PI-MPC Frequency Control of Power System in the Presence of DFIG Wind Turbines

doi:10.4236/eng.2013.59B008

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Engineering, 2013, 5, 43-50

http://dx.doi.org/10.4236/eng.2013.59B008 Published Online September 2013 (http://www.scirp.org/journal/eng)

PI-MPC Frequency Con trol of Power System in th e

Presence of DFIG Win d Turbines

Michael Z. Bernard 1, T. H. Mohamed2, Raheel Ali1, Yasunori Mitani1, Yaser Soliman Qudaih1

1Department of Electrical Engineering and Electronics, Kyushu Institute of Technology, Fukuoka, Japan

2Faculty of Energy Eng., Aswan University, Aswan, Egypt

Email: mzbe rna [email protected], [email protected], raheel.ali@hotmail.co.jp,

[email protected], [email protected]

Received July 2013

Abstract

For the recent expansion of renewable energy applications, Wind Energy System (WES) is receiving much interest all

over the world. However, area load change and abnormal conditions lead to mismatches in frequency and scheduled

power interchanges between areas. These mismatches have to be corrected by the LFC system. This paper, therefore,

proposes a new robust frequency control technique involving the combination of conventional Proportional-Integral (PI)

and Model Predictive Control (MPC) controllers in the presence of wind turbines (WT) . The PI-MPC technique has

been designed such that the effect of the uncertainty due to governor and turbine parameters variation and load distur-

bance is reduced. A frequency response dynamic model of a single-area power system with an aggregated generator

unit is introduced, and physical constraints of the governors and turbines are considered. The proposed technique is

tested on the single-area power system, for enhancement of the network frequency quality. The validity of the proposed

method is evaluated by computer simulation analyses using Matlab Simulink. The results show that, with the proposed

PI-MPC combination technique, the overall closed loop system performance demonstrated robustness regardless of the

presence of uncertainties due to variations of the parameters of governors and turbines, and loads disturbances. A per-

formance comparison between the proposed control scheme, the classical PI control scheme and the MPC is carried out

confirming the superiority of the proposed technique in presence of doubly fed induction generator (DFIG) WT.

Keywords: Doubly Fed Induct ion Generat o r; Power Syste m; Model Predictive Control); Proportional Integral

Controller; DFIG Wind Turbi ne; Wind Energ y System (WES)

1. Introduction

Two balances corresponding to two equilibrium points

namely frequency and voltage must be maintained be-

tween generation and utilization in an electric power

system. This enables generation and distribution of qual-

ity electrical power to factories and homes. Breaking or

resetting either of the two balances to a new level will

constitute floating of the equilibrium points. When either

of the two balances is broken and reset at a new level, the

equilibrium points will float. A good-quality electric

power system requires both the frequency and voltage to

remain at standard values during operation.

Thus a control system is important to mitigate the ef-

fects of the random load changes and keep the frequency

and voltage at the standard values. Although active and

reactive power affects the frequency and voltage respec-

tively, the frequency is highly dependent on the active

power while the voltage is highly dependent on the reac-

tive power. Thus the control issue in power systems can

be decoupled into two independent problems. One is

about the active power and frequency control while the

other is about the reactive power and voltage control.

The active power and frequency control is referred to as

load frequency control (LFC) [1] which is the major

concern of this paper.

LFC objectives, which determine the LF C synthesis as

a multi-objective optimization problem [2,3] are con-

cerned with, frequency regulation and tracking the load

demands, maintaining the tie-line power interchanges to

specified values in the presence of modeling uncertain-

ties, system nonlinearities and area load disturbances.

Hence, Frequency control or Load frequency control is

an important function of power system operation where

the main objective is to regulate the output power of each

generator at prescribed levels while keeping the fre-

quency fl uc tuations w i thin pre-specified limits [4].

On the other hand, energy problems and environmen-

tal issues have led to, with recent expansion of renewable

energies, power systems. WES is the fastest growing and

mostly utilized of all the renewable energies and its

M. Z. BERNARD ET AL.

global produc tion is pr edicte d to gr ow to 300GW in 2015

[5]. Hence, WES connected to the power systems has

created serious interest and concern among researchers.

In several research works, for example, in [2] it was

pointed out that the renewable integration impacts are

non-zero and can become more significant at higher size

of penetrations.

Variable speed wind turbines (VSWTs) are the most

utilized type of modern WTs. They are partially or totally

decoupled from the power network due to the power

electronic converters which limits their capacity to pro-

vide primary frequ ency support to the network in case of

disturbances. The inertial response of WTs is discussed

in details as in [ 6,7]. A detailed background of frequency

responses, including primary and secondary responses

provided in [6] where detailed comparison between

fixed-speed wind turbines (FSWTs) and doubly fed in-

duction generator (DFIG) type WTs is shown through

detailed simulations, showing that FSWTs and DFIG-

based WTs can contribute to frequency response. In [7],

it is reported that full converter (FC) type WTs are com-

pletely decoupled from the power grid and no contribu-

tion is given to the frequency regulation but pointed out

that DFIG-type WTs have some small contribution to the

power network. In the work, it is assumed that the

VSWTs have negligible inertial response and that addi-

tional control loop is necessary for a proper machine in-

ertial response.

Control system designers today are applying different

control algorithms in order to find the best controller

parameters for optimum solutions. While some of these

methods are very successful for special cases but unsuc-

cessful for other general applications, many control

strategies have been proposed and investigated by several

researchers for LFC design of power systems [8-11].

Robust adaptive control schemes have been developed in

[3,12-16] to deal with changes in system parameters.

Fuzzy logic controllers have been used in many reports

for LFC design in a two area power system [17], with

and without nonlinearities. The applications of artificial

neural network, genetic algorithms, and optimal control

to LFC have been reported in [18,19]. In their findings, it

is observed that the transient response is oscillatory and it

seems that some other elegant techniques are needed to

achieve a desirable performance.

Fixed parameters controllers, such as PI controllers,

are also widely employed in the LFC application. Fixed

parameters controllers are designed at nominal operating

points and may no longer be suitable in all operating

conditions. For this reason, adaptive gain scheduling ap-

proaches have been proposed for LFC synthesis [12,13].

This method overcomes the disadvantages of the conven-

tional PI controllers, which needs adaptation of controller

parameters, but actually, it faces some difficulties, like

the instability of transient response as a result of abrupt

changes in the system parameters in addition to the im-

possibility of obtaining accurate linear time invariant

models at variable operating points [12]. In [20-23], fast

response and robustness against parameter uncertainties

and load changes can be obtained using MPC controller

for single area load frequency control application, but

without WT participation. However, in [24] a new load

frequency control (LFC) using the model predictive con-

trol (MPC) technique in the presence of wind turbines

(WT) was presented and the results demonstrated that the

closed-loop system with MPC controller is robust against

the parameter perturbation of the system and has more

desirable performance in comparison with classical

integral control design in all of the tested scenarios. Also,

it was denoted that wind turbine has a positive effect on

the total response of the system.

Though several optimal and robust control strategies

have been developed for LFC, they all required sug-

gested replacement of the traditionally integral or PI con-

troller with a new robust control scheme. But instead of

replacing the conventional controller with a robust con-

trol scheme, this paper proposes a new robust control

technique involving the combination of a conventional PI

controller and a robust controller, precisely, the MPC, to

form a single controller known as the PI-MPC technique

for power system frequency control. This technique is

more economical, so that, a single PI-MPC scheme will

produce a stronger control signal to control the entire

area rather than using multiple controllers nor removing

or replacing traditional controllers already in the system.

This works since the MPC adapts well to different phys-

ical setups and allows for a unified approach [22-24]

while PI controller can have zero steady state error

though its disadvantage has to do with maximum over-

shoot and high settling time plus inability to adapt to

different changes in system parameters [22]. The respec-

tive PI and MPC controllers may not be new but the

combination of these two control schemes to form a single

controller is completely new in power system research.

In this paper, the load frequency control for a single

area power system in the presence of WES has been de-

veloped based on the PI-MPC technique. Each local area

includes an aggregated wind turbine model (which con-

sists of 200 wind turbine units) beside the main genera-

tion unit. With the PI-MPC technique, the MPC produces

its optimal output derived from a quadratic cost function

minimization based on the dynamic model of the single

area power system which combines with the PI signal.

The technique calculates 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 [20]. The power

M. Z. BERNARD ET AL.

system with the proposed PI-MPC technique has been

tested through the effect of uncertainties due to go vernor

and turbine parameters variation and load disturbance

using computer simulation. A comparison has been made

between the proposed PI-MPC controller, the traditional

PI controller and MPC, confirming the superiority of the

proposed technique. The simulation results proved that

the proposed controller can be applied successfully to the

application of power system frequency control including

that with WT. The rest of the paper is organized as fol-

lows: General overview of MPC and its cost function are

presented in Section 2. In Section 3, the simplified wind

turbine model, the description of the dynamics of the

power system and the overall structure of the implemen-

tation scheme as a single area power system together

with the PI-MPC technique are explained. Simulation

results and general remarks are presented in Section 4.

Finally, the paper is concluded in Section 4.

2. General Overvi e wmpc

The MPC has proved an efficient control in a wide range

of applications in industry such as chemical process, pe-

trol industry, electromechanical systems and many other

applications. Figure 1 below illustrates a Simple struc-

ture of MPC controller.

The MPC scheme uses a prediction model of the sys-

tem response to obtain the control actions by minimizing

an objective function. The objective of the optimization

is to minimize the difference between the predicted and

reference response, and the control effort subjected to

prescribed constraints.

The effectiveness of MPC is equivalent to optimal

control. At each control interval, the first input in the

optimal sequence is sent into the plant, and the entire

calculation is repeated at subsequent control intervals.

The purpose of taking new measurements at each time

step is to compensate for unmeasured disturbances and

model inaccuracy, both of which cause the system output

to be different from the one predicted by the model

[14,15].

Figure 1. Simple structure of MP C.

An internal model is used to predict the future plant

outputs based on the past and current values of the inputs

and outputs and on the proposed optimal future control

actions. The prediction has two main components: the

free response which being expected behavior of the out-

put assuming zero future control actions, and the forced

response which being the additional component of the

output response due to the candidate set of future con-

trols. For a linear system, the total prediction can be cal-

culated by summing both of free and forced responses.

The reference trajectory signal is the target values the

output should attain. The optimization is subject to con-

straints on both manipulated and controlled variables

[22]. The general object is to tighten the future output

error to zero, with minimum input effort. Therefore, the

optimizer calculates the best set of future control action

by minimizing a cost function (J) which is generally a

weighted sum of square predicted errors and square fu-

ture control values, e.g. in the Generalized Predictive

Control (GPC):

( )

( )()()

( )()

123

J[/ ]

[ 1]

NNNjykjk kj

j ukj

βω

=+ −+

+ +−

∑

(1)

where N1 and N2 are the lower and upper prediction

horizons over the output, Nu is the control horizon,

( )

βj

( )

λj

are weighting factors. The control horizon

permits to decrease the number of calculated future con-

trol according to the relation:

( )

0uK j∆ +=

for u

≥ and

( )

repre-

sents the reference trajectory over the future horizon .

Constraints over the control signal, the outputs and the

control signal changing can be added to the cost function

as follows :

( )

min max

uuk u

≤≤

( )

min max

uuk u∆ ≤∆≤∆

min k max

y yy≤≤

Details of MPC are discussed in [22-24].

3. System Configuration

3.1. System Dynamics

In this section, a simplified frequency response mode l for

a single area power system with an aggregated generator

unit is described [2].

The overall generator-load dynamic relationship be-

tween the incremental mismatch power

PP∆ −∆

and

the frequency devia t ion

f∆

can be expressed as:

.222

sfPP f

HHH

 

∆=⋅∆− ⋅∆− ⋅∆

 

 

(2)

M. Z. BERNARD ET AL.

While the dynamics of the governor can be expressed

as:

m gm

sPP P

 

⋅∆=⋅∆−⋅∆

 

 

(3)

and the dynamics of the turbine can be expressed as:

1 11

gc g

g gg

sPPf P

TRT T

 

⋅∆=⋅∆−⋅∆ −⋅∆

 

 

(6)

The block diagrams of the past equations are included

in Figure 2 where:

P∆

Change in the governor out put

P∆ Change in mechanical power

:f∆

Frequency deviation

P∆

The load change

P∆

Supplementary control action

Equivalent inertial constant

Equiva l e nt damping coefficient

Speed drop characteristics

and :

are governor and turbine time constant re-

spectively.

3.2. Simplified Wind Turbine Model for

Frequency Studies

Figu re 3 above shows a simplified model of DFIG based

wind turbine (WT) for frequency response [24]. This

simplified model can be described by the following equ-

ations:

2qr

1iV

qr qr

si T



=−⋅+⋅





(5)

Figure 2. The block diagram of a single area power system

Figure 3. Simplified model of DFIG based wind turbine [19].

.22

qr m

s iT

 

=− ⋅+⋅

 

 

(6)

3e qr

P Xi

=⋅⋅

(7)

For linearization, Equation (14) can be rewritten as:

3e optqr

P Xi

= ⋅⋅

(8)

where

opt

is the operating point of the rotational speed,

is the differential operator,

is the electromagnetic

torque,

is the mechanical power change,

is the

rotational speed, e

P is the active power of wind turbine,

is q-axis component of the rotor current,

q-axis component of the rotor voltage and

is the

equivalent inertia constant of wind turbine. Table 1

shows the detailed expressions of the main parameters

utilized for the simplified model of Figure 3.

Where:

rr ss

LL L

= +

sss m

L LL= +

rrrs m

LLL= +

is synchronous speed, m

Lis the magnetizing induc-

tance,

and

are the respective rotor and stator

resistances,

and

are the rotor and stator leakage

inductances respectively, while rr

L and ss

L are the

rotor and stator self-inductances respectively.

4. Overall System Structure

The block diagram of a simplified frequency response

model for a single area power system with aggregated

unit including the proposed PI-MPC controller is shown

in Figure 4.

The system consists of the rotating mass and load,

nonlinear turbine with GRC, and governor with dead-

band constraint [1].

The frequency deviation is used as feedback for the

closed loop control system. Initially, a PI controller in the

system receives the frequency signal ∆f , to be controlled,

and hence produces the supplementary action

. Then,

in an effort to improve system performance, the meas-

ured and reference frequency deviation

ref

f∆

(where

ref

f Hz∆=

and the reference wind rotational speed,

ref

∆

, where,

( )

ref opt

ωω

are fed to the MPC controller

in order to obtain the supplementary control action

P∆



This control action

P∆



, is then added to

Table 1. Parameters for Fi gure 3 [24].

X2 X3 T1

M. Z. BERNARD ET AL.

ΔP

. The resulting signal of the PI-MPC which is simply

the combination of the signals due to the PI and MPC

controllers respectively:

c cc

PPP∆=∆ +∆

is fed to the

governor, giving the governor valve position which sup-

plies the turbine to give the mechanical power change

P∆

. Both the active power change of wind turbine

P∆

and the load change

P∆

affect the mechanical

power change giving the input of the rotating mass and

load bloc k to provide ac tual frequency deviation

f∆

5. Results and Discussion

In order to validate the effectiveness of the proposed

scheme Computer simulations have been carried out in

the Matlab/Simulink environment. A practical single area

power system has the following nominal parameters [2]

listed below in Table 2.

Simulation studies are carried out for the proposed

controller with generation rate constraint (GRC) of 10%

p.u. per minute. The maximum value of dead band for

governor is specified as 0.05%. The parameters of the

MPC controller are set as follows:

Prediction horizon = 10, Control hor izon = 2, Weights

on manipulated variables = 0, Weights on manipulated

variable rates = 0.1, Weights on the output signals = 1

and Sampling interval = 0.0003 sec. Constraints are im-

posed over the control action, and frequency deviation.

They are considered as follows:

Max. control action = 0.25 pu, Min. control action =

0.25 pu,

Max. frequency deviation = 0.25 pu, and Min. fre-

quency de vi a tion = −0.25 pu.

The wind turbine field consists of 200 units of 2MW

rated variable speed wind turbine VSWTs, the wind tur-

bine parameters and operating point are indicated in Ta-

ble 3.

Figure 4. The block diagram of a single area power system

including the proposed P I -MPC controller

Table 2. Parameters and data of a practical single area

power system.

D (p.u/Hz) H (pu.sec) R (Hz/p.u)





(sec)



(sec)

0.015 0.08335 3.00 0.08 0.4

Table 3. Wind turbine parameter s an d op erating point [25].

Operating

point (mw) Wind

speed (m/s ) Rotational

speed (m/s )

247 11 1.17



(pu)



(pu)

X

(pu)

0.00552 0.00491 0.1

X

(pu)

X

(pu)



(pu)

0.09273 3.9654 4.5

is the magnetizing reactance wh ile lr

X and

are the leakage reactance of the rotor and stator respec-

tively.

For the simulations studies, three cases are investi-

gated. The first case is a nominal case where the power

system operates under normal operating conditions. The

second case the changed case where changes are made in

the parameters of the power system so as to carry out

robustness investigations and comparison is made be-

tween the controllers. In the third case, the effect of WT

on the power system frequency is investigated consider-

ing variable wind speed. The parameters of the PI con-

troller are K( p) = 0.37 and K(s) = −0.745.

5.1. First Case:System Performance at Nominal

Case

The system performance with the proposed PI-MPC con-

troller during WT participation at nominal parameters is

tested and comparison is made between the system per-

formances with conventional proportional integrator K(p)

= 0.37 and

( )

Ks0.745 / s= − in the presence of a step

load change

P0.02 p.u.∆=

t30 sec.=

Figure 5

shows the simulation results of the proposed PI-MPC,

MPC and only conven tional PI sys tems. The resu lts from

the top to the bottom are: the mechanical power change,

P∆

, in per unit, the frequency deviations,

f∆

, in Hertz

and the governor’s controlled input signals,

P∆

, in per

unit. It can be seen that after a step load changed is expe-

rienced by the system at t = 30 sec, the conventional

integral controller gradually brings the system back to its

reference point but took a much longer time. With the

proposed PI-MPC controller, the system is more stable

and faster as compared to the system with MPC only or

conventional PI controller only.

5.2. Second Case: Robustness Evaluat ion

To evaluate the robustness of the proposed PI-MPC

technique, changes are made in the parameters of the

power system by increasing the governor and turbine

time constants to

T0.12sec=

and t

T0.95 sec=, re-

spectively.

M. Z. BERNARD ET AL.

Figure 5. Power system response to a small load change a)

Mechanical power change, b) frequency deviation and c)

governor’s control signal.

Figure 6 depicts the system response with the respec-

tive PI, MPC and PI-MPC control schemes during this

case of study. The load change is assumed to be as de-

scribed in the first case. It has been shown that, with the

traditional controller , the system becomes unstab le while

with MPC controller, the system response is more en-

hanced. However, it can be seen that the PI-MPC is

much faster in damping the power system oscillations

and hence yields the most desirable result in enhance-

ment of the system frequency by displaying robust cha-

racteristics in the presence of load change and p arameters

uncertainties.

5.3. Third Case: Variable Wind Speed

In order to further test the effectiveness of the proposed

PI-MPC control technique. Figure 7 shows the variable

wind speed pattern in the presence of which the simula-

tion was performed. It can be seen that the wind speed

initially 12.5 m/s fluctuates between 10 m/s to 15 m/s.

The simulation was performed in the presence of variable

wind speed and the system is observed. From Figure 8, it

Figure 6. Power system response to different changes: (a)

Mechanical power change, (b) frequency deviation and (c)

governor’s control signal.

Figure 7. Simulated wind speed.

is observed that with the proposed strategy, the system is

stable which verifies the effectiveness of the proposed

control strategy. Also, the figure indicates that even

though the wind speed changes, the presence of wind

turbine lead to enhancement the system performance

with the propose P I -MPC controller, significantly.

6. Conclusion

This paper investigates robust frequency control of a

28 30 32 343638 40 424446 4850

0.005

0.01

0.015

0.02

0.025

0.03

0.035

time (sec)

(a)

∆P

(p u)

Mechanical Pow er Change

Step Load Change

MPC

PI-MPC

28 30 32 34 36 38 40 42 44 46 48 50

-0.1

-0.05

0.05

ti me(sec)

(b)

∆ f (Hz)

Frequency Deviat ion

MPC

PI-MPC

28 30 32 34 36 38 40 42 44 4648 50

0.01

0.02

0.03

0.04

0.05

time (sec)

(c)

∆ P

(p u)

Govern or Cont r ol Sign al

MPC

PI-MPC

28 3032 3436 3840 42 4446 48 50

-0.02

0. 02

0. 04

Mechanical Pow er Ch ange

time (sec)

(a)

∆ P

(p u)

MPC

PI-MPC

28 3032 34 363840 42 444648 50

-0.2

-0.1

0. 1

0.2 Frequency Dev iat ion

time(sec)

(b)

∆

f (Hz)

MPC

28 3032 34 3638 40 42 44 46 4850

-0.1

-0.05

0. 05

0. 1

0. 15

Govern or Cont r ol Sign al Change Case

time (sec)

(c)

∆ P

(p u)

MPC

PI-MPC

05101520 25 3035 40 45 50

10.5

11.5

12.5

13.5

14.5

time (s)

Wind Speed ( m / s)

WIND SPEED(m/s)

M. Z. BERNARD ET AL.

Figure 8. Power system response to variable wind speed: (a)

frequency deviation ∆f and (b) WT electrical power output.

single area power system in the presence of wind farm

based on the P I-M PC control technique. Digital simulations

have been carried out in order to validate the effectiveness

of the proposed scheme. The proposed controller has

been tested for several mismatched parameters and load

disturbance. Simulation results show that fast response,

robustness against parameter uncertainties and load

changes can be considered as some advantages of the

proposed PI-MPC controller. In addition, a performance

Comparison between the proposed controller and both

the MPC and a conventional PI control schemes are car-

ried out. It is shown that the PI-MPC controller response

is much more effective than that of the traditional PI only

and MPC only respon ses; and it is able to deal with both

uncertainties in parameters and load changes more effi-

ciently. Also, it is observed that both the MPC and the

proposed PI-MPC controllers are ro bust, but the PI-MPC

technique has the advantage over MPC with respect to

faster oscillation damping, reducing variations, frequency

enhancement and economics.

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