The 24-Pulse Three-Level Inverter Based SSSC

system structure and parameters, with the exception of some aspects of the SSSC high-level controller are the same as those in [34] in order to demonstrate the correctness of the SSSC model later in the chapter. The following section describes the modified control scheme for the three-level stand alone SSSC used to vary the inverter's ac output voltages to meet the commanded compensating reactance by adjusting the dead angle,y.

3.5.2 Stand-Alone Three-Level SSSC Controller

I I I

Phase-Locked :

I Loop Angle Control :

I : : I

L - - - ^{~ J )}

I I

I 1

1

r---,---,

1

1 I

I 1 I

I : Dead Angle Calculator I

: : <:b

Dead Angle

I Magnitude:

t

^{I Calculator}

Control I

I : Vnc

I ~---.::

I : : I

X^q

*

^{I : Vnc}* : I

I r I

__ 1 ~ , : :

I

I :

^I

I 1 DC Voltage 1

~

^I

I :

l

I

I Magnitude ¹ Regulator . 0+ I

I and Angle : I

I - - - - I

I I

I Iq I

: r - - - -I I

I ~ ^r y I

: I

1 I

82 : PatternGate Logic

Fig.3.ll: Control block diagram of a stand-alone three-level inverter-based SSSc.

Fig. 3.11 shows the high-level control block diagram of the stand-alone three-level inverter-based SSSC developed for this thesis, where the ac output voltage from the SSSC is varied by controlling the inverter's dc-to-ac gain. The diagram is once again broken down into three sub-sections according to the three control requirements of the SSSC. The synchronization of the SSSC to the bus 1 voltage and the calculation of the desired angle Byof the injected voltages for exact quadrature (the section labelled Angle Control in Fig. 3.11) is the same as in the

two-level SSSCcontroller in section 3.2. However, the subsections of the controller responsible for magnitude control and dc voltage regulation are now modified from those in the two-level SSSC controller, as explained shortly. As in the two-level SSSC controller, the final output of the high-level controls is the angle sent to the inverter's low-level firing controls, which determine the firing signals for each turn-off device within the inverter. The specific implementations of the magnitude control and dc voltage regulator in the stand-alone three-level SSSC are now explained in more detail.

3.5.2.1 Magnitude Of The Desired DC Voltage

The first important change to the dc voltage regulator from the two-level SSSC in section 3.2 is the input to the voltage regulator: in the three-level, stand-alone SSSC the desired value of the dc voltage is set by the reference input V_dc

*

which is no longer a function of the desired ac compensating voltage V_q*. The value of this reference input is determined by the operator and can be adjusted from time to time to suit the operating conditions in the transmission system.

Despite this change in the way its input is determined, the operation of the regulator itself remains the same: any error between Vde

*

^{and V}dc is passed through the error amplifier (PI controller) to determine the offset angle ~ to be added or subtracted from the angle of the injected voltages as needed to charge or discharge V_dcunder capacitive or inductive mode.

Although the reference value of the inverter dc voltage in this three-level stand-alone SSSC is now decoupled from the commanded value of ac compensating voltage Vq

*

in the controller, its value cannot be chosen completely independently of V_q*. Recall that for a given dc voltage there is a maximum ac output voltage in a three-level inverter. The magnitude of the ac compensating voltage V_q

*

required at the output of the inverter will vary depending on the range of desired magnitude of reactance X_q

*

and the magnitude of the current I flowing in the transmission line.

Therefore for a given value ofXq

*

the dc voltage needs to be sufficient to supply the requiredVq

*

at the largest value of line current envisaged. In practice, there is a maximum rating of Vdc

(based on the two physical dc capacitors used in the inverter) and of Vq

*

(based on the rating of the injecting transformers). Therefore, there would be a maximum value of Vdc that the controller can ask for based on the actual ratings of the equipment used in practice (for both types of stand-alone SSSC: two-level and three-level.)

Recall also (as discussed in Chapter Two) that at low values of ac compensating voltage (relative to the dc voltage), the dead angle 'Y is closer to 90° and the amplitudes of harmonics increase.

Hence as ac conditions in the line change, the value ofVdc

*

may have to be increased in order to

accommodate larger commanded values of Vq

*

or decreased to improve the harmonic performance at lower commanded values of V_q*. Once V_dc* is so set, V_q* can then vary independently of the inverter dc voltage provided the angleyremains in the range 0°~y::;90°.

In the stand-alone three-level SSSC, it is therefore crucial that the operator has some idea about the desired range of compensating reactance and the transmission line current in order to appropriately select the necessary magnitude of dc capacitor voltage within the inverter.

3.5.2.2 Magnitude Control

With respect to the desired ac compensating voltage V_q*, the control objectives in the three-level SSSC are the same as in the two-level SSSC described in section 3.2, and hence V_q

*

is calculated in the same way i.e. IVq*1

=

^II I x Xq*. However, now that the magnitude of the SSSC output voltage is varied using the dead-angle of the inverter, an extra stage in the magnitude controls is required to determined the correct value of ybased on the desired value of V_q

*

and the actual value of the inverter's dc voltage (as determined by the set point V_dc*).

The relationship between the magnitude of the compensating voltage vector and the dead angle,y, for a 24-pulse three-level inverter is defined [27] as

V_q =

~

^{V DC}

COs(~ )COS

^'Y

7t 24 (3.24)

Since the desired output is the dead angle, by changing the subject of the formula, Equation (3.24) becomes

'Y⁼

COS-I

_(3.25)

Therefore, depending on the desired inverter ac voltage output (i.e. the commanded value of V

q*) and the actual value ofVdc , the controller will determine the correct value ofybased on Equation (3.25). This calculation ofyfrom Vq

*

^and Vdcusing Equation (3.25) is shown as the Dead Ano-le

o

Calculator block in Fig. 3.11, although the value of V_dc used in the calculation is not shown explicitly in Fig. 3.11.

In the two-level SSSC controller described in section 3.2, the final angle sent to the low-level firing controls is 8_v + ~

=

⁸2• This angle 8₂ is the phase angle of the system-frequency ac voltages that will appear at the output of the inverter; this phase angle 82of the system-frequency ac voltages is also an output of the stand-alone three-level SSSC as shown in Fig. 3.11. However, in the three-level SSSC the required dead angle yfor the inverter is an additional output to the low-level firing controls. (In the SSSC controls of section 3.2, yis not an output of the SSSC controller since the SSSC controls are intended for a two-level inverter in which there is no capability for dead angle control.)

Dead-Angle Calculator

r---,

I I

Vq'*cos(~)~1 ~ I _~ ^{+ lacosOI i} _~y

I I

L ~ _ _ J

Fig. 3. 12: An Expanded and Detailed Diagram of Dead Angle Calculator sub-block from Fig.

3.11.

3.6 Benchmark Results For The Stand-alone Three-Level SSSC In