Effects of Grounding Configurations on Post-Contingency Performance of MTDC system: A 3-Terminal Example

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Dr Francisco M. Gonzalez-Longatt PhD | http://fglongatt.org | Copyright © 2008-2014 1/15
50thInternationalUniversitiesPowerEngineeringConference(UPEC2015)September
1st-4th,2015|StaffordshireUniversity,UK
Allrightsreserved.Nopartofthispublicationmaybereproducedordistributedinanyformwithoutpermissionoftheauthor.Copyright©2008-2015.http:www.fglongatt.org
Dr Francisco M. Gonzalez-Longatt*
Prof. M.A.M.M. van der Meijden
Dr Jose Luis Rueda

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• The power injections (Pi)
in a DC grid are controlled
by the converters.
• On a MTDC grid as
Supergrid, the power flow
into, or out of, each
converter can be
dynamically changed
without any
reconfiguration of the
HVDC grid.
• The objective of this
paper is to establish the
effects of grounding
configurations on steady-
state post-contingency
performance of multi-
Terminal HVDC System.
Created by Dr. F. Gonzalez-Longatt

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Idc
U1
Idc
b. Metallic Returna. Ground Return Idc
c. Symmetric configuration
U2
+
- +
-
+
- +
-
U1 U2
U1 U2
Idc
a. Ground Return
Idc
2Idc
Idc
Idc
2Idc
b. Metallic Return
U1
+
-
+
-
+
-
+
-
U1
U2
U2
U1
+
-
+
-
U1
U2
U2
+
-
+
-
Idc
a. Ground Return
Idc
Idc
Idc
b. Metallic return
U1
+
-
+
- U1
+
-
+
-
+
-
+
-
+
-
+
-
U2
U2
U1
U1
U2
U2
Idc
+
- Udc
Monopole configurations
Homopolar configurations
Bipolar configurations
Back-to-Back configuration
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MTDC configuration:
series or parallel
MTDC parallel configuration:
radial or meshed
I1
I2
I3
I4
I1 + I2 + I3+ I4 = 0
U1
U2
U3
U4
U1 + U2 + U3 + U4 = 0
Idc
b. Series MTDCa. Parallel MTDC
+ -Udc
+
-
+-
+
-
+-
Idc
Idc
Idc
+ -Udc
I1
Udc
+
-
+
-
+
-
+
-
I3
I2 I4
Udc
Udc
Udc
Ixy
y
x
x
+
-Udc
+
-
+
-
+
-
Udc
I1 I3
I4+
-
Ux
I2
I4
b. Mesh configurationa. Radial configuration
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• System Configuration:
• A simple MTDC test system is used in this paper for demonstratives
purposes:3-terminal, ±200kVdc, VSC-HVDC.
• Network Model: DC cable between two nodes (e.g. i and j) are
represented using a single series resistor Rij. DC side of converter stations
are modelled by an ideal dependant voltage source and ideal ground is
represented as an ideal point where voltages is zero. All electrical
quantities are represented using per unit systems. The mathematic
modelling of some grounding configuration of MTDC systems are
presented here.
GSC1
N1
GSC2
N2
N3
WFC1
PWF1 = 0.80 p.u
WF1
AC1
AC2
R12=0.0.073
Test system:
Values of resistors Rij are shown in
p.u

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• Network Model:
Test system: Circuital representation
of monopole ideal ground return
2(+)
R12
R23
R13
1(+)
3(+)
U2
U1
U3
+
-
+
-
1(0)
2(0)
3(0)
+
-
( ) (0)
1 1 1
( ) (0)
2 2 2
( ) (0)
3 3 3
U U U
U U U
U U U



    
          
         
The converter voltage (Ui) can be expressed
in terms of the terminal potentials:
Ui
(+) represents electrical potential of the
transmission terminal and Ui
(0) is used to define
potential of the neutral terminal.
For this specific case, monopolar configuration
with ideal ground return, the voltage at the neutral
point (0) is connected to ideal ground where the
electric potential is assumed zero, U(0) = 0, as
consequence: U(0) = U.
( ) (0)
 U U U
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The current injected (Ii) is written into a matrix form using the conductance matrix (G) of
the DC grid can be used:
( )
1 11 12 13 1
( )
2 21 22 23 2
( )
3 31 32 33 3
I G G G U
I G G G U
I G G G U



    
         
         
( )
I GU I GU
where the DC current vector I = [I,1, I2, ...,Idc,ndc]T, U = [U1, U2, ...,Undc]T is the DC voltage
vector and G is also known as the DC nodal admittance matrix (Gij, i, j = 1, …ndc).
The current injections I are not known prior to the power flow solution for the DC network.
The vector P = [P1, P2, ...,Pndc]T, which refers to power flow into the DC grid via the DC
terminals, is given by
where the symbol  is entry-wise (point-to-point) matrix multiplication operator.
Equation is known as the power balance equation and it can be solved in order to obtain
the classical power flow solution of the MTDC system.
I = GU
 P = U GU

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2(+)
R12
R23
R13
1(+)
3(+)
U2
U1
U3
+
-
+
-
Rgnd1
1(0)
2(0)
Rgnd2
Rgnd3
3(0)
+
-
Test system: Circuital representation
of monopole with real ground return
(Rgndi).
The potential of the neutral points (0) are calculated
based on the grounding resistors (Rgndi):
(0)
1 1 1
(0)
2 2 2
(0)
3 3 3
0 0
0 0
0 0
gnd
gnd
gnd
U R I
U R I
U R I
     
          
        
( )
1 1 1 1
( )
2 2 2 2
( )
3 3 3 3
0 0
0 0
0 0
gnd
gnd
gnd
U U R I
U U R I
U U R I



      
             
           
( ) (0)
1 1 1
( ) (0)
2 2 2
( ) (0)
3 3 3
U U U
U U U
U U U



    
          
         
(0)
 gndU R I
( )
  gndU U R I
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( )
1 1 1 1
( )
2 2 2 2
( )
3 3 3 3
0 0
0 0
0 0
gnd
gnd
gnd
U U R I
U U R I
U U R I



      
             
           
( )
  gndU U R I
1 1( ) 
       gnd gndI R U R U( )
  gndU U R I
The conductance matrix (G)
( )
I GU ( ) 1 
U G I
1 11 
       gnd gndI R G I R U
1 11            gnd gndones R G I R U
11 11
             gnd gndI ones R G R U
Finally the power balance
equations for this configuration
is described by:
11 11
               
gnd gndP = U ones R G R U

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The power balance equations of other grounding configuration are created using the same
mathematical procedure presented before.
2(+)
R12
2(-)
R23
R13
1(+)
1(-)
3(+)
3(-)
R12
R23
R13
U2
U1
U3
+
-
+
-
+
-
U1
+
-
+
-
+
-
U3
U2
Rgnd1
1(0)
3(0)
2(0)
Rgnd2
Rgnd3
2(+)
R12
2(-)
R23
R13
1(+)
1(-)
3(+)
3(-)
R12
R23
R13
U2
U1
U3
+
-
+
-
+
-
U1
+
-
+
-
+
-
U3
U21(0)
3(0)
2(0)
Test system: Circuital representation: Bipolar
ground return
Test system: Circuital
representation: Bipolar Metallic
return
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• The steady-state performance of a MTDC system is described by
the power flow, it is be described by a set of nonlinear algebraic
equations:
• where G is the set of algebraic equations define the power-balance
at network nodes as shown in previous Sections, and X is state
vector and Y is the vector of independent variable and Z is a vector
of control variables.
Bound constraints:
 , , G X Y Z 0
min maxiU U U 
Nonlinear equality constraints:
Inverter
mode
Umax
DCvoltage,Udc
Umin
Pmax0-Pmax
Uref
Rectifier
mode
DC Power, Pdc
 1
dc ref ref dc
DC
U U P P
R
  
Linear inequalities:
 max
conv dc dc convI = Y U I
Power Balance Equations

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• VSC-HVDC terminals:
• Constant power control mode on the wind farm converter station
(P3)
• DC voltage droop control on the grid side converter stations (U1
and U2, DC1 = 0.0005 and DC2 = 0.0002 p.u/MW), thus enabling
N-1 security.
GSC1
N1
GSC2
N2
N3
WFC1
PWF1 = 0.80 p.u
WF1
AC1
AC2
R12=0.0.073

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A MATLAB® R2014a (64-bit) program (m-file) has been developed for this very
specific propose. Interior-point algorithm is used to solve the optimization problem in
this paper. Bound constraints are considered in all simulations in order to ensure a secure
system operation (0.90 < Udc < 1.10 p.u).
Numerical results of N-1 contingency analysis in DIgSILENT PowerFactory v15.2.4 are
used for comparative purposes.
(Rgnd1 = 1, Rgnd2 = 2, Rgnd3 = 3).
1dc(+)
2dc(-)
3dc(-)
2dc(+)
3dc(+)
1dc(+)
3dc(-)
-106.0 kV
-1.06003 p.u.
0.0 deg
2dc(-..
-105.5 kV
-1.05533 p.u.
0.0 deg
1dc(-..
-104.7 kV
-1.04712 p.u.
0.0 deg
3dc(+)
106.0 kV
1.06003 p.u.
0.0 deg
2dc(+)
105.5 kV
1.05533 p.u.
0.0 deg
1dc(+)
104.7 kV
1.04712 p.u.
0.0 deg
3ac
100.0 kV
1.00000 p.u.
0.0 deg
2ac
100.0 kV
1.0000..
0.0 deg
1ac
100.0 kV
1.00000 p.u.
0.0 deg
fglongatt.org
PowerFactory 15.2.4
GROUNDING AND CONFIGURATION OF MTDC
Symetric Bipolar-Earth Return Multi-terminal HVDC
Prof. Francisco M. Gonzalez-Longatt
fglongatt@fglongatt.org
Project: MTDC
Graphic: Grid
Date: 6/4/2015
Annex:
Grid: SummaryGrid
Generation = 400.00 MW 0.00 Mvar 400.00 MVA
External Infeed = -394.93 MW 0.00 Mvar 394.93 MVA
Inter AreaFlow = 0.00 MW 0.00 Mvar
Load P(U) = 0.00 MW 0.00 Mvar 0.00 MVA
Load P(Un) = 0.00 MW 0.00 Mvar 0.00 MVA
Load P(Un-U) = 0.00 MW 0.00 Mvar
Motor Load P = 0.00 MW 0.00 Mvar 0.00 MVA
Losses = 5.07 MW 0.00 Mvar
Line Charging = 0.00 Mvar
Compensation ind. = 0.00 Mvar
Compensation cap. = 0.00 Mvar
Installed Capacity = 500.00 MW
Spinning Reserve = 100.00 MW
Total Power Factor:
Generation = 1.00 [-]
Load/Motor = 0.00 / 0.00 [-]
-0.0 kV
-0.00000 p.u.
0.0 deg
-0.0 kV
-0.00000 p.u.
0.0 deg
-0.0 kV
-0.00000 p.u.
0.0 deg
Rb(..
188..
Ra(..
188..
Rgnd3
0.0
GND3
0.0
0.0
0.000
Rb(..
11.1
Ra(..
11.1
Rgnd2
0.0
GND2
0.0
0.0
0.000
GSC2(-)
-11.7
-0.0
0.067
0.0
0.0
0.111
11.7
0.0
-0.111
WFC1(-)
-200.0
-0.0
1.155
0.0
0.0
1.887
200.0
0.0
-1.887
GSC1(-)209.1
0.0
1.207
0.0
0.0
-1.997
-209.1
0.0
1.997
Rb
199..
Ra
199..
Rgnd1
0.0
GND1
0.0
0.0
0.000
WFC1(+)
-200.0
-0.0
1.155
200.0
0.0
1.887
0.0
0.0
-1.887
GSC2(+)
-11.7
-0.0
0.067
11.7
0.0
0.111
0.0
0.0
-0.111
GSC1(+)
209.1
0.0
1.207
-209.1
0.0
-1.997
0.0
0.0
1.997
Cable12(-)
19.5
-58.9
0.0
0.563
59.4
0.0
-0.563
Cable23(-)
15.7
47.9
0.0
-0.452
-47.7
0.0
0.452
Cable13(-)
49.7
-150.2
0.0
1.435
152.1
0.0
-1.435
Cable12(+)
19.5
-58.9
0.0
-0.563
59.4
0.0
0.563
Cable23(+)
15.7
47.9
0.0
0.452
-47.7
0.0
-0.452
Cable13(+)
49.7
-150.2
0.0
-1.435
152.1
0.0
1.435
WF1
80.0
400.0
0.0
2.309
V
~
AC2 23.3
0.0
0.135
V
~
AC1
-418.3
-0.0
2.415
DIgSILENT

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• Minimal numerical discrepancies between the DIgSILENT
PowerFactory and proposed method. The largest numerical
difference in post-contingency states is below 0.002 p.u, as
consequence, the proposed method can be used with minor
discrepancies.
Node
Voltage (p.u)
DIgSILENT
Voltage (p.u)
MATLAB
Contingency
3dc(-) -1.0791 -1.0791 Cable13(-)
2dc(-) -1.0600 -1.0598 Cable13(-)
1dc(-) -1.0510 -1.0508 Cable23(-)
3dc(+) 1.0791 1.0791 Cable13(+)
2dc(+) 1.0600 1.0598 Cable13(+)
1dc(+) 1.0510 1.0508 Cable23(+)
DC cable outage is an important contingency because create an important change on the
power flows (magnitudes and directions) in the DC-transmission system and post-
contingency is interesting from the grounding point of view.
SIMULATION RESULTS OF N-1 CONTINGENCY ANALYSIS: CABLES OUTAGE. BIPOLAR EARTH
RETURN CONFIGURATION

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• Case I: bipolar ideal earth return (Rgnd =0).
• Case II, bipolar earth return (Rgnd1 = 1, Rgnd2 = 2, Rgnd3 = 3)
• Case III: bipolar (no ground return).
Simulations are based on simple contingency, DC cable outage.
• Case I, ideal return: the lowest post contingency DC voltages.
• It should be noticed the use of bipolar configuration without any grounding connection
provides the highest post-contingency DC voltages.
• It must recognised the benefits of using earth path return in asymmetrical DC systems.
• There are two major positive impacts: it helps to control post-contingency dc voltages
and also provided alternative current path helping on the power flow distribution on
weakly connected DC terminals.
Node Case I Case II Case III Contingency
3dc(-) -1.0783 -1.0791 -1.0884 Cable13(-)
2dc(-) -1.0590 -1.0598 -1.0706 Cable13(-)
1dc(-) -1.0512 -1.0508 -1.0595 Cable23(-)
3dc(+) 1.0783 1.0791 1.0884 Cable13(+)
2dc(+) 1.0590 1.0598 1.0706 Cable13(+)
1dc(+) 1.0512 1.0508 1.0595 Cable23(+)
RESULTS COMPARISON OF N-1 CONTINGENCY ANALYSIS: GROUNDING

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• Selection of final grounding scheme and grounding resistors
requires a complete DC system analysis.
• Grounding configuration affects the performance of the MTDC
system virtually in any possible mode: normal (asymmetrical
operation) and abnormal operation (faults), steady-state and
dynamic.
• This paper has two contribution
1. to introduce a simple optimization-based-approach to calculate the steady-
state post-contingency of MTDC systems and
2. to use that approach in order to illustrate basic effects of grounding
configurations on steady-state post-contingency performance.
• A 3-terminal HVDC system is used to formulate the main
theoretical framework for performance prediction on post-
contingency steady-state of MTDC system as well as for
demonstrative purposes.

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Effects of Grounding Configurations on Post-Contingency Performance of MTDC system: A 3-Terminal Example

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