Page 327 - Decision Making Applications in Modern Power Systems

288 Decision Making Applications in Modern Power Systems

However, it is not easy to keep the power flow as the scheduled one.
Therefore the actual power flow between two areas is measured as follows:

ΔP act 5 2πT ij ð11:21Þ
tie;ij Δf i 2 Δf j
s
The difference between the actual and scheduled power flow between
two areas determines the error in the transferred power as follows:
ΔP err 5 ΔP act 2 ΔP sch ð11:22Þ
tie;ij tie;ij tie;ij
In LFC studies, it is critical to determine the area control error of area i
(ACE i ), which is very useful in generating LFC signal. The area control error
can be determined as follows:
err
ACE i 5 β Δf i 1 ΔP ð11:23Þ
i tie;i
n
X err
err
ΔP tie;i 5 ΔP tie;ij ð11:24Þ
j51& j¼i
6
11.5.2.2 Design of load-frequency controller based on the
fractional calculus
AGC or LFC are in use in modern power system for removing or at least
mitigating both frequency and tie-line power deviations. To this end, differ-
ent types of PID controllers are utilized for controlling the frequency and tie-
line power flow in such systems. Due to its superiority, the FOPID has been
also adopted to regulate the frequency and tie-line power exchange devia-
tions [25].
In this new controllers, that is, FOPID, apart from proportional (K p ), inte-
gral (K i ), and derivative (K d ) constants, they have additional integral order
(λ) and the derivative order (μ); thus they have two further operators which
add two more DOFs to the controller and make FOPID controller has better
performance compared to the traditional PID controllers [25]. The LFC sig-
nal, u c;i , used in each control area based on the FOPID is determined as
follows:

μ
u c;i 5 k p;i 1 k D;i s 1 K I;i ACE i ð11:25Þ
s λ
It should be noted that the further two variables, that is, λ and μ, provide
much more accuracy and flexibility in designing the LFC controllers. Now,
as a next step in the procedure, the controller variables should be optimally
tuned. In the next discussion, we will show how these important variables
can be tuned using evolutionary computing methods [25].