Journal of Power and Energy Engineering, 2014, 2, 564-572
Published Online April 2014 in SciRes. http://www.scirp.org/journal/jpee
How to cite this paper: Zhao, X.D., Li, K. and Zheng, M. (2014) Analysis of Transmission Loss in Droop Control of a Multi-
Terminal HVDC System. Journal of Power and Energy Engineering, 2, 564-572. http://dx.doi.org/10.4236/jpee.2014.24076
Analysis of Transmission Loss in Droop
Control of a Multi-Terminal HVDC System
Xiaodong Zhao1, Kang Li1, Min Zheng2
1School of Electronics, Electrical Engineering and Computer Science, Queen’s University, Belfast, UK
2School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China
Received January 2014
High Voltage Direct Current (HVDC) electric power tran smission is a promising technology for in-
tegrating offshore wind farms and interconnecting power grids in different regions. In order to
maintain the DC voltage, droop control has been widely u sed. Transmission line loss c on sti tute s an
import part of the total power loss in a multi-terminal HVDC scheme. In this paper, the relation
between droop controller design and transmission loss has been investigated. Different MTDC
layout configurations are compared to examine the effect of droop cont roller design on the trans-
MTDC ; HVDC ; VSC; Transmission Loss; Droop Control
Renewable energy is predicted to supply 12% of the world’s electricity by 2020 . In order to integrate various
renewable energies such as offshore wind farms into the existing AC grid, the concept of multi-terminal HVDC
(MTDC) has been proposed. The biggest possible future project is the European Super-grid . A MTDC net-
work can connect AC power grids of different voltages, frequencies with decoupled connection and reduce the
effect of wind power fluctuation on power transmission and maximize power transmission efficiency.
Seamless integration of offshore energy into the existing power grid has brought in the utilization of HVDC
transmission, which draws little capacitive current compared with the high voltage AC (HVAC) solution .
Voltage source converter (VSC) can work as an interface between DC and AC networks. Compared with tradi-
tional line commutated converters (LCC), VSC using high voltage IGBT is capable of switching at a higher op-
Advantages of VSC-HVDC include independent control of active and reactive power, fast and reversible con-
trol of power flow, and asynchronously decoupling AC grids, etc. The control of VSC in a MTDC has been well
studied in the literature. Its operation modes can be generally classified as DC voltage control or active power
control, and reactive power or AC voltage control. For the control of DC voltages involving more than one VSC
terminal, two categories of control methods exist: master-slave control and DC voltage droop control. In a mas-
X. D. Zhao et al.
ter-slave controlled network, one VSC terminal works as a master terminal, maintaining the DC voltage at a
fixed level. Other slave terminals can be assigned to deliver power out of the DC network using active power
control. Power transmitted in the master terminal is thus influenced by other terminals’ capabilities. Its normal
operation will determine the whole system stability, so fast communication between terminals is needed. While
using voltage droop control, there is no DC voltage regulating terminals. Each terminal will maintain the DC
voltage, delivering active power at the same time -. Power transmitted by each terminal is determined by
the DC voltage so influenced by every terminal. The power transmission duties are shared between different
terminals with no communication needed, providing a more reliable network.
The idea of droop control is based on frequency-power control in the traditional AC power systems. It is more
widely used compared with the master-slave method, due to its simplicity and the ease of power sharing be-
tween different terminals. However, unlike frequency in a traditional AC system, voltage is not a universal mea-
surement of the DC network when using DC voltage droop control. DC voltage error caused by droop control
and power loss on the transmission line will add mismatch to the ideal droop control design. This impact on the
power dispatch has been analyzed in . Different power dispatch modes using voltage droop control have been
compared in  . In , a methodology to design the required droop gains is proposed to optimize system
power transmission. On the other hand, the operation and transmission cost of the MTDC network is part of the
overall power loss. In order to minimize the loss, this optimal power flow (OPF) problem of a MTDC network-
ing in traditional AC environment can be solved based on traditional optimal algorithms. In , the losses of the
different components of a VSC HVDC system and the impact of the installation on overall system losses in
meshed networks are studied. A sequential AC/DC power flow algorithm is proposed to solve networks con-
taining VSC MTDC systems in . Two different VSC control strategies, namely the constant DC voltage con-
trol (master-slave control) and DC voltage droop control, are considered in  to minimize the transmission
loss of the whole AC/DC network. Reference  combines the OPF approach with the control of a multi-ter-
minal HVDC system. The optimal power flow computes optimal voltages and communicates them to the grid-
side VSC in order to ensure minimum losses in the power transmission. However, the relation between the
droop control parameters and minimum transmission loss is not clear when OPF is involved in the operation of
MTDC using droop control.
In this paper, the dependence of transmission loss on droop control design is analyzed, i.e., the condition for
achieving a minimum loss operation point. The requirement on DC voltage is derived in order to minimize the
transmission loss and the effect of DC voltage drop is considered in achieving the best droop control design. The
paper is organized as follows. Section II introduces different control modes for grid side and wind farm side
converters. In Section III, the effect of grid side DC voltage on transmission loss is analyzed. Then DC voltage
variations caused by droop control are considered to investigate the changes in the power loss. Simulations using
Simulink are carried out in Section V. Finally Section VI is the conclusion.
2. Control Modes for Different Converters
In a typically configured MTDC system, there exist two kinds of converters: grid side converter (GSVSC) and
wind farm side converter (WFVSC). GSVSC and WFVSC have different working modes, determined by the DC
voltage and current. The voltage–current characteristics of WFVSC and GSVSC have been introduced and
studied in   .
In this paper, a four terminal MTDC network is studied, as shown in Figure 1. On the left side of MTDC is
the WFVSC integrating various wind farms, such as DIFG or full converter based induction generators. The
duty for the WFVSC is to deliver all the possible wind power collected by the wind farm to the DC cable,
meanwhile maintaining the AC side voltage or providing reactive power support if necessary.
The GSVSC will try to control the DC voltage at a desired level, delivering the power out of the DC cable.
Proper power transfer is indicated by the DC voltage. If the injected power is higher than delivered, the DC
voltage will rise, otherwise it will fall. Thus for a MTDC network in normal operation, the basic tasks are to
transfer power while maintaining the DC voltage.
2.1. Wind Farm Side Converter Control
The WFVSCs have three operation modes, characterized by Equation (1),
X. D. Zhao et al.
Figure 1. Typical four-terminal HVDC network.
where Ik is the transmitted DC current from the k-th terminal, Kk is the voltge droop, Ek is the DC voltage, Ewf L
is the maximum voltage allowed, Pk is the power injected at the k-th terminal, Ikh is the maximum current al-
lowed. In normal operation, the WFVSC delivers all the power collected from wind farm to the DC grid, as a
constant power source. If fault occurs in the onshore AC grid, the DC voltage will rise. When the DC voltage is
higher than EwfL, the WFVSC will enter droop control mode, just like GSVSC, trying to reduce the DC voltage.
Otherwise, if the current exceeds the limitation of converter, the WFVSC will also work in the current limitation
2.2. Grid Side Converter Control
Each GSVSC has two operation modes, as shown in Equation (2)
where Ek is the DC voltage, Ek0 is the reference voltage, Ikh is the maximum current limitation for the converter,
Kk is the droop control parameter.
In normal operation, each GSVSC works like constant voltage source with a pure resistance characterized by
the droop parameter Kk, so each terminal can deliver power out of the DC grid while contributing to maintain
the DC voltage. Under an AC grid fault, the power delivered will be limited by the maximum current Ikh.
3. Effect of Terminal Voltages on Transmission Loss
In a four-terminal HVDC system using droop control, the control scheme for each GSVSC in normal operation
can be represented by Figure 2.
Using the number order in Figure 1, the relation between DC current and voltage for each GSVSC and
The transmission loss is determined by the cable resistance and cable current.
P RI= Σ
where Ii is the cable DC current and Ri is the equivalent cable resistance.
X. D. Zhao et al.
Figure 2 . Droop control scheme of a VSC.
In an existing MTDC network, the cable resistance is almost unchanged and the current is determined by the
power injected from the power source such as wind farms or generators. In order to analyse the effect of droop
parameter on the transmission loss, two steps are carried out. First, each wi nd farm is simplified with a constant
current i njectio n, thus neglecting the voltage change caused by the droop control, to inspect effect of voltage
difference between droop controlled terminals on the power transmission loss. Second, the impact of voltage
change caused by droop control is analysed.
Three different layout cases are considered for a four terminal HVDC connection, with two WFVSCs and two
GSVSCs. In each case, the WFVSC is modelled with co nstant c urr e nt inje ction, thus omitting the DC voltage
variations. The requirements for grid side DC voltages are inspected to achieve the minimum transmission loss.
3.1. Case 1: With Wind Farm Interconnection
Case 1 is two wind farms interconnected by a common cable, then connected to grid side converters respectively,
as shown in Figure 3.
If we define the voltage difference between the two grid side converters as
, the power loss on the line
resistance can be calculated as
22222 32 21
12 231 12 23123 123
PIRIR IRIRIRRRR RRR
It can be easily observed that the power consumption can be minimized when
, which means the ter-
minal side voltage should be equal in order for the maximal efficiency. In this case, the minimal power loss is
22 32 21
Another important observation is that, the power loss can be further minimized when R3I2-R2I1=0, this means
that the wind farm side power should be assigned inversely to their transmission line resistance. This result can
also be verified if we assume the interconnection current between this two transmission lines is Ix,
PIIR IIRIR=− ++ +
In order to get the minimal power loss, the first order of power loss with respect to current Ix can be deduced
PIRIIR IIIR∂∂=− +++
Thus we can get the optimal current for this case with
3.2. Case 2: With No Wind Farm Interconnection
If the two wind farm locations are close enough, then the cable resistance can be omitted. This is also the case
when only one wind farm is transmitting power to two GSVSCs, or the two GSVSCs have a joint connection, as
discussed in . In both situations, the transmission loss is given a s ,
2222 32 21
12 2312 2323 23
PIR IRIR IRRRRR
It can be seen that the minimal power loss can also be achieved when the terminal voltages are the same,
which is consistent with the result in . In order to get the same terminal voltage for the two GSVSCs, it is ob-
vious that the DC current should be reversely proportional with the cable resistance, e.g.
X. D. Zhao et al.
Figure 3. Case 1: with wind
Figure 4. Case 2: with no wind
which is also true that
3.3. Case 3: With Grid Side Interconnection
Two grid side converters are connected near on-shore grid and are represented by Figure 5.
In this case, the transmission loss is
PIRIR IR= ++
We can get
P IIR∂ ∂=
Thus it is obvious that
So the minimal loss can be achieved when there is no current flow between the two GSVSCs, which means
the voltage difference between them is also zero.
It can be concluded that in all cases the minimum cost can be achieved when the voltages on the power shar-
ing terminals are balanced. However, because the voltage errors caused by droop control are neglected, this will
not be the optimal case when using voltage droop control. As the voltage rises, the optimal point will change,
and this will be demonstrated in the next sectio n.
4. Impact of Voltage Drop on Transmission Loss
In a real power system, the WFVSC normally works on the mode of constantly injecting all the available wind
power into the DC grid. The DC current injected is determined by the wind power and the DC voltage. Since
there are no voltage regulators to keep the DC voltage at a fixed level using droop control, the DC voltage will
change when the injected wind power varies. Ideally when the two GSVSCs’ DC voltages are equal, then the
transmission loss is minimized. However, when the DC voltage rises, the injected WFVSC current will decrease
if wind power is kept constant. So the transmission loss may be further decreased even though the GSVSC volt-
X. D. Zhao et al.
Figure 5. Case 3: with grid side
interco nnecti on.
ages do not match. Taking Case 2 as an example, the transmission loss can be divided into two parts, determined
by current and voltage difference respectively.
The first part is solely determined by current and will decrease with voltage rise, while the second part is de-
termined by voltage difference. So when the injected wind farm current decreases with the voltage difference,
the working point will change. The new working point for a given MTDC network with known P1, P2 and E0 can
be solved using various algorithms. Meanwhile, boundaries for the minimum loss working point can also be
found. If we assume the current injected by wind farms are I1a, I2a with no voltage drop and I1b, I2b with maxi-
mum voltage drop Ewfh-E0. The minimum power loss Pmin should be bounded by,
11 2211 22
(,) ()(,) ()
fIIf E PfIIfE
To verify the effect of terminal voltage on transmission loss and impact of droop control on the optimum tran s-
mission, simulations are carried out using Matlab SimPo werSystem package. A four terminal VSC-HVDC sys-
tem has been built in Simulink as shown in Figure 6 and system parameters are listed in Table 1.
The interconnection of HVDC cables are configured using Case 1. Two scenarios are simulated. First, the two
wind farms are injecting constant currents, and the grid side voltage var ies using droop control. In the second
situation, wind farms are working in a constant power mode, and the effect of droop control is demonstrated.
5.1. Scenario 1: Wind Farm Injecting Constant Current
When the WFVSCs inject constant current and grid side converters are under droop control, the droop parame-
ters are changed incrementally to see the effect on transmission loss. Figure 7 shows the relation between
transmission loss and the voltage difference on the two grid side terminals. It can be seen that the minimum
transmission loss can be achieved when the voltage difference is zero.
Figure 8 shows the two GSVSCs DC voltage change with droop parameters K3 and K4. Each of the hyper-
bolic lines is the grid side DC voltage varied with droop parameters. The black line shows the trace of
5.2. Scenario 2: Wind Farm Injecting Constant Power
In the second scenario, the two wind farms are modelled with constant power injectio n, thus representing the
case when wind speed is almost constant, injecting constant power. Figure 9 shows the relation between the
voltage difference and transmission loss with different K3 and K4 co mbi na tions. It can be seen that when the
voltage difference is zero, the transmission loss is not minimized since a slight voltage rise will reduce the in-
jected current into the DC cable.
Figure 10 shows the two GSVSCs DC voltage change with droop parameters K3 and K4. The solid line shows
the trace of
and dashed line is the minimum power loss trace. These two traces are not overlapped
when the wind farm is injecting constant power.
The transmission loss with constant power injection is bounded by the upper and lower current, as shown in
Figure 11, between the transmission loss with upper current limit when there is no voltage drop, and with
maximal voltage drop.
X. D. Zhao et al.
Figure 6 . A four-terminal HVDC network simulation.
Figure 7. Transmission loss via voltage differ-
ence between two GSVSCs.
Figure 8. Two GSVSCs DC voltage change
via droop parameter.
Figure 9. Transmission loss variation via vol t-
age difference between two GSVSCs.
X. D. Zhao et al.
Figure 10. GSVSCs DC voltage change via
Figure 11. Power loss range bounded by upper
and lower current.
Table 1. Simulation parameters.
Base voltage WF1 po wer WF2 power R1 R2 R3
400e3 V 600 MW 400 MW 0.5 Ω 1.2 Ω 0.8 Ω
In this paper, three different c onfi g ur a tio ns of a four terminal HVDC network have been i nve s ti ga ted to achieve
minimal transmission loss using voltage droop control. The effect of grid side DC voltage change on the trans-
mission loss has been analysed. It is found that in order to achieve the minimal transmission loss the grid side
DC voltage should be equal with an ideal constant current input from the wind farm side. However, when the
wind farm side VSC works in constant power mode, this requirement will change due to the power characteristic
of the wind farm power injection. Simulations have been carried out in Simulink and the analysis is verified by
X. Zhao would like to thank Chinese Scholarship Council (CSC) for sponsoring his research at Queen's Univer-
sity Belfast. The work is partially funded by the EPSRC under grants EP/L001063/1 and EP/G042594/1.
 E.W.E. Association and Others (2005) Wind Force 12 . CA. http://www.ewea.org
 Wikipedia, European super grid.
 Bresest i, P., Klin g, W. L. , Hend riks, R.L. and Vailati, R. (20 07) HVDC Connection of Offshore Wind Farms to the
X. D. Zhao et al.
Transmission System. IEEE Transactions on Energy Conversion, 22, 37-43.
 Xu, L. and Yao, L. (2011) DC Voltage Control and Power Dispatch of a Mu l ti -Terminal HVDC System fo r Integrating
Large Offshore Wind Farms. IET Renewable Power Generation, 5, 223. http://dx.doi.org/10.1049/iet-rpg.2010.0118
 Hail eselassi e, T. M. and Uhlen, K. (2012 ) Impact of DC Line Voltage Drops on Power Flow of MTDC Using Droop
Control. IEEE Transactions on Power Systems, 27, 1441-14 49 . http://dx.doi.org/10.1109/TPWRS.2012.2186988
 Xu, L., Yao, L. , Bazargan, M. and Yao, L. (2009 ) DC Grid Management of a Multi-Terminal HVDC Transmission
System for Large Offshore Wind Farms. 2009 International Conference on Sustainable Power Generation and Supply,
 Abdel-Khalik, A.S., Massoud, A.M., Elserougi, A.A. and Ahmed, S. (2013) Optimum Power Transmission-Based
Droop Control Design for Multi-Terminal HVDC of Offshore Wind Farms. IEEE Transactions on Power Systems, 28,
 Daele mans, G. , Srivastava, K., Reza, M., Cole, S. and Belmans, R. (20 09 ) Minimization of Steady-State Losses in
Meshed Networks Using VSC HVDC. IEEE Po we r & Energy Society General Meeting, 1-5.
 Beert en, J., Cole, S. and Belmans, R. (2010) A Sequential AC / D C Power Flow Algorithm for Networks Containing
Multi-Terminal VSC HVDC Systems . IEEE Power and Energy Society General Meeting, 1-7.
 Cao, J., Du, W., Wang, H.F. and Bu, S. (2013) Minimization of Transmission Loss in Meshed AC/DC Grids with
VSC-MTDC Networks. IEEE Transactions on Power Systems. http://dx.doi.org/10.1109/TPWRS.2013.2241086
 Aragüé s -P eñalb a, M. , Egea-Alvar e z , A. , Gomis-Bellmunt, O. and Sumper, A. (2012) Optimum Voltage Control for
Loss Minimization in HVDC Multi-Terminal Transmission Systems for Large Offshore Wind Farms. Electric Power
Systems Research, 89, 54-63 . http://dx.doi.org/10.1016/j.epsr.2012.02.006
 Lian g , J., Gomis-Bellmunt, O., Ekan a yake, J., Jenkins, N. and An, W. (2012) A Multi-Terminal HVDC Transmission
System for Offshore Wind Farms with Induction Generators. International Journal of Electrical Power & Energy Sys-
tems, 43, 54-62. http://dx.doi.org/10.1016/j.ijepes.2012.04.063
 Gomi s-Bellmunt, O., Liang, J., Ekanayake, J. and Jenkins, N. (20 11) Voltage-Current Characteristics of Multiterminal
HVDC-VSC for Offshore Wind Farms. Electric Power Systems Research, 81 , 440-450.