Page 276 - Mathematical Models and Algorithms for Power System Optimization

268 Chapter 7

Speed difference
adjustment rate

Steam turbine
governing system Steam turbine Thermal generator

Power grid

Hydro Turbine Hydro turbine Hydro generator
governing system

Fig. 7.18
Block diagram for the two-unit system.
Using Eq. (7.120), the normal random number generator is utilized to generate the load
disturbance step function ΔP L (k), as shown in Fig. 7.19. ΔP L1 and ΔP L2 shall be calculated
based on the power grid condition. To simplify the experiment, in the model testing, let:

ΔP L1 ¼ ΔP L2 ¼ 0:5ΔP L

Fig. 7.19
The given load disturbance step function.

Substitute step functions ΔP L1 and ΔP L2 into Eqs. (7.38) and (7.40), solve the foregoing
differential equations using the Runge-Kutta method, and obtain the motion traces of all state
variables. These traces are treated as the real state of the system, of which part of traces are
showed in Fig. 7.20. Take Δω j as the measurement variable, which is equal to the true value
of Δω j plus the error in measurement of Gaussian distribution, with the curves shown in
Fig. 7.20. Then use the Kalman filter Eqs. (7.51)–(7.55) to calculate the estimated curves of