Jia Hongjie

A simple method for power system stability analysis with multiple time delays

There exist significant time delays in the data of phasor measurement unit (PMU) and wide-area measurement system (WAMS). To properly evaluate the impact of time delay is very important for power system online stability assessment and controller design. In this paper, the maximum delayed time that power system can sustain without losing its stability is denoted as its delay margin. From the viewpoint of Lyapunov stability, when a dynamic system is critical stable at a given equilibrium point, there must exist critical eigenvalue on the imaginary axis. This paper presents a simple method to determine such critical eigenvalue by tracing eigenvalue loci of a transformation matrix. Then the critical eigenvalue is used to determine the delay margin of power system. Comparing with previous approaches, such as Lyapunov function/functional method, LMI method, root clustering paradigm method, the presented method can locate the exact delay margin with no conservativeness and with less computation burden. Moreover, it can be easily applied to the stability analysis of bulk power system with multiple time delays. Finally, single machine and infinite bus system (SMIB) and WSCC 3-generator-9-bus system are employed to validate its effectiveness.

An improved power system stability criterion with multiple time delays

Since there exist significant time delays in the data of phasor measurement unit (PMU) and wide-area measurement system (WAMS), to evaluate their impact is very important for power system online stability assessment and controller design in the wide-area environment. In this paper, we use Lyapunov stability theory and linear matrix inequality (LMI) method to analyze the impact of time delays on power system stability. An improved delay-dependent stability criterion for power system stability analysis with multiple time delays is presented. Based on Lyapunov-Krasovskii theory, a proper Lyapunov functional is firstly constructed. And, in deduction of its derivative function along the system trajectory, some necessary slack variables are introduced so as to reduce the method conservativeness. Then the derivative function is expressed as a set of linear matrix inequalities, which can be easily solved with LMI toolboxes in Matlab or Scilab. Finally, a typical two-dimension time-delayed system and WSCC 3-generator-9-bus system with two time delays are employed to validate the method effectiveness. It is revealed that the presented method is correct, effective and with less conservativeness. Work of this paper is helpful for power system stability assessment and control with considering time delays under wide-area environment.

Network reconfiguration for distribution system with micro-grids

Nowadays, technologies of distributed generation (DG) and distributed energy resource (DER) are developing rapidly. It has been demonstrated to be more reliable and economical that DGs or DERs are integrated into the traditional power grid based on micro-grid. So, more and more micro-grids will occur in distribution system in the future. In this paper, we mainly concern and discuss the impact of micro-grids on the distribution network reconfiguration. A model suitable for reconfiguration of distribution system with micro-grids is presented in this paper. Once a fault occurs in a distribution system, it can be applied to construct some islands so as to guarantee the power supply for some important customers and to reduce the system power loss at the same time. The problem is decomposed into a capacity subproblem and a reconfiguration sub-problem. The former is used to determine the optimal capacity for each island, and the latter is used to find the optimal reconfiguration with less power loss. They are called iteratively to get the optimal solution. Finally, some typical systems are employed to validate the effectiveness of the presented method.

Chaotic phenomena and small signal stability region of electrical power systems

In this paper, chaos phenomena and its influence on the power system small signal stability region (SSSR) are studied. We first review the studies on the SSSR, and point out that it is very important to make clear whether there exist some chaotic components on the boundary of the SSSR. Next, with some analytic skills of nonlinear dynamic system, we give a complete bifurcation diagram of a chaos existing in a sample power system, from a limit cycle (period-1) to chaotic state through cascading period-doubling bifurcation. The characteristics of the system energy varying in the continuous bifurcation are also shown. Thus a conclusion that chaos is always out of the Hopf bifurcation components (HB) on the SSSRs boundary. Based on this conclusion and some further studies, we confirm that, from the viewpoint of power system engineering, we do not need to consider the existence of chaos in the SSSR and its boundary. Therefore greatly simplifying the study of SSSR. Moreover, some aspects of the attractive regions of chaos and limit cycle are also studied, which is helpful to understanding some mistakes in some previous articles.

A novel LMI criterion for power system stability with multiple time-delays

This paper presents a novel LMI criterion for electric power system stability with multiple time-delays. Initially, the linear time-invariant model of the power system with multiple delays is constructed, subsequently, the former criteria and the novel criterion of this paper are demonstrated in this paper, and the novel criterion is fully proved according to Lyapunov direct method. Specifically, the proposed criterion utilizes a properly simplified Lyapunov-Krasovskii functional, and no free-weighting matrix is introduced in the formation of new criterion, as a consequence, the calculation efficiency is remarkably enhanced. A typical second-order delay system, a single-generator-infinite-bus system and the WSCC 3-generator-9-bus delay system are taken to validate the effectiveness and efficiency enhancement of the proposed criterion. The numerical results indicate that the criterion of this paper can generate the same stability margin with the former ones. Further, the numerical results also verify that the proposed criterion’s efficiency is substantially boosted and calculation time is greatly curtailed.

Voltage stability control based on real power flow tracing

After some disastrous instabilities and blackouts, power system voltage stability has drawn even more attention. When a serious fault occurs, proper control should be quickly adopted to terminate the system deterioration. In this paper, a control method based on power flow tracing is presented to enhance power system voltage stability. Firstly, a branch-admittance-decreasing algorithm is introduced to determine the minimum power cutting after a serious fault. Power flow tracing is then used to allocate the power to load and generator buses so as to get the corresponding load shedding and generation tripping. Comparing with the previous methods based on power flow sensitivity, the presented method can appropriately consider influence of some nonlinearities in power system, such as the discrete tap changing of OLTC, exciter hard-limit. Since power flow tracing is mainly used in the congestion management, allocation of power loss and transmission charges in the deregulation study, the presented method is compatible to the power system operation under deregulation. Finally, New-England system and IEEE 118-bus system are employed to verify the effectiveness of the presented method.

Interface control based on power flow tracing and generator re-dispatching

In recent years, economical and environmental reasons have forced the transmission systems to be operated closer to their security limits. Power utilities world-wide have become even more concerned with various power system stability problems. In this paper, we mainly concern power flow control strategy on some system critical interfaces. A control method based on power flow tracing and generator re-dispatching is presented. It can effectively control the power flow on some critical interfaces in a relatively large range. Power flow on the interface is first traced backward to locate generators to be adjusted in the sending-end subsystem. And then, it is traced forward to determine loads to be affected. Power flow tracing is adopted again from such loads to determine their supplying generators in the receiving-end subsystem, which is then used to compensate the load fluctuation on the interface. Since power flow tracing is mainly used in the congestion management, power loss allocation, node pricing in deregulation study, the presented method can not only be used in the traditional and monopolistic environment to enhance power system stability, but also can be used to mitigate power system congestion under deregulation environment. Finally, New England 39-bus system, 57-bus system and 118 bus system are employed to verify the effectiveness of the presented method.

Relationship of chaos and small signal stability region

In this paper, chaotic phenomena and its impact on the small signal stability region (SSSR) of power systems are studied. A typical period-3 trajectory in a simple power system is presented for the first time. Theorem Sarkovskii and Theorem Li-Yorke are used to identify the existence of chaos in power systems. This method can avoid the confusion caused by pseudo-chaos and incomplete period doubling bifurcation phenomena. Moreover, the influence of chaos on the small signal stability region has been investigated and we conclude that, from the engineering point of view, it is not necessary to consider the existence of chaos in the studies of SSSR and its boundary. This excludes the unnecessary complexity in the study of SSSR.

A LMI based approach to power system stability analysis with time delay

Delay margin means the maximum delayed time that power system can sustain without losing its stability. Since, there exists significant time delay in the data of phasor measurement unit (PMU) and wide-area measurement system (WAMS), to evaluate system delay margin is very important for power system online stability assessment and controller design in the wide-area environment. In this paper, we use Lyapunov stability theory and linear matrix inequality (LMI) method to evaluate power system delay margin. Lyapunov-Krasovskii criterion is firstly introduced to construct a suitable Lyapunov functional. Its derivative along the system trajectory is then expressed as a set of LMIs, which can be easily solved with LMI toolbox in Matlab or Scilab to obtain the system delay margin. In order to reduce conservativeness of the method, some slack variables are introduced in the derivation. Comparing with some existing numerical methods, such as eigenvalue based method, root clustering paradigm method, the presented method has a little conservativeness. However, it has much more flexibility and applicability in stability analysis to the time variant, nonlinear, switched and uncertain time delay systems. Finally, single-machine-infinite-bus (SMIB) system and WSCC 3-generator-9-bus system are employed to validate the effectiveness of the method.

Implementation of power system security check and its visualization system

Nowadays, with the introduction of competitive electricity markets, large scale interconnected power grids are operated closer to their operation limits, and power system operators often have a dual and conflicting responsibility for system security and for profit maximization. Insuring power grid operating safely and stably under complicated operating conditions has become a rigorous challenge to electric utilities. This paper discusses some online security check technologies, and presents a power system security check software package implemented with advanced visualization technologies. The application of power system security check is based on CIM model so as to facilitate the passing of power system data with other applications.