HVDC Link Steady-State
Description
Implement a steady-state model of a two terminal HVDC link, used
to find the DC load flow solution. Embedded in a Simulink model, the solution is reached after a certain
number of iterations or simulation steps. The solution
criteria being that the tap ratio at both terminals have reached steady-state
values.
The link is a DC line in series
with smoothing reactors where only the resistances are considered. A terminal
is constituted by one or more converter units connected in series. A converter unit comprises: a tap-changing
linear transformer connected to a 6 pulse line-commutated converter, control
systems for the converter and the tap-changer.
The block inputs and outputs are workspace constants. The
block uses as inputs, the AC converter voltages at rectifier and inverter buses and
the converters transformer tap ratio, and returns as outputs the respective AC active
and reactive powers. The load flow solution is obtained running the model for a
certain number of time steps (or iterations) until the tap ratio at both
converters remains unchanged.
The model equations are represented in Simulink and
organized as follows:
·
The basic converter equations, for both rectifier and
inverter operations, describing the relationship between the AC and DC
variables,
·
The DC link equation expressing the interdependence of
the two DC voltages (rectifier and inverter side),
·
The converters controller equations determining
the DC voltage for the minimum alpha (at rectifier) or the minimum gamma (at
inverter) control modes,
·
The transformers tap-changer controller
equations for setting the tap position to maintain AC or DC variables: alpha (rectifier), gamma (inverter), DC
voltage, Udi0 voltage within defined range,
·
The master control equations for: allocation
of the DC link power loss to one of the converters when in power control mode, switching
the current control to the inverter from the rectifier when it must operate in
the minimum alpha mode.
The modeled control modes are as follow:
·
Primary control modes: DC power flow, DC current at
rectifier, DC voltage at inverter, extinction angle gamma at inverter,
Note: In power control mode, either the rectifier or the inverter is
chosen as the slack station compensating for DC link losses.
·
Auxiliary
control modes: minimum firing angle alpha at the rectifier, minimum extinction
angle gamma at the inverter, DC current at the inverter – when the rectifier
can no longer control the current and goes in minimum alpha mode.
·
Tap
changer control modes: firing delay
angle at the rectifier, extinction angle at the inverter – when the inverter is
regulating the DC voltage, DC voltage at the inverter – when the inverter is
regulating gamma, Udi0 voltage (i.e. the secondary voltage).
Parameters
Number of 6 pulse converter
units
Specify
the number of series-connected 6 pulse converter units at the rectifier
converter station.
Power
The
transformer nominal power, in MVA, per converter unit.
Primary winding (AC
side) parameters
The phase-to-phase nominal
voltage in kV RMS, resistance, and leakage inductance in pu
for winding 1.
Secondary winding (DC
side) parameters
The phase-to-phase nominal
voltage in kV RMS, resistance, and leakage inductance in pu
for winding 2.
Minimum alpha
Firing delay angle alpha (deg.) at the rectifier
when it is no longer regulating the current.
The auxiliary minimum alpha control mode is activated when the secondary
voltage cannot be increased sufficiently by the tap changer (because outside of
its tap range) to maintain alpha within the defined angle range.
Lock tap position
If
selected, the transformer tap position is locked at the defined initial value.
Udi0 control mode
If selected, the rectifier tap changer control
regulates the ideal no-load direct voltage Udi0 of a 6 pulse converter unit.
Angle
range [min, max]
Range of the alpha angle, in deg., at the rectifier. The
tap changer control objective, when not in Udi0 control mode, is to maintain
alpha within this range. The lower limit should be set higher than the “minimum
alpha”.
Udi0 reference
Reference value, in
kV, for the tap changer control when it is in Udi0 control mode. To avoid tap
changer hunting a dead-band of 1.5 tap steps is used.
Tap step size
Step change in the transformer turn ratio (N primary / N secondary) per one tap change.
Tap
range [min, max]
Transformers
turn ratio range, in pu, at the
rectifier. The tap changer cannot step outside these limits.
Tap ratio
Initial value of the transformer turn ratio,
in pu. Equivalent to the tap
position at the primary side.
Primary AC voltage
The phase-to-phase
assumed initial voltage, in kV RMS, at the rectifier primary side.
Number of 6 pulse
bridges
Specify
the number of series-connected 6 pulse converter units at the inverter.
Power
The
transformer nominal power, in MVA, per converter unit
Primary winding (AC
side) parameters
The phase-to-phase nominal
voltage in kV RMS, resistance, and leakage inductance in pu
for winding 1.
Secondary winding (DC
side) parameters
The phase-to-phase nominal
voltage in kV RMS, resistance, and leakage inductance in pu
for winding 2.
Control mode
·
DC voltage
·
Gamma angle
Specify
the principal control mode at the inverter.
Gamma reference
Reference value, in deg., when in gamma angle control
mode. The value should be set higher than the defined “minimum gamma”.
Voltage reference
Specify the desired DC voltage, in kV, at the
measurement point, in the DC network, when in DC voltage control mode.
Minimum Gamma
Specify the minimum extinction angle gamma, in
deg. A constant minimum gamma auxiliary
control mode is activated when the secondary voltage cannot be increased
sufficiently by the tap changer (because outside of its tap range) to maintain
gamma within the defined gamma angle range.
Lock tap position
If
selected, the transformer tap position is locked at the defined initial value.
Udi0 control mode
If selected, the inverter tap changer control
regulates the ideal no-load direct voltage Udi0 that is proportional to the
secondary voltage.
Angle
range [min, max]
Range of the gamma angle, in deg., at the inverter.
The tap changer control objective, when not in Udi0 control mode, is to
maintain gamma within this range. The lower limit should be set higher than the
“minimum gamma”.
Note: When the inverter controller is regulating gamma,
the tap changer control will try to maintain the DC voltage around the reference
value. To avoid tap changer hunting a dead-band of 2 tap steps is used.
Udi0 reference
Reference value, in
kV, for the tap changer control when it is in Udi0 control mode. To avoid tap
changer hunting a dead-band of 1.5 tap steps is used.
Tap step size
Step change in the
transformer turn ratio (N primary / N secondary) per
one tap change.
Tap
range [min, max]
Transformers
turn ratio range, in pu,
at the rectifier. The tap changer cannot step outside these limits.
Tap ratio
Initial
value of the transformer turn ratio, in pu. Equivalent
to the tap position at the primary side.
Primary AC voltage
The phase-to-phase assumed
initial voltage, in kV RMS, at the inverter primary side.
Total link resistance
Specify the DC network total series resistance,
in ohms, constituted generally by the DC line (Cable/OH line, ground electrode) )and the smoothing reactors.
Resistance between voltage
measurement and converter
Specify the resistance, in ohms, of any
element (generally the smoothing reactor) placed between the voltage
measurement point and the converter controlling the DC voltage, i.e. the
inverter.
Control mode
·
Blocked
·
Power
·
Current
Specify the master control mode of operation.
The Blocked mode is used to cancel
the DC power flow. The Power mode is used to regulate either the power supplied by the
rectifier or the power received at the inverter. The Current mode is used to regulate the DC current.
Slack station
·
Rectifier
·
Inverter
Specify the converter that will compensate for the DC network power losses. The
power losses will be added at the rectifier slack or subtracted at the inverter
slack.
Power reference
Specify the desired DC power, in MW, supplied
by the rectifier (when the inverter is the slack station) or received at the
inverter (when the rectifier is the slack station).
Current reference
Specify
the desired DC current, in kA.
Inverter DC voltage
threshold in power control
Specify the lower limit of the DC voltage measurement,
in kV, used in the power control mode. The default value is 94% of the nominal
DC voltage.
Note: it is recommended not to change this value
Inverter current
margin
Specify the current margin, in kA. This value
is subtracted from the rectifier’s DC current reference to define the
inverter’s current reference. The inverter would regulate the DC current
whenever the rectifier is in the auxiliary minimum alpha control mode.
Sample time
The
sample time of the block, arbitrarily set to 1 second.
The load flow result variables are shown by clicking the “Compute and
Update” button. The variables are available in the workspace. The R
and I suffixes refer respectively to the rectifier and inverter.
Compute and Update
Button to compute the load flow and update
the shown result values.
Eac_R, Eac_I
AC voltage at
primary side, in kV.
Idc_R
DC current, in kA.
Pac_R, Pac_I
AC power into the converter station,
in MW.
Qac_R, Qac_I
Reactive power consumed by the converter unit.
Pdc_R, Pdc_I
DC power exciting the converter station
and into the DC line, in kV
Tap_pu_R, Tap_pu_I
Transformer tap ratio (Nprimary/Nsecondary), in pu.
Tap_limited_R, Tap_limited_I
Flag indicating (1/0) the tap changer
position has reached its minimum or maximum limit.
Udi0_R, Udi0_I
Ideal no load direct voltage of a (6 pulse) converter unit,
in kV.
Vdc_R. Vdc_I
DC output voltage of the converter station,
in kV.
Alpha_R, Alpha_I
Firing delay angle alpha, in deg.
Gamma_I
Exctinction delay angle gamma,
in deg.
DC_iter
Number of iterations for the load flow
solution.
Open the
Simulink model Link_A.The
HVDC Link Steady-State block
parameters default values are those for the HVDC link average model embedded in
the network model LF_AC29bus_HVDCdemo_V2_1.
In this example, the load flow solution takes in consideration a typical tap
changer control with the master unit controlling the DC power.The DC power is set at 1000 MW to be received at the inverter (the
rectifier is chosen to be the slack station). The auxiliary mode, when there is
a dip in AC voltage would be the alpha minimum mode, set to 5°. At the
inverter, the main control mode is the DC voltage, set at 500 kV. The auxiliary
mode, when there is a dip in AC voltage would be the minimum extinction angle
gamma set to 17°. The tap changer control is set to hold α angle between 14° and 17° at the rectifier and the gamma angle between
20° and 23° at the inverter. The initial tap ratios at both
ends are set to 1 pu, and the AC voltages at 1 pu.
Start the simulation to compute the load flow. Observe the recorded main
variables to see how they vary from step to step toward a solution. These variables
are available in the workspace. After 6 iterations, the solution values for the
tap ratios are 0.9375 pu at the rectifier and 0.9625
pu at the inverter. Click Update to see
in the mask the computed values.
Release MATLAB 9.1 (R2016b)