Contribution to the Optimization of the Transient Stability of an Electric Power Transmission Network Using a Universal Power Flow Compensator Controlled by a Three-Stage Inverter

The use of an electrical network as close as possible to its limits can lead to its instability in the event of a high amplitude disturbance. The damping of system oscillations can be achieved by conventional means of voltage and speed regulation but also by FACTS (Flexible AC Transmission Systems) devices, which are increasingly used in power networks. In this work, optimal control coordination between a hybrid power flow controller and a three-level inverter was used to improve the transient stability of a transmission line. The UPFC is a combination of a serial compensator (SSSC) and a parallel compensator (STATCOM) both connected to a DC-LINK DC bus. The SSSC acts as a voltage source for the network and injects a voltage that can be adjusted in phase and amplitude in addition to the network voltage; the STATCOM acts as a current source. The approach used is tested in the Matlab Simulink environment on a single machine network. Optimal controller tuning gives a better transient stability improvement by reducing the transport angle oscillations from 248.17% to 9.85%.

the development of a country. Therefore, the availability of this energy as well as the maintenance of the balance between production and consumption requires constant monitoring to ensure the quality of service (transmission problem), its security (protection problem) and its stability (regulation problem). Electrical networks until the last few years are controlled mechanically (capacitor bank, inductor, phase-shifting transformer...). These during the problems of wear and their relative slowness make them insufficient to respond effectively to these remarkable requirements. The rapid development of power electronics has a considerable effect in improving the operating conditions of electrical networks by improving the control of their parameters through the introduction of control devices based on very advanced power electronics components (GTO, IGBT) known under the acronym FACTS [1]. FACTS systems are recently discovered compensators that combine capacitor banks and inductors coils with power electronics converters. These compensators, depending on their connection to the grid, are distinguished into shunt, series and hybrid compensators such as: STATCOM, SSSC, UPFC respectively. This work complements the work of TRAN Quoc Tuan [2] who worked on the control of power flow in a network using a UPFC. In his work, he has been able to demonstrate the ability of the PI regulator to control a UPFC to improve the stability of the network and to compensate the reactive power but for small variations. Our work is then based on the use of this universal controller but controlled by a three-level inverter applied to a highly disturbed network in the optimization of the transient stability of electric power transmission networks.

Hypothesis
To carry out our work, we made the following considerations: the generator and the switches of our converter will be assumed ideal, the line will be balanced, the voltage drops across the line represented by the reactance X, the inductance of the line is represented by the inductance L. the characteristics of the line are given in the following Table 1.
Subsequently, we will proceed with the modeling of the serial converter while knowing that for the parallel converter the principle will be the same.

Dynamic Equations of the Series Compensator
The application of Kirchhoff's laws [4]. To the meshes of the circuit in Figure 1 gives us the mathematical equations governing our system as follows: In order to minimize the computing time, we have switched from the three-phase system to the two-phase system, i.e. from three-phase reference frames with coordinates a, b and c, to two-phase reference frames with coordinates d and q. The transformation matrix is the following (Park's matrix) [ So the system becomes: Using the matrix representation on the system we have: The equation above corresponds to our serial converter model. It will be used to build, under Simulink, the block that represents the serial part of the system. Therefore, this equation is represented by the following block diagram (r = R):

Dynamic Equation of the Continuous Circuit
The DC-Link connects the serial converter and the shunt converter of the UPFC.
To model the DC-Link, we will use the single-phase model of the following converter ( Figure 3).
We will first define the input/output relationships of our converters. We are going to assimilate them to a quadripole whose modulation function w(t) connects their inputs and outputs in the following way: For the shunt converter The equation verified by the quadrupole is as follows: Due to the independence of the current I e from the voltage V in and since the current I in does not depend on the voltage V e either, the matrix representation of the input system is therefore: In this quadrupole, the instantaneous power is preserved. The following relationship is therefore verified: For the serial converter In the same way as for the shunt, one can write: we obtain, from the previous equations, the following expression of DC U : this equation will be used in MATLAB/SIMULINK to form a block having the following form: (Figure 4).

Methods
Theoretically, UPFC should be treated as a multi-variable system because both serial and parallel converters are connected on one side to the transmission line and on the other side to the DC circuit and therefore each have two outputs. To facilitate the synthesis of the controllers, the two converters will be processed separately. There are several possible configurations to control this compensator.
But before that, it is necessary to determine the references to control the device.

Classic Decoupled Watt-Var Algorithm
To drive our converter correctly, we need to remove this interdependence of the d and q axes. So we are going to create a decoupling block that will reproduce the coupling signal that we want to eliminate and then we are going to introduce this signal with the opposite sign at the input of our system. Our decoupling algorithm will therefore have the following form: The association of the decoupling block and the system model will have the form of the following Figure 6 and Figure 7. We will only be left with our PI with a serial model of the system without coupling [9].

Calculation of the Parameters of the Controllers Pi
The classical proportional-integral regulator used in figure (9) ensures

Results and Discussion
In this part, we started by highlighting the model of our network in the matlab Simulink environment as shown in Figure 11.
This network will be considered to be in a three-phase configuration change process: before, during and after contingency elimination.

Simulation of the Undisturbed Network
During the pre-fault phase, the network is usually in a stable steady state. Under these conditions, the network has a very specific transport angle δ.
This angle which corresponds to the equality between the electric power and the mechanic power according to the following formula:        (Table 2).

Simulation in the Presence of the Defect
Although the system in this case is not seriously disrupted, its stability is still critical. In the absence of control, the system was subjected to unacceptable transport angle oscillations (up to 65 degrees). In this case the network tends towards instability, the course of the various network parameters is undamped oscillation (instability of several oscillations), and this is caused by the loss of the production-consumption equality.

Simulation of the Fault in the Presence of UPFC
The network plus our device is shown below: (Figure 17).
The behavior of the network in this configuration is as follows: (Figure 18 and   Another observation is that the system manages to recover its synchronism before the end of the fault, which approves the efficiency of the UPFC to converge the trajectories of the network interest parameters to an acceptable operating regime after a certain fault clearance time (Table 3).

Conclusion
The