Load Frequency Control in Single Area System
Using Model Predictive Control and Linear
Quadratic Gaussian Techniques
Abstract—This paper proposes a design and simulation of
Linear Quadratic Gaussian method (LQG) and model
predictive controller (MPC) for load frequency control in
single area power system to improve system performance.
The proposed controller has been designed such that the
effect of the uncertainty due to governor and turbine
parameters variation and load disturbance is reduced. To
account for the modeling uncertainties, the proposed
controller estimates the system interface variables and uses
these estimates and optimizes a given performance index
and allocate generating unit output. Digital simulations for a
single control area are provided to validate the effectiveness
of the proposed scheme. The performance of the proposed
controller is compared with (MPC) controller. The results
show that with proposed (MPC+LQG) technique the system
performance has good robustness in face of uncertainties
due to governor and turbine parameter variation and load
disturbance and carried out the superiority of the proposed
(MPC+LQG) technique.
Index Terms—linear quadratic Gaussian, load frequency
control, model predictive controller, Kalman estimator
I. INTRODUCTION
Load frequency controller (LFC) is very important
issue in power system operation and control for sufficient
and reliable electric power. LFC acts as a balance
between generated power and the power demanded while
keeping the net interchanged tie-line power within the
standard acceptable limit. Considerable efforts have been
made to design LFC controllers with better performance
to cope with system parameter changes using various
methodologies.
Various control strategies have been proposed and
investigated by several researchers for LFC design of
power systems. Many classical approaches have been
used to provide supplementary control which will drag
the frequency to normal operating value within very short
time, such methods include use of proportional integral
controllers [1], [2].
Manuscript received May 5, 2015; revised August 3, 2015.
Optimal control techniques based on feedback
controllers have been proposed to achieve better
performance [3], [4]. Other approach based on adaptive
neural networks has been employed to achieve better
dynamic response [5], [6]. Robust adaptive control
schemes have been developed to deal with changes in
system parameters such as Riccati equation approach [7],
H∞-control [8], μ-synthesis approach [9], robust pole
assignment approach [10]. Fuzzy logic controllers have
been used in many reports for LFC design in a two area
power system [11], [12]. The MPC controller appears to
be an efficient strategy to control many applications in
industry [13], [14]. In [15] fast response and robustness
against parameter uncertainties and load changes can be
obtained using MPC controller. Despite the fact that
controller succeeded in its target, but the door is still
opening to more techniques to improve the system
frequency in face of system power fluctuation and load
disturbance. This paper proposes a new controller for
LFC in a single area power system. The proposed control
technique produces its optimal output derived from a
quadratic cost function minimization based on the
dynamic model of the single area power system.
The technique estimates the optimal control signal
while respecting the given constrains over the output
frequency deviation and the load change.
The effects of the physical constraints such as
generation rate constraint (GRC) and speed governor
dead band are considered [16]. The power system with
the proposed (MPC+LQG) technique has been tested
through the effect of uncertainties due to governor and
turbine parameters variation and load disturbance using
computer simulation. A comparison has been made
between the (MPC+LQG) and the (MPC) controller
confirming the superiority of the proposed (MPC+LQG)
technique.
This paper is organized as follows Section 2 describes
the system dynamics and implementation scheme of
single area power system with MPC technique. Section 3
describes the general consideration about LQG technique.
Section 4 describes the implementation scheme of single
International Journal of Electrical Energy, Vol. 3, No. 3, September 2015
©2015 International Journal of Electrical Energy 141doi: 10.18178/ijoee.3.3.141-144
Tarek Hassan Mohamed, Gaber Shabib, Esam H. Abdelhameed, and Mohamed KhamiesFaculty of Energy Engineering, Aswan, Egypt
Email: {tarekhie, gabershabib, mohamedahmedmak}@yahoo.com
Yaser QudaihKyushu Institute of Technology, Japan
Email: [email protected]
area power system with proposed (MPC+LQG) controller.
Simulation results and general remarks are presented in
Section 5. Finally, the paper conclusion is in Section 6.
II. SYSTEM DYNAMICS
In this section, a simplified frequency response model
for a single area power system with an aggregated
generator unit is described in [16].
The overall generator-load dynamic relationship
between the supply error (∆Pd − ∆Pl) and the frequency
deviation (∆f) can be expressed as:
s∆f = (1
M)∆Pd – (
1
M)∆Pl − (
D
M) ∆f (1)
The dynamic of the turbine can be expressed as:
s∆Pd = (1
Tt) . ∆PG − (
1
Tt) . ∆Pd (2)
The dynamic of the governor can be expressed as:
s∆PG = (1
Tg) . ∆Pc − (
1
R.Tg) ∆f − (
1
Tg) . ∆PG (3)
Equations (1), (2), (3) can be combined in following
state space model:
[s∆fs∆Pd
s∆PG
] =
[ −
D
M
1
M0
0 −1
Tt
1
Tt
−1
R.Tg0 −
1
Tg]
[∆f∆Pd
∆PG
] + [
0 −1
M
0 01
Tg0
] [∆Pc
∆Pl]
(4)
y = [1 0 0] [∆f∆Pd
∆PG
] (5)
where:
S: differential operator.
Δ𝑃𝑔: the governor output change.
Δ𝑃𝑚: the mechanical power change.
Δf: the frequency deviation.
Δ𝑃l: the load change.
Δ𝑃𝑐: supplementary control action.
y: the system output.
H: equivalent inertia constant.
D: equivalent damping coefficient.
R: speed droop characteristic.
Tg and Tt: are governor and turbine time constants.
The block diagram of the past equation is shown in Fig.
1.
Figure 1. The block diagram of uncontrolled single area.
Fig. 2 shows the block diagram of simplified
frequency response model for single area power system
with aggregated unit including the proposed MPC
controller.
Figure 2. The block diagram of single area power system including proposed MPC controller.
III. LINEAR QUADRATIC GAUSSIAN
Load frequency control for a single area power system
has been developed based on both of MPC and LQG
techniques. The name LQG arises from the use of a linear
model, an integral cost function, and Gaussian white
noise processes to model disturbance and noise signals.
The LQG controller consists of an optimal state
feedback gain “k” and the Kalman estimator.
The optimal feedback gain is calculated such that the
feedback controls law u = -kx minimizes the performance
index:
H = ∫ (XTQX + uTRu)dt∞
0 (6)
where Q and R are positive definite or semi definite
Hermitical or real symmetric matrices [17].
The optimal state feedback u = -kx could not be
implemented without full state measurement. In our case, the states are chosen to be the frequency
deviation ∆f , mechanical power change ∆Pmi , the
governor output change ∆Pgi, and the area tie-line power
change ∆Ptie,i. The frequency deviation ∆f, the area tie-
line power change ∆Ptie,i and the supplementary control
action ∆Pci are chosen to be the only measured signals
which are fed to the Kalman estimator. The Kalman filter
estimator is used to drive the state estimation:
x̂i = [∆f̂i ∆p̂mi ∆p̂gi ∆p̂tie,i ] (7)
Such that u = -kx remains optimal for the output
feedback problem.
The state estimation is generated from:
(x̂̇) = (A − Bk − LC)x̂ + Ly (8)
where L is the Kalman gain which is determined by
knowing the system noise and measurement covariance
Qn and Rn.
However, the accuracy of the filter’s performance
depends heavily upon the accuracy of this covariance. On
the other hand the matrices A and B containing the
machine parameters are not required to be very accurate
due to the inherent feedback nature of the system.
Fortunately, the Kalman filter performs best for linear
systems. The optimal state feedback gains and the
Kalman state space model have been calculated off-line
which results in great saving in computational burden.
Fig. 3 shows the block diagram of kalman estimator.
International Journal of Electrical Energy, Vol. 3, No. 3, September 2015
©2015 International Journal of Electrical Energy 142
Figure 3. The block diagram of kalman estimator.
IV. SYSTEM CONFIGURATION
The block diagram of a simplified frequency response
model for single area power system with aggregated unit
including the proposed (MPC+LQG) controller is shown
in Fig. 4.
Figure 4. The block diagram of single area power system including the proposed (MPC+LQG) controller.
V. RESULTS AND DISCUSSION
Computer simulations have been carried out in order to
validate the effectiveness of the proposed scheme. The
Matlab/Simulink software package has been used for this
purpose. A practical single area power system having the
following nominal parameters [1] listed in Table I. The
simulation studies are carried out for the proposed
controller with generation rate constraint (GRC) of 10%
Pu. per minute. The maximum value of dead band for
governor is specified as 0.05%. The parameters of the
controller are set as follows:
Prediction horizon = 10,
Control horizon = 2,
Weights on manipulated variables = 0.8,
Weights on manipulated variable rates = 0.1,
Weights on the output signals = 0.1,
Sampling interval = 0.0003 sec.
For LQG: k = [0.1161 0.4801 0.0574],
Q=[15.8 0 00 0.000233 00 0 . 00005
], r = [150].
The system performance with the proposed
(MPC+LQG) controller at nominal parameter is tested
and compared with the system performance with MPC
controller.
TABLE I. PARAMETERS AND DATA OF PRACTICAL SINGLE AREA
POWER SYSTEM
D(PU/HZ) H(PU S) R(HZ/PU) Tg(S) Tt(S)
0.015 0.08335 3.00 0.08 0.4
A. First Case
The system is tested with load change (the ΔPL
assumed to be 0.02 Pu at t = 3 sec). Fig. 5 shows the
simulation results in this case. The results are the
governor valve position ΔPm of both proposed
(MPC+LQG) controller and MPC controller, the
frequency deviations and the governor’s controlled input
signals of both two systems following a step load change.
It has been noticed that with the proposed (MPC+LQG)
controller the system is more stable and fast comparing
with the system with MPC controller.
B. Second Case
The robustness of the proposed (MPC+LQG)
controller against parameter uncertainty is validated.
Both the governor and turbine time constants are
increased to Tg = 0.12 sec and Tt= 0.975 sec respectively.
Fig. 6 shows the simulation result of this case, it has
been indicated that a desirable performance response has
been achieved using (MPC+LQG) controller.
Figure 5.
Power system response of first case: (a) the governor valve position (b) the frequency deviation (c) supplementary control action.
International Journal of Electrical Energy, Vol. 3, No. 3, September 2015
©2015 International Journal of Electrical Energy 143
Figure 6.
Power system response of second case: (a) the governor valve position (b) the frequency deviation (c) supplementary control action.
VI. CONCLUSION
This paper investigates robust load frequency control
of a single area power system based on the (MPC+LQG)
control technique. Digital simulations have been carried
out in order to validate the effectiveness of the proposed
scheme. Simulation results show that the fast response,
robustness against parameter uncertainties and load
changes can be considered as some advantages of the
proposed (MPC+LQG) controller. In addition, a
performance comparison between the proposed controller
and a MPC control scheme is carried out. It is shown that
the (MPC+LQG) controller response is much better than
that of MPC controller response and able to deal with
both of parameter uncertainty and load changes more
efficiently.
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[16] H. Bevrani, Robust Power System Control, New York: Springer, 2009, pp. 15-61.
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T. H. Mohamed was born in Libia in 1975.
He received his B.Sc. degree in Automatic
control from Minofia University, Egypt in 1997, and his M.Sc. and PhD from Minia
University, Egypt, in 2006 and 2012
respectively. He is now a lecturer at the Faculty of Energy Engineering, Aswan
University, Egypt. His area of interest
includes control of electrical machines, and power systems.
Yaser Soliman Qudaih Graduated from the University of Engineering and Technology,
Lahore, Pakistan in 1996 as an electrical
engineer. He Completed his M.Sc. and PhD from Kumamoto University, Japan in
Electrical Engineering. He is currently a researcher (Project Assistant Professor) at the
Department of Electrical Engineering and
Electronics, Kyushu Institute of Technology (KIT), Japan. His area of interest including
power system is renewable energy and Smart Grid Applications. He is a
member of the Institute of Electrical Engineers of Japan and IEEE.
Mohamed Ahmed Khamies was born in
Sohag in 1990. He received Bachelor degree in Electrical Engineering from Aswan
University, Egypt in 2011. He is now electric
engineer in ministry of electricity and renewable energy, Egypt. His area of interest
including power system is renewable energy
and control of electric machines and power system.
International Journal of Electrical Energy, Vol. 3, No. 3, September 2015
©2015 International Journal of Electrical Energy 144