Page 237 - Mathematical Models and Algorithms for Power System Optimization

Optimization Method for Load Frequency Feed Forward Control 229

The load disturbance ΔP L is defined as follows:
ΔP L ¼ planned generation output actual generation output:

ΔP L per minute record can be obtained from the actual operation records of the power system,
from which the mathematical model can be developed. Because the order of such mathematical
model is unknown, the model identification method must be adopted to determine the order.
The current model identification methods are numerous, such as least square method, auxiliary
variable method, time series analysis method, etc., among which the time series analysis
method is widely applied in the actual engineering problem, in which the order of mathematical
model is easily characterized by the correlation function and partial autocorrelation function.
This chapter also employs such a method to develop the mathematical model of load
disturbance ΔP L . The following shows the main contents of such a method.

7.3.1 Brief Descriptions of Time Series and Stochastic Process

7.3.1.1 Time series analysis

Measuring a variable or a set of variables X(t) in the actual process, at time t 1 <t 2 <, …,<t n ,a
set of ordinal numbers with time t as a parameter is obtained:
ðÞ, ðÞ,…,Xt n
Xt 1 Xt 2 ðÞ (7.1)
Generally, it is called a time series. Here, parameter t is called time, and in practice, t may refer
to different physical meanings, and the time series are one- or multidimensional.

Measuring once a minute in the power system, some sequential number sets with independent
variablesoftcanbeobtained,constitutingthesampletimeseriesofΔP L (t).ThetimeseriesX(t)is
called definite if its value is given by a completely definite mathematical function, for instance:

XtðÞ ¼ a + bcosωt (7.2)

where a, b, and ω are the given constant values, and thus the time series are determined.
However, in practice, the time series are complicated. Generally speaking, X(t) cannot, like
Eq. (7.2), be given by a completely definite mathematical function but may be described by a
stochastic function with a certain probability distribution, as does ΔP L (t). Such time series are
called random, and the stochastic time series can simply be referred to as a time series.
The so-called analysis and forecasting of a time series, mathematically, is regarding measured
data Eq. (7.1) as a sample function of stochastic process X(t). Based on an analysis of Eq. (7.1),
by estimating the general characteristics of stochastic process X(t), the probability distribution
of future values of X(t) is estimated, thereby giving the predicted value of X(t) when t>t n :

∗
∗
X ∗ N +1 ,X N +2 ,…,X N + L