In the two-level SSSC controller described in section 3.2, the final angle sent to the low-level firing controls is 8v + ~
=
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
(alXq':Sen EMTP
-0.2 -0.3
o
I
f--
0.6 0.4
Xq': EMTDC
0.2
I
f--
L - -
0.1 0.2
-0.2 -0.3
o
'1: 0
:::J
:f
-0.10.6 0.4
0.2 0.1
0.2
§ o
:f
-0.1(b)is:Sen EMTP
2 2
'1:
~
'1::::J 0 :::J
Q; Q;
0. 0.
-1 -1
-2 -2
0 0.2 0.4 0.6 0
(clvDdSen EMTP
0.2 0.4 0.6.
0 . 5 , - - - ,
0.5 0.4 '1: 0.3 :::J
Q; 0.2
0.
0.1 0
-0.10 0.2 0.4 0.6
e2.:EMTDC 0.5
0.6 0.4
0.2
(d) e2.:Sen EMTP
f\11/
- r
n"A IV
WV
r-
1 0.4
0.1
o
0.5
-0. o
'1: 0.3 :::J
£
0.2'1: '1:
:::J 0 :::J 0
Q; Q;
0. 0.
O.q
0.2 0.4
Time (5)
-0.5 '-- ~ ~_ _- - - - J
-0.5~---~---~--~ o
o 0.2 0.4 0.6
Time (5)
Fig.3.J3:Pelformance of a two-level SSSC as modelled in EMTP[34
J
and a stand-alone three-level SSSC as modelled in PSCADIEMTDC: (a) Xq*; (b) ia; (c) VDC; (d) e2a'(e)Pq:Sen EMTP P:EMTDC q
2 2
1.5 1.5
'c 'c
::> ::>
~ 1 ~ 1
a.. a..
0.5 0.5
00 0.2 0.4 0.6 00 0.2 0.4 0.6
(f)Oq: Sen EMTP 0: EMTDC
q
0 0
-0.5 -0.5
'c 'E
::> ::>
~ ~
a.. a..
-1 -1
.1.5oL - - - -o:o"".2::---,,-O....,..4---.,-10.6 .1.50~--...,..0."::"2----:-0...,..4---:-'0.6
Time(5) Time(5)
Fig.3.B (continued): Peiformance of a two-level SSSC as modelled in EMTP [34] and a stand-alone three-level SSSC as modelled in PSCADIEMTDC: (e) Pq; (j) Qq.
Dead Angley 100
80 ID~ 60
Cl0.>
~ 0.>
Clc 40
«
20
00 0.1 0.2 0.3 0.4 0.5 0.6
Time(5)
Fig.3.14: Variation. of the dead angle rin the stand-alone three-level SSSC as modelled in PSCA DIEMTDC.
The left hand side of Fig. 3.13 shows the dynamic response of the two-level SSSC to changes in commanded compensating reactance Xq
*
as simulated using the EMTP model of Sen [34], whereas the right hand side of Fig. 3.13 shows the simulated results of the stand-alone three-level SSSC to the same changes in Xq*
using the detailed PSCADIEMTDC model presented in this chapter. As in section 3.2, in each case the sending and receiving end voltages in the transmission line are kept at constant magnitude and the transmission angle (phase betweenV,·
and Vr ) remains fixed. The SSSC is then used to alter the magnitude of the line current by changing both the size and nature of the commanded compensating reactance.At time t = 0 in Fig. 3.13, Xq
*
= 0 and the inverter injects zero volts into the line, with its dc capacitor voltage, VDC , likewise zero in the case of the two-level SSSC considered by Sen (left-hand side of Fig. 3.13(c)). On the other hand, the dc voltage is set at 60kV (0.53 pu) for the y-controlled SSSC shown on the right-hand side of Fig. 3.13(c) throughout the entire analysis.Because of this non-zero dc voltage, the dead angle y is adjusted to 90° (i.e. zero on-pulse for the turn-off devices in the inverter), in order to achieve zero ac output voltage in the case of the y-controlled SSSC when Xq
* =
O. The transmission line is thus initially operating with no series reactive compensation in the case of both SSSC models in Fig. 3.13. (Fig. 3.14 shows the value of y in the three-level SSSC at each stage during the transient response shown in Fig. 3.13.)At t = 50ms, the desired reactance Xq
*
is stepped up to 0.15 pu inductive (i.e. Xq* = -0.15).Immediately, the line currentiaand both the active (Pq) and reactive (Qq) powers at the receiving end decrease because of the increase in net reactance between the sending and receiving ends of the transmission line. The inverter output voltage, eza , of phase a leads the line current, ia> by almost 90°, and therefore mimics the desired inductive characteristic. When Xq
*
is increased to 0.3 pu inductive at t = 175ms, the magnitudes of inverter dc voltage and ac injected voltage increase accordingly in the case of the two-level SSSC. For the three-level SSSC, y decreases from 65.2° to approximately 48.5° thus increasing the width of the on-pulse of each turn-off device and therefore increasing the fundamental magnitude of the compensating voltage.At t=300 ms, the commanded reactance Xq* is step-changed to 0.1 pu capacitive (i.e. Xq* =+0.1).
Due to this step change from a negative to a positive value, Xq
*
momentarily passes through zero which results in y shooting up to almost 90° then settling to approximately 59°. The net reactance of the line is now lower than its uncompensated value and therefore the line current, active power and reactive power increase; the inverter output voltage, eZa> of phaseanow lags the line current, ia> by almost 90°. The injected ac voltage magnitude decreases with the reduced magnitude ofXq*. WhenXq* is increased to 0.15 pu capacitive at t=
450ms, the injected ac2.5 2.5
2 2
1.5 1.5
=-
'c=-
::::> '2:
.... 0.5 0.5 ::::>
c..(I) ....
--
~(I)c.. 0
I- 0 U
~. 0
LU I-
~ -0.5 -0 5 ~
(/) . w
..Cl> .:":Cl>
'-
-1 -1-1.5 -1.5
-2 -2
-2.5 -2.5
0 0.1 0.2 0.3 0.4 0.5 0.6
Time (s)
Fig. 3.J5: The line current, ia : two-level SSSC in EMTP [34Jvs. three-level SSSC in PSCADIEMTDC.
voltage, line current and the power flow in the transmission line all increase in magnitude due to this higher degree of compensation.
Inthe simulation results shown in Fig. 3.13, both forms of compensator (three-level and two-level SSSC) are commanded to provide the same dynamically-varying compensating reactance to the
~ame transmission system. Thus, despite the differences in internal control approach in the two SSSCs, the ac performance in the line should be the same in each case. One transmission variable, the line current ia, is chosen to demonstrate this. Fig. 3.15 shows this same variable from the three-level SSSC case and the two-level SSSC case plotted on the same axes. Fig. 3.15 confirms that the steady state and dynamic performance of the ac line variables is virtually identical as the two forms of SSSC compensation are used to vary the effective reactance of the line.
Recall that in the case of the two-level SSSC, there is no change in the dead angle of the inverter, so the variable magnitude of ac compensating voltage is achieved by varying the dc voltage of the inverter. However, in the case of the three-level SSSC, the inverter dc voltage Vdc is fixed at 60kV (0.53 pu) and the dead angleyis varied to change the magnitude of the ac compensating voltages. This section has thus confirmed that despite this difference in control approach, the three-level stand-alone SSSC developed in this chapter is able to provide the same dynamic variation of compensating reactanceXqas the stand-alone two-level SSSC of Sen, but with a fixed de voltage.