Performance analysis of a model predictive unified power flow controller (MPUPFC) as a solution of power system stability by IJASCSE


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									                                                  IJASCSE, VOL 1, ISSUE 4, 2012

Dec. 31

              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
         School of Engineering and Computer Science (SECS), Independent University Bangladesh (IUB), Bashundhara
                                               R/A, Baridhara, Dhaka, Bangladesh.
            Department of Electrical and Electronic Engineering, Islamic University of Technology (IUT), BoardBazar,
                                                   Gazipur-1704, Bangladesh.
        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                                                                                               Page 56
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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
             [ 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
      E fd  K A ((Vref  v  U pss )  E fd )    … (4)                Where
      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                                                                                                             Page 57
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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 >
      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
                                                                                               for all x, where xeq is some desired equilibrium and
                                                                                               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
                                                                    Manipulated u(k)           Fig 3 shows a complete block representation of
                                                                                               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
          Fig 2: The receding horizon principle of model                                                +       x    Quadratic Programming                                  u                         y
                                                                                                                                                                                 Power System (SMIB)
                                                                                                                          (QP) Problem
                        predictive control                                                       yref
                                                                                                                                                       Cost Function and
      At a current instant k, the MPC solves an                                                                                                       Constraints Equation

      optimization problem over a finite prediction horizon
      [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                                                                                                                                                         Page 58
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      information about the plant (system matrix A,B) are                         v    xtE   vEt
                                                                                                                                    vBt              vb
      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
      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                                                                                                             Page 59
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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                                                                                                             Page 60
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Dec. 31

           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                                                                                                             Page 61
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Dec. 31
      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.

                                                                   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


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