Investigation of the structure of dynamic stabilization problems of power pool

1. Investigation of the structure of dynamic stabilization problems of power pool N. N. Lizalek, A. N. Ladnova, M. V. Danilov Institute of Power System Automation Siberian Branch of JSC R&D Center for Power Engineering

2. Introduction • In this article the prerequisites of the structural analysis power systems stability are considered as a result of grand disturbance. On an example of short circuits the approach to structural investigations of the stability, founded on the analysis of oscillatory structures of system and an estimation of their limit excitation up to stability is stated. • A complete stability analysis of an electric power system necessitates answering not only the question "Will there be a violation of stability at this or that disturbance?", but also the question: "Along which section will be a loss of stability and how the spatial position of this section depends on the disturbance?" • Structural researches of an electrical power system stability we will base on the analysis of electromechanical transient oscillatory structure. Basic introduced concepts: • An oscillatory / wave structure; • An oscillatory degrees of freedom for a power system; • A structured motion ; • A potential and an actual trajectories. • We will relate the processes leading to the loss of stability with some stability-ultimate (critical) disturbance of at least one of the oscillatory degrees of freedom. As a quantitative characteristics of the ultimate excitation intensity, we can use, for instance, the stability-ultimate oscillation energy of this oscillatory degree of freedom under some disturbing action.

3. Basic concepts • A wave structure – this is the constant oscillatory structure of a certain free ocsillatory motion in the linearized system with the "switched off" damping • Structural model of system (structure of system) – is the partition of system into the subsystems and their uniting intersystem links. A quantity of subsystems, entering the structure, gives its dimensionality R (S). • The motion of system, described as a hierarchical system of relative processes, we will call structural organized on S. • We can apply the notion of oscillatory degrees of freedom to the development of algorithms for evaluating the stability conditions for power systems based on the consideration of power system motion in structured forms. • An oscillatory structure – it is the form of the idea of wave motion. It describes such partition of system into the subsystems, in which in every two adjacent of them (at the given instant) the displacement of all vectors emf of synchronous machines relative to the coordinate of the center of inertia of system has opposite directions. • An oscillatory degrees of freedom for a power system – is a the structural mapping of laws governing the free oscillatory motions in the power system. • A potential trajectory – is a trajectory on which are carried out the equations of balance and the law of momentum conservation.

4. Examples of the oscillatory structures The chained structure 0.2-0.5 Hz 0.5-1.1 Hz More than 1.1 Hz • In the region of low frequencies the oscillatory structures have the chained structure (0.2 - 0.5 Hz). On the measure increases in the frequency of the vibrations (0.5 - 1.1 Hz - more than 1.1 Hz) of structure are re-formed and acquire the branched out chained structures, are formed rings and star-shaped structures. • For the fluctuations with frequencies of about 1 Hz a quantity of subsystems in maximally developed directions of wave structures does not exceed 12 - 15. 1 2 3 4 5 The branched out chained structure 3 4 6 9 1 2 5 7 8 4 1 The star-shaped structure 2 3 6 5

5. Estimation of the critical on the stability excitation of oscillatory degrees of freedom for a power system. Estimation of the time of propagation of the traveling waves in the EES of Russia As a quantitative characteristics of the ultimate excitation intensity, we can use, for instance, the stability-ultimate oscillation energy of this oscillatory degree of freedom under some disturbing action. The nature of the developing instability in this case will be determined by the comparative rates of the processes of the racing of the objects of oscillatory degrees of freedom for a power system to the maximum on the stability deviations from the position of equilibrium. Calculations of stable transients in the UES of Russia spent on nonlinear model with "switched off" damping for the purpose of definition of running wave passage time for various frequencies, yield rather close results to the received estimations. It confirms the made assumption of possibility of revealing of directions and an estimation of speeds of wave propagation not only "small", but also nonlinear waves on the basis of wave structures for "small" standing waves.

6. Equations of relative motions We represent the speed of rotation of the j-th synchronous machine as the sum of a time independent component (speed of rotation in the initial regime) and three relative processes: гj(t)= 0+гjs(t)+ s0(t)+ 0(t), (1) here, 0(t)= 0(t)- 0; s0(t)= s0(t)- 0(t); гjs(t)= гj(t)- s0(t); Irrespective of the manner used to divide the whole system into subsystems, there hold the following equalities (momentum conservation law): (2) here,- is the total moment of inertia of the i-th subsystem.

7. Equations of relative motions The angular-velocity components satisfy the following equations of relative motion: (3) The components of the incremental kinetic energies are due to the works done over incremental displacements : (4)

8. Estimation of maximum impulse disturbances for the objects of one oscillatory degree of freedom The response of the system at equilibrium to an impact (pulsed) disturbance acting on the system during a short time interval t : Provided that the energy of the object at the time t0is equal to, or greater than, the estimated margin in terms of deceleration work, it can be expected that the stability will be violated under an angular displacement equal to the critical one in a time interval: (5) Here, is the critical energy of the object at the time t0, and is the deceleration work for the object as a function of its deflection from the position at time t0.

9. The “Area method”

10. The identification algorithm for instability structures of a power system at finite-duration shunt faults The calculated data for several oscillatory degrees of freedom can be conveniently represented as an energy-time diagram

11. The energy-time diagram

12. The energy-time diagram

13. Conclusions

14. Conclusions