1 chapter 8: procedure of time-domain harmonics modeling and simulation contributors: c. j....
TRANSCRIPT
1
Chapter 8: Procedure of Time-Domain Harmonics Modeling and Simulation
Chapter 8: Procedure of Time-Domain Harmonics Modeling and Simulation
Contributors: C. J. Hatziadoniu, W. Xu, and G. W. Chang
Organized by
Task Force on Harmonics Modeling & Simulation
Adapted and Presented by Paulo F Ribeiro
AMSC
May 28-29, 2008
2
OUTLINEOUTLINE
1. Introduction: Relevance of the Time Solution Procedures
2. The Modeling Approach• Harmonic Sources in the Time Domain• Apparatus Modeling• Formulation of the Network State Equation• Harmonic Solution Procedure
3. Software Demonstration of Harmonic Simulation
4. Summary and Conclusion
3
INTRODUCTIONINTRODUCTION
• Why Time Domain Solution?
• When is Time Domain Solution Appropriate?
• How Accurate is Time Domain Solution Compared to Direct Methods?
• What are the General Characteristics of a Time Domain Solution Procedure?
4
Why Time Domain Solution?Why Time Domain Solution?
• “Time Domain Simulation is preferable to direct methods in certain line varying conditions involving power converters and non-linear devices.”– It allows detail modeling, especially of non-linear
network elements;
– It allows the assessment of non-linear feedback loops onto the harmonic output (e.g. study of harmonic instability in line commutated converters).
• Example of Direct Methods– PCFLOH;
– SuperHarm.
5
When is Time Domain Solution Appropriate?
When is Time Domain Solution Appropriate?
• Calculations of non-characteristic harmonics from power converters.
• Calculation of harmonic instability and harmonic interactions between power converters and the converter control.
• Harmonic filter design and harmonic mitigation studies.
• The effect of harmonics on equipment and protection devices.
• Real time digital simulations-RTDS of harmonics such as hardware-in-loop simulations.
6
Accuracy of Time Domain Simulation v. Direct Methods
Accuracy of Time Domain Simulation v. Direct Methods
• The time response of the system must arrive at a periodic steady state.
– Quasi periodic or aperiodic response possible under non-linear feedback control.
• Sampling and integration errors. The sampling step is dictated by the highest harmonic order of interest.
• Modeling errors approximating the non-linear characteristic of certain apparatuses (e.g. transformer magnetization and arrester v-i characteristics)
7
What are the General Characteristics of a Time Domain Solution Procedure?
What are the General Characteristics of a Time Domain Solution Procedure?
• Slow Transient Modeling. May use programs such as EMTP, PSCAD, and SIMULINK. May incorporate local controls of power converters.
• Describe a limited part of the system around the harmonic source.
• Run simulation until steady state Use FFT within the last simulation cycle to compute harmonics.
8
Modeling ApproachModeling Approach
• Harmonic Sources
– Power Converters Detail representation including grid control and, possibly,
higher level control loops.
Equivalency: Represent as rigid source.
– Non-Linear Devices Transformer magnetizing and inrush current.
Arrester current in over-voltage operation.
– Background harmonics: Rigid source representation.
9
Power Converters: Detail RepresentationPower Converters: Detail Representation
• Detail Valve model
• Surge arrester representation in studies of harmonic overvoltages
• Representation of the grid control
SurgeArrester
Ls
Snubber
10
Power Converters: Switching FunctionPower Converters: Switching Function
• Voltage-Sourced inverters are more suitable for this representation.
• Switching function approach:
– Voltage:
– Current:
va
vc
vb
ia
ic
ib
id
+vd
-
dccdbbdaa vtsvvtsvvtsv )(,)(,)(
ccbbaad itsitsitsi )()()(
11
Non-Linear Devices: TransformerNon-Linear Devices: Transformer
• Piece-wise Linear representation of the core inductance.
• Switching inductance model (flux controlled switches).
l(i)
i
Lo
L2
L1
iA iB
lA
lB
Aircore Inductance
Saturation Characteristic
Uns
atur
ated
Seg
men
t
Sat
urat
ed
Seg
men
t
i
v Lo LA LB
SA SB
12
Formulation of the Network EquationsFormulation of the Network Equations
• Pre-integrated Components: Algebraic Equations
• State Equations: Numerical Integration– Piece-wise Linear Equations
– Time Varying Equations
)(
),(0
)(
0
),(),(),(
),(
),(
tu
txB
B
B
xf
x
x
x
txAtxAtxA
txAAA
txAAA
x
x
x
C
N
L
C
N
L
CCCNCL
NCNNNL
LCLNLL
C
N
L
13
Summary of The Time Domain ProcedureSummary of The Time Domain Procedure
Run Slow Transient Program
Network and
converter data
Steady State?
Sart
Slow Transient Modeling
No
Run FFT
Met Criteria?
Fine-Tune Model
End
Yes
No
Yes
14
SIMULINK DemonstrationsSIMULINK Demonstrations
• Converter Simulation Using the Switching Function
• Non-Linear Resistor
• Rigid Harmonic Source
• Impedance Measurement
• Network Equivalency
15
Converter Simulation Through the Switching Function
Converter Simulation Through the Switching Function
Switching Function Generation Inverter DC Side
Inverter AC Side
Measurements from network
Continuous
powerguiV
s
-+
Vc
s
-+
Vb
s
-+
Va
ABC
A
B
C
A
B
C4
Multimeter
s -+
Id
[Ic]
[Ib]
[Ia]
[Vd]
[Sc][Sb][Sa]
[Ic][Ib][Ia] [Sc][Sb][Sa]
[Sc]
[Sb]
[Sa]
[Vd]
P1
P2
Discrete 3-phasePWM Generator
Cd
A
B
C
A
B
C
(a)
(b)
+Vd
-
• Linear Network.
• Insert the converter as:– Voltage source on ac
side.
– Current source on dc side.
• Incorporate high level converter controls.
16
Example of Non-Linear Resistor Using User-Defined Functions
Example of Non-Linear Resistor Using User-Defined Functions
+v-
Voltage Controlled Resistor
Continuous
pow ergui
s -+
i(v)
v+-
Series RLC Branch
Scope
node 0
node 1
node 1
Lookup TableDescribing i(v)
[i]
Goto
[i]From
C'
v i(v )
RT
+-
+
v
-
i(v)
V(x)
Network Thévenin Equivalent
Non-linear voltage controlled resistor
• Voltage Controlled Element: Parasitic capacitance C’
• User-defined function describing the i(v) function
)()( xVviRv T
17
Rigid Harmonic Source Using the s-Function
Rigid Harmonic Source Using the s-Function
• S-Function: Calculation of the harmonic current:
• Simulation time slows down with increasing order N
Nn
nna ntnItIti,..,5,3
111 )cos()cos()(
3
C
2
B
1
A
sfHarm_3ph
Rigid Source
s
-+
Phase C
s
-+
Phase B
s
-+
Phase A
18
Impedance Scans Using Rigid Harmonic Sources
Impedance Scans Using Rigid Harmonic Sources
• Basic assumptions:– Linear Network Model.
– Single driving point (e.g. location of harmonic source).
– The harmonic source is represented by a rigid current source at pre-defined harmonic orders.
• Driving point impedance
• Transfer impedance
Procedure:1. Inject positive, negative, or
zero sequence current separately at unit amplitude;
2. Arrive at steady state
3. Obtain bus voltage
4. Apply FFT1. Driving point impedance
2. Transfer Impedance
)()(
)(1
1
11
jnV
jnI
jnVjnZ k
k
kkk
)()(
)()( 1
1
11
jnV
jnI
jnVjnZ m
k
mmk
19
Impedance Scan: Transfer Function Method
Impedance Scan: Transfer Function Method
• Basic Assumptions– The impedance is
defined as a current-to-voltage network (transfer) function:
– Network is driven by a signal-controlled current source. More than one inputs can be used.
• Procedure
1. Define network as a subsystem;
2. Define the controlling signals of the current sources as the inputs;
3. Define the voltages at the buses of interest as the outputs;
4. Use the LTI tool box to obtain the driving and transfer impedances.
)(
)()(
sI
sVsZ
k
mmk
20
Impedance Scan: Transfer Function Method—Example
Impedance Scan: Transfer Function Method—Example
• Inputs: Signal node 1 (array input: number of input signals is three).
• Outputs: Voltage at network nodes 1, 2, and 3 (each is an array of three). Voltage is measured by the voltmeter or the multimeter block
Line Impedance datar'=0.278 Ohm/mix'=0.733 Ohm/mi
Injection Source
Input
3
Vb32
Vb2
1
Vb1
Continuous
ABC
ABC
A B C
Load 34MW1.4MVAR
A B C
Load 22MW0.7MVAR
A B C
Load 12MW
0.7MVAR
s
-+
I1c
s
-+
I1b
s
-+
I1a
V_bus1 V_bus3V_bus2
ABC
ABC
Feeder 2-3: 2mi
A
B
C
A
B
C
Feeder 1-2: 2 mi
A
B
C
a
b
c
Bus 3
A
B
C
a
b
c
Bus 2
A
B
C
a
b
c
Bus 1
A B C
750kVAR
A B C
700kVAR
1
I1
21
Network EquivalencyNetwork Equivalency
• It is often desirable to represent a part of the network (referred to as the external network) by a reduced bus/element equivalent preserving the impedance characteristic at one or more buses (interface or interconnection buses).
• The part of the network that is of interest can be represented in detail.
22
Network Equivalency Using SIMULINKNetwork Equivalency Using SIMULINK
• The procedure replaces the external network by a TF block representing the driving point impedance at the interface bus.
• The TF block is embedded into the network of interest:
1. Drive the block input by the interface bus voltage;
2. Connect the block output to the input of a signal driven current source;
3. Connect the current source to the interface bus;
23
Network Equivalency: ExampleNetwork Equivalency: Example
• Method becomes cumbersome for multiple interface buses.
• Mutual phase impedances are omitted.
Injection Source
ContinuousA B C
Load 12MW
0.7MVAR
s
-+
I1c
s
-+
I1b
s
-+
I1aV_bus1
A
B
C
a
b
c
Bus 1
(s+0.1)(s+100)
(s+100)(s+40-800i)(s+40+800i)
Admittance Phase c
(s+0.1)(s+100)
(s+100)(s+40-800i)(s+40+800i)
Admittance Phase b
(s+0.1)(s+100)
(s+100)(s+40-800i)(s+40+800i)
Admittance Phase a
A B C
700kVAR
AB
C
Ih
24
SummarySummary
1. Time domain harmonic computation is useful in cases where detail modeling of the harmonic source is required;
2. The modeling approach is the same as the slow transient modeling approach;
3. The size of the network simulated is limited to a few buses around the harmonic source;
4. Software like SIMULINK combine several useful features that can provide insight into a problem, especially for educational purposes.