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DIgSILENT Technical Documentation Static Generator

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Page 1: TechRef_ElmGenstat

D I g S I L E N T T e c h n i c a l D o c u m e n t a t i o n

Static Generator

Page 2: TechRef_ElmGenstat

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Rev. Nr. Author Date Reviewed by Date PF Version

01 S.Weigel 15.04.2010 14.0.516

DIgSILENT GmbH

Heinrich-Hertz-Strasse 9

D-72810 Gomaringen

Tel.: +49 7072 9168 - 0

Fax: +49 7072 9168- 88

http://www.digsilent.de

e-mail: [email protected]

Static Generator

Published by

DIgSILENT GmbH, Germany

Copyright 2009. All rights

reserved. Unauthorised copying

or publishing of this or any part

of this document is prohibited.

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T a b l e o f C o n t e n t s

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Table of Contents

1 General Description ............................................................................................................................. 4

1.1 Basic Data ............................................................................................................................................. 4 1.1.1 Zero/Negative Sequence Model........................................................................................................... 5

1.2 Load-Flow Analysis ................................................................................................................................. 6 1.2.1 Local Voltage Controller Options ......................................................................................................... 6 1.2.2 External Station Controller .................................................................................................................. 8 1.2.3 Primary frequency bias ...................................................................................................................... 9 1.2.4 Reactive Power Limits ........................................................................................................................ 9 1.2.5 Active Power Limits ......................................................................................................................... 10

1.3 Short-Circuit Calculations ...................................................................................................................... 10 1.3.1 VDEC/IEC Short Circuit .................................................................................................................... 10 1.3.2 Complete Short Circuit ..................................................................................................................... 13 1.3.3 ANSI Short Circuit ........................................................................................................................... 15 1.3.4 IEC 61361 ...................................................................................................................................... 17

1.4 Harmonics ........................................................................................................................................... 17

1.5 RMS Simulation .................................................................................................................................... 18 1.5.1 Current Source Model ...................................................................................................................... 18 1.5.2 Voltage Source Model ...................................................................................................................... 19 1.5.3 Negative/Zero Sequence Model......................................................................................................... 20

1.6 EMT Simulation .................................................................................................................................... 20 1.6.1 Current Source Model ...................................................................................................................... 21 1.6.2 Voltage Source Model ...................................................................................................................... 22 1.6.3 Zero Sequence? .............................................................................................................................. 22

2 Input/Output Definition of Dynamic Models .................................................................................... 23

2.1 Stability Model (RMS) ........................................................................................................................... 23 2.1.1 Current Source Model ...................................................................................................................... 23 2.1.2 Voltage Source Model ...................................................................................................................... 24

2.2 EMT-Model .......................................................................................................................................... 25 2.2.1 Current Source Model ...................................................................................................................... 25 2.2.2 Voltage Source Model ...................................................................................................................... 26

3 Input Parameter Definitions .............................................................................................................. 27

3.1 *.ElmGenstat ....................................................................................................................................... 27

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1 General Description

The Static Generator is an easy-to-use model of any kind of static (no rotating) generator. Applications are:

Photovoltaic Generators

Fuel Cells

Storage devices

HVDC Terminals

Reactive Power Compensators

Wind Generators

Wind generators, which are connected through a full-size converter to the grid, can also be modelled as static

generators, because the behaviour of the plant (from the view of the grid side) is determined by the converter.

1.1 Basic Data

Figure 1: Basic Data for the Static Generator

The specific application of the static generator can be selected in the category box.

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Figure 2: Categories

The number of parallel machines can be entered, as well as the MVA rating of a single generator. In general, the

total MW and Mvar outputs of the static generator will be the rating of a single generator multiplied by the

number of parallel machines specified. In the specific case of the Wind Generator category, the output will

additionally be affected by the Wind Generation Scaling Factor of the zone to which it belongs.

Figure 3: Zone

1.1.1 Zero/Negative Sequence Model

The negative sequence current is always set to zero. The zero sequence depends on the settings:

Input Parameter:

iearthed : Earthed (option)

- r0 : Zero-sequence Resistance, r0 (hidden if ieathed is disabled)

- x0 : Zero-sequence Reactance, x0 (hidden if ieathed is disabled)

Figure 4: Negative Sequence Model

u2

i2 = 0

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Figure 5: Zero-sequence Model if option “Earthed” is enabled

If the option is disabled the zero-sequence current is zero.

1.2 Load-Flow Analysis

1.2.1 Local Voltage Controller Options

The local voltage controller could be set to three different modes (cos, V, droop) that are described in the the

following sub chapters.

1.2.1.1 Power Factor control

This option corresponds to a PQ bus type and its block diagram is shown in Figure 7 (1). With the power factor

control the user can specify active and reactive power outputs at which the static generator will be operated (PQ

bus). The way to specify these values will depend on the Input Mode selected.

Figure 6: Input Mode

The voltage and droop value boxes are disabled for the Power Factor control option. Psum and Qsum will be controlled in unbalanced load flow.

u0

i0 r0 x0

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UU ,

x I

ir UU ,

)cos(,)1( P

UP,)2(

droopU ,)3(

maxQ

minQ

UU ,

x I

ir UU ,

)cos(,)1( P

UP,)2(

droopU ,)3(

maxQ

minQ

Figure 7: Voltage Controller - Options

1.2.1.2 Voltage control

This option correspondes to a PV bus type and its block diagram is shown in Figure 7 (2). Voltage control can be

done locally, i.e. the reactive power output of the generator is controlled to achieve the specified local voltage at

its terminal. The active power output is constant for the dispatch.

When this option is selected, the voltage setpoint box is enabled and its value must be entered.

1.2.1.3 Droop control

This option corresponds to a DV bus type and its block diagram is shown in Figure 7 (3). The generator can be

set to control the local voltage at its terminal to a specified setpoint. With droop control the setpoint is not

reached in any case because the setpoint is moved (by dudroop) as more reactive power is needed to reach the

original voltage setpoint of the static generator. The advantage of the droop control is that more than one

machine at one busbar could control the voltage. As well as the participation of the single machine could be

configured with the setting of the droop value.

When set to voltage control, a droop value can be entered. The voltage at the local busbar is then controlled

according to the following equations this equations are shown graphically in Figure 8:

droop

SQ

Q

QQdu

duuu

nomdroop

droop

setpoint

droop

droopsetpoint

100

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Where:

u is the actual voltage value at the terminal busbar

usetpoint is the specified voltage setpoint of the stataic generator

Q is the actual reactive power output of the static generator

Qsetpoint is the specified dispatch reactive power of the static generator

Snom is the nominal apparent power

droop is the droop value specified in percentage.

puu

setpu

u

setpQ Q puQ

droop

puu

setpu

u

setpQ Q puQ

droop

Figure 8: Droop Voltage Control

1.2.2 Static Generator as Slack

For load flow only it is also possible to use the static gernator as slack. For that the „Active Power Control‟ on the

load flow command has to be set „as Dispatched‟, the balancing has to be set „by Static Generator at Reference

Bus‟, a static generator has to be connected to the selected busbar. The local voltage controller of the slack-static

generator has to be set either to „Voltage‟ or to „Droop‟.

1.2.3 External Station Controller

The static generator can also be part of a station controller. In such a case, the external station controller has

priority over the local voltage controler of the static generator.

The way the station controller dispatches the static generators depends on the settings of the Load Flow page for the station controller. See technical reference of the station controller.

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1.2.4 Primary frequency bias

Shortly following a disturbance, the governors of the units participating in primary control will increase/decrease

their turbine power and drive the frequency close to its nominal value. The change in the generator power is

proportional to the frequency deviation and is shared among participating units according to the gain (Kpf) of

their primary controllers, this is depicted in Figure 9. If the Active Power Control According to Primary

Control option is selected in PowerFactory's load flow command, the power balance is established by all

generators having a primary controller gain (parameter Prim. Frequency Bias from the Load Flow tab of

the static generator), according to the corresponding frequency droop.

puf

nf

f

dispP P puP

P

f

puf

nf

f

dispP P puP

P

f

Figure 9: Primary Freqncy Bias

The actual dispatched real power of the generator is calculated as:

P = Pdispatch + dP

where

dP = dF * Kpf

dP is the change in generator output

dF is the change in frequency

Kpf is the primary controller gain parameter for the generator

1.2.5 Reactive Power Limits

The reactive power limits can be specified in two ways:

Minimum/maximum constant limits. In the case of the minimum/maximum limits, these are originally set equal to

the minimum and maximum value of the nominal reactive power. Note that the reactive power limits are

operational data and will be saved to the operation scenario if active. Along these values, a scaling factor for each

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limit can be specified, which can be used in conjunction with the option „Consider Reactive Power Limits Scaling

Factor‟ in the Basic Options of the Load Flow Calculation dialog.

Capability Curve objects (IntQlim) allows the consideration of distinct minimum / maximum values of the

reactive power at different levels of active power injection. Capability curves are stored inside the 'Mvar Limits

Curves' folder in the Operational Library. Synchronous generators (ElmSym) and static generators (ElmGenstat)

defined in the network model can use the same Capability Curve object that is stored in the operational library.

When a capability curve is used, the dispatch of the generator always stays within its minimum and maximum

range if the option „Consider Reactive Power Limits‟ on the Load Flow command is activated.

How to create a new capability curve object is explained in the help of PowerFactory.

1.2.5.1 Applying Mvar Limits Curve from Operational Library

To apply an existing generator capability curve to a generator:

Locate the “Reactive Power Limit” section in the load flow page of the static generator dialog.

Press next to “Capability Curve”.

Choose “Select…” to look for a suitable curve in the “Mvar Limit Curves” folder in the “Operational

library” folder.

1.2.6 Active Power Limits

There are two ways to set a limit for the active power. If one of the two limits is exceeded during a load flow

calculation a warning massage will be dispayed in the output window.

The “Active Power: Operational Limits” are the minimum and maximum MW output limits of the generator from

an operational perspective. They have a higher prirority than the “Active Power Rating” limits.

The “Active Power: Ratings” is the maximum active power output of the generator and it is established by

multiplying the generator nameplate MVA rating by the power factor and the rating factor.

1.3 Short-Circuit Calculations

1.3.1 VDEC/IEC Short Circuit

There are three different possibilities to consider a static generator in the VDE/IEC short circuit calculation:

No Short-Circuit Contribution (according to the standard)

Static Converter-Fed Drive

Individual Max. Fault Contribution

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Figure 10: VDE/IEC Short Circuit Page

1.3.1.1 No Short-Circuit Contribution

In the VDEC/IEC short circuit calculations, the static generators are normally disregarded, according to the

standard (Option: “No Short-Circuit Contribution”).

1.3.1.2 Static Converter-Fed Drive

With the option “Static Converter-Fed Drive” activated the Static Gernator behaves during the VDE/IEC short

circuit calculation like a static converter-fed drive according to the IEC 60909 (VDE 0102). The static converter-

fed drives are considered for three-phase short circuits only. They only contribute to the initial symmetrical short-

circuit current Ik” and to the peak short-circuit current ip. They do not contribute to the symmetrical short-circuit

breaking current Ib and to the steady-state short-circuit current Ik. As a result, static converter-fed drives are

treated for the calculation of short-circuit currents in a similar way as asynchronous motors. The equivalent model

is shown in Figure 11.

The impedance is calculated as follow:

rM

rM

rMLRrM

rM

rMLR

MS

U

III

U

IIZ

21

3/

1

with:

3/ rMLR II

1.0/ MM XR with MM ZX 995.0

where:

UrM is the rated voltage

Irm is the rated current

SrM is the rated apparent power

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The Index „rM‟ specifies the rating of the static converter transformer on the network side, or the rating of the

static converter if no transformer is present.

2)/(11

MM

M

XR

ZX

1/1 XXRR MM

Figure 11: Equivalent Generator Model, for Static Converter-Fed Drive Option

1.3.1.3 Individual Max. Fault Contribution

If neither “No Short Circuit Contribution” nor “Static Converter-Fed Drive” is enabled then the user can input the

Maximum Short Circuit Contribution. It is calculated according to a equivalent generator model.

Figure 12: Equivalent Generator Model, Positive sequence circuit diagram

The impedance is calculated as follow:

2max

11

XRS

cx

k

11 xXRr

cmax is the voltage factor c.

i1 R1 X1

~ c*Un/√3

i1 r1 x1 F

~ c*Un/√3

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Note that cmax in the calculation of x1 is needed because the current is calculated with x1 and cmax*u. The factor

cmax will cancel down. So that finally the subtransient short circuit apparent power is equal to the entered value.

The model is considered for the symmetrical short-circuit breaking current Ib like an external grid:

IkIkIb ''

For the steady-state short-circuit current Ik is the same value as for Ik‟‟ used. This is the same approach as for

the asynchronous machine.

The Inputparameters are:

Ik‟‟ or Sk‟‟

X‟‟/R or R/X‟‟

For minimum short-circuits is the model completely neglected and has no short-circuit contribution.

MODEL FOR UNBALANCED FAULTS

For unbalanced faults uses the static generator the zero and negative sequence model that is already described in

section 1.1.1 Zero/Negative Sequence Model.

For minimum short-circuits is the model completely neglected and has no short-circuit contribution.

1.3.2 Complete Short Circuit

With the Complete Mehod is it possible to define a user-specific level for the subtransient and the transient short

circuit. Either as short circuit power or as short circuit current, and the R/X‟‟ ratio (alternatively the X‟‟/R ratio).

The static generator model for the short-circuit calculation using the “complete” method is adapted as follows:

Figure 13: Model for Complete Short Circuit Calculation

The short-circuit impedance is calculated as follow for the transient and sub-transient

u1

i1 r1 x1

uint Yldf

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211

XRS

cx

k

for Sk = Sk” or Sk‟ respectively

XRxr 11

The c factor and the Yldf admittance are only used for the complete method with load flow initialization. So the c

factor reflects the actual voltage at the static generator from load flow in per unit.

ldfuc and ldfuu int

ldf

ldf

ldfu

iY

For a short-circuit at the terminal of the generator the short-circuit current is equal to the entered value of the Ik”

and Ik‟. For short-circuit far away the short-circuit current is nearly equal to the load flow current.

MODEL FOR UNBALANCED FAULTS

For unbalanced faults uses the static generator the zero and negative sequence model that is already described in

section 1.1.1 Zero/Negative Sequence Model.

For minimum short-circuits is the model completely neglected and has no short-circuit contribution.

1.3.2.1 “Complete” without load flow initialization

If the Complete Short-Circuit method is used without the option “Load Flow Initialisation” on the Advanced

Options page of the short-circuit calculation command the following model is used.

Figure 14: Positive sequence circuit diagram for sub-transient faults

The positive sequence transient impedance is calculated as follow:

u1’’

i1’’ r1’’ x1’’

uo’’

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21

""1

XRS

cx

k

XRxr "1"1

"" cuo

c” is the c-factor (voltage factor)

If the transient short-circuit level (Ik‟, Sk‟) is zero, the model is represented only through the subtransient

impedance. The transient impedance and the internal voltage source uo‟ are ignored.

Figure 15: Positive sequence circuit diagram for transient faults

The positive sequence transient impedance is calculated as follow:

21

''1

XRS

cx

k

XRxr '1'1

c‟ is the c-factor (voltage factor)

MODEL FOR UNBALANCED FAULTS

For unbalanced faults uses the static generator the zero and negative sequence model that is already described in

section 1.1.1 Zero/Negative Sequence Model.

For minimum short-circuits is the model completely neglected and has no short-circuit contribution.

u1’

i1’ r1’ x1’

uo’

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1.3.3 ANSI Short Circuit

There are two possibilities to use the static generator in an ANSI short circuit calculation:

No Short-Circuit Contribution (according to the standard)

Individual Fault Contribution

If “No Short-Circuit Cinstribution” is activated the static generator will be neglected in the calculation.

If the option “No Short-Circuit Contribution” is not enabled the Maximum Short Circuit Contribution could be

entered.

Figure 16: Positive sequence circuit diagram

The impedance is calculated as follow:

211

XRS

ux

k

prefault

11 xXRr

uprefault is the prefault voltage in p.u.

The static generator is considered as follows for the corresponding short-circuit currents:

Momentary Current (First-cycle)

r1, x1 is used (as defined in the equations above)

Interrupting Current

like for the first-cycle study and always considered as “remote contribution”

30-cycle short-circuit

No short-circuit contribution, the model is neglected (disconnected)

i1 r1 x1 F

~ uprefault

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1.3.4 IEC 61361

The IEC 61361 short circuit for the static generator is calculated according to the specification. The specification

could be found in the chapter for IEC 61361 in the handbook.

1.4 Harmonics

The static generator behaves like a current source during harmonic analysis. The used equivalent model is

therefore a current source.

The harmonics tab allows to specify or select the harmonic sources object. The spectrum of harmonic infeeds

may be entered according to one of two options: balanced or unbalanced.

Figure 17: Harmonics Balanced - Unbalanced

Also, the harmonic current can refer to either the Fundamental Current or to the Rated Current.

If „Rated Current‟ is selected (Figure 18) then the phase angle is used from the initial bus voltage angle obtained

from load flow.

Figure 18: Harmonic current referred to

More information about the definition of harmonic current sources could be found in the corresponding chapter of

the handbook.

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1.5 RMS Simulation

The static generator supports two different models:

current source model

voltage source model

Depending on which input signals are connect the current or the voltage source model is used. If both signal

combinations are connected the voltage source model is used. If no input signal is connected the static generator

behaves like a constant current source. The current values from the load flow are used.

Figure 19: Model Input (RMS)

The user can specify in both models a Minimum Operation Voltage threshold. For unbalanced simulation the

zero/negative sequence is calculated as described in chapter 1.1.1.

1.5.1 Current Source Model

Input Signals:

• id_ref: d-Axis Current Reference in p.u.

• iq_ref: q-Axis Current Reference in p.u.

• cosref: Cos(dq-Reference-Angle)

• sinref: Sin(dq-Reference-Angle)

The cosref, sinref signal can be connected from a PLL model.

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Figure 20: Current Source Model

The following equations are used:

uiuijuiuii refqrefdrefqrefd cossinsincos1 ____

If the input signals “cosref” and “sinref” are connected:

refu coscos and refu sinsin

If the input signals are not connected the sinu and cosu quantities are internally calculated by using the terminal

positive sequence voltage u1:

|1|

)1Re(cos

u

uu and

|1|

)1Im(sin

u

uu

If the voltage under-runs the “Min. Operating Voltage”:

01i

The machine is switched on again, if the voltage is 5% higher as the “Min. Operating Voltage”.

1.5.2 Voltage Source Model

Input Signals:

u1r_in : Voltage Input, pos. Sequence Real Part in p.u.

u1i_in : Voltage Input, pos. Sequence Imaginary Part in p.u.

Input Parameter:

uk : Series Reactor, Short Circuit Impedance in %

i1

id_ref iq_ref u1

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Pcu : Series Reactor, Copper Losses in kW

The voltage source model is used if the two input signals “u1r_in” and “u1i_in” are connected otherwise the

current source model is used.

Figure 21: Voltage Source Model

The following equations are used:

11_1_1 izuiniujinru

with: XjRz

The quantities R and X are calculated from the input parameter “uk” and “Pcu”.

If the voltage under-runs the “Min. Operating Voltage”:

01i

The machine is switched on again, if the voltage is 5% higher as the “Min. Operating Voltage”.

1.5.3 Negative/Zero Sequence Model

See chapter 1.1.1. Zero/Negative Sequence Model of the load flow calculation.

1.6 EMT Simulation

Fot the EMT Simulation are also two models available like in the RMS simulation.

u1r_in u1i_in u1

i1

~ U

R X

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1.6.1 Current Source Model

The current source model is implemented as a voltage source with a controlled current. The current is controlled

with a build in current controller:

Figure 22: Build in Current Controller (Parameter)

The current controller is defined as follows:

sTK

d

d

11

sTK

q

q

11

dui

qui

refdi _

refqi _

di

qi

sTK

d

d

11

sTK

q

q

11

dui

qui

refdi _

refqi _

di

qi

Figure 23: Build in Current Controller

The voltage of the internal voltage source is calculated in the d-q-frame as follows:

qshcnomdu ilfidu 21

dshcnomqu ilfiqu 21

with:

lshc is the short circuit inductance in p.u.

The voltage is transformed back to the system coordinates and applied to the voltage source:

quuduuru 1sin1cos1

quuduuiu 1cos1sin1

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Figure 24: Model used for EMT-current source

1.6.2 Voltage Source Model

The voltage source model of the EMT Simulation is equal to the model of the RMS Simulation (1.5.2 Voltage

Source Model).

1.6.3 Zero Sequence

See chapter 1.1.1. Zero/Negative Sequence Model of the load flow calculation.

u1r u1i u

Id iq

~ U

2f lshc

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2 Input/Output Definition of Dynamic Models

2.1 Stability Model (RMS)

2.1.1 Current Source Model

Figure 25: Input/Output Definition of the HVDC converter model for stability analysis (RMS-

simulation)

Table 1: Input Definition of the RMS-Model

Parameter Description Unit

id_ref d-Axis Current Reference p.u.

iq_ref q-Axis Current Reference p.u.

cosref Cos(dq-Reference-Angle)

sinref Sin(dq-Reference-Angle)

Table 2: Output Definition of the RMS-Model

Parameter Description Unit

xspeed Frequency p.u.

id Current, d-Axis p.u.

iq Current, q-Axis p.u.

id_ref

iq_ref

cosref

xspeed

iq sinref

id

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2.1.2 Voltage Source Model

Table 3: Input Definition of the RMS-Model

Parameter Description Unit

u1r_in Voltage Input, Real Part p.u.

u1i_in Voltage Input, Imaginary Part p.u.

Table 4: Output Definition of the RMS-Model

Parameter Description Unit

xspeed Frequency p.u.

id Current, d-Axis p.u.

iq Current, q-Axis p.u.

u1r_in

u1i_in

xspeed

iq

id

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2.2 EMT-Model

2.2.1 Current Source Model

Figure 26: Input/Output Definition of the HVDC converter model for stability analysis (EMT-

simulation)

Table 5: Input Definition of the EMT-Model

Parameter Description Unit

id_ref d-Axis Current Reference p.u.

iq_ref q-Axis Current Reference p.u.

cosref Cos(dq-Reference-Angle)

sinref Sin(dq-Reference-Angle)

Table 6: Output Definition of the EMT-Model

Parameter Description Unit

xspeed Frequency p.u.

id Current, d-Axis p.u.

iq Current, q-Axis p.u.

id_ref

iq_ref

cosref

xspeed

iq sinref

id

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2.2.2 Voltage Source Model

Table 7: Input Definition of the EMT-Model

Parameter Description Unit

u1r_in Voltage Input, Real Part p.u.

u1i_in Voltage Input, Imaginary Part p.u.

Table 8: Output Definition of the EMT-Model

Parameter Description Unit

xspeed Frequency p.u.

id Current, d-Axis p.u.

iq Current, q-Axis p.u.

u1r_in

xspeed

iq

id

u1i_in

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3 Input Parameter Definitions

3.1 *.ElmGenstat

Table 9: Input Parameter Definitions of the Static Generator Element

Parameter Description Unit

loc_name Name

bus1 Terminal (StaCubic)

bus1_bar Terminal

cpZone Zone

cpArea Area

outserv Out of Service

aCategory Category

ngnum Number of Parallel Machines

sgn Rated Apparent Power MVA

cosn Rated Power Factor

bustp Corresponding Bus Type

iv_mode Local Voltage Controller

c_pstac External Station Controller

mode_inp Dispatch: Input Mode

pgini Dispatch: Active Power MW

qgini Dispatch: Reactive Power Mvar

sgini Dispatch: Apparent Power MVA

cosgini Dispatch: Power Factor

pf_recap Dispatch: Power Factor

usetp Dispatch: Voltage p.u.

ddroop Dispatch: Droop %

Kpf Dispatch: Primary Frequency Bias MW/Hz

pQlimType Reactive Power Limits: Capability Curve

q_min Reactive Power Limits: Min. p.u.

q_max Reactive Power Limits: Max. p.u.

cQ_min Reactive Power Limits: Min. Mvar

cQ_max Reactive Power Limits: Max. Mvar

scaleQmin Reactive Power Limits: Scaling Factor (min.). %

scaleQmax Reactive Power Limits: Scaling Factor (max.). %

Pmin_uc Active Power: Operational Limits: Min. MW

Pmax_uc Active Power: Operational Limits: Max. MW

Pnom Active Power: Operational Limits: Pn. MW

P_max Active Power: Ratings: Max. MW

pmaxratf Active Power: Ratings: Rating Factor.

c_pCtrlHV Controlled HV-busbar

Uctrl HV-Voltage Setpoint kV

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Qmin_a Qmin (act.) Mvar

Qmax_a Qmax (act.) Mvar

Pmin_a Pmin (act.) MW

Pmax_a Pmax (act.) MW

iconfed Static Converter-fed Drive

Skss Fault Contribution: Subtransient Short-Circuit Level MVA

Sks Fault Contribution: Transient Short-Circuit Level MVA

Ikss Fault Contribution: Subtransient Short-Circuit Level kA

Iks Fault Contribution: Transient Short-Circuit Level kA

rtox Fault Contribution: R to X” Ratio

xtor Fault Contribution: X” to R Ratio

iearthed Earthed

r0 Earthed: Zero-sequence Resistance p.u.

x0 Earthed: Zero-sequence Reactance p.u.

iAstabint A-stable Integration Algorithm

umin Min. Operation Voltage p.u.

uk Short Circuit Impedance %

Kd Current Controller: Kd: d-Axis, Proportional Gain

Td Current Controller: Td: d-Axis, Integration Time Constant s

Kq Current Controller: Kq: q-Axis, Proportional Gain

Tq Current Controller: Tq: q-Axis, Integration Time Constant s

phmc Harmonic Injections

icurref Harmonic Current Referred to

ictqg Optimal Power Flow Controls: Reactive Power

iOPFCQmin Optimal Power Flow Reactive Power Limits: Min

iOPFCQmax Optimal Power Flow Reactive Power Limits: Max

pBMU Commitment Automatic Dispatch: Virtual Power Plant

iestp State Estimation: Estimate Active Power

iestq State Estimation: Estimate Reactive Power

pStoch Stochastic Model