Page 303 - Mathematical Models and Algorithms for Power System Optimization

Local Decoupling Control Method for Transient Stability of a Power System 295

state space applied in the power system; Section 8.3.3.4 describes the dynamic relation in
observation decoupled state space; Section 8.3.3.5 gives the formulation of norm reduction
control criterion and its expression for a typical network structure; and Section 8.3.3.6 gives the
formulation of norm reduction control criterion in other observation decoupled state space.

8.3.3.1 The concept of observation decoupled reference state vector

It is known that the power angle δ 0i in an equilibrium state for the generator sets of the power
system, which is determined by its operation mode that depends on three factors: the unit power
output of system, network structure, and load. That is, a change in any factor will change the
operation mode, and δ 0i will also change accordingly. Thus, a different operation mode will
correspond to a different power angle δ 0i in the equilibrium state.
When the power system is operated in a steady-state, the input mechanical power of the
generator is in balance with the output electromagnetic power, and each generator rotor
operates at synchronous speed ω 0 . In case of fault, the power balance will be disrupted, so
generator speed ω i will increase or decrease, thus deviating from synchronous speed ω 0 .
Meanwhile, the power angle δ i will deviate from the power angle δ 0i in a prefault stable
equilibrium state as well.

As the operation mode of the system often changes prior to and after the fault, prefault δ 0i cannot
beusedasthestabilitycriterionforthepartsofthesystem.Asamatteroffact,evenifthesystemis
in a steady-state prior to the fault, its operation does not remain unchanged, so the prefault δ 0i is
not constant. The operation mode after the fault is often unknown. Even if the change of the
network structure is known after the fault, it is impossible to accurately determine the postfault
operation mode and the corresponding power angle in a postfault equilibrium state in advance
due to the correlation and interaction of generator sets among systems, as well as the stochastic
fluctuation of the load. Moreover, the power angle δ i of each generator bus is a relative quantity
with one point in the system as the coordinate reference point 0, and because the power system is
an interconnected system with complex coupling relations, the local disturbance of the system
will even shift the coordinate of the reference point. Therefore, it becomes impossible to
determine the final stability goal for the change of δ i in advance.
To sum up, the power angles in a steady-state at each part of the system after the fault cannot be
determined; thus, it is impossible to determine the final stability goal for each part of the system
in advance. So, for δ i , which keeps changing because of the power unbalance, what criterion
will be followed to reach stability? This is the most urgent problem to face and the key to
solving the problem lies in whether stability criterion for δ i can be found.

As mentioned earlier, the power equilibrium is disrupted after a system fault. Assume that at
least one generator (set to the Nth unit) maintains power balance; the rest of the power
system forms up to N 1 local systems. In addition, if δ ei is further defined as the rotational