Investigating the impacts of the SVCs and the SCs affecting to the transient stability in multi-machine power system

A new algorithm simulating the impacts of the VAR supporting devices such as the static var compensators (SVCs) and the synchronous condensers (SCs) under condition of symmetrical disturbances in multi-machine power system is mentioned. Some typical numerical examples are presented in this article. The comparisons of variation of the state parameters, such as the voltage, frequency, reactive power outputs and asynchronous torques...are simulated under condition of the action of the automatic voltage regulation systems of generators and of the VAR supporting devices. The transient energy margins are calculated and compared to assess the transient stability in multi-machine power system. Basing on this algorithm, the PC program uses the elements of the eigen-image matrix to bring the specific advantages for the simulation of the transient features of state variables.


INTRODUCTION
The control of voltage levels is accomplished by controlling the production, absorption and flows of reactive power.The device use for voltage control may be the static var systems (SVCs), the synchronous machines/condensers or regulating transformers...
The synchronous condensers and SVCs provide reactive power compensation, together with the generators they have specific influence to the steady-states and the transient states in the power system.
A synchronous condenser (SC) is a synchronous machine running without a prime mover or a mechanical load.By controlling the field excitation, the SC can generate or absorb reactive power.During electro-mechanical

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oscillation there is an exchange of kinetic energy between a SC and the power system.A static VAR system is an aggregation of Static VAR Compensator, the mechanically switched capacitors and reactors.whose outputs are coordinated.In contrast to the SC, the SVC, being composed of the thyristor-switched reactors and capacitors, becomes a fixed capacitive admittance at full output.Thus, the maximum attainable compensating current of the SVC decreases with the square of this voltage.
The SVC can enhance the transient stability and the damping of system oscillations.Referring to (Prabha Kundur, 1993) the performance of the SVC is instantaneously provide an amount of reactive power to hold the voltage at a specific bus in power network with its V/I characteristic showing in fig. 1  The composite characteristic of SVC -Power System, within the control range defined by the slope KS with reactance XSL may be expressed as

as follow
where EThe is thevenin e.m.f. ; XThe is thevenin reactance at the bus of SVC locating in multi-machine power system.

MATHEMATICAL MODELLING
Commonly, the technical movement is described by a set of differential equations.depending on a set of different parameters such as the i-th elements of the eigen-image matrix, the phase angles t i  at the t-th time interval, the voltages t i V at the i-th observing bus in power network at the t-th tim interval, the subtransient time constants d T " , q T " , the transient and and the rated frequency of the power system.
Developing the flowchart in [5] and referring to [6],[7] and [8], the set of equations ( 2) can be solved by a numerical method using formulas relating to the Taylor's series expansion.

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Referring to [2], [3], [4], using the transient energy margin (TEM) to comparatively assess the dynamic stability in case of SVCs operation with those in case of SCs operation where V t KE is kinetic energy function depending on i th inertia constant (Hi) and i th angular frequency (ω t i) at t th instance of time; V t PE is potential energy function depending on i th turbine power (P t m i), i th electrical power (P t e i) calculating by e.m.f.E t iδ t i and equivalent bus admittance matrix Y t e at t th instance of time.
The TEM is larger the system is more stable.

NUMERICAL EXAMPLE
Let's survey the electro-mechanical transient process in a 21-bus power system consisting of 2 power plants with 5 synchronous generators (SGs), 3 SCs (may be replaced by SVCs of the same rating powers) and 11 composite loads.The basic power is 100 MVA.The positive-sequence line-data and load busdata are given in the table 1

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The data of the synchronous machines are given in the tables 3, 4 and 5 as follows

Another studying cases:
There are two studying cases are realized in the same manner with the first studying case.The second and third studying cases are effectuated under condition of fault type of 3 phase short circuit, the main investigating conditions of which are shown in the table 4.

Figure 1 .
Figure 1.Equivalent circuit and V/I characteristic of SVC

Figure 2 .
Figure 2. V/I characteristic of SVC 14 and SVC 15 First studying case: A high voltage transmission line (1-5), connecting the buses 1 and 5, is chosen to simulate the fault type of 3 phase short circuit to assess the transient stability of the power system.Let's suppose that the fault occurs near the bus 1 and will be cleared at 0.2sec by removing of the fault line, causing a transient condition, under which the frequencies of generator of SCs-Configuration are changed more than those of the SVCs-Configuration, as shown in the fig.5a and fig.5b, and the transient energy margin (TEM) of

Figure 5c .
Figure 5c.Comparing the TEM of the first studying case.

Figure 5e .
Figure 5e.Voltage Variation at the bus 16 relating to the SVCs-Configuration.

Table 4 .Figure 6b .
Figure 6a.Comparing the TEM of the second studying case

Figure 6c .
Figure 6c.Network Voltage Profile relating to the SVCs-Configuration.

Figure 6d .
Figure 6d.Q power output of SC at the bus 16 relating to the SCs-Configuration.

Figure 6e .Figure 7a .
Figure 6e.Q power output of SC at the bus 16 relating to the SVCs-Configuration.

Figure 7b .
Figure 7b.Accelerating Torque Profile relating to the SVCs-Configuration.

Figure 7c .
Figure 7c.Comparing the TEM of the third studying case.

Figure 7d .
Figure 7d.Asynchronous Torque Variation relating to the SCs-Configuration.

Figure 7e .
Figure 7e.Asynchronous Torque Variation relating to the SVCs-Configuration.
studying cases results in the outcome following: the SCs operation causes more vulnerability of losing of the transient stability of power system in comparison with the SVCs operation under the same conditions of disturbance.The SCs replaced by SVCs will increase the critical clearing time, bring the specific advantages for the relay protection operating in multi-machine power system under transient conditions.The transient energy margins allow to compare the impacts of SVCs with those of SCs affecting to the transient prosecces under condition of symmetrical disturbances and to assess the dynamic stability in multi-machine power system.

Table 1 .
and table 2 as follows Line-data

Table 2 .
Load bus-data

Table 3 .
Initial generation bus-data

Table 5 .
Time and Inertia Constants.