In the paper the simplified criterion of a steady – state stability of electric power systems (EPS) is justified on the basis of Lyapunov functions in a quadratic form ensuring necessary and sufficient conditions of its performance. Upon that, use of the node – voltage equations allows reducing study of a steady – state stability of complex EPS to study of the generator – bus system. The obtained results facilitate studies of a steady – state stability of the complex systems and have the practical importance.
[1]
Allaev K. R., Power Plants, Networks and Systems Faculty, Tashkent State Technical University, Tashkent, Republic of Uzbekistan.
[2]
Mirzabaev A. M., PV Solar Plants Faculty, International Solar Energy Institute, Tashkent, Republic of Uzbekistan.
[3]
Makhmudov T. F., Power Plants, Networks and Systems Faculty, Tashkent State Technical University, Tashkent, Republic of Uzbekistan.
[4]
Makhkamov T. A., Power Plants, Networks and Systems Faculty, Tashkent State Technical University, Tashkent, Republic of Uzbekistan.
Steady – State Stability, Matrix Method, Lyapunov Function, Node – Voltage Equations
[1]
A.M. Lyapunov, “The general problem of the stability of motion” in collections of “Selected works of A.M. Lyapunov”, Moscow – Leningrad, Academy of Sciences of USSR, 1948.
[2]
A. Bacciotti, L. Rosier, “Lyapunov Functions and Stability in Control Theory”, 2nd edition, Springer–Verlag Berlin, Heidelberg, 2005.
[3]
V.A. Venikov, “Electromechanical transient phenomena in electrical power system”, Higher School, Moscow, 1984.
[4]
E.A. Barbashin, “Lyapunov function”, Science, Moscow, 1970.
[5]
P.M. Anderson, Fouad A.A., “Power system control and stability”, 2nd Edition, IEEE, Wiley–interscience, USA, 2003.
[6]
M.Sh. Misrikhanov, V.N. Ryabchenko, “Quadratic problems of eigenvalue in EPS”, A&T, No. 5, 2006, pp. 24 – 47.
[7]
Y.N. Andreev, “Finite – dimensional linear object control”, Science, Moscow, 1976.
[8]
O.S. Aladishev “Super Computers: field of application and performance requirements”, Electronics, No. 1, Moscow, 2004.
[9]
K.R. Allaev, A.M. Mirzabaev, “Small fluctuations of electrical power system. Matrix approach”, Science and Technologies, Academy of Sciences Republic of Uzbekistan, Tashkent, 2011.
[10]
P.C. Parks, “A new proof of the Routh – Hurwitz stability criterion using the second method of Lyapunov”. Proc. Camb. Phil. Soc. Math. Phys. Sci., Vol 58, 1962, pp.694 – 702.
[11]
R.E. Kalman, “On the Hermite – Fujiwara Theorems in stability theory”, Quart. Appl. Math, Vol. 23, 1695, pp.
[12]
R.E. Kalman, I.E. Bertram, “Control System Analysis and Design Via the «Second Method» of Lyapunov. 1. Continuous – Time Systems”. Trans. ASME J. Basic Engr., 1960, pp.371–393.
[13]
Y.N. Adreenv, “Algebraic state – space methods in linear objects control theory”, A&T, No. 3, Moscow, pp. 5 – 50.
[14]
Hl. M. Power, “The companion matrix and Lyapunov Functions for linear multivariable time–invariant system”, J. Franklin Inst., Vol. 283, 1967, pp. 214 – 234.
[15]
K.R. Allaev, “Lyapunov function in a quadratic form as the tool for study of steady–state stability in EPS” Science and Technologies, No. 5, Tashkent, 1984, pp. 13 – 17.
[16]
S.A. Sovalov, “Operating conditions of Unified Energy System”, Energoatomizdat, Moscow, 1983.
