Special Issue on Power Electronics & Systems: Modeling, Analysis, Control, and Stability, 2017
Optimal Design of Controller Parameters for Improving the Stability of
MMC-HVDC for Wind Farm Integration
Jing Lyu
1
, Marta Molinas
1
, Xu Cai
2
1. Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim 7491, Norway
2. Wind Power Research Center, Shanghai Jiao Tong University, Shanghai 200240, China
Abstract—A subsynchronous oscillation (SSO) phenomenon has been observed in a modular multilevel converter-based
high-voltage DC (MMC-HVDC) transmission system for wind farm integration in the real world, which is independent of
the type of wind turbine generator. This kind of oscillation appears different from those in DFIG-based wind farm with
series-compensation line or wind farm integration through two-level VSC-HVDC transmission system, because the internal
dynamics of the MMC may have significant impact on the oscillation. By far, however, very few papers have reported it.
In this paper, the generation mechanism of the SSO phenomenon in an MMC-HVDC transmission system for wind farm
integration is revealed from an impedance point of view. The harmonic state-space (HSS) modeling method is applied to
model the multi-frequency behavior of the MMC, based on which, the ac-side small-signal impedance of the MMC is
analytically derived according to harmonic linearization theory. As a general rule, the controller parameters of the wind
power inverter and the HVDC converter are designed separately, to meet the performance requirements of the single
converter under ideal conditions, but this practice does not guarantee the stability of the interconnected system. Therefore,
an optimal design method for controller parameters is proposed in this paper in order to guarantee the stability of the
interconnected system from a system point of view. Finally, time-domain simulations validate the effectiveness of the
theoretical analysis and the proposed optimal design method.
Index Terms—Modular multilevel converter (MMC), HVDC, wind farm, stability, controller parameter design.
Statement: This paper is original and has never been submitted to any other journals or conferences.
Jing Lyu is the corresponding author for this work.
Address: Department of Engineering Cybernetics, NTNU, Trondheim-7491, Norway
Phone: +47 92297235, E-mail: jing.lyu@ntnu.no
I. INTRODUCTION
Modular multilevel converter-based high-voltage dc (MMC-HVDC) transmission technology is a promising solution for
integrating large-scale and long-distance offshore wind farms into onshore power grid, due to its high modularity, low switching
loss, low distortion of output voltage, decoupling control of active and reactive power, and so on [1], [2]. However, because of the
complex internal structure of MMC, the modeling and control of MMC is much more complex than that of two-level voltage-
source converters (VSCs) [3], [4]. Moreover, the internal dynamics of MMC such as capacitor voltage fluctuations and harmonic
circulating currents may have harmful effects on the stable operation of MMC-based interconnected systems, especially for
renewable energy integration applications [5], [6]. Fig. 1 demonstrates the on-site recorded waveforms of the wind farm side MMC
(WFMMC) in a certain MMC-HVDC project for wind farm integration in China [7], where the output power of the wind farm is
approximately 20% of the rated power. As can be seen, there is an obvious subsynchronous oscillation (SSO) phenomenon in the
ac- and dc-side currents, and the dominant oscillation frequency is approximately 20 Hz in the ac-side and 30 Hz in the dc-side.
When the output power of the wind farm further increased, the MMC-HVDC system was shut down by the protection system,
leading to the outage of the wind farm. Furthermore, it is worth noting that there are several different types of wind farms in the
project, including fixed speed induction generator (FSIG)-based wind farm, doubly-fed induction generator (DFIG)-based wind,
and permanent magnet synchronous generator (PMSG)-based wind farm, and a similar oscillation phenomenon appeared when
each type of wind farm was separately connected to the MMC-HVDC transmission system.
Fig. 1. On-site recorded waveforms in a real MMC-HVDC project for wind farm integration
So far, very few papers have discussed the stability of wind farms integrated with MMC-HVDC transmission systems. An SSO
phenomenon in an MMC-HVDC transmission system for wind farm integration was reported in [5], in which the distribution and
propagation mechanisms of the SSO currents in the MMC-HVDC system were investigated and an SSO current suppression
strategy was also proposed, but the mechanism by which these oscillations are generated in the MMC-HVDC system with wind
farms wasn’t deeply analyzed nor identified. The impedance-based analysis method was used to analyze the small-signal stability
of wind farm integration through MMC-HVDC in [6], [8], where the impacts of power transfer level, circulating current control,
and controller parameters on the stability of the interconnected system were discussed. However, neither controller parameter
design methods or stabilization control methods for enhancing the stability of the interconnected system were deeply discussed in
those above papers. In addition, voltage stability of offshore wind farms integrated with a VSC-HVDC transmission system was
studied by using impedance-based method in [9], in which, however, the VSC-HVDC system is based on two-level VSC that lacks
internal dynamics, so the instability mechanism might not be able to exactly explain the SSO phenomenon in the MMC-HVDC
connected wind farms.
The eigenvalue-based analysis method is commonly used to investigate the small-signal stability of MMC-based power systems
[10]-[15]. However, most of the authors have overlooked the internal dynamics of MMC in the course of developing small-signal
models, which leads to the small-signal model analogous to that of the two-level VSC. Besides, a few authors have built the small-
signal model of MMC in the rotating dq frames at different frequencies so as to have the internal dynamics of MMC been
considered [13]-[15], and then the impact of the internal dynamics on MMC stability was analyzed using eigenvalue analysis. In
addition, nonlinear analysis methods such as Lyapunov [16], [17] and Floquet [18] theory have also been introduced to analyze
the MMC stability, which, however, have some important disadvantages, such as complexity of analysis, difficulty in application,
inconvenience for guiding control system design, etc.
This paper focuses on the small-signal stability of MMC-HVDC connected wind farms by using impedance-based analysis
method. In order to obtain an accurate MMC model, the harmonic state-space (HSS) modeling method [19], which is based on the
linear time periodic (LTP) theory and is able to include all the harmonic dynamics, is introduced to model the MMC in this work.
On the basis of the HSS model, the ac-side small-signal impedance of MMC is then derived according to the harmonic linearization
principle [20]. The derived MMC impedance model in this paper is able to include the effects of all the internal harmonics on the
impedance response. Next, the generation mechanism of the SSO phenomenon in the MMC-HVDC connected wind farm is
revealed based on the terminal impedance characteristics. On the basis of the instability mechanism analysis, an optimized design
method on the ac voltage controller of WFMMC is proposed from a systemic perspective in order to guarantee the stability of the
interconnected system. Finally, time-domain simulations are carried out in MATLAB/Simulink to validate the effectiveness of the
theoretical analysis and the proposed optimization design method.
The rest of the paper is organized as follows. Section II describes the configuration and control of the system under study.
Section III presents the HSS modeling of MMC, and the impedance modeling and verification for MMC are elaborated in Section
IV. The instability mechanism is first revealed, and on this basis, the optimized design method for the ac voltage controller of
WFMMC are then proposed in Section V. Time-domain simulations are carried out in Section VI. Section VII concludes the paper.
II. CONFIGURATION AND CONTROL OF THE INTERCONNECTED SYSTEM
A. System Configuration under study
Fig. 2 shows the structure diagram of wind farm integration through an MMC-HVDC transmission system. Fig. 2(a)
demonstrates the overall structure of the system, where the wind farm consists of full-power wind turbines based on two-level
VSCs, and the MMC-HVDC transmission system comprises a WFMMC, a grid side MMC station (GSMMC), and dc transmission
lines. In addition, T1 and T2 are the converter transformers, and T3 is the step-up transformer of the wind farm. Fig. 2(b) presents
the MMC topology used for both WFMMC and GSMMC. Each phase-leg of the MMC consists of one upper and one lower arm
connected in series between the dc terminals. Each arm consists of N identical series-connected submodules (SMs), one arm
inductor L, and an arm equivalent series resistor R. Each SM contains a half-bridge as a switching element and a dc storage
capacitor C
SM
.
(a)
(b)
Fig. 2. Structure diagram of wind farm integration through an MMC-HVDC transmission system. (a) Overall structure. (b) MMC topology.
For simplification of analysis, the wind farm is modeled by an aggregated full-power wind turbine. Furthermore, since the grid
side converter of the wind turbine is decoupled with the generator side converter by the dc link capacitor, the generator side
dynamics have less impact on the grid side dynamics, so the turbine mechanical and generator side converter can be replaced with
a constant power source [9]. In addition, it is assumed that the ac power grid is strong and the control bandwidth of the dc voltage
loop of the GSMMC is less than the SSO frequency under study (i.e. 20 Hz in this paper), which means the dc voltage control
dynamics of the GSMMC have little effect on the ac-side dynamics of the WFMMC. Consequently, the GSMMC can be simply
replaced with a dc voltage source. The simplified circuit structure diagram of the interconnected system is presented in Fig. 3,
where T4 is the step-up transformer of the wind turbine, and L
w
is the ac filter inductance of the wind turbine.
Fig. 3. Simplified circuit structure of the interconnected system.
B. System Control
Since the WFMMC has to supply an ac voltage source for the wind farm, a single-loop ac voltage control in the three-phase
stationary abc frame is employed in the WFMMC, as shown in Fig. 4, where H
v
(s) is an ac voltage regulator, a proportional-
resonant (PR) regulator is used to achieve the zero steady-state error for the sinusoidal quantities; k
f
is a feed-forward gain for
improving the dynamic response of the control system. The nearest level modulation (NLM) [21] and sorting-based capacitor
voltage balancing control [22] are used in the MMC.
The transfer function of the ac voltage regulator is
( )
( )
22
1
pv
v pv
iv
Ks
Hs K
Ts
ω
= +
+
(1)
where K
pv
and T
iv
are the proportional gain and integral time constant of the PR regulator, respectively; ω
1
is the fundamental
angular frequency.
The conventional current vector control strategy in a rotating dq frame with feedforward and decoupling terms is used for the
wind power inverter, as presented in Fig. 5, where a PLL ensures that the d-axis of the rotating dq frame is aligned with the grid
voltage vector. Fig. 5(a) shows the current control, where
*
wd
i
is the active current reference which is given as a constant value
according to the active power command,
*
wq
i
is the reactive current reference which is set as zero in this paper, and H
i
(s) is a current
regulator based on a proportional-integral (PI) regulator, which is given by
( )
1
1
i pi
ii
Hs K
Ts
= +
(2)
where K
pi
and T
ii
are the proportional gain and integral time constant of the current PI regulator, respectively.
Fig. 5(b) shows the PLL diagram, where H
PLL
(s) is a PI regulator, which is given by
