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: yaser_qudaih@yahoo.com

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.

REFERENCES

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International Conference on Control, Mar. 1994, pp. 409-415.

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[16] H. Bevrani, Robust Power System Control, New York: Springer, 2009, pp. 15-61.

[17] A. A. Hassan, Y. S. Mohamed, and T. H. Mohamed, “Robust control of a field oriented linear induction motor drive,” in Proc. 11th International Middle East Power Systems Conference, Cairo

University, Egypt, Dec. 19-21, 2010.

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