Analysis of harmonics and resonances in hvdc mmc link connected to AC grid

H. Saad, Y. Fillion
Abstract - High-frequency responses of HVDC-MMC links are
essential to study because harmonic and resonance phenomena
may impact the AC grid. In this paper, EMT-type simulations are
used to analyze converter station’s frequency response. Several
MMC station and AC network parameters are varied to analyze
their impact. In addition, an EMT-type test case, based on a
recent installed HVDC project, is used to illustrate potential
resonances that can occur between converter stations and AC
networks.
Keywords: EMTP, Harmonic, Resonance, Impedance Analysis,
HVDC, Modular multilevel converter (MMC), Voltage source
converter (VSC)
I. INTRODUCTION
igh Voltage Direct Current (HVDC) systems based on
the Modular Multilevel Converter (MMC) [1] is the
predominant topology used in recent and upcoming HVDC-
VSC projects. For instance, several HVDC-MMC projects are
currently planned or operated by RTE (French TSO), such as
the INELFE, FIL, IFA2, etc.
Harmonic emissions and resonances in a system may reduce
the use of power and damage the insulation of the system
components if they are not limited properly. Furthermore, a
system malfunction may occur if the system has high voltage
or current harmonic amplitudes. The harmonics which
propagate in the AC network and to power electronic
components can cause overheating of equipment and
interferences with communication circuits.
Power electronic converters can cause instabilities and/or
resonances when interacting with other equipment in a power
system. These phenomena can occur in a wide range of
frequencies (up to few kHz). Low and high frequency
resonances have been registered in several power electronics
based projects: in offshore HVDC link high frequency
resonances [2] were noted. Instability with converters of a
photovoltaic plant [3] and in traction applications [4] are
reported. In [5] low frequency oscillations are studied between
power electronic and power system devices. Power electronic
converters inject harmonics in the grid mainly due to
modulation and switching commutations. For a MMC station,
the injected harmonics depend mainly on the number of
H. Saad and Y. Fillion are with Réseau de Transport d'Electricité (RTE),
Paris, France (e-mail: hani.saad@rte-france.com).
Paper submitted to the International Conference on Power Systems
Transients (IPST2017) in Seoul, Republic of Korea June 26-29, 2017
submodules (SMs) per arm and their modulation strategies,
which is specific to the manufacturer and/or project.
In HVDC projects, vendors and utilities perform harmonic
and resonance studies. These studies are conducted in
frequency domain and/or using electromagnetic transient
(EMT) tools. Frequency domain studies are used to assess
system stability [6] and are convenient for simulating a wide
range of configurations and scenarios. To derive the frequency
response of a converter, analytical or small signal approaches
are commonly used. In [7]-[11] an analytical development of a
VSC station is presented. However, during real HVDC and
FACTS projects, the EMT-type model provided by the
manufacturer is often hidden (or black-boxed) due to
intellectual property issue. Therefore, the analytical model
derivation is not possible or not sufficiently accurate. In
addition, model linearization and derivation are challenging
and complex tasks since the MMC includes several variables
and complex control structures. In this paper, the derivation of
the frequency response of a converter station based on a black-
box EMT model, presented in [18], is used. Since this EMT
model includes the detailed representation of the converter
station with its control system, this approach is more practical
than with an analytical model.
This paper is an extended version of [18]. Several test cases
are performed to analyze the impact of MMC station
parameters (as MMC levels, control system, AC filter, etc.) on
the high-frequency response (i.e. harmonics and impedance).
In addition, the generic EMT test case where high frequency
resonances can occur between the AC network and the
converter station presented in [18] is analyzed in this paper.
Parametric sensitivity studies of the AC network is conducted
in order to assess the impact on system stability.
The paper is structured as follows. Section II recalls
harmonics and resonance phenomena. Section III presents the
generic MMC-401-Level station and its control structure.
Section IV illustrates the derivation of the frequency response
based on the EMT-type model. Section V simulation results of
the impact of converter station and ac network parameters are
presented.
II. MMC STATION OVERVIEW
The generic EMT model includes the detailed
representation of the converter station with its control system,
see Figure 1 [5]. The equivalent detailed MMC model where
each SM is represented, (i.e. Model #2 as defined in [13]) is
considered. The control system uses an upper level control
including inner/outer controllers and a lower level control to
Analysis of Harmonics and Resonances in
HVDC-MMC Link Connected to AC grid
H

regulate MMC internal variables: capacitor balancing
algorithm (CBA) to balance SM capacitor voltages in each
arm, modulation to convert the reference voltage to a number
of inserted SMs and circulating current control (CCC) to
regulate converter internal energy. More details can be found
in [17].
+
-
1 2
gate signal
measurements
ref
conv j
v
Lowerlevelcontrol
Outer Control
Inner Control
Upperlevelcontrol
StartPoint
Reactor
CBA and
Modulation
CCC
400 / 320kV
0.12trfL pu=
0.001trfR pu=
0.075armL pu=
PCC j
v
ji
Measurements
filter
640dcV kV=
40 /C kJ MVA=
400N SM=
Figure 1: Generic control structure of MMC station
III. HARMONICS AND RESONANCES
We can distinguish two different high frequency phenomena
that can take place between power electronics and surrounding
AC networks; harmonic emissions and resonances:
• Harmonics emissions are mainly associated with
semiconductor switches and therefore continuously
transmitted by the system which may affect the wave
quality.
• The resonances are mainly related to the control system,
filters, delays, etc. Resonances have usually higher order of
magnitude than harmonics but their time intervals are
shorter since system protection is used to trip network
devices.
Figure 2 illustrates these two different aspects. The voltage
source ( convh
v ) or current source ( convh
i ) represents the
harmonic emissions and the impedance Z(f) (where f stands for
frequency) depends on control loops and physical equipment
which includes system resonances [14]. Since a converter
station with its control system, is a nonlinear system,
equivalent circuit values depend on the set-point operation of
the system and will vary when the converter configuration
changes.
( )Z s convh
v
1convv convv
++
( )Z s
1conviconvh
i
a) Equivalent Thevenin circuit b) Equivalent Norton circuit
Figure 2: Equivalent circuit for frequency response
Determination of Z(f) and convh
i (or convh
v ) is achieved in
two ways: by means of an analytical approach or by EMT
simulations. The analytical approach offers the capability to
use classical modal analysis tools in order to study the
converter behavior [6]. However, analytical models may
become complex depending on the studied system and must be
validated as several approximations are introduced. On the
other hand, the EMT simulations include the detailed models
of the control system and power equipment. The obtained
results are more realistic than with an analytical model,
however simulation time constitutes the main drawback.
This article uses the EMT simulation approach to derive
Norton equivalent values at each harmonic rank h.
IV. FREQUENCY RESPONSE BASED ON EMT SIMULATION
The derivation of the equivalent Norton circuit (Figure 2)
based on time domain EMT simulation is briefly described in
this section. The circuit setup is shown in Figure 3 and the
flow chart computation for each h is depicted in Figure 4. The
converter station is connected to an equivalent AC grid and a
controlled ideal current source injh
i at the PCC. The injected
current injh
i are varied during time domain simulations in
order to compute Z(f) and convh
i (Figure 2.b) [18]. The
amplitude of injh
i should be a fraction of the nominal current of
the system to guarantee a small-signal perturbation and to
avoid any excitation of the control and protection system. The
important feature of this method is that the control system is in
normal operation, therefore, a realistic set point can be
considered [14]. Norton equivalent values change according to
the set point operations.
injh
i
PCCh
v
gridh
i
Equivalent
AC grid
hi
HVDC-MMC link
+
Figure 3: Model setup to derive the equivalent Norton
circuit
Time
domain
+ iinjh
Measure
vPCCh & ih
Compute
iconvh & Zh
Frequency
domain
studies
Figure 4: Block diagram, Norton equivalent computation
The derivation of the Norton equivalent circuit is also
useful for frequency domain studies in power grid systems,
since the computation time is much faster than with the
detailed EMT-model.
It should be highlighted that this approach can be also used
in real-time simulators with hardware-in-the-loop simulation
including the real-physical control system (or replicas). Such
approach can provides faster simulation time and more
realistic results since the real and complete control system is
used.
V. FREQUENCY RESPONSE STUDIES
In this section, the impact of the converter station
parameters on the frequency response is analysed. The test
case used is a point-to-point HVDC-MMC 401-Level link with
a transmission capacity of 1,000 MW. The AC grid is modeled

as an equivalent source with a short-circuit level (SCL) of
20 GVA. Converter station data can be found in Figure 1 and
control data is provided in the Appendix. All model
developments and simulations are performed using the EMTP-
RV software.
A. Harmonic studies
In this sub-section, converter station parameters that impact
the harmonic emissions are considered.
1) Impact of MMC levels
Harmonics emitted from the MMC station are known to be
low in amplitude. In order to show the impact of MMC levels,
the MMC-401-Level is compared with a MMC-11-Level, in
this section. Voltage references, harmonic distorsions (i.e.
convh
i ) and Z(f) are compared in Figure 5. Obviously,
harmonic emissions produced from 11-Level MMC are higher
than those produced by a 401-Level MMC which are
negligible. For such MMC 11-Level, it is expected that an AC
filter will be installed at the converter station in order to limit
those harmonics. Based on Z(f) responses in Figure 5, one can
notice that the impedance is not affected by the MMC levels.
This was expected since control loops are identical (except the
CBA and modulation) between thoses two MMC levels.
0.91 0.915 0.92 0.925 0.93 0.935
0
0.2
0.4
0.6
0.8
1
vPCCa
(pu)
Time (s)
MMC 11L
MMC 401L
100 400 700 1000 1300 1600 1900 2200 2500 2800
0
5
10
15
iconv
(A)
Frequency (Hz)
MMC 11L
MMC 401L
100 400 700 1000 1300 1600 1900 2200 2500 2800
0
500
1000
1500
2000
|Z|(ohm)
Frequency (Hz)
MMC 11L
MMC 401L
Figure 5: Impact of MMC levels
2) CBA impact
In this section, the impact of the CBA over the frequency
response is investigated. The capacitor value and the threshold
activation [15] of the CBA are varied to get the extreme cases:
- CBA #1: threshold is set at 1% and C= 45 kJ/MVA
- CBA #2: threshold is set at 50% and C =25 kJ/MVA
Similar test case as in [18] has been used, however, a MMC
including 401-Level is simulated instead of MMC-11-Level.
Figure 6 shows some of the 400 SMs capacitor voltages of
phase A upper arm, using CBA #1 and CBA #2. It can be
observed that CBA #2 has higher amplitude fluctuation and
higher differences between capacitor voltages.
Figure 7 shows the impact of capacitor fluctuations and
CBA configurations over the frequency response, i.e. Z(f) and
convh
i . It can be observed that these parameters have mainly an
impact on the harmonic injection convh
i rather than on Z(f).
Note that with CBA #2, high harmonic emissions are noticed
at lower frequency (around 250 Hz and 350 Hz). This shows
that CBA and capacitor voltage fluctuations have an impact on
the harmonic emissions. This results shows also the
importance of a detailed EMT model (even for MMC-401
Level) to account for such harmonics.
0.6 0.61 0.62 0.63 0.64 0.65 0.66
0.8
0.9
1
1.1
1.2
vCi(pu)
Time (sec)
a) CBA#1 and C=45 kJ/MVA
0.6 0.61 0.62 0.63 0.64 0.65 0.66
0.8
0.9
1
1.1
1.2
vCi(pu)
Time (sec)
b) CBA#2 and C=25 kJ/MVA
Figure 6: CBA impact, Capacitor voltages of SMs
100 300 500 700 900 1100 1300 1500 1700 1900 2100
0
2
4
6
8
iconv
(A)
Frequency (Hz)
CBA #2
CBA #1
100 400 700 1000 1300 1600 1900 2200 2500 2800
0
500
1000
1500
2000
|Z|(ohm)
Frequency (Hz)
CBA#1
CBA#2
Figure 7: CBA impact, frequency response ( convh
i and Z )
3) CCC impact
To analyze the circulating current control impact, the
reference value of the second harmonic circulating current
control is varied between 0 and 0.1 pu, for CCC #1 and CCC
#2 respectively. Similar test case as in [18] has been used,

however, a MMC including 401-Level is simulated in this
paper, instead of MMC 11-Level. Figure 8 shows the
circulating current variation impact. Figure 9 shows the results
of convh
i and Z(f). Since the frequency response of both CCC
configurations are close, it can be concluded that the
circulating current has a minor impact on the frequency
response from the AC side (as highlighted in [16]).
0.6 0.61 0.62 0.63 0.64 0.65 0.66
-0.5
-0.4
-0.3
-0.2
-0.1
Current(pu)
Time (sec)
CCC #2 CCC #1
Figure 8: CCC impact, circulating current phase A
100 300 500 700 900 1100 1300 1500 1700 1900 2100
0
2
4
6
8
iconv
(A)
Frequency (Hz)
CCC #2
CCC #1
100 400 700 1000 1300 1600 1900 2200 2500 2800
0
500
1000
1500
2000
|Z|(ohm)
Frequency (Hz)
CCC#1
CCC#2
Figure 9: CCC impact, frequency response ( convh
i and Z )
B. Impedance studies
In this section, the impact of control system parameters on
Z(f) is studied.
1) Inner control loop and time delay
Inner control loop dynamic and time delay have an impact
on Z(f). Results and analysis are provided in [18]: The impact
of the inner control is increased when the dynamic response of
the control loop is fast.
2) Impact of AC filter at PCC
Depending on Manufacturers and project specifications, AC
filter equipment can be installed at PCC. To show the impact
of this device over the frequency response, in this section a
low-pass filter is added at PCC to the MMC station model.
Parameters of the low-pass filter are based on [19]. Note, that
in practice, this low-pass filter will be tuned according to
project specification, however, the scope of this section is only
to illustrate the impact of such equipment. Result comparisons
between converter station with and without the installation of
the AC filter is depicted in Figure 10. It can be noticed that the
Z(f) is mainly affected by the AC filter installation for
frequencies above 400 Hz.
100 400 700 1000 1300 1600 1900 2200 2500 2800
0
500
1000
1500
2000
|Z|(ohm)
Frequency (Hz)
with AC filter
without AC filter
100 400 700 1000 1300 1600 1900 2200 2500 2800
-100
-50
0
50
100
∠Z(deg)
Frequency (Hz)
without AC filter
with AC filter
Figure 10: Impact of AC filter at PCC
VI. STABILITY ANALYSIS
In [12] and [18], it has been shown that low-pass filters and
delays in converter station control can lead to negative
resistance in high frequency range. Therefore, this negative
resistance can lead to resonances or instability depending on
the AC network configuration and parameters.
To analyze the stability of a system, the considered circuit
can be represented as a feedback loop system in the small-
signal domain. Therefore, the following Laplace equation can
be deduced [3]:
( )
( ) ( )
1 ( ) / ( )
grid
PCC conv
grid
Z s
i s v s
Z s Z s
=
+
(1)
where ( )gridZ s is the equivalent impedance of the AC grid.
From equ. (1), the system is stable if the expression
( ) / ( )gridZ s Z s is lower than one at each frequency. However,
if the Nyquist criterion is not met, and in addition, the angle
( ) / ( )gridZ s Z s∠ is higher than ±1800
, then the system
becomes unstable or sustained resonances will occur.
Using the EMT time domain simulation, both ( )Z s and
( )gridZ s can be computed, and system stability tools can be
used.
The generic EMT test case where resonances can occur
between the AC network and the converter station presented in
[18] is analyzed in this section. Parametric sensitivity studies
of the AC network is conducted, in order to assess the impact
on system stability. The HVDC-MMC 401 Level link is
connected to an AC network (Figure 11). Network 1 includes:
AC overhead lines, AC breaker “BRK”, shunt compensator of
400 MVar and an equivalent Thevenin source with SCL equal
to 20 GVA. Active power of 1,000 MW is transmitted from
Grid 1 to 2. The outer control strategy considers a DC
voltage/reactive power control on Station 2 and active/reactive
power control on Station 1.

HVDC-MMC link
50km
Overhead line
Network 1
Station 1Station 2
Grid2
Grid1
PCC1
Cshunt
+
+
Figure 11: EMT test case
In the following subsections, the impact of AC network
parameters is elaborated.
A. Impact of AC line length
The impact of the line length parameter on the system
stability is analyzed. AC overhead line length is varied ±10%
from the initial 50km value. Figure 12 shows the EMT
simulation results of the ( ) / ( )gridZ s Z s amplitude and angle.
Line length has mainly an impact on the frequency
resonance value. However, the frequency bandwidth that
exceeds the amplitude of one (threshold that guaranties the
stability) is the same. In addition, the phase margin
( ) / ( )gridZ s Z s∠ is close (and even slightly higher) to -1800
,
which shows that resonances can occur in this specific
frequency range. Indeed, in [18], time domain waveforms
illustrate such resonances.
100 400 700 1000 1300 1600 1900 2200 2500 2800
10
-2
10
0
10
2
|Zgrid
/Z|(ohm)
Frequency (Hz)
ACline=50km
ACline=55km ACline=45km
100 400 700 1000 1300 1600 1900 2200 2500 2800
-180
-140
-100
-60
-20
20
60
100
140
∠(Zgrid
/Z)(degree)
Frequency (Hz)
ACline=45kmACline=55km
ACline=50km
Figure 12: Impact of AC line length
B. Impact of shunt compensator
Shunt capacitors have also an impact on the stability of the
system. In Figure 13, the impact of the capacitor value on
( ) / ( )gridZ s Z s is depicted. Capacitor values of 800MVar,
400MVar, 100MVar and 0MVar are considered. It is noticed
that when no shunt capacitor is included in the system, the
system is stable since the phase margin ( ) / ( )gridZ s Z s∠ is
lower than ±1800
. When the capacitor value increases,
( ) / ( )gridZ s Z s amplitude increases and ( ) / ( )gridZ s Z s∠
tends to -1800
which makes the system unstable.
100 400 700 1000 1300 1600 1900 2200 2500 2800
10
-2
10
0
10
2
|Zgrid
/Z|(ohm)
Frequency (Hz)
100MVar
0MVar
400MVar800MVar
100 400 700 1000 1300 1600 1900 2200 2500 2800
-180
-140
-100
-60
-20
20
60
100
140
∠(Zgrid
/Z)(degree)
Frequency (Hz)
100MVar
0MVar400MVar
800MVar
Figure 13: Impact of Cshunt
C. Impact of short-circuit level
Short-circuit level (SCL) of the Thevenin source (Grid 1) is
varied in this subsection. Figure 14 shows the result of
( ) / ( )gridZ s Z s for three different values: 50, 20 and 5 GVA.
Based on this result, it can be concluded that for high
frequency resonances (>1 kHz), the short circuit level has a
minor impact on the stability of the system.
100 400 700 1000 1300 1600 1900 2200 2500 2800
10
-2
10
0
10
2
|Zgrid
/Z|(ohm)
Frequency (Hz)
SCL=20GVA
SCL=5GVA
SCL=50GVA
100 400 700 1000 1300 1600 1900 2200 2500 2800
-180
-140
-100
-60
-20
20
60
100
140
∠(Zgrid
/Z)(degree)
Frequency (Hz)
SCL=5GVA
SCL=20GVA
SCL=50GVA
Figure 14: Impact of SCL
D. Impact AC lines in parallel
The impact of the number of AC lines connected in parallel
is depicted in Figure 15: one line to three lines in parallel has
been considered. It is noticed, that when the number of AC
lines connected in parallel increases, the stability of the system
increases. In fact, with one AC line is connected, the frequency
range that leads to instability is as large as 100 Hz (1750 to
1850 Hz), however when three AC lines are in parallel, the
frequency range of instabilities tend to zero.

100 400 700 1000 1300 1600 1900 2200 2500 2800
10
-2
10
0
10
2
|Zgrid
/Z|(ohm)
Frequency (Hz)
1 AC line
2 AC lines
3 AC lines
100 400 700 1000 1300 1600 1900 2200 2500 2800
-180
-140
-100
-60
-20
20
60
100
140
∠(Zgrid
/Z)(degree)
Frequency (Hz)
3 AC lines
2 AC lines
1 AC line
Figure 15: Impact of AC lines in parallel
VII. CONCLUSIONS
This paper presents the impact of MMC station parameters
on the frequency response (Z and convh
i ) of the converter on
the AC side. It uses the EMT simulations approach and a
detailed MMC-401 Level model to derive these results.
Several parameters were considered to analyze their impact
on the frequency response: MMC levels, CBA, circulating
current, AC filter installation. Based on the presented results, it
can be concluded that MMC levels and CBA have the main
impact on the harmonic emissions. The circulating current
impact seems negligible on the frequency response at the AC
side. On the other hand, the paper showed that AC filters have
an impact on the impedance Z(f).
Parametric sensitivity studies have been also presented to
shows the impact of the AC network on the stability of the
system: AC line length, shunt capacitor and the number of AC
lines in parallel play a role on the stability of the system.
However, the short circuit level does not seem to affect such
high frequency resonances.
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[3] J. Sun, "Impedance-Based Stability Criterion for Grid-Connected
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[6] R. D. Middlebrook, “Input Filter Considerations in Design and
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