INTRODUCTION
The concept of Flexible Alternating Current Transmission Systems (FACTS)
has recently gained much attention in the electric industry community
and has been an area of interest and technology development during these
last years.
An important FACTS device is the UPFC, which can control all three principal
parameters (voltage, impedance and phase angle) that determine the power
flow of a transmission line. A UPFC consists of two forcedcommutated
voltage inverters which are connected through a common dc link provided
by a storage capacitor as shown in Fig. 1, (Gyugyi,
1992; Edris et al., 1995; Tuttas, 1999). One converter is shuntconnected
and the other is connected in series with the transmission line.
Each inverter can independently generate reactive power at its own ac
terminal. The dc link allows an active power exchange between both electronic
circuits. Inverter 2 operates as a series compensator and injects an ac
voltage V_{c} with variable amplitude and phase angle at power
system frequency.

Fig. 1: 
Basic circuit configuration of a UPFC 
The active and reactive power flow of the transmission line can be controlled.
Inverter 1 provides the real power demand of inverter 2, regulates the
capacitor voltage V_{dc} and provides reactive power.
Sen and Keri (2003) compared field results of the Inez UPFC project to
an EMTP simulation. There are no details on the design of the controllers
utilized, or the presence of any disturbances or uncertainties. Zhengyu
et al. (2000) have discussed four principal control strategies
for UPFC series element main control and their impacts on system stability. Ma (2003) demonstrated
the feasibility of using a centralized optimal control scheme using an
evolutionary programming algorithm. Sukumar (2006) has used a Radial Basis
Function neural Network (RBFNN) as a control scheme for the UPFC to improve
the transient stability performance of a multimachine power system. Schoder
et al. (2000) have proposed a Fuzzy damping controller. In last
years, the application of neural networks (NNs) for adaptive control has
been a subject of extensive study (Xie et al., 2006; Chau
et al., 2005, 2007; Lin et al., 2006).
The method proposed in this study is novel. It combines two different
approaches, namely intelligent techniques that seem to work but do not
provide a formal proof and analytical techniques that provide proofs under
some restricted conditions and for simple systems. These limitations have
been a central driving force behind the creation of hybrid systems (Henriques
and Dourado, 1999) where two or more techniques are combined in a manner
that overcomes the limitations of individual techniques. So, the hybrid
systems are important when considering the control of the unified power
flow through a transmission line using a PWMbased UPFC, because, it is
a complex application. The present study intends to be a contribution
in this direction. It considers the application of a Generalized Predictive
Controller (GPC), with neural networks in an electric power system.
MODELLING OF A UPFC SYSTEM
The series and shunt inverters are represented by voltage sources V_{c}
and V_{p}, respectively. The transmission line is modelled as
a series combination of resistance, R and inductance, L, whereas the parameters
R_{p} and L_{p} represent the resistance and leakage inductance
of shunt transformer, respectively. The nonlinearities caused by the switching
of the semiconductor devices and transformer saturation are neglected
in the equivalent circuit shown in Fig. 2. It is assumed
that the transmission system is symmetrical.

Fig. 2: 
Equivalent circuit of UPFC system 
After the dq transformation, a mathematical model of the transmission
system including the series part of UPFC is given in (1)
and (2) where i_{sd}, i_{sq} are the
transmission line currents (Yu et al., 1996).
Similarly, the mathematical model of shunt connection of the UPFC system
can be determined from Fig. 2 and is given in Eq.
3 and 4 where i_{pd}, i_{pq} are
the shunt currents.
Using the power balance principle and neglecting the inverter losses,
the dc bus voltage can be expressed as (5) .
The dc link capacitor in Fig. 1 must be selected to
be large enough to minimize the dc voltage ripple. Having derived the
real and reactive power references P* and Q*, the following Eq.
6 can be used to determine the corresponding direct and quadrature
axes reference currents at the sending and receiving ends of the two bus
power system
where the * superscript defines the reference quantities.
To control the UPFC system, ordinary simple PIDecoupling (PID) controller
for UPFC is good enough (Fig. 3).
Unfortunately, The PIcontrol fails to solve problems where it is not
possible to obtain sufficiently precise processes and disturbances models.

Fig. 3: 
Current step response of PI with decoupling 
CONTROL DESIGN
This section describes one of the most popular predictive control algorithms:
Generalized Predictive Control (GPC) (Peri and Petrori, 1999).
The basic idea of GPC is to calculate a sequence of future control signals
in such a way that it minimizes a multistage cost function defined over
a prediction horizon (Fig. 4).
A CARIMA model is given by:
with
A, B and C are the polynomials in the backward shift operator z^{1}.
For simplicity, in the Fig. 5 the C polynomial is chosen to be 1.
The Generalized Predictive Control (GPC) algorithm consists of applying
a control sequence that minimizes a multistage cost function of the form:
y(t+j) is an optimum jstep ahead prediction of the system output on
data up to time t, where N_{1} ≤ j ≤ N_{2} (j =
1). There is no reason for choosing it smaller because first predictions
depend upon past control inputs only and thus cannot be influenced. On
the other hand it is not recommended to choose it bigger since this can
lead to quit unpredictable results.

Fig. 4: 
The principle of predictive control 

Fig. 5: 
Representation of the CARIMA model 
N_{1} is the minimum prediction
horizon, N_{2} is the maximum prediction horizon and N_{u} is the control horizon, λ is the weighting sequence and w(t + j)
is the future reference trajectory.
The objective of predictive control is to compute the future control
sequence u(t), u(t+1),…in such a way that the future plant output
y( t+j ) is driven close to w(t + j). This is accomplished by minimizing
J (N_{u}, N, λ).
The following set of j ahead optimal predictions can be written as:
Notice that only the first element of u is applied and the procedure
is repeated at the next sampling time. The algorithm to obtain the control
law described in the previous section will be used on the neural networks
GPC (NNGPC). Obtaining numerical results for the parameter values a_{1}
= 0.9231, b_{1} = 9.6095.10^{4} and b_{2} =
2.1617.10^{7}, the horizons being: N_{1} = 1;
N_{2} = 2; N_{u} = 1 and λ = 10^{9}.
The control signal is a function of the desired reference and of past
inputs and outputs and is given by:
The training of the network consists in modifying the weights and bias
in order to minimize the quadratic errors at the output by using the WindrowHoff
law (Nguyen and Widrow, 1990). The reason for this specification choice
of network is justified by the fact that in general recurrent networks
are considered more suitable for modelling dynamical systems. With each
step of training, the error at the output is calculated as the difference
between the required target y and the estimate output y of the network.
The quantity to be minimized, with each step of training k, is the variance
of the error at the output of the networks. Equation 13
can be expressed as:
where,
P, w et w_{ 0} design, respectively, the input vector,
the weight and the bias.
CONTROL PERFORMANCE
Simulations are performed on a Pentium PC under MATLAB/Simulink. The
transmission line and the UPFC (series and shunt inverters) system are
implemented with Simulink blocks.
The neural network generilized predictive controller (NNGPC) are implemented
as a Ccoded Sfunctions as shown in Fig. 7.
For each of the control systems, a simulation model is created which
makes use of PWMinverters as interface to the power system.
The parameters of the simulation model are selected to be equal to the
parameters of a laboratory UPFC model (Yu et al., 1996), which
are listed in Table 1.

Fig. 6: 
Simulation result of step response of the series UPFC
system 

Fig. 7: 
Error prediction (GPC) 
Table 1: 
The parameters of the laboratory UPFC model 

The PWM switching frequency is selected to be 750 Hz. The control system
described above was derived by assuming that the series and shunt inverters
are ideal controllable voltage sources.
Simulation results show the behaviour of the closed loop system.
The Fig. 6 shows the step response of the UPFC system.
Initially the system is in steady state with a real power of the receiving
end of 1000 W and reactive power of 500 VA.

Fig. 8: 
Real power response of UPFC variables 

Fig. 9: 
Reactive power response of UPFC variables 
At a time 1 sec, the reactive power reference Q* is changed to 500 VA
while the real power reference P* is kept constant at 1000 W until t
= 0.5 sec where the real power reference P* is changed to 1000 W.
The control system has a fast dynamical response. The error prediction
is equal to 0.0002 Fig. 7.
One major advantage of NNGPC is its robustness against parameter variations.
This is demonstrated by change the UPFC line impedance by±25% Fig.
8 and 9.
A repeating sequence is added to the system UPFC as a perturbation. The
time of this perturbation is equal to 0.02 sec with amplitude 2.
As can be seen, the controller rejected the external perturbation quite
rapidly Fig. 10 a and b.
The PID control for UPFC has been used successfully with precise models
and no disturbances. In cases of model uncertainties and disturbances,
the PIcontrol fails as shown in Fig. 11; hence, the
proposed controller is designed to handle these conditions.
The objective is to keep the sending bus voltage at its prespecified
value and to keep the reactive power constant0.15 p.u while tracking
the step changes in the real power: at time 0.2 sec real power flow reference
is changed from 1.6 1.8 p.u, at time 0.35 sec reference is set to 1.3
pu and at time 0.8 sec system returns to the initial operating condition
as shown in Fig. 12.

Fig. 10: 
System response in the presence of external disturbance 

Fig. 11: 
PID power responses at  15% X_{L} 
A step at the reactive power affects slightly the measured real power
in Fig. 12. It can be seen that the NNGPC controller
acts correctly with a quite perfect decoupling between real power, reactive
power and dclink voltage.
It is natural that disturbances at both voltage and current affect the
power flow, as seen in Fig. 12, despite of keeping
the power reference values constant.
However, phase control voltage and phase currents responses (Fig.
13 and 14) performs well since it is able to maintain
the outputs P, Q and V_{dc} at the desired values.

Fig. 12: 
Step change in receiving end active and reactive power 

Fig. 13: 
Phase control voltage response 

Fig. 14: 
Phase currents response 
CONCLUSION
The performance of the UPFC under classical and hybrid method control
was investigated. A UPFC located at the middle of the transmission line
was modeled realistically by transforming its variables into a rotating
synchronous reference frame. The developed control concept shows an excellent
dynamic behaviour and behaves robust to parameter changes of the power
system. Hybrid control systems may contribute to the establishment of
an unifying control theory merging traditional analyticalgebraic methods
with artificial intelligent tools. It is believed that neural networks
can be effectively used for control design of nonlinear systems and they
must be seen as an extension, rather than replacement, of linear identifiers
and controllers that may be already working.