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DIgSILENT PowerFactory Technical Reference Documentation

Rectifier / Inverter ElmRec, ElmRecmono, TypRec

DIgSILENT GmbH Heinrich-Hertz-Str. 9 72810 - Gomaringen Germany T: +49 7072 9168 0 F: +49 7072 9168 88 http://www.digsilent.de [email protected] Version: 2016 Edition: 1

Copyright © 2016, DIgSILENT GmbH. Copyright of this document belongs to DIgSILENT GmbH. No part of this document may be reproduced, copied, or transmitted in any form, by any means electronic or mechanical, without the prior written permission of DIgSILENT GmbH. Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

1

Contents

Contents 1 General Description

3

1.1 Fundamental Frequency Model . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.1.1 Converter Transformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

1.1.2 Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

1.1.3 Unbalanced Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

1.2 Basic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

1.2.1 Basic Type Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

2 Load Flow Analysis 2.1 P-setpoint Adaption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14 15

3 Short-Circuit Calculations

17

4 Harmonics

18

5 Dynamic Simulation

20

5.1 RMS Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

5.2 EMT Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

A Parameter Definitions

23

B Signal Definitions

25

List of Figures

26

List of Tables

27

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

2

1

General Description

General Description General Description

1

General Description 11General Description General Description

Figure 1: HVDC Converter including Built-In Transformer

Figure 1.1: HVDC converter including built-in transformer Figure 1: HVDC Converter including Built-In Transformer

Figure 2: Detailed Circuit with Commutation Reactance and DC Reactance (not part of the model) This converter model basically represents two different three-phase converters: •

the three-phase diode rectifier

• the2: three-phase Figure Detailedline-commutated Circuit with rectifier/inverter Commutation Reactance and DC Reactance (not part of the model)

Figure 1.2: Detailed circuit with commutation reactance and DC reactance (not part of the The diode rectifier is a full-bridge diode rectifier, which is rectifying the three-phase AC voltage to a 6-pulse DC model) This converter represents twobedifferent voltage. Due to the model usage ofbasically diodes, which can neither turned-onthree-phase nor turned-off converters: externally, the DC voltage or DC current of the rectifier can not be controlled.

•

the three-phase diode rectifier

•

the three-phase line-commutated rectifier/inverter

The model can be configured as: The controlled converter model consists of six power thyristors, arranged as shown in Figure 2. These valves can be turned-on by an external control signal (one dash), but only turns-off, when the current flowing through them becomes negative. This converter can operate as rectifier or as inverter, depending on the control signals applied.

The diode rectifier is a full-bridge diode rectifier, which is rectifying the three-phase AC voltage to a 6-pulse DC • Three-phase diode rectifier

voltage. Due frequency to the usage of diodes, which canis neither be turned-on nor turned-off the DC voltage or The fundamental representation of this model used for load-flow calculations and stabilityexternally, analysis.

DCis current rectifier can not be controlled. and describedof in the section 1.1. The detailed modelling of all six thyristors is only necessary for EMT simulations, • Three-phase line-commutated rectifier/inverter where the converters are modelled as shown in Figure 2.

The controlled converter model consists of six power thyristors, arranged as shown in Figure 2. These valves can turned-on by an external control signal (oneis dash), but only turns-off, when the current through The diode rectifier is abefull-bridge diode rectifier, which rectifying the three-phase ACflowing voltage to them becomes negative. This converter can operate as rectifier or as inverter, depending on the control signals applied. a 6-pulse DC voltage. Due to the usage of diodes, which can neither be turned-on -or turned-off 6-Pulse Bridge 4externally, the DC voltage or DC current of the rectifier cannot be controlled. The fundamental frequency representation of this model is used for load-flow calculations and stability analysis. and is described in section 1.1. The detailed modelling of all six thyristors is only necessary for EMT simulations,

The controlled converter consists of six power thyristors, arranged as shown in Figure where model the converters are modelled as shown in Figure 2. 1.2. These valves can be turned-on by an external control signal, but only turned-off when the current flowing through them becomes negative. This converter can operate as rectifier or as inverter, depending on the timing of the gate signal relative to the AC voltage wave. 6-Pulse Bridge

-4-

A fundamental frequency model is used for load flow calculations and stability analysis, and is described in section 1.1. The detailed modelling of all six thyristors is only necessary for EMT simulations, where the converters are modelled as shown in Figure 1.2.

1.1

Fundamental Frequency Model

The models for load flow calculation and RMS-simulation are based on a fundamental frequency approach. The equations of the thyristor converter and the diode rectifier are identical if the diode rectifier is assumed as an uncontrolled thyristor converter (hence the firing angle α is set to zero).

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

3

1

General Description

During steady-state operation the converter can be modelled as a load with constant active and reactive power P and Q. The following equations describe the converter in a detailed way and give hints for the layout of an HVDC system. The transmitted DC power of the high-voltage DC system is given by:

P d = Ud · Id

(1)

The DC voltage of the ideal and uncontrolled converter, without load, is called the “ideal no-load direct voltage” Ud0 , which is defined as follows:

Ud0

s0 · q = · sin π

  √ 2 π · √ · ULL q 3

(2)

where s0 defines the number of commutation groups, q is the number of branches in a commutation group and ULL is the AC voltage supplied to the converter station. For a 6-pulse converter there are two commutation groups (s0 = 2) and q is equal to 3, hence the Ud0 is

Ud0

√ 3· 2 ULL ≈ 1.35 · ULL = π

(3)

This equation is valid for the uncontrolled thyristor converter (α = 0) as well as for the diode bridge. The gate control of the thyristors can be used to delay the ignition of the valves. The time delay due to the turn-on signal applied is defined to be ωt = α. Then the DC voltage depends on the ignition angle α

Udα = Ud0 · cos(α)

(4)

The effect of the ignition angle α is shown in Figure 1.3, where the AC voltage, the phase currents and the DC voltage can be seen for an idealized operation with the DC current Id assumed to be constant. The ignition angle is also indicated in the figure. Here the time between the transfer of the current from one valve to the next is assumed to be zero, i.e the leakage reactance of the transformer is neglected and the commutation angle µ is zero. To study more realistic converters the current commutation from one valve to the next must be considered. The commutation leads to a drop in the DC voltage ∆Ud :

Ud = Ud0 · cos(α) − ∆Ud

(5)

∆Ud is defined as a function of Id and the commutation reactance Xc according to equation 6, where Rc is the “equivalent commutating resistance”. Rc does not represent a real resistance and thus has no associated power losses. ∆Ud is defined as:

∆Ud = −Rc · Id = −

3 3 · ω · Lc · Id = − · Xc · Id π π

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

(6)

4

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General Description

DIgSILENT

General Description

1.50 1.00 0.50 -0.00 -0.50 -1.00 -1.50 0.000

0.004

0.008

0.012

0.016

[s]

0.020

0.012

0.016

[s]

0.020

0.012

0.016

[s]

0.020

Rectifier: Phase Voltage A/Terminal AC in p.u. Rectifier: Phase Voltage B/Terminal AC in p.u. Rectifier: Phase Voltage C/Terminal AC in p.u.

1.50

α

1.00 0.50 0.00 -0.50 -1.00 -1.50 0.000

0.004

0.008

Rectifier: Phase Current A/Terminal AC in p.u. Rectifier: Phase Current B/Terminal AC in p.u. Rectifier: Phase Current C/Terminal AC in p.u.

1.25

1.00

0.75

0.50

0.25

0.00 0.000

0.004

0.008

Cub_1\Ud_R Measurement: Output Voltage, Real Part in p.u.

DIgSILENT

Three-Phase Thyristor Rectifier alpha = 30°, overlap angle u = 0°

TechRef

Date: 4/7/2004 Annex: 1 /1

Figure 1.3: 3: Phase voltages, phase currents and DC voltage of a three-phase rectifier rectifier operating with Figure Phase voltages, phase currents and DC voltage of a three-phase operating ◦ zero overlap angle μ α = 30° and with α = 30 and zero commutation angle µ Here the time between the transfer of the current from valve i to the next valve is assumed to be zero, i.e the leakage reactance of the transformer is neglected and the commutation angle μ is zero.

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec) 6-Pulse Bridge

5 -6-

1

General Description

Combining equations 5 and 6, the DC voltage can be expressed as:

Ud = Ud0 · cos(α) +

3 · Xc · Id π

(7)

Figure 1.4 shows the equivalent circuit for the rectifier including the effects of commutation. Note in the figure and in the equations above, that the DC current is negative for the rectifier operation due to the representation with load-orientation.

Rcr

Id Udr

Udo cos α

Figure 1.4: Rectifier equivalent circuit commutating resistance Rcr Rloss Vdrop Rcr with equivalent

Id The reactance of the converter transformer is usually the biggest part of total reactance on the AC side, hence it can be assumed that Xc is approximately that reactance: Udr

Udo cos α Xc = Xr,sec =

2 ukr Ur,sec · 100 Sr

(8)

where ukr , Ur,sec and Sr are the converter transformer short-circuit voltage (in %), rated voltage on the secondary side and rated power respectively. With the DC current being equal to its rated value Id , the DC voltage can be written in a different form as:

Ud = Ud0 · (cos(α) − dxr )

(9)

with

dxr =

1 ukr · 2 100

(10)

The term dxr has been calculated from the following relationship:

dxr =

3 |Id | · Xc · π Ud0

(11)

assuming the converter transformer rated current Ir is equal to sqrt(2)/sqrt(3) · Id (see section 1.1.1) and expressing Udo according to equation 3. The phase voltages and currents, as well as the DC voltage of a thyristor rectifier, including effects of commutation can be seen in Figure 1.5. The ignition angle α and the commutation angle µ are indicated in the figure. Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

6

1

General Description

DIgSILENT

General Description

1.50 1.00 0.50 -0.00 -0.50 -1.00 -1.50 0.000

0.004

0.008

0.012

0.016

[s]

0.020

0.012

0.016

[s]

0.020

0.012

0.016

[s]

0.020

Rectifier: Phase Voltage A/Terminal AC in p.u. Rectifier: Phase Voltage B/Terminal AC in p.u. Rectifier: Phase Voltage C/Terminal AC in p.u.

α

1.50

μ

1.00 0.50 0.00 -0.50 -1.00 -1.50 0.000

0.004

0.008

Rectifier: Phase Current A/Terminal AC in p.u. Rectifier: Phase Current B/Terminal AC in p.u. Rectifier: Phase Current C/Terminal AC in p.u.

1.25

1.00

0.75

0.50

0.25

0.00 0.000

0.004

0.008

Cub_1\Ud_R Measurement: Output Voltage, Real Part in p.u.

DIgSILENT

Three-Phase Thyristor Rectifier alpha = 30°, overlap angle u = 20°

TechRef

Date: 4/7/2004 Annex: 1 /1

Figure Phase voltages, phase currents andvoltage DC voltage of a three-phase operating Figure 1.5: 5: Phase voltages, phase currents and DC of a three-phase rectifierrectifier operating with ◦ ◦ with α = 30 and an overlap angle of µ = 20 α = 30° and an overlap angle of μ = 20° Using these two angles two other angles can be defined, used in the HVDC theory. γ is called the extinction angle, which is normally used to control the inverter side of the HVDC.

0 = π −α − μ −γ The ignition advance angle β is specified as

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec) 6-Pulse Bridge

7 -8-

1

General Description

Using these two angles two other angles can be defined. The extinction angle γ, which is normally used in the control on the inverter side of the HVDC, is defined as:

γ =π−α−µ

(12)

The ignition advance angle β is defined as

β =π−α

(13)

β is often used in the HVDC controllers for both the rectifier and inverter side. Using these different angles the DC voltage can be calculated differently for the rectifier and for the inverter respectively:

Udr = Ud0 ·

cos(α) + cos(α + µ) 2

(14)

cos(β) + cos(γ) 2

(15)

and

Udi = Ud0 ·

The DC voltage for the inverter case is considered positive in equation 15. Using equations 14 and 9, the term dxr can be expressed as:

dxr =

cos(α) − cos(α + µ) 2

(16)

The phase currents of the 6-pulse bridge are shown in Figure 1.3 and Figure 1.5. In the literature the AC current is often calculated approximately from the ideal rectifier current with the commutation angle neglected. In PowerFactory the amplitude of the fundamental frequency current IL1 is calculated using the Fourier analysis of the phase current waveform, so the effect of the commutation is taken into account. This leads to the following relationship between the RMS value of the fundamental frequency component and the direct current: √ IL1 = k ·

6 · Id π

(17)

where k is equal to

p k=

[cos(2α) − cos 2(α + µ)]2 + [2µ + sin(2α) − cos 2(α + µ)]2 4 · [cos(α) − cos(α + µ)]

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

(18)

8

1

General Description

This factor is close to unity for small values of µ, but if the angle becomes larger, the error increases up to 4% at µ = 60◦ . For unsymmetrical operation the phase currents have to be calculated differently, which is described in section 1.1.3. The power factor cos(ϕ) can then be calculated, given the power equivalence on the AC and DC side and using equations 3, 14 and 17:

√

√ 3 2 cos(α) + cos(α + µ) 3 · ULL · IL1 · cos(ϕ) = Ud · Id = · ULL · · Id π 2

cos(ϕ) =

1.1.1

1 · [cos(α) + cos(α + µ)] 2k

(19)

(20)

Converter Transformer

There are two possibilities to model the converter transformer in PowerFactory : • Built-in transformer • External converter transformer The built-in transformer features a tap-changer on the HV side to control the secondary voltage. The built-in transformer can be configured as Fixed Tap, to control the firing (alpha-control) or extinction (gamma-control) angle of the converter. The commutation reactance is always assumed to be on the secondary side of the transformer. Hence Xc is calculated as follows:

Xc =

2 ukr Ur,sec · 100 Sr

(21)

where ukr , Ur,sec and Sr are the converter transformer short-circuit voltage (in %), rated voltage on the secondary side and rated power respectively. If an external transformer is used for the converter model, the AC voltage drop over the transformer is estimated using the commutation reactance specified in the converter dialog window. If the parameters specified in the external transformer and in the rectifier/inverter fit together, the same results are obtained as with the built-in transformer. If the rated DC voltage of the converter is known, the rated secondary voltage of the converter transformer can be calculated using the following equation, which can derived from the equations above:

Ud π Ur,sec = √ · 3 2 cos(α) − dxr

(22)

The rated AC current on the converter side of the transformer equals the RMS value of the total AC current which, neglecting commutation effects, consists of rectangular pulses with amplitude equal to the rated DC current Id and duration of 120◦ . The rated AC current on the converter side of the transformer is found as: Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

9

1

General Description

r Ir,sec =

2 · Id 3

(23)

Note that this current is the RMS value of the total AC current, and not of only its fundamental frequency component, which is calculated instead as in equation 17. Hence the rated power can be calculated as

√ √ π Pd Sr = 3 · Ir,sec · Ur,sec = 2 · Id · Ur,sec = · 3 cos(α) − dxr

1.1.2

(24)

Losses

The model of the HVDC does not include the effects of losses so far. The losses in the converter bridge are caused due to the different components, i.e. the resistances of valves, transformers, smoothing reactances. An exact representation of the losses associated with the converter station is very sophisticated, so it is common practice to model the losses in the Load Flow analysis as an equivalent series resistance on the DC side. Two more terms accounting respectively for the forward voltage drop in the thyristors and no-load losses depending on the DC voltage are also considered. In PowerFactory , rectifier/inverter losses are specified in fundamental frequency models as: • No-load losses: specified with the parameter P nold in [kW]. • Forward voltage drop losses: specified with the parameter swtLossF actor in [KW/A]. • Resistive losses: specified with the parameter resLossF actor in [Ohm]. Total losses are calculated as:

Losses = Gnoload · Ud2 + resLossF actor · Id2 + Vdrop · Id

(25)

with: • Vdrop = sign(Id ) · swtLossF actor · (1 − exp−200·|Id | ) • Gnoload =

Pnold where UDCnom is expressed in kV 2 1000 · Unom,DC

• Losses: Converter losses in MW To take into account losses, equation 7 must be modified, both for rectifier and inverter, as:

Ud = Ud0 · cos(α) +

3 Xc · Id + resLossF actor · Id + Vdrop π

(26)

The representation of station losses of a rectifier for load flow calculations is shown in Figure 1.6. Note in the figure and in the equation above, that the DC current is negative for the rectifier operation due to the representation with load-orientation. Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

10

Rcr

Id Udr

Udo cos α 1

General Description

Rloss

Rcr

Vdrop

Id Udr

Udo cos α

Figure 1.6: Simplified modelling of losses for a 6-pulse converter 1.1.3

Unbalanced Operation

When the network voltages are unsymmetrical, the periods for natural conduction of the valves are not the same and the DC voltage will be made of six pulses with different duration and amplitude. The ideal no-load DC voltage can be calculated by taking the average of the pulses over half a period. As an example, with reference to Figure 1.7, at ωt = θca + π the DC current starts flowing in phase a and returns back through phase b until ωt = θbc . For a thyristor converter, these angles can be delayed by αa and αc respectively. During this period, the DC voltage is equal to the line-line voltage Uab . The angles θab , θbc and θca , at which the corresponding line-line voltages cross zero and become positive, are calculated internally in the model, given the terminal voltage phasors. This holds only for load flow and RMS simulations.

Uab Ubc Uca Ud

Ua Ub Uc

Ia Ib Ic

θca

θbc-π

θab θca+π

θbc

θab+π θca+2π

Figure 1.7: Currents and voltages for diode bridge rectifier with unbalanced network voltages and smoothing reactor on the DC side By taking the average of the resulting three pulses over half a period, the ideal no-load DC voltage is calculated in load flow and RMS simulations as:

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

11

1

General Description

Ud =

1  · Uab · [cos(θca + π + αa − θab ) − cos(θbc + αc − θab )]+ π Ubc · [cos(θab + π + αb − θbc ) − cos(θca + αa − θbc )]+ Uca · [cos(θbc + π + αc − θca ) − cos(θab + αb − θca )]

(27)

In unsymmetrical load flow and RMS simulations, a PLL will measure the angle θ1 of the positive zero-crossing of the positive sequence line-line voltage. The firing angles of the valves are then calculated in order to obtain an interval between the firing pulses of 60◦ . Therefore, the firing angles αa , αb and αc will not be identical but differ according to the phase-shift of the phase voltages. The firing angles of the three phases are calculated internally in the model as (the negative sign is due to the fact that negative angles imply a lagging phase in equation 27):

αa = −[α + (θca − (θ1 − 4π/3))]

(28)

αb = −[α + (θab − θ1 )]

(29)

αc = −[α + (θbc − (θ1 − 2π/3))]

(30)

In general it is not possible to obtain a 60◦ interval between the firing pulses, since this would require leading firing angles. As a consequence, the pulses will still have different length even after applying different firing pulses for each phase. The AC currents are affected by the different length of the pulses. Assuming a constant DC current, the amplitude of the fundamental frequency component of the phase currents is no longer equal because the conduction periods for each phase are different, as can be seen in Figure 1.7. Let θIi represent the conducting time of phase i. The RMS value of the fundamental frequency component of each phase current is easily calculated by Fourier series expansion as:

IL1i = k ·

θIi 4 Id · √ · sin( ) π 2 2

(31)

The DC power is then calculated as the sum of the real power of all phases on the secondary side of the transformer:

Pdc = Pa + Pb + Pc

1.2

(32)

Basic Data

On the Basic Data page a name for the element has to be entered. A type has to be selected or defined for the element. Furthermore, the orientation has to be specified to allow representation of either a rectifier or an inverter.

1.2.1

Basic Type Data

In the basic data page of the type of the inverter/rectifier, the main parameters of the converter layout have to be entered. You can choose between rated AC or DC voltage and between rated Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

12

1

General Description

DC power and DC current. Furthermore the kind of converter can be defined (uncontrolled diode rectifier or thyristor converter). If the built-in transformer is chosen (which is advisable for most types of converters), there is as well the necessity to enter the turns-ratio of the converter transformer, which is given by the ratio of secondary to primary voltage, and the nominal firing angle α. Also the limits of the turns-ratio are given to specify the tap-changer ranges. The maximum and minimum turns-ratio is given in per unit of the nominal turns-ratio (t2/t1) of the converter transformer.

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

13

2

2

Load Flow Analysis

Load Flow Analysis

In load flow analysis, it is common practice not to specify control variables directly but to define the controlled variables instead. The control variable (the firing angle α) is then resulting from the Load Flow calculation. In the Load Flow command, several common control characteristics are supported by the HVDC converter model. Meaning and typical application of the various control modes are the following: • Vdc: The firing angle is adjusted to obtain a predefined value for the DC voltage of the converter. This control mode is typically used at the inverter side of an HVDC transmission system. • Vac: Specifies the magnitude of the AC voltage at the converter terminals, when the DC voltage is controlled externally. No typical application. • P: The transmitted DC power is held constant. Typically used for rectifier side in HVDC systems. • Q: Specifies the amount of reactive power absorbed by the converter. No typical application. • I: The DC current of the converter is held constant. Typically used for rectifier control of an HVDC transmission system. • Gamma: The extinction angle γ is specified. Normally the inverter side of an HVDC system is controlled to a minimum γ. • EXT: The firing angle α is specified as an input to the model, provided by a Controller which must be specified with the parameter pctrl. The Controller is a line-commutated rectifier/inverter element (ElmRec or ElmRecmono) as well. The EXT control mode is useful in a 12-pulse arrangement with two converters: one converter is the Controller performing one of the other control modes, while the second converter is in EXT control mode. These control modes are enabled if the flag Automatic Firing Angle Control is selected. Otherwise, the firing angle α is set equal to the Actual Firing Angle, specified with the parameter alpha set. Minimum and maximum firing angle limits can be specified. If the converter reaches one of these limits, the firing angle will remain constant at the limit and the converter cannot perform the chosen control function. A minimum value of the extinction angle, gammamin, can also be entered. The angle gammamin represents a safe value of γ in order to avoid commutation failure in normal operating conditions; it does not represent the limiting value for commutation failure. If the inverter extinction angle γ reaches this limit, a warning is printed in the output window. For inverters in Vdc (EXT) control mode, the option Consider minimum extinction angle (gammamin) for control is available. If the option is selected, the inverter will no longer control the DC side voltage but will switch to a gamma-control mode with gammamin as setpoint if gammamin is reached. In load flow calculations, commutation failure is assumed to take place only when the sum of the firing angle α and of the overlap angle µ would be higher than 180◦ (negative γ). A warning for commutation failure is printed in the output window. In this case, the load flow is still calculated assuming the overlap angle equal to zero. However, this may not represent a feasible operating point.

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

14

2

Load Flow Analysis

During load flow calculation, if the thyristor converter current is very low, the converter current is set to zero. The thyristor converter voltage is set to zero with the firing angle equal to 90◦ . A message is sent to the output window warning about zero current flowing in the converter. Furthermore the control of the tap-changers of the converter transformer can be chosen between: • Fixed Tap: The position of the tap-changers is fixed to a given winding ratio. • alpha-control: The secondary voltage is adjusted by the tap-changers to obtain a specified setpoint of the firing angle. This is typically used at the rectifier station of the HVDC. • gamma-control: The tap-changers are controlled to obtain a specified setpoint of the extinction angle. This is typically used at the inverter station of the HVDC. Besides the firing angle control modes, the load flow page of the converter also comprises additional information for the converter transformer. Here the commutation reactance Xc is specified as the leakage reactance of the transformer, which is important for the calculation of the commutation angle. Also the phase-shift of the converter transformer can be entered here. This information is needed, when designing 12-pulse thyristor bridges with 30◦ phaseshift between two converters in series to reduce harmonic currents fed into the network. Attention: This information is also needed, when no built-in transformer is selected in the converter type! The value of the commutation reactance is specified as the reactance of the converter transformer, modelled externally. The value of the commutation reactance is used to estimate the voltage on the transformer primary side, given the converter terminal voltage and current. The estimated voltage is used to calculate the ideal no-load DC voltage. Specifying the correct value of the commutation reactance is also important to get realistic values for the commutation angle.

2.1

P-setpoint Adaption

When the converter is in P control mode, usually the rectifier side in an HVDC system, the active power setpoint can be modified by the following controllers if selected: • Angle-difference dependent P-droop • Active power participation When the Angle-difference dependent P-droop option is selected, the active power setpoint is modified for the rectifier and inverter case according to:

Pr = Pr,set + Kpphi · (phiulocal − phiuremote ) Pi = Pi,set − Kpphi · (phiulocal − phiuremote ) When the Active power participation option is selected, the active power setpoint is modified for the rectifier and inverter case according to:

Pr = Pr,set + Kpart · Pmeas Pi = Pi,set − Kpart · Pmeas Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

15

2

Load Flow Analysis

where: • Pr,set is the active power setpoint, rectifier case. • Pi,set is the active power setpoint, inverter case. • Pr is the modified active power setpoint, rectifier case. • Pi is the modified active power setpoint, inverter case. • Kpphi is the specified factor for Angle-difference dependent P-droop. • Kpart is the specified factor for Active power participation. • phiuremote is the positive-sequence voltage angle of the remote busbar. • phiulocal is the positive-sequence voltage angle of the local busbar. • Pmeas is the active power measured (assumed positive with load orientation) at a specified cubicle/boundary. The Angle-difference dependent P-droop and Active power participation options can be used to adapt the active power of the converter depending on the active power flow on a parallel AC line. When the Active power participation option is selected, the sign of the parameter Kpart depends on the orientation of the power flow at the point where the parameter Pmeas is measured. Figure 2.1 shows how to correctly define the sign of Kpart. In the example, the converter INV is performing the active power control and has the Active power participation option selected.

Figure 2.1: Active power participation example for converter INV. Active power setpoint is P=10MW.

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

16

3

3

Short-Circuit Calculations

Short-Circuit Calculations

Typically the line-commutated converters are neglected during short-circuit calculations due to the effect, that the thyristors are automatically blocking during very low voltages at the AC side. This results in low short-circuit currents supplied by the converter. The calculation methods using the VDE, IEC or ANSI standards do neglect the contribution of the converters. If a complete method short-circuit calculation is executed, the short-circuit current of the converter will not be neglected but defined being the rated AC current of the converter. Enabling the option Static converter-fed drive, the element can be used to represent in shortcircuit studies reversible static converter-fed drives, with the converter having then a different layout than a six-pulse bridge. In this case, the contribution of the converter to the short-circuit current is no longer neglected in the VDE 0102/0103 and IEC 60909 calculation method. According to these standards the converters are assumed to be asynchronous machines having a short-circuit current ratio of Ishc /Irated = 3 and an R/X-ratio of R/X = 0.1. The short-circuit current contribution is only considered in symmetrical short-circuits. In case of asymmetrical short-circuits the current contribution of static converter drives is neglected. The contribution is only used to calculate the initial and the peak short-circuit current (I” and ip ). The ANSI and the complete calculation method are not affected by this option. Only the ElmRecmono is considered in the calculation of DC short-circuits according to IEC 61660 and ANSI/IEEE 946. Additional parameters required to perform DC short-circuit calculations according to the standards can be entered in the DC Short-Circuit page of the element ElmRecmono and of the type TypRec. In these pages, data about the commutation resistance, AC side impedance, DC side resistance and inductance, converter connection type and voltage factor are specified.

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

17

4

4

Harmonics

Harmonics

The currents of the 6-pulse thyristor-controlled converter, which are shown in Figure 1.3 with the commutation effect neglected and in Figure 1.5 including commutation, are characteristic waveforms. From these curves it can easily be seen, that the currents not only have a large 50-Hz-component but also cause a flow of harmonic currents of higher orders. Hence the most accurate harmonic model of the HVDC converter is a harmonic current source. The order of the harmonic currents is calculated as

h=6·n±1

(33)

(where n = an integer) The assigned amount of current injected is

Ih =

IL1 h

(34)

Typically the 6-pulse converters have a characteristic spectrum of harmonic currents injected to the AC system. If the Ideal Rectifier on the Harmonics page of the element is used, this typical spectrum of the converter is assumed up to a specified number (normally 31) using the above two equations with the commutation reactance neglected. This assumption usually causes the harmonic currents to be larger than in reality, but gives a good approximation to use. The polarity of the harmonics (angle) is 180◦ for the 5th , 11th , etc. harmonics (represented in the negative sequence) and 0 for the 7th , 13th , etc. harmonics (represented in the positive sequence). To represent the converter in a more realistic way, a harmonic current source can be defined and the amplitude and angle of the harmonic currents can be defined as shown in Figure 4.1. Here you can choose between a balanced and unbalanced representation. More information can be derived from the Technical Reference of the type “Harmonic Sources” (TypHmccur ).

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

18

4

Harmonics

Figure 4.1: Example for a converter representation as harmonic current source

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

19

5

Dynamic Simulation

5 5.1

Dynamic Simulation RMS Simulation

The stability model uses the same equations as described in section 2 (Load Flow analysis). The converter transformer data, commutation reactance and phase shift, are identical with the values specified on the load flow page of the element. A separate minimum extinction angle for commutation failure gammamindyn can be specified in the RMS page. This angle specifies the minimum extinction angle below which commutation failure is assumed to take place. When the extinction angle γ reaches the specified gammamindyn, a message warning for commutation failure is printed in the output window, the DC side is short-circuited and the converter current is assumed equal to zero. Notice that the gammamindyn angle has a different meaning than the gammamin angle specified for control purposes in the load flow page. With the signal short dc is possible to short-circuit the DC side of the element, in order to bypass the valves. The DC voltage and the AC current go to zero during active short dc. With the signal block all all thyristors will be blocked. The AC and DC current are then both zero. It is possible to select the way the extinction angle γ is handled when the converter is blocked through the parameter gammaMode: The angle can either be set to zero or kept constant. The zero sequence current is always zero in RMS simulations.

alpha tap fref short_dc

gamma RMS Simulation

gamma_min

block_all

Figure 5.1: Input/Output definition of the HVDC converter model for stability analysis (RMSsimulation)

gamma gamma_min

alpha

Ip_A/B/C

tap Fmeas short_dc

EMT Simulation

block_all

Im_A/B/C Upc_A/B/C Umc_A/B/C U0

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

20

1.6 RMS Simulation

The stability model uses the same equations as described in section 1.3 of the load-flow analysis. Ther further information needed.

5

Dynamic SimulationThe commutation reactance and its angle are identical with the values specified on the load-flow page element.

5.2

EMT Simulation

1.7 EMT Simulation

For the electro-magnetic transient simulation the detailed modelling of all six thyristors or diodes is necessary. Here theFor converters are modelled as shown in Figure 1.2. This detailed the electro-magnetic transient simulation the detailed modelling of allmodel six thyristors is necessary. H represents the discrete converters valves including onand off-resistances of the switches (R , G ) and the discrete valves i on of f are modelled as shown in Figure 2. This detailed model is representing the elements of the snubber-circuits in parallel (shown in Figure 5.2). These values can be on- and off-resistances of the switches (Ron, Goff) and the elements of the snubber-circuits in parallel (s defined in the EMT page of the type TypRec. Figure 10).

Figure 10: Detailed Valve Representation for EMT-Simulations

Figure 5.2: Detailed valve representation for EMT-simulations

For triggering the valves the built-in trigger-circuit is used, which converts the firing angle supplied by

For triggering the valves the built-in trigger-circuit can be used, which converts the firing angle converter controller to the six correct firing signals of the discrete thyristors. supplied by the converter controller to the six correct firing signals of the discrete thyristors.

an exact triggering of the the timesofofthe zero-crossing of the AC to voltages For an exact triggering For of the valves, the times of valves, zero-crossing AC voltages have be have to be measure the 6-pulse converter doesnot nothave have aa built-in measurement, a PLLa element measured. Since the 6-pulse converter does built-inphase phase measurement, PLL (*.ElmPhi__pll) has is required byisthe converter provided. This meansThis the means output ofthe a PLL “Fmeas element (ElmPhi pll) has to be provided. output of a” PLL Fmeas required byfor accurate operation the converter for accurate operation.

With the signal short dc is possible to short-circuit the DC side of the element, through a valve with resistance equal to Ron . With the signal block all all thyristors will be blocked. The AC and Attention: Modelling the converter transformer externally (i.e. the “Built-In Transformer” is not used) DC current are then both zero.

problems due to the exact value of commutation reactance specified on the load-flow pag

additional reactance inserted the transformer element. with Only the small errors of this value a The converter transformer data, commutation reactance and by phase shift, are identical commutation angle andThe hence the EMT extinction simulation angle can notgammacalculate the right initial condit values specified on the load flow page of the element. minimum mindyn is not used in EMT simulations. it is recommended to use the built-in transformer of the converter element instead to get results in the EMT-simulation!

If the built in transformer is used the zero sequence current is always zero. Attention: Modelling the converter transformer externally (i.e. the flag Built-In Transformer in TypRec is not selected) can cause problems due to the exact value of commutation reactance specified on the load flow page and the additional reactance inserted by the transformer element. Only small errors of this value affect the commutation angle and hence the EMT simulation can not calculate the right initial conditions. Here it is recommended to use the built-in transformer of the converter element instead to get correct results in the EMT-simulation!

6-Pulse Bridge

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

21

5

Dynamic Simulation

alpha tap fref short_dc

gamma RMS Simulation

gamma_min

block_all

gamma gamma_min

alpha

Ip_A/B/C

tap Fmeas short_dc

EMT Simulation

block_all

Im_A/B/C Upc_A/B/C Umc_A/B/C U0

Figure 5.3: Input/Output definition of the HVDC converter model for stability analysis (EMTsimulation)

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

22

A

Parameter Definitions

A

Parameter Definitions Table A.1: I/O Signals of the PWM-converter model

Parameter loc name typ id busac busac bar busdp busdm busdc busdc bar outserv mode bstp uset Pset Qset Iset gamma set pctrl alphacn alpha set alphamin alphamax gammamin gammaminCtrl ntrcn nntap Xd nt2ag iPphidrp Kpphi p b1phiu p b2phiu iPpart Kpart p pmeas iconfed i int maxorder phmc cTypHmc icurref Inom iAstabint gammamindyn gammaMode comres Racmax Xacmax Racmin Xacmin

Description Name Type (Typrec) Terminal AC (StaCubic) Terminal AC Terminal DC+ (StaCubic) Terminal DC- (StaCubic) Terminal DC (StaCubic) Terminal DC Out of Service Orientation (Rectifier/Inverter) Firing Angle (alpha-)Control: Control-Characteristic Firing Angle (alpha-)Control: Voltage Setpoint Firing Angle (alpha-)Control: Power-Setpoint Firing Angle (alpha-)Control: Reactive Power-Setpoint Firing Angle (alpha-)Control: Current Setpoint Firing Angle (alpha-)Control: Extinction Angle (gamma) Setpoint Firing Angle (alpha-)Control: Controller Firing Angle (alpha-)Control: Automatic Firing Angle Control Firing Angle (alpha-)Control: Actual Firing-Angle Firing Angle (alpha-)Control: Minimum Firing Angle Firing Angle (alpha-)Control: Maximum Firing Angle Firing Angle (alpha-)Control: Minimum Extinction Angle Consider minimum extinction angle (gammamin) control Converter Transformer: Tap-Changer Converter Transformer: Actual Winding Ratio Converter Transformer: Commutation Reactance Converter Transformer: Phase Shift Angle difference dependent P-Droop Kpphi Remote AC busbar (ElmTerm*) Local AC busbar (ElmTerm*) Active power participation Participation factor P(AC) measured at (StaCubic*,ElmBoundary) Static converter-fed drive Ideal Rectifier Maximum Harmonic Order Harmonic Currents (TypHmccur) Type of Harmonic Sources Harmonic Current Injections referred to Rated Harmonic Current Injection A-stable integration algorithm Min. extinction angle for commutation failure Handling of extinction angle if rectifier is blocked Commutation resistance (Only ElmRecmono) Max. values: AC resistance (Only ElmRecmono) Max. values: AC reactance (Only ElmRecmono) Min. values: AC resistance (Only ElmRecmono) Min. values: AC reactance (Only ElmRecmono)

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

Unit

p.u. MW Mvar kA deg

deg deg deg deg

p.u. Ohm *30deg MW/degree

kA

Ohm Ohm Ohm Ohm Ohm 23

A

Parameter Definitions

volfac

IEC parameters: Voltage factor, c (Only ElmRecmono)

Table A.2: Parameters of the HVDC Converter Type Parameter

Description

loc name Unom Unomdc Pnom Imax tapnom alphanom i diode i trf tapmin tapmax Pnold swtLossFactor resLossFactor Rthy Goff Gs Cs rres rind fr way

Name Rated AC Voltage Rated DC-Voltage (DC) Rated Active Power Rated DC-Current Nominal Turns-Ratio (t2/t1) Nominal Firing Angle Diode-/Thyristor Converter Converter Transformer: Built-In Transformer Converter Transformer: Minimum Turns-Ratio Converter Transformer: Maximum Turns-Ratio Losses: No-load losses Losses: Switching loss factor Losses: Resistive loss factor Thyristor-Resistance (at On) Thyristor-Conductance (at Off) Snubber-Conductance Snubber-Capacity Rectifier resistance (DC-side) Rectifier inductance (DC-side) ANSI/IEEE Parameters

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

Unit kV kV MW kA deg

p.u. p.u. kW kW/A Ohm Ohm S S uF mOhm uH

24

B

Signal Definitions

B

Signal Definitions Table B.1: Input/Output signals

Name

Description

Unit

Type

Model

alpha tap short dc block all fref Fmeas gamma gamma min Ip A Ip B Ip C Im A Im B Im C Upc A

Firing Angle Tap-Position DC Bypass AC Blocking Reference Frequency Frequency Extinction Angle Extinction Angle (Min. in one cycle) Thyristor Current (pos Thyristor, Phase A) Thyristor Current (pos Thyristor, Phase B) Thyristor Current (pos Thyristor, Phase C) Thyristor Current (neg Thyristor, Phase A) Thyristor Current (neg Thyristor, Phase B) Thyristor Current (neg Thyristor, Phase C) Capacitive Voltage (pos Snubber Capacity, Phase A) Capacitive Voltage (pos Snubber Capacity, Phase B) Capacitive Voltage (pos Snubber Capacity, Phase C) Capacitive Voltage (neg Snubber Capacity, Phase A) Capacitive Voltage (neg Snubber Capacity, Phase B) Capacitive Voltage (neg Snubber Capacity, Phase C) Zero Sequence Voltage

rad

p.u. Hz rad rad kA kA kA kA kA kA kV

IN IN IN IN IN IN OUT OUT OUT OUT OUT OUT OUT OUT OUT

RMS, EMT RMS, EMT RMS, EMT RMS, EMT RMS EMT RMS, EMT RMS, EMT EMT EMT EMT EMT EMT EMT EMT

kV

OUT

EMT

kV

OUT

EMT

KV

OUT

EMT

kV

OUT

EMT

kV

OUT

EMT

kV

OUT

EMT

Upc B Upc C Umc A Umc B Umc C U0

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

25

List of Figures

List of Figures 1.1 HVDC converter including built-in transformer . . . . . . . . . . . . . . . . . . . .

3

1.2 Detailed circuit with commutation reactance and DC reactance (not part of the model) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.3 Phase voltages, phase currents and DC voltage of a three-phase rectifier operating with α = 30◦ and zero commutation angle µ . . . . . . . . . . . . . . . . . . .

5

1.4 Rectifier equivalent circuit with equivalent commutating resistance Rcr . . . . . .

6

1.5 Phase voltages, phase currents and DC voltage of a three-phase rectifier operating with α = 30◦ and an overlap angle of µ = 20◦ . . . . . . . . . . . . . . . . . .

7

1.6 Simplified modelling of losses for a 6-pulse converter . . . . . . . . . . . . . . . .

11

1.7 Currents and voltages for diode bridge rectifier with unbalanced network voltages and smoothing reactor on the DC side . . . . . . . . . . . . . . . . . . . . . . . .

11

2.1 Active power participation example for converter INV. Active power setpoint is P=10MW. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

4.1 Example for a converter representation as harmonic current source

. . . . . . .

19

5.1 Input/Output definition of the HVDC converter model for stability analysis (RMSsimulation) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

5.2 Detailed valve representation for EMT-simulations

. . . . . . . . . . . . . . . . .

21

5.3 Input/Output definition of the HVDC converter model for stability analysis (EMTsimulation) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

26

List of Tables

List of Tables A.1 I/O Signals of the PWM-converter model . . . . . . . . . . . . . . . . . . . . . . .

23

A.2 Parameters of the HVDC Converter Type . . . . . . . . . . . . . . . . . . . . . .

24

B.1 Input/Output signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

Rectifier / Inverter (ElmRec, ElmRecmono, TypRec)

27