorial optimization problem. However, the combinatorial explosion of the solution space that occurs for large power systems increases the complexity of solving it. This paper proposes a two-step controlled islanding algorithm that uses spectral clustering to find a suitable islanding solution for preventing the initiation of wide area blackouts by un-damped electromechanical oscillations. The objective function used in this controlled islanding algorithm is the minimal power-flow disruption. The sole constraint applied to this solution is related to generator coherency. In the first step of the algorithm, the generator nodes are grouped using normalized spectral clustering, based on their dynamic models, to produce groups of coherent generators. In the second step of the algorithm, the islanding solution that provides the minimum power-flow disruption whilst satisfying the constraint of coherent generator groups is determined by grouping all nodes using constrained spectral clustering. Simulation results, obtained using the IEEE 9, 39 and 118-bus test systems, show that the proposed algorithm is computationally efficient when solving the controlled islanding problem, particularly in the case of a large power system.

A new controlled islanding algorithm based on spectral clustering

When islanding operation of system is unavoidable, controlled islanding need determine proper splitting strategies and split the entire interconnected transmission network into islands ensuring generation/load balance and generator coherency. For a large-scale power system, the controlled islanding problem is very complex in general because a combinatorial explosion of strategy space happens. This paper mainly studies how to find proper splitting strategies of large-scale power systems using a two-step spectral clustering based method. In the first step, the machine nodes (generators and dynamic loads) will be grouped by normalized spectral clustering with dynamic models to satisfy the dynamic constraint, and the machine grouping results will be served as prior knowledge of the next step. In the second step, all the nodes will be grouped by constrained spectral clustering with power flow data to satisfy the static constraint and get the minimal cut set solution. Simulation results on IEEE 9- and 118-bus networks show that this method is efficient for controlled islanding of large-scale power systems.

Graph Spectra Based Controlled Islanding for Low Inertia Power Systems

The inertia of modern power systems is decreasing and becoming more variable as more inverter-connected renewable energy sources and loads are integrated. This leads to a low and time-varied inertia power system that is more sensitive to disturbances and may not be robust enough to survive large disturbances. How to protect such a low and time-varied inertia system from blackouts is in question. This paper tries to answer this question using a graph spectra-based controlled islanding method. Eigenvector sensitivity, with respect to inertia, is used to identify the impact of reduced inertia on the spectral properties of power system graphs and, thus, coherent generator grouping. Constrained spectral clustering is then used to find the islanding boundary with minimal power-flow disruption to island low inertia systems. Simulation results, obtained using the IEEE 9-bus and 118-bus test systems, validate the effectiveness of the proposed algorithm in the case of low inertia systems.

Optimal placement of Phasor Measurement Units to Improve Parallel Power System Restoration

This paper proposes a new method for optimal placement of Phasor Measurement Units (PMUs) across the weak areas of the power system to monitor the status of the boundary buses during Parallel Power System Restoration (PPSR). The proposed PMU placement method is based on an Integer Linear Programming (ILP) methodology. For validation purposes, the proposed method is implemented across the weak areas of the following two test systems: New England 39-bus test system and IEEE 118-bus test system.

A novel controlled islanding algorithm based on constrained spectral clustering

Controlled islanding, which splits the whole power system into islands, is an effective way of limiting blackouts during severe disturbances. Finding islanding solutions in real time is difficult because of the combinatorial explosion of the solution space occurs for large power system. This paper proposes a computationally efficient algorithm based on constrained spectral clustering to solve controlled islanding problem. The objective function used in this algorithm is the minimal power- flow disruption. The main constraints applied are related to generator coherency and transmission line availability. An undirected edge-weighted graph is constructed based on power flow data, and constraints related to transmission line availability and generator coherency are included by modifying the graph weights and using a subspace approach. Spectral clustering is then applied to the constrained solution subspace to find the islanding solution. To improve the clustering quality, a robust k-medoids algorithm, which is less sensitive to outliers than the traditional k-means algorithm, is used for clustering. Simulation results show that the proposed algorithm is computationally efficient when solving a controlled islanding problem in real-time.

Closure to Discussion on “Two-Step Spectral Clustering Controlled Islanding Algorithm”

The method proposed in the procedure of the first step of the spectral clustering controlled islanding (SCCI) is actually equivalent to the application of slow coherency. The slow coherency method is very useful for ofiline analysis. However, the following two questions must be answered before slow coherency can be applied to identify suitable generator groups: 1) have the generators lost synchronism, or will they, i.e., is the separation of generator groups necessary? 2) How many generator groups should be formed? This means that there are distinct drawbacks when applying slow coherency online; however, the method can still be adapted to this purpose to a certain extent [1]. We think a better way is using an online algorithm to replace the slow coherency method [2], [3]. The drawbacks and limitations of the first step of the SCCI have been discussed in Section III-A.

Dynamic performance comparison of different controlled islanding methods

Controlled islanding can be used as an efficient emergency action to prevent blackouts. Steps of controlled islanding methods implementing include graph modelling, objective function establishing, and the splitting solution finding. Researchers now concern about static constraints such as reactive power compensation and restoration capability when solving the objective function, but few papers have analyzed dynamic performance of splitting algorithms comprehensively. This paper investigates detailed dynamic responses with three typical methods: a) Ordered Binary Decision Diagram (OBDD), b) Weak Connection and c) Spectral Clustering islanding. To compare their differences, this paper separates the responses creatively into two phases from the perspective of time. In the first phase, characteristics of oscillations among generators and duration of transient process are taken into consideration. Maximum frequency shift and steady frequency shift in the second phase are compared then. Feasibility of different splitting solutions are also analyzed to compare the three methods. Time domain simulation of IEEE 118 case is carried out with PSS\E.

Two-step spectral clustering controlled islanding algorithm

Controlled islanding is an active and effective way of avoiding catastrophic wide area blackouts. It is usually considered as a constrained combinatorial optimization problem. However, the combinatorial explosion of the solution space that occurs for large power systems increases the complexity of solving it. This paper proposes a two-step controlled islanding algorithm that uses spectral clustering to find a suitable islanding solution for preventing the initiation of wide area blackouts by un-damped electromechanical oscillations. The objective function used in this controlled islanding algorithm is the minimal power-flow disruption. The sole constraint applied to this solution is related to generator coherency. In the first step of the algorithm, the generator nodes are grouped using normalized spectral clustering, based on their dynamic models, to produce groups of coherent generators. In the second step of the algorithm, the islanding solution that provides the minimum power-flow disruption while satisfying the constraint of coherent generator groups is determined by grouping all nodes using constrained spectral clustering. Simulation results, obtained using the IEEE 9-, 39-, and 118-bus test systems, show that the proposed algorithm is computationally efficient when solving the controlled islanding problem, particularly in the case of a large power system.