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

Rectifier Tab

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.  
 X secondary voltage(ph-ph)

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.

Inverter Tab

 

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.

 

DC network Tab

 

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.

 

Master Control Tab

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.

 

Result  tab

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.

 

Example

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)