Yu Xiaodan

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.

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.

ON an improved delay-dependent robust stability criterion and application to power system statbility analysis with time delays

In this paper, Lyapunov stability theory and linear matrix inequality (LMI) method are used to analyze the delay-dependent robust stability of power systems with multiple time delays. An improved delay-dependent robust stability criterion for power system with multiple time delays is presented. A proper Lyapunov functional is firstly constructed based on Lyapunov-Krasovskii theory. And, in the deduction of its derivative function along the system trajectory, some necessary slack variables are introduced so as to reduce its conservatism. Then the method is applied to the robust stability analysis for power system with time-varying delays and uncertainties. It can be found the present method is correct, effective and with less conservatism.

A Method to Determine Oscillation Emergence Bifurcation in Time-Delayed LTI System with Single Lag

One type of bifurcation named oscillation emergence bifurcation (OEB) found in time-delayed linear time invariant (abbr. LTI) systems is fully studied. The definition of OEB is initially put forward according to the eigenvalue variation. It is revealed that a real eigenvalue splits into a pair of conjugated complex eigenvalues when an OEB occurs, which means the number of the system eigenvalues will increase by one and a new oscillationmode will emerge. Next, a method to determine OEB bifurcation in the timedelayed LTI system with single lag is developed based on Lambert W function. A one-dimensional (1-dim) time-delayed system is firstly employed to explain the mechanism of OEB bifurcation. Then, methods to determine the OEB bifurcation in 1-dim, 2-dim, and high-dimension time-delayed LTI systems are derived. Finally, simulation results validate the correctness and effectiveness of the presented method. Since OEB bifurcation occurs with a new oscillation mode emerging, work of this paper is useful to explore the complex phenomena and the stability of time-delayed dynamic systems.One type of bifurcation named oscillation emergence bifurcation (OEB) found in time-delayed linear time invariant (abbr. LTI) systems is fully studied. The definition of OEB is initially put forward according to the eigenvalue variation. It is revealed that a real eigenvalue splits into a pair of conjugated complex eigenvalues when an OEB occurs, which means the number of the system eigenvalues will increase by one and a new oscillation mode will emerge. Next, a method to determine OEB bifurcation in the time-delayed LTI system with single lag is developed based on Lambert W function. A one-dimensional (1-dim) time-delayed system is firstly employed to explain the mechanism of OEB bifurcation. Then, methods to determine the OEB bifurcation in 1-dim, 2-dim, and high-dimension time-delayed LTI systems are derived. Finally, simulation results validate the correctness and effectiveness of the presented method. Since OEB bifurcation occurs with a new oscillation mode emerging, work of this paper is useful to explore the complex phenomena and the stability of time-delayed dynamic systems.