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A Static VAR compensator (SVC) is Flexible ac Transmission System (FACTS) device used to regulate the voltage on a transmission line. The SVC uses reactive compensation in order to control the voltage. The SVC is made up of a Thyristor Controlled Reactor (TCR) and a Thyristor Switched Capacitor (TSC). The TCR is used to absorb MVArs from the transmission line in order to decrease the system voltage. The TSC is used to supply MVArs to the transmission line in order to increase the system voltage. The SVC is made up of one or more of these devices depending on the system requirements and installation of the SVC. These devices are connected in parallel to the bus through a transformer.
This report details the design of the TCR as well as its switching of the thyristors and control scheme. The design of the harmonic filters used to eliminate the harmonics caused from the switching of the TCR is included. The design was modeled on the computer software program PSCAD. Tests were done on the model to measure the performance of the TCR and the reliability of the control scheme.
The problem of the project is to design a SVC for voltage stability control. This means that a SVC must be designed to the given specifications in order to maintain the required voltage at the receiving on of the transmission line.
SVCs are used in to increase active power transfer capacity, to damp power oscillations and to achieve effective voltage control.  SVCs have a faster response over the simple mechanically switched compensation schemes. They are more reliable as they consist of no moving parts, hence the term static.
The SVC is made up of a TCR and TSC. "When TCRs and TSCs are placed in parallel with each other and have the firing angles of their thyristors adjusted by a controller, the device is referred to as a SVC." 
The TCR uses thyristors connected back-to-back as a bidirectional switch, in series with an inductance to switch the inductor in for a certain period of time. A TSC consist of one or more capacitor banks in series with a bidirectional thyristor switch and a small inductor. The inductor is used to limit the transients caused form switching of the TSC. 
If the load on the transmission line is a capacitive load, the SVC will use the TCR to absorb MVArs from the system, in turn lowering the system voltage. If the connected load is an inductive load, the SVC will use the TSC to inject MVArs into the system therefore increasing the system voltage. The SVC can supply or consume MVArs depending on the load connected to the system. The SVC is able to handle the varying loads because of the fast response of the controller.
The SVC will be connected to a simple transmission system rated at 400kV. The majority of electricity transmission is done at this kV rating.
Information can be obtained from journals and thesis found in the library or on the IEEE website. Textbooks have information regarding the SVC and the modelling and control thereof. PSCAD will be used as the simulation tool to model the design and is available on majority of the computers within the university computer lans.
THYRISTOR CONTROLLED REACTOR
Figure . Basic structure of thyristor 
The operation of a thyristor (silicon controlled rectifier) can be explained by referring to Figure 1 above. The thyristor consist of four layers of a semiconductor material making up p-n-p-n layers. Three junctions are produced designated J1, J2 and J3, and there are three terminals, the Anode, Cathode and Gate. The thyristor can be thought of as pnp transistor (J1 and J2) connected to a npn transistor (J2 and J3). To forward bias the thyristor, a voltage is applied to be positive on the anode and negative on the cathode. If no gate current is supplied, both transistors remain cut off. When a negative gate-cathode voltage is applied both transistors remain off. A positive gate-cathode voltage applied will forward bias npn transistor (J2 and J3) and cause it to conduct. Once this has started conducting it will cause the pnp transistor (J1 and J2) to conduct. The first pnp junction then keeps the second npn junction conducting, even when the gate pulse has been removed. The ability for the thyristor to remain on once the gate pulse has been removed is known as latching. Only a brief pulse to the gate is needed to switch the thyristor on. The thyristor switches off on the negative half cycle of the supply voltage when the anode to cathode voltage becomes zero. 
When two thyristors are connected in parallel with the anode of one connected to the cathode of another, the thyristors form a bidirectional switch.  Applying a sinusoidal voltage across the two thyristors will cause the one thyristor to conduct on the positive half cycle, and the other thyristor will conduct on the negative half cycle. When the voltage across the thyristor becomes negative, it will stop conducting and the other thyristor will start conducting. With this method the thyristors are said to be "naturally commutated" . The thyristors are turned on by firing pulses sent to their respective gates 180Ëš apart. This enables the thyristor to be controlled as a switch. A firing angle Î± is used which causes the thyristors to conduct for a portion of the sinusoidal voltage.
Figure . Basic elements of a TCR
Figure 2 above illustrates the basic elements of a TCR. A TCR is a reactor in series with a bidirectional thyristor switch. The thyristors conduct on opposite half cycles of the fundamental frequency depending on the firing angle alpha Î± which is used as a delay to trigger the thyristors to switch on. Alpha is measured from a zero crossing of voltage. A firing angle of 90° results in full conduction of the thyristors. Partial conduction is obtained with firing angle between 90° and 180°. "Firing angles between 0° and 90° are not allowed as they produce asymmetrical currents with a dc component." 
A TCR acts as a controllable susceptance, as. Full conduction of the thyristors at 90° results in the maximum value of susceptance from the TCR. The thyristors are none conducting as 180° resulting in a zero susceptance from the TCR. The susceptance of the TCR varies as a function of Î± as shown by Equation (1). 
The susceptance is switched into the system by the TCR for a "controllable fraction of every half cycle depending on the firing angle".  Changing the amount of susceptance switched into the system determines the amount of MVAr that will be absorbed by the TCR. The TCR requires a control system to determine the firing angle of the thyristors to achieve the correct susceptance value. The control system responds to an error signal in the voltage between a reference voltage Vref and a measured voltage Vmeasured.
INITIAL DESIGN SPECIFICATIONS
TRANSMISSION LINE PARAMETERS
Figure . Single line diagram of transmission line with SVC connectedFigure 3 above shows the SVC connected to a simple transmission line. The transmission line parameters are given below in table 1. The transmission line is fed from a 400kV 50 Hz source and is connected to a varying load. The transmission line is 200km long. The SVC is connected in shunt with the transmission line through a transformer. The object of the SVC is to match the magnitude of the receiving end voltage VR with sending end voltage VS within a certain percentage while the load varies. (Either being capacitive or inductive and at different MVAR ratings).
Table . Transmission line parameters
RL is the resistance, XL the inductive reactance and BC the capacitive susceptance. These values are given per km of the transmission line and must be multiplied by the line length in order to get the total values. These values are calculated  in equations (2-4) below and are shown above in Figure 3.
The model of the SVC will be built in the computer simulation package PSCAD. The model considers the SVC as a shunt-connected variable susceptance BSVC, which changes automatically due to the controller to achieve voltage control. The equivalent susceptance Beq needed for reactive compensation is determined by the firing angle Î± of the thyristors. The switching of the thyristors causes harmonics which must be reduced using harmonic filters. The reduction of harmonics will be discussed in more detail in following sections.
TCR's conduct between a firing angle of Î±=90Ëš to Î±=180Ëš. When the firing angle is at Î±=90Ëš the thyristors are fully conducting and when the firing angle Î±=180Ëš, the thyristors are not conducting. By controlling the firing angle of the thyristors, the susceptance is controlled and hence the device is able to control the amount of MVAr consumed from the system. Controlling the amount of MVAr being absorbed in turn controls magnitude of the voltage at the bus that it is connected to. As the load changes, the firing angle must change by means of a control system. As the load increases (capacitive load), the firing angle must decrease from 180Ëš towards 90Ëš so that more reactive power is consumed. The receiving end voltage VR, must be within range of 5% with respect to the sending end voltage VS.
Figure 3 above illustrates a simple transmission line with a varying load connected. This load was varied for different ratings of MVAr and at different power factors. This allowed for a range of loads to be tested in order to determine the limits of the SVC. The surge impedance loading or SIL was calculated and used as a reference to determine the loads that the SVC will be able to compensate for. The SIL of a transmission line is defined as "the MW loading of a transmission line at which a natural reactive power balance occurs."  This means that there is no reactive power flow along the transmission line at the SIL. A transmission line produces its own reactance due to the reactive capacitance of the line (XC). The transmission line is also able to absorb some of the reactance produced because of its inductive reactance (XL). The point where the amount of reactive power produced by the transmission line is equal to the amount of reactive power absorbed is shown below by Equation (5) .
At this point there is no net reactive power flow into or out of the line.
The SIL can be calculated by Equation (6) below:
Using the parameters given in table 2 above, the SIL of the transmission line was calculated using equations (5) and (6).
When the load from the transmission line is P0=537.456 MW, there will be no reactive power flow through the transmission line. Using this point as the reference, different loads can be calculated for the transmission line for different ratios of MVA/P0, as shown in Table 3 below.
Table . Varying loads for transmission line
These calculated loads were then used in the PSCAD model. Each load was tested in the model to see how it affects the receiving end voltage Vr. Vr was measured and tabulated as shown below in Table 4. The voltages were measured to obtain a range that the SVC will operate at.
Table . Receiving end voltages for different loads
The voltages in table 4 above were then plotted against the MVA/P0 and the result is shown below. This graph illustrates the range of Vr against the MVA/P0 for different loads connected in shunt to the transmission line.
A: Maximum capacitive
B: Maximum inductive
Figure . Limits of operation of the SVC
The above graph illustrates the change in the voltage at the receiving end for the different loads. The greatest difference in Vr exists for the 0.9 leading load and the 0.9 lagging load as shown in Figure 4 above. Point A shows the maximum value that Vr reaches with the capacitive load and point B shows the minimum value that Vr reaches with the inductive load. The magnitudes of the loads at these two points are shown below in Table 5. These two points determine the maximum reactive compensation needed for the TCR (point A) and TSC (point B).
Table . Maximum limits of operation
Point on Curve
The sending end voltage Vs and the receiving end voltage Vr were measured at these two different loads shown in the table above to determine the amount of MVAr to correct the voltage difference. The capacitive loads results are depicted in Figure 5.
Figure .Vs and Vr for point A load
The voltages shown above are in per unit (pu). The purpose of the SVC is to inject or absorb reactive power into or from the transmission line. The amount of MVAr required by the TCR to decrease Vr to 1 pu is 245 MVAr. This amount can be confirmed by Figure 6 below.
Figure .Vs and Vr for point A load
Figure 7 below illustrates the difference in Vs and Vr for the maximum inductive load.
Figure .Vs and Vr for point B load
The amount of MVAr needed for the TSC to increase Vr to 1 pu is 1260 MVAr. This can be confirmed in Figure 8 below
Figure .Vs and Vr for point B load
The size of the transformer used will be a 1300MVA 400kV/20kV star-delta. 1300 MVA is used to be able to supply the 1260 MVAr and 245MVAr from the TSC and TCR respectively.
Design of SVC parameters
THYRISTOR CONTROLLED REACTOR (TCR) VALUES
The TCR consist of an inductance which value needs to be calculated in order to switch in the correct amount of reactance. The amount of MVAr needed (QTCR) to decrease Vr to 1 pu is 245MVAr.The TCR will be connected in delta (to eliminate triple harmonics) so the amount of reactive power that each inductor can absorb (QL) must be calculated.
The TC R will need to supply a maximum of 81.667 MVAr across each phase of the delta connection. The size of the inductor (L) was calculated as follows:
A 15.591 mH inductor will be connected in each phase of the TCR to absorb the correct value of reactance needed to decrease Vr to 1 pu. This value of inductance will cause the TCR to absorb 245 MVArat full conduction of the thyristors. Values below 245MVAr will be absorbed by changing the firing angle of the thyristors.
COMPARISON OF TCR SUSEPTANCE vs FIRING ANGLE
The TCR susceptance (BTCR) was compared against the firing angle Î± to see how the susceptance changes as the firing angle changes. The theoretical comparison was done by using equation (1). The equation was used in MATLAB to plot the results. The susceptance vs firing angle curve is shown below in Figure 9. The MATLAB code required to plot this curve can be found in Appendix A.
Figure .Theoretical Comparison of BTCR and Î±
Table . Susceptance values at varied firing angles
The simulated results were plotted as shown below in Figure 10. These were simulated in PSCAD by measuring the voltage and the current in the line for different firing angles, and calculating BTCR (BTCR =ILINE/VSOURCE) from these values..
Figure . Simulated comparison of BTCR vs alpha
OPERATION OF TCR
The inductance value calculated in Equation (9) is the size of the inductor that will be used in the TCR. The inductor in each phase of the TCR is split into two halves, one on each side of the anti-parallel connected thyristor pair, to prevent the full ac voltage appearing across the thyristor valves and damaging them if a short circuit fault occurred across the reactors two end terminals. The switching of the inductors at different firing angles changes the value of the susceptance, which causes a change in the amount of VARs absorbed.
The switching of the thyristors is based on the following circuitry shown in Figure 11 below. A PLL (phase locked loop) generates a ramp signal theta, which varies between 0° and 360°. This signal theta is synchronized in phase with the input voltages. The outputs from the PLL are compared with the firing angle Î± in the interpolated firing pulse (IFP) to generate the correct switching of the thyristors. The IFP generates an output pulse to turn on the thyristors. The output of the interpolated firing pulse is based on a comparison of high and low input signals. The low input is the firing angle ¡ and the high input is theta from a phase-locked loop.
The circuit diagram of the TCR connected to the transmission line can be found in Appendix B. Figure 11 below illustrates the firing scheme.
Phase B', FP4
Phase C, FP5
Phase A, FP1
Phase A', FP2
Phase B, FP3
Phase C', FP6
Figure . PLL and Interpolated Firing Pulse Generation signals
The inputs from to the PLL are the line voltages from the secondary side of the transformer. These are used instead of the line voltages of the transmission line to prevent the phase shift of the voltages through the transformer from affecting the firing scheme. A transformer is used to connect the TCR to the transmission line so that the TCR operates at lower voltages; therefore the components in the SVC are smaller, saving on cost. The IFP generates the firing pulses based on the phase rotation. Phase A receives firing pulses FP1 and FP2. Phase B receives FP3 and FP5. Phase C receives FP4 and FP6.
7.3.4 THYRISTOR SWITCHING
Figure 12 illustrates the firing scheme of phase A when Î±=90°. At a firing angle of 90°, there is full conduction of the thyristors. This can be seen by the bottom graph in figure 12. It shows that the current is sinusoidal.
Figure . Phase A at alpha = 90 degrees
Figure 13 below illustrates the switching of the thyristors at Î±=135°
Figure . Phase A at Alpha = 135 degrees
Figure . Phase A at alpha = 180 degrees
Figure 14 illustrates the switching of the thyristors at 180Ëš. It can be seen from the current curve that no current is flowing and hence the thyristor is not conducting.
DESIGN OF HARMONIC FILTERS
Harmonic currents in power systems shorten the equipment's life expectancy and can interfere with communication lines and sensitive equipment. The TCR generates harmonics from the switching of the thyristors. In a three phase system the TCR is connected in delta to prevent all triple harmonics from entering the line, the delta causes the triple harmonics to circulate in the closed delta. A filter is needed to remove the lowest order harmonics that are not trapped by the delta connection. A filter will be needed to trap the 5th and 7th harmonics.
The size of the harmonic filter (MVAr rating) is set to be 19% to that of the size of the TCR. This was selected as the optimum value. Specifically tuned filters were used to diminish the 5th and 7th order harmonics.
Qfilter=0.19 QTCR, the size of the TCR was determined in the previous section to be 245 MVAr. The following equations  are used to calculate the size of the harmonic filters.
Qfilter= 45 MVAr
Qfilter(5th) = 30 MVAr
Qfilter(7th) = 15 MVAr
5th ORDER HARMONIC FILTER
From equation (10),
From equation (11),
From equation (a),
Sub equation (b) in equation (a),
7th ORDER HARMONIC FILTER
From equation (10),
From equation (11),
From equation (c),
Sub equation (d) in equation (c),
COMPARISON OF HARMONICS
The harmonics were measured before and after the filters were placed into the circuit. A comparison was then made on hoe effective the filters are at reducing the 5th and 7th order harmonics. A FFT (fast fourier transform) block was used in PSCAD to measure the harmonics. The FFT receives the line current as the input and outputs the corresponding harmonics in that line. Figure 15 below shows the harmonics in each phase of the transmission line for a firing angle of 130Ëš. The first column shows the current at the fundamental frequency (50Hz). The second column shows the 5th order harmonic and the third column shows the 7th order harmonic.
Figure . Harmonics with no filter, Alpha=130 degrees
Figure 16 below shows the magnitude of the harmonics when the filters have been placed into the circuit. The harmonics were measured at a firing angle of 130Ëš.
Figure . Harmonics with filters, alpha = 130 degrees
As can be seen from Figure 15 and 16 above, the harmonics have decreased with the inclusion of the filters. The 5th harmonic has decreased by 95% and the 7th harmonic has decreased by over 99%. Using tuned filters to the correct frequency of the harmonics, results in the harmonics being eliminated. The filters are connected as shunt filters, and act as a short to earth at the respectively tuned frequencies. The circuit diagram showing the connections of the harmonic filters can be found in Appendix B.
ABSORBTION MODE CONTROL
The TCR uses a control circuit to determine the amount of MVAr to be absorbed form the system. A voltage regulator loop continuously monitors the systems variables and generates an output signal that is proportional to the desired reactive power compensation. The following voltage regulator loop shown in Figure 17 below was used as the switching control for the TCR.
Figure . Voltage regulator for absorption mode control
Vref is the reference voltage and is set to be 1 pu. Vmeasured is the measured voltage on the HV side of the transformer. G is the static gain and is defined as the reciprocal of the current droop characteristic. The current droop is 1% so G was set at 100. T is defined as the thyristor firing delay and is set to be 200ms . These values were chosen for a critical damped system response. The Transfer function was limited in per unit between Bmax at 1pu and Bmin at 0.02pu . The base used for susceptance was 0.204S calculated from Equation (8). This transfer function acts on the voltage error between Vref and Vmeasured to produce a susceptance value within the range of limits. The non-linear transfer characteristic outputs the correct firing angle depending on the susceptance value that is obtained from the error signal in voltage. The non-linear characteristic was measured in Section 6.3.2 and table 6 was used to provide values for the non- linear relationship.
Figure 18 below illustrates the relationship between the susceptance and the firing angle. If the output from the transfer function is BTCR=1pu the non-linear characteristics will send an output of 90° to the interpolated firing pulse. The minimum output of Bmin=0.02 pu will correspond to a firing angle between 155° and 160°.
Figure . Non-Linear transfer characteristic table
TESTING ON CAPACITIVE LOAD VARIABLES
The first test was done without the TCR connected to the transmission line. A load was placed on the receiving end of the transmission line as shown below in Figure 19.
Figure . Capacitive loads
Figure . Voltage measured at receiving end with no TCRAt time t=0s, Circuit Breaker 1 (CB1) was closed, CB2 was open and CB3 was open. At t=1s, CB1 was opened. At t=1.3s CB2 was closed. At t=2s CB2 was opened and CB3 was closed. This resulted in the following voltage at the receiving end.
As can be seen from figure 20 above, the voltage measured at the receiving end increases to 1.12pu as more capacitive load is added to the transmission line. With the TCR included, the measured voltage stabilizes back to 1.017pu, shown below in Figure 21. This is within the acceptable limits of 5%.
Figure . Voltage measured at receiving end with TCR included
Figure 22 below illustrates the response of the controller to this variation in load. The circuit breaker operations, BTCR and Î± are shown.
Figure . Response of controller with variation in load
VARIATION IN REFERENCE VOLTAGE
A step change was applied to the reference voltage to view how the system responds. The receiving end voltage VR must follow Vref. Vref was initially set to 1.05pu. At a time t=0.5s Vref was changed to 0.95pu. At t=1.5s, Vref was changed to 1pu. Figure 23 below illustrates the step in Vref and the response caused by the controller on VR.
Figure . Variation in Vref and response of Vr
The project specifications have been presented in the report. The goal of the SVC is to stabilise the voltage at the receiving end of the transmission line. The SVC parameters were calculated based on the specifications given for the transmission line and the required loads that it will need to compensate for. The TCR was designed to the given specifications and the control system to control the amount of MVArs being absorbed by the TCR was designed. The harmonic filters to eliminate the 5th and 7th harmonics was designed and tested to prove that the harmonics are eliminated. The next phase of the design involves the design of the TSC and the TSC control scheme to control the amount of MVArs being injected into the system.
MATLAB CODE FOR PLOTTING SUSCEPTANCE VS FIRING ANGLE
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