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Transcript
Combined Transient and Steady State
Simulation
November 2007
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]
Published by
DIgSILENT GmbH, Germany
Copyright 2007. All rights
reserved. Unauthorised copying
or publishing of this or any part
of this document is prohibited.
Combined Transient and Steady State Simulation
Table of Contents
Table of Contents
1 Introduction ......................................................................................................................................... 4
2 Theoretical Background ....................................................................................................................... 4
3 PowerFactory Setup............................................................................................................................. 5
3.1 General description ................................................................................................................................ 5
3.2 Starting PowerFactory ............................................................................................................................ 7
3.3 Synchronizing the Slave with the Master................................................................................................... 7
3.4 Transmitter and Receiver Input Data ....................................................................................................... 9
3.5 Starting the Simulation ......................................................................................................................... 12
4 Example .............................................................................................................................................. 13
4.1 UKss Calculation, RMS Side ................................................................................................................... 16
4.2 Pext, Qext Calculation, RMS Side ........................................................................................................... 16
4.3 Convert_I, EMT Side ............................................................................................................................. 16
4.4 Convert_U, EMT Side ............................................................................................................................ 17
Combined Transient and Steady State Simulation
1 Introduction
Combined transient and stability simulation means splitting the simulation of a power system into two parts, one
performed in transient mode and the other in stability mode.
The nonlinear nature of the power system implies that the responses at different frequencies are not completely
decoupled. The steady-state behaviour of a component, which internally works with fast frequencies, may change
as a result of interaction between fast and slow dynamics, hence changing the overall operating point of the
system. The common practice is to use average steady-state models for such devices in system studies, but the
question arises as to whether those models properly portray this interaction or not. The equivalent question for
the new methodology is whether the partitioning of equations and solving them successively rather than
simultaneously can reflect the phenomena of interest with enough accuracy.
While the above issues deserve attention, they are not the main concern here. Rather our focus is to describe the
implementation of RMS-EMT simulation in PowerFactory. In this report:
The nature of data exchange between the simulators is explained in Theoretical Background. Then in
PowerFactory Setup, it is shown how the communication between two PowerFactory simulators must be
configured. A simple example is considered last.
2 Theoretical Background
In stability simulation the electrical network is represented by phasors whereby only the synchronous frequency
data is considered. This simplification yields conservative results, but is necessary in order to deal with the
analysis of large-scale power systems. In transient simulation, on the other hand, the network is modelled by
differential equations, and therefore, the electrical variables contain all the natural and forced frequencies.
Stability simulation deals with the solution of differential-algebraic equations. The differential equations describe
the mechanical as well as the rotor electrical dynamics, while the algebraic equations describe the network. It is
helpful to review the nature of this combination as a similar situation arises when combining RMS and EMT
simulations.
The most important simplification in stability simulation is done with regard to synchronous machine modelling.
The more accurate model of synchronous machine consists of a set of differential equations both in the rotor and
in the stator. By neglecting the differential terms in the stator equations, the terminal voltage of the machine is
represented by a phasor that can be used in the algebraic equations of the network. These equations yield the d
and q components of the stator currents which are then used to calculate the internal voltage of the machine
(voltage behind reactance). The internal voltage of the machine is treated as a state variable and used in
differential equations together with the excitation voltage (see for example Kundur p.181).
Combined Transient and Steady State Simulation
As a result of this simplification, effect of fast transients of the network on the rotor variables is neglected. The
slow frequencies, however, are represented well enough, and the slow variations of the rotor speed about the
synchronous speed are calculated using a differential equation that includes the mechanical and electrical powers.
For the range of frequencies of interest in stability studies (much below the synchronous frequency) the
simplifications described above are reasonable.
How is the combined RMS-EMT simulation justified?
If the detailed model of a part of the network for example an electronic converter is available, and it is expensive
or not straightforward to derive the average steady-state model, then the RMS-EMT simulation allows for the
detailed model to be used for system studies. Instead of using an equivalent RMS model for the converter, it is
represented in detail using an EMT model and interfaced with the rest of the network, which due to its size, is
represented by an RMS model. Furthermore, if these periodically-switched devices go to their nonlinear region as
the result of shift in the operating point (which is determined by the steady state of the whole system) or get
disconnected from the system by protective devices which trigger upon fast transients, it might be important
even from the stability point of view to take these fast phenomena into account for modelling.
One obvious limitation of this simulation strategy is when at the point of split, the subsystems have loading effect
on each other at frequencies other than the synchronous frequency (for example subsynchronous resonance).
The combined simlulation method implemented in PowerFactory has a feedback nature. The master simulator
(RMS) feeds voltages into the slave simulator (EMT), and receives currents from it. In the next section the setup
details are explained.
3 PowerFactory Setup
This section explains the settings that need to be done in order to establish communication between two
PowerFactory simulators.
3.1 General description
The simulation setup is depicted in Figure 1.
Combined Transient and Steady State Simulation
Bus
RMS
NETWORK
EMT
NETWORK
PowerFactory 1 (Master)
PowerFactory 2 (Slave)
Transmits voltage
Receives voltage
Receives current
Transmits current
Figure 1- Splitting the task of simulation between two instances of PowerFactory
The network to the left of Bus is simulated in the stability mode, and the network to the right of Bus in the
transient mode in two PowerFactory simulators. The transfer of data between the simulators is realized through
RPC (Remote Procedure Calls) which is based on a TCP/IP (Transmission Control Protocol/Internet Protocol). Two
PowerFactory objects are used for this purpose; the transmitter (ElmTransm) and the receiver (ElmReceiv).
The RMS network contains a load whose active and reactive currents are sent over by the EMT side. Similarly, the
EMT network contains a sinusoidal voltage source whose magnitude and angle are sent over by the RMS side.
Figure 2 shows this communication.
Bus
RMS
NETWORK
Load controlled
from EMT side
Z
Bus
EMT
NETWORK
Voltage controlled
from RMS side
Figure 2 – Communication between RMS and EMT networks
Each network has a DSL model containing an ElmReceiv object and an ElmTransm object. In the RMS network
the DSL model is connected to the load through the signals Pext and Qext. In the EMT network the DSL model
is connected to the voltage source through the signals U_A, U_B, and U_C.
Combined Transient and Steady State Simulation
Since the RMS simulation only deals with one frequency, the currents calculated in the EMT section have to be
filtered before being passed. Filtering the decaying DC component of the short circuit currents is of special
importance, because the response of the RMS model to DC excitation is simply wrong.
Z is the equivalent impedance of the RMS network at synchronous frequency. Inserting Z in the model means
that the subtransient voltage (voltage behind reactance) has to be sent over from the RMS to the EMT side
instead of the Bus voltage. This is advantageous because subtransient voltages are linked to the state variables
and their values do not jump.
3.2 Starting PowerFactory
When you start PowerFactory, make sure the “Master in Distributed Simulation” flag is checked for the master
simulator, and unchecked for the slave simulator. This flag is found in the “Advanced” page of the logon window
(Figure 3).
Figure 3: Starting PowerFactory in master mode
3.3 Synchronizing the Slave with the Master
The EMT simulator (slave) should be synchronized with the master. This is done in the “Real-Time” tab-page of
the “Calculation of Initial Conditions” window. The settings are shown in Figure 4.
Combined Transient and Steady State Simulation
Figure 4: Settings of the Real-Time tab-page of Initial Conditions of the slave simulator
Combined Transient and Steady State Simulation
3.4 Transmitter and Receiver Input Data
Figure 5: Transmitter input data pages in RMS simulator
Combined Transient and Steady State Simulation
Figure 6: Receiver input data pages in RMS simulator
Combined Transient and Steady State Simulation
Figure 7: Receiver input data pages in EMT simulator
Combined Transient and Steady State Simulation
Figure 8: Transmitter input data pages in EMT simulator
3.5 Starting the Simulation
After the simulators are initialized, master must be started first. After advancing one time step, it sends the
results to the slave and stops to receive signals from the other side before continuing.
Combined Transient and Steady State Simulation
4 Example
The network in this example is trivial, and is meant only to show the modelling details with regard to RMS-EMT
communication. Basically, the RMS and EMT networks are the same, as shown in Figure 9 and Figure 10.
20 kV
Load
~
V
Vrms
Const. Current
plini=10 MW
qlini=0.1 MVAr
Bus
usetp= 1.0 p.u.
X1=31.416 Ohm
Source
Controlled Load
Figure 9: RMS network
Load
~
Vemt
V
Reactor
Const Current
plini=10 MW
qlini=0.1 MVAr
xrea=31.416 Ohm
Bus
usetp=1.0 p.u.
Controlled Source
Load
Figure 10: EMT network
The load is a constant current load, so it represents a current source. Figure 11 and Figure 12 show the
composite frames used to set up the communication.
Combined Transient and Steady State Simulation
Figure 11: Composite frame of the communication on the RMS side
Combined Transient and Steady State Simulation
Receiver
*
Reference Frq
*
RMS V_Meas
*
RMS I_Meas
*
1
0
1
0
1
0
iq
id
ui
ur
ii
ir
1
0
3
2
1
0
ComRMS: Communication on the RMS side
ConvPQ
*
1
0
Ukss
*
1
0
Qext
Pext
1
0
Load
*
fref
u2
u1
2
1
0
Transmitter
*
DIgSILENT
Figure 12: Composite frame of the communication on the EMT side
Combined Transient and Steady State Simulation
EMT i_Meas
*
EMT v_Meas
*
Receiver
*
1
0
1
0
2
1
0
ii
ir
ui1
ur1
fref
ui
ur
ComEMTframe: Communication in the EMT side
3
2
1
0
2
1
0
Convert_I
*
Convert_U
*
1
0
2
1
0
u2
u1
U_C
U_B
U_A
1
0
2
1
0
Transmitter
*
Voltage
*
DIgSILENT
The voltage and current are measured (using StaVmea and StaImea) at Bus on both simulators. The current
measurement on both RMS and EMT networks is inserted in the cubicle facing the voltage source.
4.1 UKss Calculation, RMS Side
ussr = ur - rs*ir + xss*ii
ussi = ui - rs*ii - xss*ir
inc(ussr) = ur - rs*ir + xss*ii
inc(ussi) = ui - rs*ii - xss*ir
vardef(rs)='Ohm';': Equivalent Resistance'
vardef(xss)='Ohm';': Equivalent Reactance'
4.2 Pext, Qext Calculation, RMS Side
Pext = -id*Unom*sqrt(3)
Qext = iq*Unom*sqrt(3)
inc(id) = -Pext/Unom/sqrt(3)
inc(iq) = Qext/Unom/sqrt(3)
! The following two lines are needed to initialize the
! system when the load type is not specified. If
! the load type is set to Constant Current, the
! initialization is done without the following.
!inc0(Pext) = 0
!inc0(Qext) = 0
vardef(Unom)='kV';': Load Nominal Voltage'
4.3 Convert_I, EMT Side
umag = sqrt(ur*ur+ui*ui)
cosphi = ur/umag
sinphi = ui/umag
id1 = ir*cosphi+ii*sinphi
iq1 = -ir*sinphi+ii*cosphi
idd = delay(id1,0.01)
iqd = delay(iq1,0.01)
Combined Transient and Steady State Simulation
id = (id1+idd)/2
iq = (iq1+iqd)/2
! Initialization
inc(id) = ir*cosphi+ii*sinphi
inc(iq) = -ir*sinphi+ii*cosphi
inc(idd)=id
inc(iqd)=iq
inc(id1)=id
inc(iq1)=iq
inc(fref)=1
4.4 Convert_U, EMT Side
phiref. = 2*pi()*fref*Fnom
ualpha = ur*cos(phiref) - ui*sin(phiref)
ubeta = ur*sin(phiref) + ui*cos(phiref)
U_A=ualpha*Unom/sqrt3*sqrt2
U_B=(-0.5*ualpha+0.5*sqrt3*ubeta)*Unom/sqrt3*sqrt2
U_C=(-0.5*ualpha-0.5*sqrt3*ubeta)*Unom/sqrt3*sqrt2
sqrt3 = sqrt(3)
sqrt2 = sqrt(2)
! Initialization
!inc(phiref)=7.5*pi()/180
inc(phiref)=0.0
inc(ualpha)=ur*cos(phiref)-ui*sin(phiref)
inc(ubeta)=ur*sin(phiref)+ui*cos(phiref)
inc(U_A)=ualpha*Unom/sqrt3*sqrt2
inc(U_B)=(-0.5*ualpha+0.5*sqrt3*ubeta)*Unom/sqrt3*sqrt2
inc(U_C)=(-0.5*ualpha-0.5*sqrt3*ubeta)*Unom/sqrt3*sqrt2
inc(fref)=1
inc(ur)=19.55125 !1
inc(ui)=-2.477702 !0
vardef(Unom)='p.u.';': Nominal Line-Line Voltage'
Combined Transient and Steady State Simulation
! ur and ui are in kV, therefore Unom = 1
! If ur and ui are passed from the RMS simulator in p.u.
! then the value of Unom should be specified in kV
vardef(Fnom)='Hz';': Nominal Frequency'
Combined Transient and Steady State Simulation