Page 252 - Mathematical Models and Algorithms for Power System Optimization

244 Chapter 7

7.4.4 Equivalent Generator Model of the Power System

Suppose there are n generators in the system, and the equation for the K-th generator is:

(7.41)
M K Δ _ ω K + D K Δω K ¼ ΔP TK ΔP LK
Add the n equations in the system together as the following equation:
n n n n
X X X X
M K Δ _ ω K + D K Δω K ¼ ΔP TK ΔP LK (7.42)
k¼1 k¼1 k¼1 k¼1
Now, it is required to transform Eq. (7.42) into an equivalent generator equation of n generators,
which can be completed by different transformation types. The following parameters are
defined for the equivalent system:
X
M e ¼ M K ¼ Inertia constant of equivalent generator
X
M K Δω K
Δω e ¼ ¼ Relative rotation speed of equivalent generator
M e
X
D K Δω K
D e ¼ ¼ Damping coefficient of equivalent generator
Δω e
and

M e Δ _ ω e + D e Δω e ¼ ΔP Te ΔP Le (7.43)
can be obtained,

where
X X
ΔP Te ¼ ΔP TK , ΔP Le ¼ ΔP LK

Under small disturbance, some effects can be generally neglected, such as the electromagnetic
damping torque caused by the rotor damping winding and the mechanical damping caused by
the prime mover and motor rotation loss, due to the small change in the unit rotation speeds.
These effects should be considered only in the case of great changes in the rotation speed or
under circumstances where accurate calculation results are required. Hence, the damping terms
in Eq. (7.43) can be generally neglected, namely assume D e ¼0.

Taking into account the static effect of the system load ΔP Le as follows:

ΔP Le ¼ DΔω e + ΔP L

That is, ΔP Le is the sum of static load response DΔω e and stochastic load disturbance ΔP L
irrelevant to Δω, where D is static response coefficient of load correlated to Δω e .