Identification of Coherent Generators in Multi-Machine Power Systems

Dynamic estimation of rotor angle deviation of a generator in multi-machine power systems

This paper illustrates a new technique that identifies coherent clusters of synchronous generators in multi-machine power systems. The technique can be easily implemented in a wide-area measurement system. The importance of fast identification of coherent groups of generators based on wide-area signal measurements lies in its contribution to the design of wide-area based stability control schemes that aim to enhance the overall performance of the power system. The method uses a hierarchical clustering technique (Agglomerative Method) to classify any number of synchronous generators into a number of coherent groups. A new technique is proposed to take into account the influence of the type of events on the clustering. The clustering is based on coherency measures obtained from the time domain responses of the generators following system disturbances. These measures are used to evaluate the degree of coherency between any pair of generators. Thereafter, the clustering algorithm is used to cluster these coherent generators into coherent groups. It is suggested that generators' rotor measurements can be obtained and therefore synchronised measurements of these quantities using Phasor Measurement Units (PMUs) technology can be acquired. Hence, the proposed clustering method could be integrated into a wide-area measurement system that enables fast identification of coherent clusters of generators. The proposed method is tested on the standard 16 generator 68 bus system.

The development of the modern Global Positioning System (GPS) technique makes the real time monitoring of the generator status workable. However it is impractical and unnecessary to install GPS devices at all generators due to the high cost. Observations and calculations indicate that most of the generators in a large power system have some similar transient power angle characteristics. Therefore the generators can be grouped according to the similarity of their power angle characteristics, and within each group only one generator is required to install GPS device to monitor the real time status of all the generators in the group. Based on the coherence group theory, the coherence groups of the generators are irrelevant to the magnitude of disturbance and the details of the generator unit model. Therefore, by building a classical synchronous generator linear system model, an accessible Gram matrix model can be derived. Then according to the generator identification rule of ε-coherence (or coherent group), the generator coherence groups can be identified in a large power system. The methodology can facilitate the real time monitoring of generators' status and the real-time control based on the GPS technique.

A new approach for online coherency identification in power systems based on correlation characteristics of generators rotor oscillations

This paper presents the application of fuzzy c-means (FCM) clustering to the recognition of coherent generators in power systems. A coherency measure, which is derived from the time-domain dynamic responses of generators, is first proposed for evaluating the property of generator coherency. From the coherency measure a fuzzy relation matrix describing the degree of coherency between any pair of generators is constructed. Fuzzy c-means clustering analysis is applied on coherency measure. The result of various coherent generator groups can thus be obtained, showing results of clustering for different prescribed number of coherent groups. Application results of a sample power system are presented to show the validity and effectiveness of the proposed method.

In multi-machine power systems, synchronous generators tend to oscillate in several coherent groups, each group being equivalent to a virtual generator. Coherency analysis is fundamental to wide area control of large power systems. Usually, coherency analysis is carried out in an offline mode. However, in response to various events at different operating conditions, the coherent groups may differ. Thus, it is important to develop the analysis to be online. In this paper, K-harmonic means clustering (KHMC) approach is introduced for online analysis. This approach is insensitive to initialization of group centers and is fast. Besides, a second algorithm is developed to automatically determine the optimal number of groups during the online analysis for KHMC. Simulation results are presented using the IEEE 68-bus 16-machine power system. The results indicate that KHMC approach correctly identifies the group centers and assigns each generator to its corresponding group.

Power systems with synchronous generators and solar photovoltaic (PV) experience frequency and power fluctuations due to high variability of PV power. Automatic generation control is implemented to control power outputs of the generators and stabilize the system frequency. It is desirable with increasing levels of PV penetration to have foresight of frequency fluctuations to empower advanced control systems. A new methodology is presented in this paper for predicting frequency of synchronous generators in a power system with solar PV. A cellular computational network (CCN) is used to perform the frequency prediction over multi-time scale. CCNs are decentralized and distributed computing paradigms. Thus, CCNs are suitable for fast prediction of frequency of synchronous generators distributed spatially across a power system. The inputs to cells of the CCN are derived from phasor measurement unit (PMU) measurements of frequency and voltage phasor at the respective generator buses. Past, current and predicted measurements enable multi-timescale predictions of synchronous generator frequencies in a power system. Typical multi-time scale frequency predictions using the CCN are illustrated on a two-area four machine power system with solar PV integrated.

The design of the under-excitation limiters (UEL) in the multi-machine Singapore power system is considered. Based on the technique described by the authors previously (see IEEE Trans. Power Syst., vol.14, no.4, p.1279-84, 1999), the frequency response method has been extended to include the interactions between generators in the power system such that the design of the UEL can be carried out in a systematic manner. By coordinating the reactive power compensation scheme with the generator reactive power absorption capability, a more effective utilization of the network resources can be achieved.

When the generators of a coherent group in a power system are equivalenced for transient stability studies, it is logical that the associated controllers—excitation controllers and the speed governing systems—are also equivalenced. Depending upon various design features and capacity, the time constants of the transfer functions of different controllers may be different. This paper presents a Walsh function approach for equivalencing the controllers in multi-machine power systems, taking into account the above differences. The approach has an elegant mathematical base and provides any desired level of accuracy.

The frequency is one of the instruments for measuring the health status of the power system, due to its ability to anticipate any imbalance between generations and loads. If the generated power is adequate for the system load and losses, then, the system will be in a steady state, otherwise frequency deviates from nominal value due to the mismatch between the generation and load. If the frequency continues to deviate from nominal value, the system may collapse. The assessment of frequency stability level becomes an essential aspect of power system operation and also for projecting the ability of the power system to maintain nominal frequency when subjected to any disturbance. In this paper, a method is proposed to evaluate frequency security of multi-machine power system using transient frequency deviation index (TFDI) which is based on Center of Inertia (COI) referred frequency. The proposed method has been tested on the New England 39- bus test system. Results show that the proposed method takes the advantage of TFDI in accumulating the effect of frequency trajectory deviations. These frequency trajectories may be obtained from the time domain simulation or Wide Area Measurement System (WAMS). The results also show the advantages of COI referred frequency in representing the equivalent frequency of the system. The method would provide a reliable and efficient base for load shedding relays adjustment and operation control.

This note has proposed a novel concept, called dynamic COI-tracking concept, in which the power angle and frequency of each generator track the dynamic COI (center of inertia) of the power system. A salient feature of the suggested concept is that it pulls all generators towards the real-time COI of the system, in the end it drives the system to a stable state with an acceptable frequency. Besides, it is built on a control structure which is decoupled. To make a comparison between the proposed concept and the conventional one, we will first establish the control system models based on the two concepts respectively. Then, using the back-stepping method, two robust controllers will be designed to achieve the control objectives of the two concepts. At last, dynamic simulations will be carried out based on a 2-area-4-machine test power system, and the control effects of the two robust controllers, together with that of the conventional AVR+PSS excitation system, will be compared to show the advantages of the proposed concept in improving transient angle stability. (6 pages)

This paper presents a general approach for coherency detection in bulk power systems using the projection pursuit (PP) theory. Supported by the concept of center of inertia (COI) in power systems, the PP theory is employed to model the wide-area coherency detection as an optimization problem. In the proposed method, the optimal projection direction in high dimensional orthogonal space is explored in order to detect the coherent groups via the data from synchronous phasor measurement units (PMUs). Two quantitative indices constructed with projection assessment index (PI), the objective of the optimization model, are then defined in order to determine the critical coherent group and the dominant coherent groups. The coherency detection criterion and the implementation framework for the proposed approach are also presented. Simulation data from the 16-machine 68-bus test system and China Southern power Grid (CSG), along with actual field-measurement data retrieved from WAMS database in the CSG, are employed to demonstrate the effectiveness and applicability of the proposed algorithm under different disturbances. It is shown that the proposed methodology successfully detects the dominant coherent groups of generators and buses in bulk power system via the wide-area field-measurement data.

Starting from normalized generators’ equations of rotor motion with respect to the center of inertia of power systems, post-fault power system dynamic is analogized as a motion of a particle with 1.0 mass in an n-dimensional Euclidean space. A rotational coordinate axis is defined for the moving particle. Transient stability of a multi-machine power system is transformed into a simple one-dimensional motion of particle on the axis. Based upon the above new idea, a new concept transient energy function (NCTEF) is proposed for transient stability assessment of power systems. Case studies on the 10-generator New England power system verified the rationality of NCTEF.

In this paper, a novel and robust Power System Stabilizer (PSS) is proposed as an effective approach to improve stability in electric power systems. The dynamic performance of proposed PSS has been thoroughly compared with Conventional PSS (CPSS). Both the Real Coded Genetic Algorithm (RCGA) and Particle Swarm Optimization (PSO) techniques are applied to optimum tune the parameter of both the proposed PSS and CPSS in order to damp-out power system oscillations. Due to the high sufficiency of both the RCGA and PSO techniques to solve the very non-linear objective, they have been employed for solution of the optimization problem. In order to verify the dynamic performance of these devices, different conditions of disturbance are taken into account in Single Machine Infinite Bus (SMIB) power system. Moreover, to ensure the robustness of proposed PSS in damping the power system multi-mode oscillations, a Multi Machine (MM) power system under various disturbances are considered as a test system. The results of nonlinear simulation strongly suggest that the proposed PSS significantly enhances the power system dynamic stability in both of the SMIB and MM power system as compared to CPSS.

In this paper, a nonlinear excitation controller is designed for multimachine power systems in order to enhance the transient stability under different operating conditions. The two-axis models of synchronous generators in multimachine power systems along with the dynamics of the IEEE Type-II excitation systems are considered to design the proposed controller. The partial feedback linearization scheme is used to simplify the multimachine power system as it allows decoupling a multimachine power system based on the excitation control inputs of synchronous generators. A receding horizon-based continuous-time model predictive control scheme is used for partially linearized power systems to obtain linear control inputs. Finally, the nonlinear control laws, which also include receding horizon-based control inputs, are implemented on the IEEE 10-machine, 39-bus New England power system. The superiority of the proposed scheme is evaluated by providing comparisons with a similar existing nonlinear excitation controller, where the control input for the feedback linearized model is obtained using the linear quadratic regulator (LQR) approach. The simulation results demonstrate that the proposed scheme performs better as compared to the LQR-based partial feedback linearizing excitation controller in terms of enhancing the stability margin.