Modeling of Time-Delayed Distributed Cyber-Physical Power Systems for Small-Signal Stability Analysis

Abstract

Compared with a power system under centralized control, a power system under fully distributed control has stronger interdependence between its physical side and cyber side. Such a system is a typical cyber-physical system (CPS). The time delay problem is one of the most critical issues in the application of distributed control for power systems. First, a distributed information flow model is established considering multiple sources of time delay, especially the communication delay between neighboring agents. Second, combining the dynamics of physical power systems, a general model of time-delayed CPS under fully distributed control is proposed, especially for inverter-based microgrids. Third, the stability of the time-delayed CPS is analyzed based on the proposed model with a critical eigenvalue tracking algorithm. A real-world microgrid with DGs under fully distributed frequency control is tested for small-signal stability analysis. The findings show that the stability of the distributed CPS with multiple sources of time delay depends on not only the absolute value of time delays but also the coordination of time delays, and the delay merging property in centralized mode is not relevant in a distributed CPS. The accuracy of the model and the obtained stability margin are verified by Simulink simulations.

Stability-Oriented Minimum Switching/Sampling Frequency for Cyber-Physical Systems: Grid-Connected Inverters Under Weak Grid

“…K represents feedback factor. Additionally, the instantaneous active power p sour and reactive power q sour are provided through equations ( 9)- (10). The low-pass filter is applied to the grid-connected inverter to obtain the average active power P sour and reactive power Q sour .…”

“…According to the literature [10], the foresaid section can be simplified as e −1.5T s = 4 f −3s/4 f +3s, where f represents the system sampling or switching frequency. The droop controller can be expressed as:…”

“…Traditionally, the system stability of cyber-physical systems was widely studied, which could be divided into two parts, i.e., stability analysis with network attack and stability analysis without network attack [7][8][9][10][11]. From the viewpoint of stability analysis with network attack, the current researches have constructed one relatively complete research system from the perspectives of network attack [7], attack cascade reaction [8], network attack defense [9].…”

“…From the viewpoint of stability analysis with network attack, the current researches have constructed one relatively complete research system from the perspectives of network attack [7], attack cascade reaction [8], network attack defense [9]. From the viewpoint of stability analysis without network attack, the current researches focused on the time delay regarding distributed/centralized communication network [10][11]. The literatures [10] and [11] respectively designed delay time threshold conditions for communication delay time caused by cyber-physical material integration in cyber-power system and cyber-energy system.…”

“…From the viewpoint of stability analysis without network attack, the current researches focused on the time delay regarding distributed/centralized communication network [10][11]. The literatures [10] and [11] respectively designed delay time threshold conditions for communication delay time caused by cyber-physical material integration in cyber-power system and cyber-energy system. Since the power system with digital control system is one simplest cyber-physical system, the stability of this control system without communication network should be studied, which belongs to small-signal stability analysis.…”