Abstract
This paper derives the initial value calculation of a multi-machine power system with a detailed sixth-order model of synchronous generator equipped with exciter and turbine systems. The method is generalized that can be used for any model including the reduced model of synchronous generators such as two-axes, one-axis, and classical model. A Matlab-based package was developed for calculating the initial values and simulating a multi-machine power system. The test system used in the study is IEEE 16-machine 68-bus system.
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Abbreviations
- \( R_{\text{s}} \) :
-
Stator resistance in pu
- \( X_{d} \) :
-
d-axis reactance in pu
- \( X_{d}^{{\prime }} \) :
-
Transient d-axis reactance in pu
- \( X_{d}^{{\prime \prime }} \) :
-
Sub-transient d-axis reactance in pu
- \( X_{q} \) :
-
q-axis reactance in pu
- \( X_{q}^{{\prime }} \) :
-
Transient q-axis reactance in pu
- \( X_{q}^{{\prime \prime }} \) :
-
Sub-transient q-axis reactance in pu
- \( H \) :
-
Shaft inertia constant in second
- \( w_{s} \) :
-
Generator synchronous speed in rad per second
- \( T_{do}^{\prime } \) :
-
d-axis time constant associated with \( E_{q}^{{\prime }} \) in second
- \( T_{do}^{\prime \prime } \) :
-
d-axis time constant associated with \( \varPsi_{1d} \) in second
- \( T_{qo}^{\prime } \) :
-
q-axis time constant associated with \( E_{d}^{{\prime }} \) in second
- \( T_{qo}^{\prime \prime } \) :
-
q-axis time constant associated with \( \varPsi_{2q} \) in second
- \( T_{A} \) :
-
Amplifier time constant in second
- \( T_{\text{CH}} \) :
-
Incremental steam chest time constant in second
- \( T_{\text{SV}} \) :
-
Steam valve time constant in second
- \( K_{A} \) :
-
Amplifier gain
- \( {\text{K}}_{E} \) :
-
Separate or self-excited constant
- \( E_{q}^{{\prime }} \) :
-
q-axis transient internal voltages in pu
- \( E_{d}^{{\prime }} \) :
-
d-axis transient internal voltages in pu
- \( E \) :
-
Internal voltage in pu
- \( \varPsi_{1d} \) :
-
Damper-winding 1d flux linkages in pu
- \( \varPsi_{2q} \) :
-
Damper-winding 2q flux linkages in pu
- \( \delta \) :
-
Rotor angle in rad
- \( w \) :
-
Angular speed of generator in rad per second
- \( \bar{V}_{i} \) :
-
Complex voltage phasor
- \( V \) :
-
Magnitude of bus voltage in pu
- \( \theta \) :
-
Angle of bus voltage in rad
- \( \bar{I}_{Gi} \) :
-
Generator complex current phasor
- \( I_{Gi} \) :
-
Generator current magnitude in pu
- \( \gamma_{i} \) :
-
Generator current angle in rad
- \( I_{d} \) :
-
d-axis current in pu
- \( I_{q} \) :
-
q-axis current in pu
- \( \alpha_{ik} \) :
-
Angle of admittance \( Y_{ik} \) in rad
- \( E_{fd} \) :
-
Field voltage in pu
- \( V_{R} \) :
-
Exciter input in pu
- \( R_{\text{F}} \) :
-
Rate feedback in pu
- \( T_{M} \) :
-
Mechanical input torque in pu
- \( P_{\text{SV}} \) :
-
Steam valve position in pu
- \( P_{\text{C}} \) :
-
Control power input in pu
- \( R_{\text{D}} \) :
-
Speed regulation quantity in Hz/pu
- \( V_{\text{ref}} \) :
-
Reference voltage input in pu
- \( S_{E} \) :
-
Saturation function
- \( T_{\text{FW}} \) :
-
Frictional windage torques
References
Anderson PM, Fouad AA (2003) Power system control and stability. IEEE Press, Hoboken
Dandeno PL (1991) IEEE guide for synchronous generator modeling practices in stability analyses. In: IEEE Std 1110-1991, vol 1
Eremia M, Shahidehpour M (2003) Handbook of electrical power system dynamics. IEEE Press, Hoboken
Ilić M, Zaborszky J (2000) Dynamic and control of large electric power systems. Wiley, Hoboken
Kundur P (1994) Power system stability and control. McGraw-Hill, New York
Machowski J, Bialek JW, Bumby JR (1997) Power system dynamics and stability. Wiley, Chichester
Padiyar KR (2008) Power system dynamics stability and control. BSP, Hyderabad
Pai MA, Stankovic A (2005) Robust control in power systems. Springer, New York
Sauer P, Pai MA, Chow JH (2017) Power system dynamics and stability, 2nd edn. Wiley IEEE Press, Hoboken
Weckesser T, Jóhannsson H, Stergaard J (2013) Impact of model detail of synchronous machines on real-time transient stability assessment. In: 2013 IREP symposium bulk power system dynamics and control, Rethymno
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Abdulrahman, I., Radman, G. Initial Value Calculation of a Multi-machine Power System with a Detailed Model of Synchronous Generator. INAE Lett 3, 257–263 (2018). https://doi.org/10.1007/s41403-018-0057-9
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DOI: https://doi.org/10.1007/s41403-018-0057-9