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  • Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 2 (3): 456-461 (ISSN: 2141-7016)


    Coherent generator based Transient Stability Analysis of the 16 machines,

    330KV �igeria Power System

    Izuegbunam F. I., Okafor E. �. C., Ogbogu S. O. E.

    Department of Electrical and Electronic Engineering Federal University of Technology, P.M.B. 1526, Owerri, Nigeria

    Corresponding Author: Izuegbunam F. I

    ___________________________________________________________________________ Abstract

    This paper assesses the transient stability analysis of the expanded 16 machines, 330KV �igeria Grid System

    through coherent generators aggregation based on equal acceleration and velocity concept. The technique

    involves performing the electrical proximity test on the system generators under fault condition to select the

    study area generators, subjecting these generators to coherency check through inertia and damping indices

    conditions; and construction of dynamic equivalents representing each pair of coherent generators. The result

    led to reduction of 16 machines system to 13, thereby simplifying the network complexity and requires minimal

    computer time as well as memory space.

    __________________________________________________________________________________________ Keywords: transient stability, coherent generators, dynamic equivalents, expanded grid, swing curve. __________________________________________________________________________________________ I�TRODUCTIO�

    The large interconnections that constitute the present day power networks has further added to its complexity hence requiring a simplified but accurate method of transient stability analysis with minimal computing time and memory space. The method of transient stability analysis of a large power system via simplified dynamic equivalents is attracting increased attention by researchers across the globe (Rau and Hussian, 1998). The coherent generator technique is an elegant and powerful tool for system simplification through construction of simplified reduced order dynamic models which can represent the entire system without loss of system significant characteristic. The reduction is based on the impact of large disturbances in a particular area known as the study system, while system external to study area are not of direct interest in stability analysis; and are thus represented by dynamic equivalents in recognition of its influence on the response of the study area to disturbances. Available literature shows that different authors applied variant principles of determining coherent generators. Lee and Schweppe, (Lee and Schweppe, 1993), used the concepts of distance measure such as admittance distance, reflection distance and acceleration distance to identify coherent generators for construction of dynamic equivalents. Also the concept of power variation of the generators at the instant of initiated fault is applied to classify the machines into inner circle (study area) machines and outer circle (external area) machines. Spalding, Yee, and Goudie, (Spalding et al., 1977), applied the principle of singular points in coherency identification. The singular points include the post-fault Stable Equilibrium Point (SEP) and Unstable Equilibrium Point (UEP). This approach

    compares system’s differential equations describing change in relative machine angles from the stable equilibrium point to that of unstable equilibrium point corresponding to the system instability anticipated from the fault condition under investigation. Podmore, (1978), applied a simplified linear model of power system known as clustering Algorithm using linearized network and dynamic equations deemed clustered to determine the angular deviation of the machines. Al-Fuhaid, (1987), deployed the properties of exponential matrix and Cayley-Hamilton theorem using the state transition matrix to determine the linearized system dynamic equations. Rudmick, Patino, and Brameller, (1981), applied the principle based on rate of change of kinetic energy, relating the power system behaviour to its potential energy and kinetic energy transition. Krishnaparandhama et al., (1981), and Sankaranarayanan et al., (1983), applied coherent generators identification based on equal acceleration principle using a linearized acceleration equation with the damping coefficient neglected. In this paper, the coherent generator based transient stability analysis of the 16 machines expanded Nigeria power system was conducted through the following steps: electrical proximity test, coherent generator identification, construction of dynamic equivalents of coherent generator pairs, and re- integration of the aggregated generators with the rest of system machines. The purpose is to assess the transient stability condition of the expanded Nigerian 330KV Grid system using a technique that reduces the model order of the Network without altering the characteristic structure and it is justified because

    Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 2 (3): 456-461 © Scholarlink Research Institute Journals, 2011 (ISSN: 2141-7016)

  • Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 2 (3): 456-461 (ISSN: 2141-7016)


    most of the generating plants and transmission lines in this grid are still under construction, but its response to large disturbance has been simulated. A practical power network has been used to test the effectiveness of the coherent generator technique.

    Multimachine Power System Modeling

    Figure 2.1 represents a large power network Figure 2.1 Large power network The rotor dynamic equation for ith machine of an n- generator system is given by,

    (2.1) For ith and j

    th generators to be coherent,

    (2.2) where,

    Pre-fault value of the difference between the ith and jth rotor angles. Linearizing equation (2.1) on the assumption that the power variation is small and that the generator coherency is independent of the magnitude of the disturbance (Podmore, 1978), gives,

    (2.3) Where,

    = the change in acceleration of the ith machine

    = change in the velocity of the ith machine The mechanical power input to the machine is assumed constant for a short duration of the fault, hence the term in equation (2.3) becomes zero. The change in electrical power of the ith generator due to a small change in the angle of the jth generator evaluated at the time of initiating the fault (Lee and Schweppe, 1993), gives,




    The following assumptions are made: 1. Internal voltages of the machines are equal

    to 1.0 pu 2. The angular difference is within


    3. The network is highly reactive, while the conductances are not neglected. The above assumption simplifies equation (2.6) to,


    Substituting equation (2.7) into (2.3) gives, (2.8)

    Let , and (2.9)

    Putting (2.9) into (2.8) gives,


    Electrical proximity for any two machines depends upon their mutual admittance (Sankaranarayanan et al., 1983). As the mutual admittance between two machines becomes larger, that pair of machines is considered more close to each other (Rau and Hussian, 1998). Therefore, the mutual admittance between a pair of machines is a measure of coupling between them (Rau and Hussian, 1998), (Monticelli, 1999).

    Electrical Proximity index

    Electrical proximity index αįj is defined by the expression,


    The generators that satisfy equation (2.11) qualifies for coherency pair check with the ith machine. The modified linearized acceleration equation for ith and jth machines can be written as,



    For equal acceleration of the ith and jth machines, equations (2.14) and (2.15) must be satisfied.

    (2.14) Where,


    From the equations (2.14) and (2.15) the two vital indices β and γ for coherency check are obtained as :


    (2.17) where, = Inertia index for ith and jth machines

    = Damping index for ith and jth machines

    X΄d1 E ΄ 1

    X΄dn E ΄ n




    X΄d2 E

    ΄ 2

    X΄d3 E

    ΄ 3

    X΄d4 E

    1 4

    Fictitious Point

  • Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 2 (3): 456-461 (ISSN: 2141-7016)


    In a situation where machines i and j are absolutely coherent, both β and γ becomes equal to zero. But when one of the inertias tends to infinity, then both β and γ will tend to unity (1.0), which indicates the machines deviation from each other. The tolerance values of 0.2 for β and 0.5 for γ are found to give acceptable results (Rau and Hussian, 1998). In a situation whereby the damping coefficient is zero or the ratio D/M becomes uniform, the coherency grouping is conducted based on β criterion alone.

    Construction of Dynamic Equivalents

    The concept of dynamic equivalent construction


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