1. IJASCSE, VOL 1, ISSUE 4, 2012
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Performance analysis of a model predictive unified power flow
controller (MPUPFC) as a solution of power system stability
Md. Shoaib Shahriar1, Md. Saiful Islam2, B. M. Ruhul Amin3
1
School of Engineering and Computer Science (SECS), Independent University Bangladesh (IUB), Bashundhara
R/A, Baridhara, Dhaka, Bangladesh.
2
Department of Electrical and Electronic Engineering, Islamic University of Technology (IUT), BoardBazar,
Gazipur-1704, Bangladesh.
3
Department of Electrical and Electronic Engineering, Bangladeh University of Business and Technology (BUBT),
Mirpur-1216, Bangladesh.
Abstract— This paper addresses model predictive attractive and effective features. It is capable of
controller (MPC) as a powerful solution for providing simultaneous control of voltage magnitude
improving the stability of an FACTS device like and active and reactive power flows, in adaptive
unified power flow controller (UPFC) connected fashion. It has the ability to control the power flow in
single machine infinite bus (SMIB) power system. transmission line, improve the transient stability,
UPFC is mainly used in the transmission systems mitigate system oscillation and provide voltage
which can control the power flow by controlling support [1, 4].
the voltage magnitude, phase angle and A number of researches had been done to find out the
impedance. And as a controller, MPC, not only control schemes for performing the oscillation-
provides the optimal control inputs, but also damping task of UPFC. Among the controllers which
predicts the system model outputs which enable it are used to control the FACTS devices, model
to reach the desired goal. So, model predictive
predictive controller (MPC) has got a wide range of
unified power flow controller (MPUPFC), a
attractive and versatile features. Now a day, this
combination of UPFC and MPC along with
controller is widely used in the field of industry as it
proper system model parameters can provide a
satisfactory performance in damping out the has the ability to implement constraints in control
system oscillations making the system stable. process system. A good overview of industrial linear
Simulation is done in Matlab. Response is shown MPC techniques can be found in [5-7].
for 4 different states. Effects are shown for 4 In this paper, model predictive Controller (MPC) has
control signals of UPFC operating individually been chosen to control UPFC. Attractive features of
and combining 2 at a time. these two tools jointly provide a very satisfactory
solution to the system stability. System model of
Keywords— Power system stability, system model, SMIB system along with UPFC is controlled here
UPFC, FACTS, MPC. with MPC for four different control signals of UPFC.
Impact of the system for different combinations of
I. INTRODUCTION control signals is also investigated.
Power system oscillations are an inevitable
phenomenon of the system. Faults and weak
protective relaying operation can cause the oscillation II.SYSTEM DYNAMIC MODEL
to collapse the system [1]. In order to damp these
power system oscillations, different devices and The power system [8] that is studied in this paper
control methods are used [2]. FACTS technology is consists of a synchronous generator connected to
the newest way of improving power system operation transmission lines and an infinite bus via two
transformers. The UPFC consists of an excitation
controllability and power transfer limits which has
transformer (ET), a boosting transformer (BT), two
been added in the stream with the progress in the
three-phase GTO based voltage source converters
field of power electronics devices. FACTS devices (VSCs); which are connected to each other with a
can cause a substantial increase in power transfer common dc link capacitor [1].
limits during steady state operation [3]. Among the Fig. 1 shows a SMIB system equipped with an
FACTS devices, UPFC is the one having very UPFC. The four input control signals to the UPFC
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2. IJASCSE, VOL 1, ISSUE 4, 2012
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are mE, mB, δE, and δB. Where, mE is the excitation By applying Park’s transformation and neglecting the
amplitude modulation ratio, resistance and transients of the ET and BT
mB is the boosting amplitude modulation ratio, transformers, the UPFC can be modeled by the
δE is the excitation phase angle, and following equations (5-7):
δB is the boosting phase angle.
 mE cos  E vdc 
vEtd  iEd   2 
  [ ]  +  
vEtq  iEq   mE s in E vdc 

 2 

…… (5)
 mB cos  B vdc 
vBtd  iBd   2 
  [ ]  +  
vBtq  iBq   mB s in B vdc 

 2 

Fig 1: SMIB power system equipped with UPFC …… (6)
3mE 3m
In stability and control studies of power system vdc  (cos  E iEd  sin  E iEq )  B (cos  BiBd  sin  BiBq )
4Cdc 4Cdc
oscillations, the linearized model can be used. In this
paper dynamic model of the system for small signal
………………….. (7)
stability improvement is used. Nominal parameters Where, vEt , iE , vBt , and iB are the excitation voltage,
used for system modeling are given in Appendix-I. excitation current, boosting voltage, and boosting
current, respectively; Cdc and vdc are the DC link
The nonlinear model of the SMIB system of Fig 1 capacitance and voltage.
can be expressed by the following differential
equations (1-4) [8]: By combining and linearizing the equations (1-7)
  base (  1) … … … … … … … … (1) state space equations of system will be obtained
which are present in equations (8). In this process
1
 [ Pm  Pe  D(  1)] … … … … (2) there are 28 constants denoted by k are being used.
2H = AΔX + BΔU ………………. (8)
1 where the state vector ΔX and control vector ΔU are
Eq  ' [ E fd  Eq  ( xd  xd )id ] … … … (3)
' ' '
ΔX = [Δδ Δω ΔEʹq ΔEfd ΔVdc]T
Tdo ΔU = [ΔUpss ΔmE ΔδE ΔmB ΔδB]T
1
E fd  K A ((Vref  v  U pss )  E fd ) … (4) Where
TA
where Pm and Pe are the input and output power,  0 b 0 0 0 
respectively. P  vd id  vqiq , vt
e  v 2
d v 2
q , 
  K1 
D K2
 0 
K pd  
 M M 
vd  xqiq  xq  iiq  ilq  , vq  Eq ' xd ' id ,
M M
 K qd 
K K3 1
A  4 0   
id  iEd  iBd , iq  iEq  iBq ,  T 'd 0 T 'd 0 T 'd 0 T 'd 0 
 
M and D the inertia constant and damping  K A K5 0 
K A K6

1 K K
 A vd 
coefficient, respectively; ωbase the synchronous speed;  TA TA TA TA 
δ and ω the rotor angle and speed, respectively; E′q ,  
 K7 0 K8 0  K9 
Efd, and v the generator internal, field and terminal
voltages, respectively; T′do the open circuit field time
constant; xd and x′d the d-axis reactance, d-axis
transient reactance respectively; KA and TA the
exciter gain and time constant, respectively; Vref the
reference voltage; and uPSS the PSS control signal.
and
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3. IJASCSE, VOL 1, ISSUE 4, 2012
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 0 0 0 0 0  prediction horizon is infinite, one could apply the
 K pe K pde K pb K pdb  control strategy found at current time k for all times.
 0      However, due to the disturbances, model-plant
 M M M M 
 mismatch and finite prediction horizon, the true
K qe K qde K qb K qdb 
B 0     system behavior is different from the predicted
 T 'd 0 T 'd 0 T 'd 0 T 'd 0  behavior. In order to incorporate the feedback
  information about the true system state, the computed
 KA K A K ve K A K vde K A K vb K K
    A vdb  optimal control is implemented only until the next
 TA TA TA TA TA 
  measurement instant ( k , k  1 ), at which point the
 0 K ce K cde K cb K cdb 
entire computation is repeated [10].
III. DAMPING CONTROL
MPC approach can be expressed considering the
The unique feature of MPC which has made it following finite horizon cost function [10]
H 1
J ( xt ,[u0 (t ),..., uH 1 (t )])   h( xt iT (u), ui (t ))  g ( xt  H T (u))
different from other controllers is the ability to rh
predict the future response of the plant. At each
control interval an MPC algorithm attempts to i 1
optimize future plant behavior by computing a
sequence of future manipulated variable adjustments
where t is the current time; H is the length of the
[9]. Figure 2 shows the basic working principle of
optimization horizon; ΔT is the sample period. If i >
MPC.
Prediction horizon (TP) is the time range which, 0, then xt  iT (u ) denotes the controlled trajectory
at time t  iT from xt under piecewise controls
future system outputs are predicted in it. Control
horizon (Tc) is the time steps number that input
control sequence calculations for the prediction u  [u0 (t ),..., ui 1 (t )] U H ; h is the running cost;
horizon are done [9]. In this plant model, value of and g is the terminal cost. We assume that h is non-
prediction horizon is taken 20 and control horizon is
negative function and g satisfies g ( x)   x  xeq
2.
for all x, where xeq is some desired equilibrium and
Set-point
α>0 is some positive constant. That is, g is an
past future trajectory ‘upward’ function whose lowest point is at the
system equilibrium. This condition on g(.) ensures
Predicted Output
that the control design attempts to reach the system
equilibrium.
Manipulated u(k) Fig 3 shows a complete block representation of
Inputs
UPFC connected SMIB system controlled with MPC.
k k+1 k+Hc k+Hp
Input horizon A,B
Linearized System Model
Output horizon x  Ax  Bu

y
-
Fig 2: The receding horizon principle of model + x Quadratic Programming u y
Power System (SMIB)
(QP) Problem
predictive control yref
Plant
Cost Function and
At a current instant k, the MPC solves an Constraints Equation
optimization problem over a finite prediction horizon
MPC
[k , k  H P ] with respect to a predetermined
objective function such that the predicted state Fig 3: Block diagram representation of UPFC
ˆ ˆ
variable x or output y can optimally stay close to a connected SMIB system controlled with MPC
reference trajectory. The control is computed over a
The UPFC connected SMIB power system plant is
control horizon [k , k  H C ] , which is smaller than connected here with the MPC block. The output of
the prediction horizon ( H C  H P ). If there were no the plant (y) enters into the summing junction where
it has been compared with the reference value (yref).
disturbances, no model-plant mismatch and the Subtracted result (∆y) goes into the MPC block. The
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4. IJASCSE, VOL 1, ISSUE 4, 2012
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information about the plant (system matrix A,B) are v xtE vEt
vBt vb
xBV
already given to the MPC block. So, the linearized iB xB
system model of the plant gives the future output (u) it
VSC  E VSC  B
iE BT
with the help of Quadratic Programming (QP)
function of MPC and proper constraints of the MPC xE
block. Predicted output of the controller, u enters into
ET
the plant and creates the next result y′. Thus the loop vdc
will continue until it reaches the desired reference
trajectory of the plant. mE  E mB  B
Figure 4 show the circuital representation of UPFC
connected SMIB system controlled with MPC which
MPC Controller
is actually the modification of Fig 1.
Four control signals of UPFC (mE, mB, δE, and δB) are Change in speed or
power output
entering into the UPFC connected SMIB plant Fig 4: Circuital representation of UPFC connected
through MPC. Thus MPC is connected with the SMIB system controlled with MPC (modification of
system model through UPFC. Fig 1)
IV. SIMULATION RESULTS
A disturbance of pulse type signal is given in the Response of MPC on proposed model is observed for 4
system’s ΔPe. Disturbance duration (period) is 0.1 sec, different states ∆δ, ∆ω, ∆E′q and ∆Efd. Individual effects
disturbance amplitude (size) is 1 unit and disturbance of 4 different control signals mE, δE, mB and δB on system
occurring time is 1 sec. states are observed first in figure (5-8)
Value of prediction horizon is taken as 10, control
horizon is 2 and control interval is chosen as 0.5 in
Matlab MPC toolbox.
Fig 5: Responses for control signal mE for states (i) ∆δ, (ii) ∆ω, (iii) ∆E′q,and (iv) ∆Efd
Fig 6: Responses for control signal mB for states (i) ∆δ, (ii) ∆ω, (iii) ∆E′q,and (iv) ∆Efd
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Fig 7: Responses for control signal δE for states (i) ∆δ, (ii) ∆ω, (iii) ∆E′q,and (iv) ∆Efd
Fig 8: Responses for control signal δB for states (i) ∆δ, (ii) ∆ω, (iii) ∆E′q,and (iv) ∆Efd
It has been seen that mE (Fig. 5) and δE (Fig. 7) give the worse applications involve plants having multiple inputs and outputs.
response. They can bring stability only in state ∆ω. Control Here, combination of different control signals of UPFC is now
signal δB also doesn’t have a good response characteristics applied as input to the plant to observe the responses on
(Fig. 8). It can stable several states but takes a long time for different states.
that. Among the four signals, mB gives the best output making Then, the responses are observed for different combinations of
all the 4 states stable at a reasonable time of below 6 seconds control signals two at a time. Four different combinations of
(Fig. 6). two control signals are observed in this paper in fig (9-12).
An exceptional and effective feature of MPC is the ability to
provide support to the MIMO plants. Most MPC toolbox
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Fig 9: Responses for control signal mB and mE together for states (i) ∆δ, (ii) ∆ω, (iii) ∆E′q,and (iv) ∆Efd
Fig 10: Responses for control signal δB and δE together for states (i) ∆δ, (ii) ∆ω, (iii) ∆E′q,and (iv) ∆Efd
Fig 11: Responses for control signal mB and δB together for states (i) ∆δ, (ii) ∆ω, (iii) ∆E′q,and (iv) ∆Efd
Fig 12: Responses for control signal mB and δE together for states (i) ∆δ, (ii) ∆ω, (iii) ∆E′q,and (iv) ∆Efd
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Observing the combined effect of two different time to settle ∆δ (Fig. 10). But the other 4 states are
control signals, it has been found that the responses settled down within 3 seconds. Combination of mB-δB
are significantly improved for every case than (Fig. 11), mE-mB (Fig. 9) and mB-δE (Fig. 12) show
applying them individually. Among the 5 the best responses here making all the 5 states stable
combinations, combination of δE and δB takes a long within a short time of 3 seconds.
CONCLUSION
proposed model is the use of MPC with four control
In this paper by linearizing and combining the signals of UPFC at a time.
equations of single machine infinite bus power
system and unified power flow controller, a complete Appendix:
state space model of SMIB power system including
UPFC was presented. Effect for model predictive The parameters used in system model:
controller for stability analysis is observed then for Generator: M = 8 MJ/MVA, T′d0 = 5.044 s, D =
different states of the system model. Different 0 , Xq = 0.6 pu, Xd = 1.0 pu, X´d = 0.3 pu
combinations and individual impacts of four different Transformers: XT = 0.1 pu, XE = 0.1 pu, XB = 0.1 pu
control signals of UPFC are analyzed. It has been Transmission line : XL = 0.1 pu
found that the system performs better if MPC is Operating condition: Pe = 0.8 pu,Q=.1670pu , Vb = 1
allowed to operate with multiple control signals of pu, Vt = 1 pu
UPFC. Impact of MPC as MIMO plant is thus DC link parameter: VDC = 2 pu, CDC = 1.2 pu
evident. Best solution of stability analysis for the
REFERENCE
[1] Shayeghi H. - Jalilizadeh S. - Shayanfar H. - [6] Qin S.J. and Badgwell T.A. “An overview of
Safari A. : “Simultaneous coordinated designing of industrial model predictive control technology”, In F.
UPFC and PSS output feedback controllers using Allg¨ower and A. Zheng, editors, Fifth International
PSO”, Journal of ELECTRICAL ENGINEERING, Conference on Chemical Process Control – CPC V,
VOL. 60, NO. 4, 2009, 177–184 pages 232–256. American Institute of Chemical
Engineers, 1996.
[2] Anderson P. M. - Fouad A.A., “ Power System
Control and Stability” : Ames, IA: Iowa State [7] Qin S.J. and Badgwell T.A. : “An overview of
Univ.Press, 1977. nonlinear model predictive control applications”, In
F. Allg¨ower and A. Zheng, editors, “Nonlinear
[3] Keri A. J. F. – Lombard X. – Edris A. A. : Predictive Control”, pages 369–393. Birkh¨auser,
“Unified power flow controller: modeling and 2000.
analysis”, IEEE Transaction on Power Delivery 14
No. 2 (1999), 648-654.[4] Hingorani N. G. – Gyugyi [8] Al-Awami A. T. - Abdel-Magid Y. L. - Abido M.
L. : “Understanding FACTS: concepts andtechnology A. : “Simultaneous Stabilization of Power System
of flexible AC transmission systems”, Wiley-IEEE Using UPFC-Based Controllers”, Electric Power
Press, 1999. Components and Systems, 34:941–959, 2006.
[4] Tambey N. - Kothari M.L. : “Unified power flow [9] Ahmadzade B. – Shahgholian G. - Mogharrab
controller based damping controllers for damping Tehrani F. – Mahdavian M. : “Model Predictive
low frequency oscillations in a power system”, IEE control to improve power system oscillations of
Proc. on Generation, Transmission and Distribution, SMIB with Fuzzy logic controller”.
Vol. 150, No. 2 (2003), 129-140.
[10] Eduardo F, Camacho and Carlos Bordons:
[5] Dash P. K. - Mishra S. – Panda G : “A radial “Model Predictive Control Advanced Textbooks in
basis function neural network controller for UPFC,” Control and Signal Processing”, Springer Publication,
IEEE Trans. Power Systems, vol. 15, no. 4, pp. 1998.
1293–1299, November 2000.
www.ijascse.in Page 62