| Abstract |
We will consider a mathematical model that describes the transients in the electrical system, and represents the following system of nonlinear differential equations:
(dδ_i)/dt=S_i, H_i (dS_i)/dt=-D_i S_i-E_i^2 Y_ij sin〖α_ij 〗-P_i sin〖(δ_i-α_i )-∑_(j=1,j≠i)^l▒〖 P〗_ij 〗 (δ_ij-α_ij )+u_i, i=(1,l) ̅, t∈[0,T] (1)
δ_ij=δ_i-δ_j, P=E_i UY_(i,n+1),〖 P〗_ij=E_i E_j Y_(i,j)
where δ_i is angle of rotation of the rotor of i-th generator with respect to some synchronous rotational axis (the axis of rotation of constant voltage tires, it makes 50 rev / sec); S_i is sliding of the i-th generator; H_i is constant inertia of i-th machine; u_i is electromotive force i-th machine; Y_ij is mutual conductance of i-th and j-th system branches; U=const is the voltage on constant voltage tires; Y_(i,n+1) is characterizes the contact (conductivity) of i-th oscillator with constant voltage tires; D_i=const≥0 is mechanical damping, α_ij α_i,α_j are constants, taking into account the influence of active resistances in the generator stator circuits. The complexity of model (1) consists in considering analysis α_ij with the following property α_ij=α_ji. We believe that the conditions δ_ij=-δ_ji are realized. In this case, the model (1) is not conservative; so it isn’t possible to build for it the Lyapunov function in the form of the first integral. This creates an additional difficulty for its research. System (1) is traditionaly called the positional model, and it belongs to non-conservative class.
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