06290374

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 6, JUNE 2013 2429

A Novel Distributed Direct-Voltage Control Strategyfor Grid Integration of Offshore Wind Energy

Systems Through MTDC NetworkRodrigo Teixeira Pinto, Student Member, IEEE, Pavol Bauer, Senior Member, IEEE,

Sílvio F. Rodrigues, Student Member, IEEE, Edwin Jan Wiggelinkhuizen,Jan Pierik, and Braham Ferreira, Fellow, IEEE

Abstract—Although HVDC transmission systems have beenavailable since mid-1950s, almost all installations worldwide arepoint-to-point systems. In the past, the lower reliability and highercosts of power electronic converters, together with complex con-trols and need for fast telecommunication links, may have pre-vented the construction of multiterminal DC (MTDC) networks.The introduction of voltage-source converters for transmissionpurposes has renewed the interest in the development of super-grids for integration of remote renewable sources, such as offshorewind. The main focus of the present work is on the control andoperation of MTDC networks for integration of offshore windenergy systems. After a brief introduction, this paper proposesa classification of MTDC networks. The most utilized controlstructures for VSC-HVDC are presented, since it is currentlyrecognized as the best candidate for the development of super-grids, followed by a discussion of the merits and shortcomingsof available DC voltage control methods. Subsequently, a novelcontrol strategy—with distributed slack nodes—is proposed bymeans of a DC optimal power flow. The distributed voltage control(DVC) strategy is numerically illustrated by loss minimization inan MTDC network. Finally, dynamic simulations are performedto demonstrate the benefits of the DVC strategy.

Index Terms—Control design, HVDC transmission, offshorewind farms, optimization algorithms.

I. INTRODUCTION

THE INTENTION to build dc networks for the trans-mission of electricity is not something completely new.

Thomas Edison patented, in the end of the XIX century, the firstelectric distribution system for the transmission of electricity.Edison’s transmission system, which was somewhat essentialto broaden the use of his most famous invention—the electriclamp—made use of direct current. By 1884, the Pearl Streetpower plant in Manhattan, NY, was providing dc electricity

Manuscript received January 31, 2012; revised April 27, 2012 and July 2,2012; accepted August 8, 2012. Date of publication September 4, 2012; dateof current version February 6, 2013. This work was supported by the Ministryof Economic Affairs, Agriculture and Innovation of the Netherlands within theEOS-LT program of Agentschap-NL under the “North Sea Transnational Grid”(EOS LT 08019) project.

R. Teixeira Pinto, P. Bauer, S. F. Rodrigues, and B. Ferreira are with thePower Processing Group (EPP), Delft University of Technology, 2628 CDDelft, The Netherlands (e-mail: [email protected]).

E. J. Wiggelinkhuizen and J. Pierik are with the Energy Research Center ofthe Netherlands, 1755 LE Petten, The Netherlands (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2012.2216239

for lightning around ten thousand lamps from 508 differentconsumers [1].

Nevertheless, at that time, low-voltage dc transmission, dueto its losses and high voltage drop (which forced Edison tobuild generating plants near the loads), was proved inefficientwhen compared to ac transmission systems. In fact, only twodecades later, there were more than 50 ac transmission sys-tems in service, operating with voltage ratings from 70 to150 kV [2], [3].

Despite the success of ac transmission, the efforts for thedevelopment of practical dc transmission continued. However,it was not until the mid-1950s, with improvements in the high-voltage mercury-arc valve, that this type of technology wasmade technically feasible and economically attractive. The firstcommercial HVDC transmission system was built in Sweden,in 1954, to connect the mainland with the island of Gotlandthrough a submarine cable, which used ground return, for adistance of approximately 100 km. The project used mercury-arc valves and had a power rating of 20 MW with ±100-kVdirect-voltage transmission level [4].

During the following decades, a great increase in researchand development brought to HVDC the use of high-power-solid-state switching devices. Indeed, thyristor valves had al-ready, by 1970s, substituted the mercury-arc valves for newHVDC applications [5].

The advent and consolidation of current-source convert-ers (CSCs) for HVDC applications—also known as HVDCclassic—helped to increase the interest of interconnecting morethan two terminal stations in order to form multiterminal dc(MTDC) networks. Until 1980, more than 70 different articleshad already been published with studies covering differentaspects of MTDC systems such as network topology, the needfor interrupting devices, system stability, control strategy, andeconomic analysis [6]–[9].

The outlook at that time was very optimistic that MTDCnetworks were technically and economically feasible. However,only two multiterminal CSC-HVDC transmission systems wereever built: the Hydro-Québec/New England scheme, in Canada,and the SACOI-2 scheme, between Italy and France [5], [10].This may have been due to the fact that, when the numberof converter stations—rectifiers and inverters—grows in anHVDC transmission system with CSC technology, also thecomplexity of the master control increases. Since the master

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2430 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 6, JUNE 2013

control is responsible for proper coordination between theterminals, also the need for a fast telecommunication link in-creases. Telecommunication is needed for the synchronizationof the converter current orders, identifications, and actions forclearing dc faults and start-up of the system after a poweroutage [11], [12].

Even without being able to build meshed networks, around80.000 MW of HVDC transmission capacity is installed, orunder construction, in over 100 projects throughout the world[10], while the total installed capacity is continuously growingwith countries such as China, India, and Brazil, building longdc transmission lines to integrate remotely located generationsources. China alone plans to build more than 30 HVDC linksup to 2020 [13], [14]. Hence, HVDC has become a reality, andit represents nowadays an important share in the transmissioncapacity in many countries around the world.

With further progresses in the power electronics industry,HVDC transmission systems have reduced in size and improvedin reliability. Modern state-of-the-art voltage-source convertersfor transmission applications make use of modulation schemesand/or multilevel topologies, which allow them to have smallerspace requirements than the classic HVDC. Due to its physicalcharacteristics and improved controllability, the developmentof VSC-HVDC transmission systems has brought back theinterest in the establishment of MTDC networks for differentapplications, such as supergrids, electronic power distributionsystems, and transnational networks for integration of offshorewind farms [15]–[17]. Several studies have shown that, forlarger amounts of power (e.g., > 500 MW) and for long sub-marine transmission distances (e.g., > 60−80 km), the use ofdc systems for the transmission of the generated electricityoffshore is both economically and technically more convenientthan using ac systems [18]–[20].

II. CLASSIFICATION OF MTDC NETWORKS

Multiterminal HVDC transmission systems are character-ized by having more than two converter stations somehowinterconnected on the dc side of the transmission system. Thesituation where two (or more) HVDC converter stations becomeinterconnected by the ac side of their transmission systemsis known as multiple infeed of HVDC into ac networks. TheMTDC configurations can be classified according to the type ofHVDC technology implemented at the converter stations andthe network topology. A classification according these criteriais shown in Fig. 1.

A. Network Topology

To form a multiterminal network, the converter stations canbe connected either in series or in parallel. When connected inseries, all the converter stations share the same current, whilefor the parallel connection, the converters share the same dctransmission voltage [9]. Even though the possibility exists,no series-connected MTDC transmission system has ever beenbuilt; only parallel configurations have been applied [5], [10].The series connection may not be the best choice for largeMTDC networks. Permanent line faults would cause an in-

Fig. 1. Classification of MTDC transmission systems according to the HVDCtechnology and network topology. Initially, MTDC networks will probably beconstituted of a small number of VSC terminals radially connected to later onorganically evolve into hybrid-meshed MTDC networks.

terruption in the complete system, while in a parallel system,only the faulted converter would have a service disruption[21]. However, in a parallel MTDC, circuit breakers may benecessary for clearing faults in the dc line or stations [21].

Moreover, parallel connections can still be grouped into twocategories: radial and meshed networks. In radial networks, thepermanent loss of a section of the dc transmission system wouldresult in total service interruption of the interested converterterminals. For meshed MTDC networks—provided that theremaining elements of the network are capable of carryingthe additional power—normal operation would still be possibleeven though with higher transmission losses. However, due tothe extra cables, meshed topologies will tend to be more costlythan the radial ones.

B. HVDC Technology

The MTDC configurations can be classified according tothe type of HVDC technology implemented at the converterstations, i.e., line-commutated CSC or forced commutatedvoltage-source converter.

1) CSC-MTDC: All the converter stations use the line-commutated CSC-HVDC technology.

2) VSC-MTDC: All the converter stations use the forcedcommutated voltage-source converter HVDC technology.

3) Hybrid-MTDC: Both HVDC technologies, CSC-HVDCand VSC-HVDC, are used together.

In parallel CSC-MTDC networks, power-flow reversal of oneconverter terminal involves mechanical switches since power-flow inversion can only be achieved by changing the voltagepolarity of the converter station valves [4], [5].

One possible solution to avoid this issue would be to buildparallel VSC-MTDC networks instead. Since VSCs are capableof inverting the direction of the dc current, mechanical switchesare not needed for the reversal of the power flow. However,VSCs are not capable of extinguishing dc line faults by merelytaking control actions as CSCs; thus, HVDC circuit breakersmight be needed to assure proper system operation under dccontingencies.

Like any initiative of such dimension and complexity, futureMTDC networks will have to organically grow with time froman inherently simple initial phase. In the beginning, they mightcomprise just a few terminals radially connected with only onetype of HVDC system. The most probable initial candidate, for

TEIXEIRA PINTO et al.: VOLTAGE CONTROL STRATEGY FOR GRID INTEGRATION OF OFFSHORE WIND ENERGY SYSTEMS 2431

its flexibility, is the VSC technology. These initial topologieswill then be able to evolve with time as the characteristics ofMTDC networks and the different modules inside it becomebetter understood. In this manner, much more complex topolo-gies, e.g., a meshed-hybrid MTDC network, may be developed.

In order to allow MTDC networks to grow with time, focuswill have to be given to the development of control strategieswhich will not limit the system expansion and are thereforecapable of operating inside any dc network regardless of itssize.

III. CONTROL STRATEGIES FOR VSC-HVDC

The basic operation of a VSC-HVDC transmission systemcan be described by considering each converter terminal asa controllable-voltage source connected to an ac transmissionnetwork by means of a series reactor [22], [23].

The VSC can control the active and the reactive powerthrough the transmission system in an independent way. Thegoal of the VSC controller is to set the amplitude, the angle, andthe angular frequency of the converter’s phase voltage. Thereare usually two main possible control strategies to achievethat objective: direct control and vector control [5], [24], [25].Recently, another control strategy has been proposed, known aspower-synchronization control, which augments the maximumtransferable power through the VSC link [26], [27].

A. Direct Control

The direct control strategy is very straightforward as it dealswith the converter’s alternating currents and voltages directlyin the three-phase (abc) frame, without the need for coordinatetransformations. The control principle is simple, and the currentreferences are calculated based on the load-flow equationsbetween two nodes [28].

However, as the current references are calculated directly, thedirect control strategy does not contain an inner-current loop.Therefore, it is not possible for the direct control to limit thecurrent to protect the converter’s valves. This is probably themain reason why this kind of control strategy is usually notemployed in VSC-HVDC systems as, generally, there is verylittle room for current overloads.

B. Vector Control

In the vector control strategy—the most commonly em-ployed control method for VSC-HVDC systems—the convertercurrents and the three-phase voltages are transformed to therotating direct-quadrature (d, q) frame, which will be thensynchronized with the ac network voltage by means of a phase-locked loop. The control system will determine the convertervoltage reference in the (d, q) axes via an inner-current con-troller, and this signal will be fed back to the converter afterretransforming it again to the three-phase frame [29]–[32].

A well-designed closed-loop current controller, with a suffi-ciently high control bandwidth, improves the system’s responseby providing damping effect [33]. In addition, it helps, in steadystate, to eliminate the cross-coupled interactions between the

Fig. 2. Simplified diagram representation of a vector control strategy for oneterminal of a VSC-HVDC transmission system. The vector control strategy isthe most commonly used VSC-HVDC control method.

d- and q-axes and reduces the effect of the grid-side voltagevariations on the converter current [23], [25]. A simplifieddiagram representation of the vector control structure is shownin Fig. 2.

C. Power-Synchronization Control

The main idea behind power-synchronization control is tomake the grid-connected VSC have a dynamic response whichis similar to that of a synchronous machine in order to overcomesome of the difficulties of vector-current control, namely, whenthe VSC is connected to weak (low short-circuit ratio) acnetworks [34].

Power-synchronization control allows the VSC-HVDC tomaintain steady operation for higher load angles. As a re-sult, the VSC is then able to exchange more power withthe ac network. The converter maximum transferable poweris a very important criterion for control design and stabilityanalysis [27].

However, regardless of the control strategy and convertertopology employed, it is always possible to consider the VSCas an ideal voltage source where the control system has thefreedom to specify the magnitude, phase, and frequency of theproduced sinusoidal voltage waveform.

Moreover, in VSC-HVDC transmission systems, at least oneof the converter stations has to control the direct voltage, whilethe other converters can control other parameters, such as theexchanged active power or the frequency of the connected acnetwork.

Nevertheless, it is only through a stiff dc-system voltagecontrol that the active power being exchanged between all thestations is balanced. That is why the development of direct-voltage control methods is of extreme importance for successfulutilization of VSC-HVDC transmission systems in the con-struction of future large MTDC networks.

IV. DIRECT-VOLTAGE CONTROL METHODS

Inside a VSC-MTDC network, voltage control is certainlyone of the most important tasks given to VSC-HVDC stations.


A well-controlled direct voltage on an HVDC link requirespower balance between all the interconnected nodes [35]. Ifthe dc-system voltage starts to increase excessively, it maytrigger protective equipment, such as dump resistors. On theother hand, a large direct-voltage drop might generate nonlinearphenomena, creating difficulties for the control systems, andcan also temporarily limit the capability of the ac systemvoltage controller [27].

The control of point-to-point HVDC transmission systems istypically arranged so that one terminal controls the dc-link volt-age while the other operates in current—or power—regulationmode. This control philosophy—of having only one convertercontrolling the direct voltage—can be extended to MTDC net-works. However, disregarding losses, the net sum of the activepowers of all the converters operating in current regulationmode has to be, at all times, lower than the maximum ratingsof the direct-voltage-controlling station. Mathematically, thiscontrol strategy for MTDC networks can be translated as

PmaxVdc ≥

N−1∑i=1

P iIdc(t) (1)

where PmaxVdc is the maximum rating of the VSC controlling the

dc-system voltage (N th node) and P iIdc(t) is the actual power

of the ith VSC terminal operating in current regulation mode.As it can be seen from (1), as the network grows, it will

be increasingly difficult to assure balance by having only oneterminal responsible for voltage regulation. Thus, for largeMTDC networks, controlling the voltage at a single terminalis not desirable. In addition, if an outage would affect theonly voltage-controlling station, direct-voltage control wouldbe lost until somehow transferred, e.g., after a defined over-voltage threshold, to another node in the network. This is,however, also not desirable. The fast nature of dc phenomenacould trigger protection equipment, within only a few cyclesof the ac network. Therefore, for its successful developmentand operation, MTDC networks will require a control strategycapable of sharing the direct-voltage control among more thanone network node. Next, the most common dc-system voltagecontrol methods for VSC-HVDC are presented and discussed.

A. Voltage Droop

Even though the droop control strategy was first proposedfor controlling CSC-MTDC networks, this method can also beapplied for VSC-MTDC networks [36], [37]. The droop controlscheme for MTDC networks works similarly to the one im-plemented in traditional ac systems, where the load-dependentfrequency variations are used as an input signal for the controlsystem to adjust the generated power to meet demand at alltimes [38]. In MTDC networks, the control employs the droopmechanism to regulate the direct voltage within the system byadjusting the converter current in such a way that power balanceis guaranteed [38].

Extending the droop control method to MTDC networks withmore terminals should be straightforward, and the synchroniza-tion of the several VSC stations would happen without the needfor fast communication. However, the main downside of droop

control is the fact that power-flow control is limited [39]. Forinstance, in an offshore grid, steering the power produced bythe wind farms to a particular node in the network would not bepossible without communication [37], [40].

B. Ratio Control

The ratio control is a modification of the droop control toaddress the difficulty of steering the power flow in the network.On this control strategy, a power ratio between two or moredc-system voltage-controlling stations is established, and theconverters will then share the generated power according to thispre-established ratio [41].

The difference between the ratio controller and the droopcontroller is that, by varying the slope of the droop charac-teristic, a system operator can vary the power ratio betweenthe terminals in the transmission system. However, in the ratiocontrol, the direct voltage can display an oscillatory or evenunstable behavior, if the slope of the droop characteristic ismade too low, which is equal to having a high control gain.This stability issue then limits the ratio range that can be usedto share power among the terminals [39].

Another downside of the ratio control approach may be itsexpandability. It might be difficult to find an analytic expressionthat correctly shares the power for the case where more thantwo stations are controlling the direct voltage inside the MTDCnetwork. In addition, the analytic expression depends on theresistance of the dc cables, which may vary, further affectingthe method’s accuracy [42].

C. Priority Control

In the priority control method, one VSC terminal has prece-dence over the other terminals for the generated power. Theterminal with the precedence will control the dc-system voltage,by means of a proportional–integral (PI) regulator, until itreaches its rated capacity or a maximum power set point estab-lished by system operators. The other terminals controlling thedirect voltage will only start transmitting power after the firstterminal has reached its limit [42]. A voltage droop controlleris then provided to the other VSC terminals so that they receiveall the remaining power that could not be transmitted by the firstterminal.

The priority control strategy is interesting for small MTDCnetworks, for instance, in a small offshore MTDC, where aspecific country wishes to have precedence over the powerproduced by its wind farms and is willing to sell the exceedingpower to neighboring countries. However, it is not clear howthis control method can be extended to larger MTDC networks.In addition, operation of MTDC networks by assigning priorityto certain terminals is not effective as it may generate a largenumber of idle converters.

D. VMM

The voltage margin method (VMM) was first proposed in1999 by Nakajima and Irokawa. In this control strategy, eachconverter station in the system is given a marginal offset in its


TABLE ICOMPARISON BETWEEN AC AND DC NETWORKS

direct-voltage reference [43], [44]. This control scheme is dualto the current margin method proposed for controlling CSC-MTDC networks [4]. Similarly, the voltage margin is definedas the difference in the direct-voltage reference between the ter-minals. The modified two-stage VMM scheme is more suitablefor multiterminal systems, as it reduces the need for commu-nication between the terminals [45]. However, the VMM hastwo main drawbacks: Because of its controller architecture, thedynamic response is slower than other methods, and only oneVSC is controlling the dc-system voltage at a given time [46].Still, extending the VMM to larger MTDC networks would beeasier to accomplish than for the ratio or priority controllers.

However, with a limited direct-voltage operating range, e.g.,±10% the nominal voltage, the maximum number of VSCterminals that can be controlled by the VMM may be limited.That is to avoid adverse interaction between the controls of eachterminal generated by possibly too low voltage margins.

V. DISTRIBUTED DC VOLTAGE CONTROL STRATEGY

A more suitable control strategy for large MTDC networkswould be to assign each dc-voltage-controlling VSC terminalwith a specific voltage set point. In this way, any predefinedload-flow scenario can be achieved while no single converteris left alone with the responsibility of balancing the powerinside the transmission system, i.e., the control of the dc-system voltage is distributed between several nodes insidethe MTDC network. This novel method of controlling VSC-MTDC networks, here presented, is called distributed voltagecontrol (DVC). Distributed control is a common practice inac networks, where no single power station is left alone withthe task of guaranteeing system balance. Table I displays abrief comparison between different quantities for ac and dcnetworks [47].

The main difference concerning the control of both systemsis the synchronization parameter: It is the frequency for acnetworks whereas voltage for dc ones. While ac controllers willtry and make sure that the frequency is fixed through the entireac system, the same cannot happen for dc controllers. With theexception of superconducting networks, if the direct voltageis the same throughout the network, there will be no powerflow. In order to assign each dc-voltage-controlling VSC witha specific voltage set point, it is first necessary to solve a load

Fig. 3. Control topology flowchart diagram for the DVC control strategy,showing the steps in the calculation of the direct-voltage reference values tobe sent to the onshore VSC-HVDC terminals.

flow. As the DVC strategy relies only on a power-flow solution,there is no need for a fast communication link between thenetwork terminals. The information for the dc power flow canbe gathered by an Independent System Operator through use ofthe Supervisory Control and Data Acquisition communicationsystems just like it is regularly done for the control of powerplants in ac networks. The advantage of the DVC strategy isthat, in practice, a certain load-flow scenario can be kept fora fixed amount of time (e.g., 15-min control cycle); hence,a fast communication link is not needed. Nevertheless, it isnecessary to be able to send the voltage references to the VSC-HVDC stations onshore once every control cycle. A flowchartdiagram for the DVC strategy is shown in Fig. 3. The mainsteps in the DVC strategy are discussed next. The focus isparticularly on the distributed dc-load-flow algorithm and thepower-flow optimization, which are of great importance forthe development of control strategies which are capable ofoperating in large MTDC networks.

A. DC Load Flow

The classical load-flow iteration process can be written as

X(k + 1) =X(k) + ΔX(k)

with ΔX(k) = − J(k)−1 · g (X(k)) (2)

where X contains the state variables, J is the Jacobian matrix,and g holds the mismatch equations. In comparison with the


classical ac load flow, since the phase angle is not defined in dcnetworks, the state variables are simplified as

X = [Vi, . . . , VN−1]T (3)

with the slack node considered to be the last node (N th node)of the dc network.

The vector that holds the mismatch equation is also simpli-fied as, in dc networks, there is no need to write equations forthe reactive power. In addition, during steady state, only theresistive part of the transmission cables plays a role; thus, theload-flow equations become

g (x(k)) = [gP1, . . . , gPN−1

]T

gPi=PGi − PLi −

∑j �=i

ViVjYij − YiiV2i (4)

where PGi is the generated power, PLi is the load power, andVi is the voltage of the ith network node. The Yij and Yii

coefficients come from the dc network admittance matrix andare calculated based on the conductance of the dc cables.

The simplified Jacobian matrix J, which is defined as thevariation of the mismatch equations with respect to the statevariables, becomes

J(k) =∂gP

∂V

=

⎛⎜⎝

∂gP1/∂V1 . . . ∂gP1

/∂VN−1

.... . .

...∂gPN−1

/∂V1 · · · ∂gPN−1/∂VN−1

⎞⎟⎠

while∂gPi

∂Vk=

{−YikVi, for k �= i−

∑j �=i

VjYij − 2YiiVi, for k = i. (5)

B. OPF for DC Networks

Optimal power flow (OPF) is a common tool used for theoptimization of a given ac power system network. The ideabehind it is to find the optimal values of the network parameterswhich will optimize the system’s functionalities, such as systemlosses, total generation cost, operational limits, or system secu-rity [48]–[50]. Before solving the OPF for an MTDC network,it is first necessary to define the state variables (X) and thespecified variables (Y). In addition, the specified variables canbe separated as control variables (U) and fixed variables (W),such as [Y] = [U W]T.

Generally, in ac systems, the state variables (X) are definedas the load angle and the voltage on each PQ bus (where thenode voltage is unknown) or only as the load angle on PV buses(where the voltage is known). Table II shows a comparisonbetween the different types of network buses in ac and dcnetworks.

In a dc system, as shown in (3), the state variables canonly be the nodal voltage of P-type buses (unknown voltage).Therefore, according to Table II, the control variables (U) arethe voltage references of the V-type buses, while the net powerof the P-type buses is the fixed variables (W).

TABLE IICOMPARISON BETWEEN AC AND DC NETWORK BUSES

After defining the state and specified variables, the OPF,without inequality constraints, can then be defined as a mini-mization problem

min f(X,U)

s.t. g(X,U,W) = 0 (6)

where f(X,U) is the function to be optimized andg(X,U,W) denotes the load-flow equations as given in (4).

C. Steepest Gradient Method

To solve the OPF problem, the gradient method, also knownas the method of steepest decent, can be used. Constructing theunconstrained Lagrangian function yields

L(X,U,W) = f(X,U) + λTg(X,U,W) (7)

where λ is the vector of the Lagrangian multipliers and its sizeis given by the number of load-flow equations. The minimiza-tion conditions of the unconstrained Lagrangian function arethen given by⎧⎪⎪⎪⎨

⎪⎪⎪⎩∇LX = ∂L

∂X = ∂f∂X +

[∂g∂X

]T· λ = 0

∇LU = ∂L∂U = ∂f

∂U +[

∂g∂U

]T· λ = 0

∇Lλ = ∂L∂λ = g(X,U,W) = 0.

(8)

The solution steps of the OPF algorithm with the steepestgradient method are as follows [48].

1) Assign an initial value to control vector U0.2) Solve the load-flow equation: ∇Lλ = g(X,U,W) = 0.3) With X and J = ∂g/∂X from step 2), solve ∇LX

w.r.t. λ

λ = −[JT]−1 ∂f

∂X.

4) With the new value of λ, compute ∇LU.5) If |∇LU| ≥ ε, go to the next step. Otherwise, the opti-

mization is achieved.6) Compute the new control vector U: Uk+1 = Uk −

β|∇LU|. Restart, from step 2), with Uk+1.

D. Inclusion of Inequality Constraints

In order to minimize the system losses but still obtain a fea-sible power-flow solution, it is necessary to integrate inequality


constraints of the system variables into the optimization pro-cess. Examples of inequality constraints for MTDC systemscould be, among others, the nodal voltages in the network, thepower flow in the network lines, and the VSC-HVDC powerratings.

Inequality constraints on control variables (U), such as thereference value of the VSC stations set to control the MTDCvoltage, can be handled by the optimization algorithm withoutthe need to alter the objective function.

If a particular variable of the new set of control variablesUk+1 infringes a limit, then that variable is set to the vio-lated limit, i.e., Uk+1

i = Umaxi , if Uk+1

i > Umaxi and Uk+1

i =Umini , if Uk+1

i < Umini . In case a control variable violates

the constraints, the Kuhn–Tucker theorem gives the necessaryconditions for a minimum, if the objective function involved isconvex [48], [49].

The inclusion of inequality constraints on state and depen-dent variables is done by the use of a penalty function. Thepenalty function is usually described as the quadratic differencebetween the violated variable and its limit as

Wi = rpi(xi − xLIM

i

)2(9)

where rpi is the penalty factor.If a variable is not violating a constraint, then its penalty

factor is zero. Using penalty functions, inequality constraintsare introduced, only when active, as equality constraints. In thisway, the OPF can still be solved by the gradient method usingan augmented optimization function

L(X,U,W) = f(X,U) +∑i

Wi(X,U) + λTg(X,U,W).

(10)

VI. MINIMIZATION OF THE SYSTEM LOSSES IN AN

MTDC NETWORK

Let us apply the gradient method for the OPF problem usingthe losses in an MTDC network as the objective function. Thetotal losses in an MTDC grid can be written as

f(X,U) = PL(X,U) = ITRI = (IMV)TYP(IMV) (11)

where YP is the network’s primitive admittance matrix and IMits incidence matrix.

It is important to describe the losses in the MTDC system asa function of the nodal voltages rather than the nodal currents.This is due to the fact that the state variables are given bythe voltages of P-type buses, as previously shown in (3). Thenext step is the inclusion of the inequality constraints. Takinginto account only the MTDC nodal voltages as inequalityconstraints, the penalty functions may be written as

WVi= rVi

(Vi − V Lim

i

)2. (12)

In this case, when building the augmented function, it is notnecessary to include a function for the control variables. Aspreviously mentioned, the control variables can have their value

restricted directly, during the OPF. Finally, by combining (10)with (11), the Lagrangian function becomes

L(X,U,W) = PL(X,U) +∑i

WVi(X) + λTg(X,U,W).

(13)

A. Numerical Example

The dc network to be considered in this example is shownin Fig. 4, whereas the system’s rated parameters are given inTable III. For the network shown in Fig. 4, the offshore windfarms, as well as the middle nodes, are generation nodes and arethen considered as P-type buses. The onshore VSC stations willbe controlling the MTDC network voltage and are consideredthen as V-type buses, i.e., slack buses. The system variables aretherefore assigned as follows:

1) state variables: X = [V1 V2 V3 V4 V5]T;

2) control variables: U = [V6 V7]T;

3) fixed variables: W = [P1 P2 P3 P4 P5]T.

The total system losses for the considered MTDC networkcan be calculated as

PL(X,U)=Y11(V1−V4)2+Y22(V2−V4)

2+Y33(V4−V6)2

+Y44(V4 − V5)2 + Y55(V3 − V5)

2 + Y66(V5 − V7)2. (14)

On the other hand, the inequality constraints may bewritten as

5∑i=1

WVi(X) = rV1

(V1 − V Lim

1

)2+ · · ·+ rV5

(V5 − V Lim

5

)2.

(15)

During normal operation, the voltage range of the MTDCnetwork is considered to be ±10% the nominal value. Finally,the Lagrangian multipliers are λT = [λ1 . . .λ5], whereas thefive load-flow equations are given by

gi(X,U,W) = Pi−5∑

j=1

ViVjYij ∀ i = 1,. . ., 5. (16)

B. Results

Table IV gives the results of the OPF problem solved withthe steepest gradient method. The values are presented in aper-unit (p.u.) basis, with the base voltage being equal to theVSC dc-side voltage, i.e., ±200 kV, whereas the base power isequal to the installed capacity of the offshore wind farms, i.e.,500 MW, as shown in Table III.

In order to provide a comparison between nonoptimal andoptimal results, the obtained data are presented for three dif-ferent case studies. In the first one, the optimization was notconducted. Instead, a dc load flow was performed consideringVSC1 as a fixed load P6 = −0.9 p.u., while VSC2 was leftwith the responsibility for controlling the network’s voltage.In the second case study, the losses in the MTDC network areoptimized, but only VSC2 is a slack node, meaning that VSC1


Fig. 4. Radial VSC-MTDC network with seven nodes and six lines.

TABLE IIIMTDC NETWORK RATED PARAMETERS

TABLE IVLOAD-FLOW RESULTS OF THE LOSS OPTIMIZATION

is still left as a fixed load and it is not helping with voltageregulation. Finally, in the last case study, the optimization wasperformed considering both onshore VSCs as slack nodes.

As one would expect, without any optimization, the trans-mission losses in the MTDC network are at its highest, with12.3 MW or 2.46%. This is mainly because the voltage set pointof VSC2 is not optimized and it is assigned to 1.0 p.u. In thesecond study case, with the optimization already in place—andVSC2 solely responsible for the voltage control—the transmis-sion losses are reduced by almost half percent to 2.03% whencompared to the nonoptimal scenario. After the optimization,a voltage set point of 1.0969 p.u. was assigned to VSC2,bringing the voltage of the offshore wind farms very close to themaximum permissible voltage. In fact, the reason why the directvoltages on the VSCs of the offshore wind farms are slightlyabove 1.10 p.u. is because the penalty functions do not imposea rigid limit on the objective function; rather, they show theweakest points of the optimization problem [49]. To implementrigid limits, one possible solution is to use heuristic methodssuch as the genetic algorithm [50].

The transmission loss optimization was last performed withboth onshore VSCs working together in order to control thevoltage inside the MTDC network. As a result of the optimiza-tion, the power assigned to VSC1 was reduced from 0.9 to0.5205 p.u. This is a direct result from the fact that the VSC1is now also a slack node. Indeed, in order to further minimizethe transmission losses, the optimization algorithm assignedthe same voltage set point of 1.0867 p.u. both to VSC1 andVSC2. Therefore, the lowest losses happen when both onshoreVSCs are controlling the system voltage at equal referencevalues. In this way, the system losses were reduced by 1.09% incomparison with the nonoptimized results.

However, in order to optimize the transmission losses, thedirect voltage on the offshore wind farms is brought close totheir operational limit of 1.10 p.u. During normal operation,having the wind farm voltage close to the maximum allowablevoltage is not of concern. Nonetheless, a possible outage insome node of the MTDC network could give rise to an overallincrease in the voltage profile, causing problems to the networknodes that are operating close to the voltage limit.

A possible solution to this issue is to integrate an N − 1contingency analysis into the optimization algorithm. In orderto do so, only a minor change to the steepest gradient method is


TABLE VLOAD-FLOW RESULTS OF THE LOSS OPTIMIZATION WITH BUILT-IN N − 1 NETWORK SECURITY

required. After solving the load flow (step 2 of the algorithm),it is now necessary to verify whether the obtained solution isN − 1 secure or not. The network is N − 1 secure if, after anoutage on an arbitrary node, the parameters of the remainingoperational nodes do not surpass the stipulated constraints. Ifthe network is N − 1 secure, the algorithm can proceed; other-wise, the optimization is halted, and the last feasible solution istaken as the optimization result.

Table V contains the results of the loss optimization in theMTDC network taking into consideration the N − 1 contin-gency analysis. The results are shown for two cases: when onlyone onshore VSC is controlling the voltage and when bothVSCs are operating as slack nodes.

As it can be seen from Table V, when all the network nodesare operational, the new voltage reference set point assignedto VSC2 is 1.0731 p.u. Before, when the N − 1 contingencyanalysis was not included in the optimization algorithm, thevoltage reference was 1.0969 p.u., as shown in Table IV.

As a result, the optimized losses rose from 2.03% to 2.13%.Nevertheless, including the N − 1 analysis still provided betterresults than the base case (2.46% losses) and made the networkN − 1 contingency proof. The maximum permissible voltageof 1.10 p.u. happens on the offshore wind farm 1 (WF1) whilethe VSC1 terminal is faulted.

For case study 4, the last row of Table V cannot be filledbecause VSC2 is the only slack node in the network. In reality,if only VSC2 would be working as a slack node, a fault inthat terminal would disrupt the power balance in the MTDCnetwork, giving rise to overvoltages which would then triggerprotective equipment to safeguard the HVDC terminals.

As previously discussed, a better way to control MTDCnetworks is to distribute the responsibility of the voltage controlamong more terminals. The second case in Table V—casestudy 5—shows the results of the transmission loss optimiza-tion when both onshore VSCs are sharing the voltage controlinside the MTDC network. However, different from the resultsof case study 3 shown in Table IV, this time, also the N − 1contingency analysis is taken into account.

As before, with two slack nodes, the optimization algorithmassigned the same voltage set point to both VSC1 and VSC2,although, due to the inclusion of the N − 1 contingency anal-ysis, the set point was reduced from 1.0867 to 1.0661 p.u.

The reduction in the voltage reference comparatively increasedthe transmission losses. For the optimization with two slacknodes, the losses were 1.37% without the N − 1 contingencyanalysis (case study 3 in Table IV), whereas they were 1.42%with the security-modified optimization algorithm (case study 5in Table V). Nevertheless, the results from case study 5 arestill more than 1% lower than the base scenario without anyoptimization. In the end, having an increase in the transmissionlosses of 0.05% is a minor drawback when compared with theadvantage of having an MTDC network that is optimized andN − 1 secure. In fact, with the distributed dc-system voltagecontrol strategy (DVC), as shown in Table V, if both onshoreVSCs are controlling the MTDC network voltage, the systemcan successfully maintain operation even if one node of the net-work is lost while still operating with optimized transmissionlosses.

However, if we assume that the network shown in Fig. 4 isused to connect two countries, it is most likely that the powerflow between them will be set by an operator, and thus, it willnot always be possible to assign it in order to optimize thenetwork losses. Nevertheless, the DVC strategy can still be usedto establish the desired load flow while keeping the networkN − 1 secure. The method has shown to work regardless of thenetwork size and can be extended to cases with more countryconnections while actually benefiting from the increase in thenumber of slack nodes.

VII. DYNAMIC SIMULATIONS

Hitherto, only steady-state phenomena have been analyzed.Dynamic simulations are needed in order to confirm the ob-tained load-flow results and to evaluate the dynamic behaviorof the complete system operating under the proposed DVCstrategy. Once more, the simulated network is the one shownin Fig. 4, and the MTDC network dynamic parameters are theones given in Table III. The dynamic model utilized is shownin Fig. 5, and the simulation results are given in Fig. 6.

For the dynamic simulations, the wind farms are modeledas the sum of the aggregated capacities of the single windturbines [51]. The turbine model is based on the mathematicalexpression of the mechanical power that the turbine generatesfrom a given wind speed [52]–[54]. The ac grids are modeled as


Fig. 5. Modular representation of the MTDC network dynamic model for theintegration of offshore wind farms.

infinite buses behind short-circuit impedances, and the MTDCnetwork is modeled as lumped impedances in a state-spacematrix representation [55], [56]. The VSC model utilized is alossless model used to simulate the dynamics of the HVDCterminals, and a vector-current control, as the one shown inFig. 2, is implemented [46].

The OPF algorithm only takes into consideration the MTDCnetwork transmission losses. The losses shown in Fig. 6(c) arethe transmission losses only, not the total losses in the MTDCnetwork, which would include the converter losses. However,the DVC strategy sets the voltage in the MTDC network ashigh as possible to guarantee the desired power flow, to ensurethat the network remains N − 1 secure and to minimize thetransmission losses. Therefore, it can be expected that the lossesin the VSC-HVDC converters should also be optimized sincethe converters would always operate with the highest possibledirect voltage for a given desired power-flow scenario.

The offshore VSC terminals are set to control the ac sys-tem voltage and frequency of the wind farms to fixed values,whereas the onshore VSC terminals are set to control the ex-changed reactive power with the ac grids and the voltage of theMTDC network. On the onshore VSC terminals, PI regulatorsare employed for the direct-voltage outer controller in order toannul steady-state errors. The controller is made to operate onthe error of the energy stored in the VSC capacitance, insteadof operating directly on the direct voltage. In the latter case,the closed-loop dynamics of the dc-system voltage controllerwould be nonlinear and dependent on the operating point [23].

A. Simulation Results

At the beginning of the simulation, no power is being trans-mitted, and all the nodes inside the network have 1.0-p.u. directvoltage. The VSCs at the offshore wind farms are unblockedat t = 0.5 s, and the offshore wind farms start transmittingpower. The offshore wind farms are generating 0.4, 0.3, and0.5 p.u., respectively. The wind farm power varies stepwiseat different times t = 0.5, 1.0, and 1.5 s for WF1, WF2, andWF3, respectively. This shows that the DVC method is capableof controlling the dc-system voltage in a stable way, even whenthere is a step in the wind power being transmitted throughthe VSC1 or VSC2. Initially, the VSC2 is controlling its directvoltage at 1.0 p.u., and the VSC1 is receiving the power beinggenerated offshore up to 0.9 p.u. At simulation time t = 1.5 s,the system losses are 2.46%, as displayed in Table IV andshown in Fig. 6(c).

Fig. 6. Simulation results: (a) dc-system voltages and (b) active power at theonshore and offshore wind farms VSCs and (c) total system transmission losses.

At t = 2 s, the optimization algorithm sends a new referencevoltage set point to VSC2, and its voltage is raised from 1.0to 1.069 p.u. The system response is very fast, and the voltage


transient lasts for less than 200 ms. During the transient, thepower in VSC2 drops to about 0.80 p.u. but is restored to itsinitial value of 0.90 p.u. after the transient is finished. As aconsequence of a higher dc-system voltage profile, the systemlosses are now reduced to 2.03%.

At this point, the MTDC network is being operated withonly VSC2 as a slack node. If a fault would occur at thatterminal, the power balance inside the network would be lost,and the offshore wind farms would have to quickly apply somefast power reduction method. In addition, dc choppers in theonshore HVDC terminals would also have to be activated oncethe voltage would have risen to dangerous values [57].

Therefore, at t = 3 s, the onshore VSC1 is also called inby the optimization algorithm to help with the voltage reg-ulation inside the MTDC network and to reduce the overalltransmission losses. At that moment, the voltage referencesof both VSC1 and VSC2 are made equal to 1.0867 p.u. As aconsequence, the losses in the transmission system are furtherreduced to 1.37%.

However, as it can be seen from Fig. 6, from t = 2 to 4 s,the voltages at the offshore wind farm nodes are being operatedvery close to the maximal permissible limit of 1.10 p.u. This isdue to the fact that, up to that point, no consideration regardingthe N − 1 contingency analysis had been implemented in theoptimization algorithm.

Then, at t = 5 s, new voltage reference set points, which takeinto account N − 1 security constraints, are sent to VSC1 andVSC2. Accordingly, the voltage on both nodes is reduced from1.0867 to 1.0661 p.u., while on the wind farm terminals, thevoltage is reduced from around 1.10 to circa 1.08 p.u.

Due to the reduction in the network voltage profile, thelosses in the transmission system are increased. Nevertheless,the losses are still optimized, and the increase from 1.37%to 1.42% is, as shown in Fig. 6(c), practically insignificant.The advantage of this new operating point is that the MTDCnetwork is now N − 1 secure. In order to demonstrate theinclusion of the N − 1 security analysis in the DVC strategy,a three-phase fault is applied to the ac grid connected to VSC2at simulation time t = 6 s. The fault duration is 500 ms.

It is worth noting that, during the fault, the current controlon the VSC2 terminal is set to provide full reactive currentsupport (1 p.u., i.e., up to the rated converter capability), asrequired by the most stringent grid codes [58]. This is shownin Fig. 6(b), where the active power going through the VSC isinstantaneously zeroed to provide full reactive current supportduring the ac network voltage dip.

As previously mentioned, if this was the only direct-voltage-controlling node, the power balance in the MTDC networkwould have been lost, and the dc-system voltage would startto rise, an event which could potentially power down the wholeMTDC transmission system. Instead, with the DVC strategy,once the VSC2 terminal is faulted, in order to maintain powerbalance, the VSC1 terminal increases its power inversion from0.52 to 1.17 p.u. after a short transient, which lasts less than200 ms. During the fault, the direct voltage on the third offshorewind farm (WF3) has an overshoot peak of circa 1.13 p.u.However, being only 3% over the nominal range, these briefovervoltages are not of concern [57]. In fact, once the transients

are over, the direct voltage at the WF3 is successfully broughtback by VSC1 to 1.10 p.u., i.e., inside the normal operatingrange, showing that, with the DVC strategy, the MTDC networkis indeed N − 1 secure. After the fault is cleared, the MTDCnetwork successfully returns to the previous operating pointafter a brief transient.

VIII. CONCLUSION

Currently, the best candidate for the development of atransnational grid for the connection of offshore wind farms isthe VSC-HVDC transmission technology. However, up to now,almost all HVDC projects around the world have been point-to-point systems. As a consequence, presently available controlstrategies for VSC-HVDC are not designed for operation insidelarge MTDC networks. In this paper, a new control strategy,called DVC, has been proposed. In the DVC strategy, theresponsibility of balancing the power inside the MTDC networkis shared between several VSC terminals. In so doing, the taskof controlling the voltage inside the MTDC is no longer left toa single network node. Through an optimization algorithm, theproposed control strategy is capable of operating MTDC net-works with an arbitrary number of nodes while optimizing thesystem’s functionalities such as system losses, total generationcost, operational limits, and network security. In this paper, thesteepest descent method has been used to optimize the MTDCtransmission losses while guaranteeing N − 1 security. Load-flow results and dynamic simulations have been provided tosupport the findings and to demonstrate that the DVC strategycan successfully be applied for the control of large MTDCnetworks.

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Rodrigo Teixeira Pinto (S’10) was born in Brazilin 1983. He received the B.Sc. degree in electricalengineering from the Escola Politécnica da Universi-dade de São Paulo, São Paulo, Brazil, and the M.Sc.degree (cum laude) from the Politecnico di Torino,Torino, Italy, in 2008.

From May to November 2008, he was withSiemens PTI, Erlangen, Germany, as a Diplomandin the Network Dynamics Studies Department.Since 2010, he has been a Ph.D. Researcher ofthe North Sea Transnational Grid project with the

Electrical Power Processing Group, Delft University of Technology, Delft,The Netherlands.


Pavol Bauer (S’91–M’00–SM’07) received the M.S.degree in electrical engineering from the TechnicalUniversity of Kosice, Kosice, Slovakia, in 1985,and the Ph.D. degree from the Delft University ofTechnology, Delft, The Netherlands, in 1995.

Since 1990, he has been with Delft University ofTechnology, teaching power electronics and electri-cal drives. He received the title Professor from thePresident of Czech Republic at the Brno Universityof Technology, Brno, Czech Republic, in 2008. Hepublished over 60 journal and 250 conference papers

in his field and is an author or coauthor of six books. He is the holderof international patents, and he organized several tutorials at internationalconferences.

Prof. Bauer is the Chairman of the Benelux IEEE Joint Industry ApplicationsSociety and the Power Electronics and Power Engineering Society chapter, amember of the EPE-PEMC council, an EPE member, and also a member ofinternational steering committee at numerous conferences.

Sílvio F. Rodrigues (S’12) was born in Portugal in1988. He received the B.Sc. degree in electrotech-nical engineering and computer science from theInstituto Superior Técnico, Lisbon, Portugal, and theM.Sc. degree from the Energy Department, InstitutoSuperior Técnico. He is currently working towardthe Ph.D. degree at the Electrical Power ProcessingGroup, Delft University of Technology, Delft, TheNetherlands, working on the Flow research project.

His research interests include the modeling andoptimization of offshore wind farms and multitermi-

nal DC grids.

Edwin Jan Wiggelinkhuizen was born in Soest,The Netherlands, in 1968. He received the M.Sc.degree in electrical engineering from the TechnicalUniversity Eindhoven, Eindhoven, The Netherlands,in 1992.

From 1993 to 1996, he was Lecturer withHogeschool Zeeland, Vlissingen, The Netherlands.Since 1996, he has been a Research Scientist withthe Energy Research Center of the Netherlands,Petten, The Netherlands. His main technical interestsinclude wind energy grid integration and wind farm

control.

Jan Pierik was born in The Netherlands in 1954. Hereceived the M.Sc. degree in chemical engineeringfrom the Technical University Twente, Enschede,The Netherlands, in 1978.

Since 1980, he has been with the Energy ResearchCenter of the Netherlands, Petten, The Netherlands,where he is currently a Senior Research Scientist. Hismain technical interest is modeling and control ofelectrical systems for wind turbines and wind farms.

Braham Ferreira (M’88–SM’01–F’05) received theB.Sc.Eng., M.Sc.Eng., and Ph.D. degrees in elec-trical engineering from Rand Afrikaans University,Johannesburg, South Africa, in 1981, 1983, and1988, respectively.

From 1986 until 1997, he was with RandAfrikaans University, where he held the Carl andEmily Fuchs Chair of Power Electronics in lateryears. Since 1998, he has been a Professor with DelftUniversity of Technology, Delft, The Netherlands.

Dr. Ferreira is a member of the IEEE Power Elec-tronics Specialists Conference Adcom and has been the Treasurer of the IEEEPower Electronics Society (PELS) since 2005. He was the Founding Chairmanof the IEEE Joint Industry Applications Society/PELS Benelux chapter in 1999.He served as the Chairman of the CIGRE SC14 National Committee of theNetherlands and was a member of the executive committee of the EPE Society.

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Documents

transmission of electricity

introduction of voltage

dc electricitymanuscript

netherlands email

student member

ieee transactions

edisons transmission

dc optimal power flow