1

Communication-Less Frequency Support fromOffshore Wind Farms Connected to

HVdc via Diode RectifiersOscar Saborío-Romano , Student Member, IEEE, Ali Bidadfar , Member, IEEE, Jayachandra N. Sakamuri ,

Lorenzo Zeni, Member, IEEE, Ömer Göksu , and Nicolaos A. Cutululis , Senior Member, IEEE

Abstract—Before diode rectifier (DR) technology for connect-ing offshore wind farms (OWFs) to HVdc is deployed, in-depth studies are needed to assess the actual capabilities of DR-connected OWFs to contribute to the secure operation of thenetworks linked to them. This study assesses the capability ofsuch an OWF to provide communication-less frequency support(CLFS) to an onshore ac network. It is shown that the HVdclink’s offshore terminal direct voltage can be estimated frommeasurements at the OWF’s point of connection with the DRplatform. Two different methods are proposed for implementingCLFS in the OWF active power controls. In Method 1, theestimated offshore terminal direct voltage is used for estimatingthe onshore frequency deviation. In Method 2, the actual offshoreterminal direct voltage measurement is used instead. Uniquefeatures of the provision of CLFS from OWFs connected toHVdc via DRs are highlighted, and the dynamic and staticperformance of the CLFS control scheme is compared to that ofthe communication-based frequency support scheme. To assessthe impact of parameter estimation errors on the provision ofCLFS, a parametric sensitivity study is presented as well, andrecommendations are given to increase accuracy.

Index Terms—Diode-rectifier-based HVdc transmission, fre-quency support, grid-forming wind turbine control, offshore windenergy integration, primary frequency response

I. INTRODUCTION

EXPLOITING Europe’s offshore wind resources furtherrequires the development of electrical infrastructure con-

necting offshore wind farms (OWFs) and onshore networks.To date, only a few OWFs are connected via HVdc, whilethe majority export their production through HVac. However,as the distance from shore and OWF size increase and theassociated costs decrease, the amount of HVdc-connectedOWFs is widely expected to increase.

Since its introduction in 1997, HVdc transmission technol-ogy using voltage source (forced-/self-commutated) converters(VSCs), based on insulated-gate bipolar transistors, has de-veloped significantly. VSC-based HVdc transmission (VSC-HVdc) offers advantages such as independent control of active

This work has received funding from the European Union’s Horizon 2020research and innovation programme under grant agreement No 691714.

O. Saborío-Romano, A. Bidadfar, Ö. Göksu and N. A. Cutululis are withthe Department of Wind Energy, Technical University of Denmark, Frederiks-borgvej 399, 4000 Roskilde, Denmark (e-mail: osro@dtu.dk; abid@dtu.dk;omeg@dtu.dk; niac@dtu.dk).

L. Zeni is with Ørsted Offshore, Nesa Allé 1, 2820 Gentofte, Denmark(e-mail: lorze@orsted.dk).

J. N. Sakamuri is with Vattenfall, Jupitervej 6, 6000 Kolding, Denmark(e-mail: jayachandranaidu.sakamuri@vattenfall.com).

and reactive power, smaller footprints, fast reversibility ofactive power flow and the (grid-forming) capability to formac networks, i.e. to control their ac-side voltage magnitudeand frequency. Owing to such advantages, the use of VSC-based offshore HVdc terminals has enabled the developmentof HVdc-connected OWFs with the prevailing grid-followingapproach to controlling wind turbines (WTs), in which WTsrely on other (grid-forming) units (e.g. VSC-based offshoreHVdc terminals) forming their ac network.

Recently suggested as a feasible alternative for connect-ing OWFs to HVdc, (uncontrolled, line-commutated) dioderectifiers (DRs) have prompted increasing interest from bothacademia and industry [1]–[6]. DR-based offshore HVdc ter-minals offer advantages such as higher reliability, lower costs,higher efficiency and smaller footprints [3], [5]. Since diodesare passive devices, however, such offshore HVdc terminalsare inherently devoid of the grid-forming capability of VSCs.WTs have therefore been suggested as feasible candidates totake over such responsibility. This entails fundamentally dif-ferent WT and WF controls, changing their control approachfrom that of grid-following units to that of grid-forming units[1], [4].

HVdc-connected OWFs and the corresponding HVdc powertransmission networks can be required to contribute to thesecure operation of the onshore ac networks connected to themby means of e.g. fault ride-through, black start and restoration,rotor angle stability-related control, reactive power/alternatingvoltage control and active power/frequency control. The capa-bilities of VSC-HVdc-connected OWFs and the correspondingHVdc power transmission networks to provide such servicesare well established. In-depth studies are, however, needed toassess the actual capabilities of DR-connected OWFs to con-tribute in the provision of such services before such technologyis deployed [7].

A control strategy for the provision of frequency support(FS) from HVdc-connected WFs was first developed in [8],based on the long-distance communication of the remote acnetwork’s frequency to the WF-side HVdc terminal, here-inafter referred to as communication-based frequency support(CBFS). To avoid the need for long-distance communica-tion, communication-less schemes have been subsequentlyproposed for the provision of FS, hereinafter referred to ascommunication-less frequency support (CLFS), from VSC-HVdc-connected OWFs [9], [10]. The term communication-less means, in this context, without long-distance communi-

2

cation, i.e. all quantities needed by each controller can bemeasured locally. For an OWF, locally means at its point ofconnection, which may be extended for DR-connected OWFsto include the DR platform.

The capability of DR-connected OWFs to provide CBFSto onshore ac networks by means of plant-level controlssimilar to those devised for VSC-connected OWFs has beeninvestigated in [11], using models and grid-forming WT front-end converter (FEC) controls based on those in [1]–[3], and anaggregated representation of the OWF as a single equivalentWT. The analysis has been extended in [12], using moredetailed component models based on those in [13], a semi-aggregated representation of the OWF and improved grid-forming WT FEC controls based on those in [6].

To date, CLFS from DR-connected OWFs has only beenstudied in [14], where supplementary WT controls have beenproposed to detect the onshore frequency event via the corre-sponding change in the magnitude of the voltage in the off-shore ac network (clamped to the HVdc network voltage) andchange the WT active power output by manipulating the pitchangle, once the fluctuation in voltage magnitude surpasses acertain threshold value. The performance of such controls hasbeen illustrated by simulation results corresponding to twooperating points very close to each other, not considering theaccuracy with regards to the expected changes in WF activepower output in response to the changes in the frequency ofthe onshore ac network. However, since the voltage drop overthe DRs varies with the operating point, an accurate provisionof CLFS with such controls over the whole operating rangeof the OWF will inevitably require that:

• such WTs receive information about the operating point(e.g. WF active power or current output) that is notavailable from measurements local to the WTs, and that

• some parameters of the proposed supplementary WTcontrols (e.g. voltage magnitude threshold, droop) varywith the operating point.

The main contribution of this work, extending the assess-ment conducted in [12], is to include the capability of the DR-connected OWF to provide CLFS to an onshore ac network bymeans of plant-level controls similar to those devised for VSC-connected OWFs. It is shown that the HVdc link’s offshoreterminal direct voltage can be estimated from measurementsat the OWF’s point of connection with the DR platformand offline estimation of parameters corresponding to the DRplatform. Furthermore, it is shown that the onshore frequencydeviation can in turn be estimated from the offshore terminaldirect voltage estimation and the coordinated selection of thecorresponding droops in the onshore terminal and OWF activepower controls.

Two different methods are proposed for implementing CLFSin the WF active power controls. In Method 1, the estimatedoffshore terminal direct voltage is used for estimating theonshore frequency deviation. In Method 2, the actual offshoreterminal direct voltage measurement is used instead.

Through the proposed controls, the OWF modifies its activepower output according to the estimation of the onshorefrequency deviation. Focus is given to primary frequencyresponse (PFR), based on an active-power-frequency droop,

with reserves from curtailed operation considered as the sourceof additional active power during onshore underfrequencyevents [13]. Unique features of the provision of CLFS fromOWFs connected to HVdc via DRs are highlighted, and thedynamic and static performance of the CLFS control schemeis compared to that of the CBFS scheme. To assess theimpact of parameter estimation errors on the provision ofCLFS, a parametric sensitivity study is performed as well,and recommendations are given to increase the accuracy inthe estimation of such parameters.

The rest of the paper is organised as follows. In Section II,the studied system is detailed and the main control algorithmsare described. In Section III, the considered cases are de-scribed, and corresponding simulation results are presentedand discussed. Finally, concluding remarks are made in Sec-tion IV.

II. MODELLING AND CONTROL

Fig. 1 shows the studied system. The system is based onthat described in [7], [13] and consists of one of three 400 MWOWFs connected to an onshore ac network by means of a200 km long ±320 kV monopolar HVdc link and correspond-ing onshore HVdc terminal, operating at a third of the ratedvoltage (i.e. the nominal voltage is approximately 213 kV,and the nominal power is 400 MW). Balanced/symmetricoperation is assumed. The system is modelled in PSCAD.System parameters are given in Table I.

The onshore ac network is represented by a lumped three-phase resistive load and a lumped three-phase synchronousmachine (SM) with its electrohydraulic governor and hydraulicturbine (with a non-elastic water column and no surge tank),using the corresponding models from the PSCAD MasterLibrary. The share of wind power generation at the connectionpoint is 50 %, i.e. the WF is rated at 400 MW, for a totalinstalled capacity of 800 MW. The offshore HVdc terminal:one of three diode rectifier platforms (one per OWF), consistsof two (uncontrolled, line-commutated) diode-based 12-pulserectifiers (DRs) connected in series on their dc side, withcorresponding reactive power shunt compensation and filterbank on their ac side.

The OWF has 50 grid-forming type-4 (full-converter) 8 MWWTs, laid out in 6 strings. The first string, comprised of WTs1–9 is represented in detail. The other 5 strings, consisting ofWTs 10–50, are aggregated into an equivalent 328 MW WTand corresponding cable equivalent π circuit using the methodproposed in [15].

The represented WT dynamics focus on the WT front-end(grid-/line-side) network. Dynamics in each WT dc link andbehind it are not considered, as they are not relevant to thecase in question. The corresponding voltage is thus assumedconstant, i.e. ideally regulated by the back-end/machine-sideconverter [7]. Pulse-width modulation (PWM) is assumed tobe done in the linear range, switching effects and any delaydue to the implementation of the PWM are neglected, andaverage value models are used to represent all VSCs (includingthe VSC-based onshore HVdc terminal). Focus is given todynamics not faster than the VSC (inner/lower) current control

3

PF , QF

UF

10–50

1

Offshoreac

Network

9

Idc

Onshoreac

Network

OnshoreTerminal

HVdc Link

+ER−

+EI−

DiodeRectifierPlatform

(a) Overview

Uk UT,k

PT,k , QT,kPk , Qk

Ik IT,k UW,k

Lk RkCk

P ∗T,k

U0

PT,k

QT,k

ω0

Q∗T,k Ik

UT,k

IT,k

dcLink

Front-EndConverterFilter

Offshoreac

Network

Front-EndConverterControls(Fig. 3)

(b) kth wind turbine front-end (grid-/line-side) networkFig. 1. Studied system

f∗

on

fon +

− 1

1 + sTfE

LPF

fE

−fE

Deadband

kfE

Frequency Support

E∗

R

Idc+

+

−

+

Rdc

E∗

IE

∆fon

∆E

Fig. 2. Onshore terminal outer control loop; parameter values and limits givenin Table II

loops, the fastest of which are designed to have a bandwidthof 200 Hz.

A. Onshore Terminal Controls

The VSC-based onshore HVdc terminal regulates the volt-age on its dc terminals, EI, and the reactive power injected intothe onshore ac network by means of the controls described in[3]. To study the capability of such an OWF to provide CLFSto an onshore ac network, the onshore terminal controls are ex-tended to include the outer control loop shown in Fig. 2, basedon those used in [9], [10], [16] for OWFs connected to HVdcvia VSCs. In such loop, the base direct voltage reference, E,is determined by subtracting the estimated voltage drop on theHVdc link from the offshore terminal direct voltage reference,E∗

R, which is set to the nominal value. The voltage drop onthe HVdc link is calculated using the onshore terminal currentmeasurement, Idc, and the estimated HVdc link resistance, Rdc.

When CLFS is provided, E is modified by means of anadditional direct voltage reference, ∆E, which is determinedby a given droop acting on the onshore frequency deviationsignal, ∆fon, i.e.

∆E = kfE∆fon . (1)

∆fon is generated by applying a first-order low-pass filter(LPF) and a deadband to the subtraction of the correspondinginput signals. Values for the control parameters and limits aregiven in Table II. Assuming perfect control of the onshoreterminal direct voltage, EI ≈ E∗

I , and perfect estimation ofthe HVdc link resistance, Rdc ≈ Rdc,

ER − E∗R = ∆ER ≈ ∆E = kfE∆fon . (2)

B. Offshore Terminal Direct Voltage Estimation

When the (4 diode bridges of the two 12-pulse) DRsare conducting, the relation between alternating and directvoltages on both sides of the DR platform is [17]

ER =12√

6

πNTRUF −

12

πXTRIR,dc , (3)

where ER is the average direct voltage, NTR is the DRtransformer turns ratio, UF is the rms line-to-neutral alternatingvoltage, XTR is the DR transformer leakage reactance, and IR,dcis the direct current flowing out of the DR platform. Moreover,the relation between alternating and direct currents in the DRs(with losses neglected) is [17]

IR,ac cosφ ≈ 2√

6

πNTRIR,dc (1 + cosµ) , (4)

where IR,ac is the rms fundamental alternating line currentflowing into the DRs, φ is the angle by which the alternat-ing current associated with IR,ac lags the alternating voltageassociated with UF, and µ is the DR commutation overlapangle. Neglecting shunt losses in the DR platform,

IR,ac cosφ ≈ PF

3UF, (5)

where PF is the three-phase active power flowing out of theOWF and into the DR platform. Using (4) and (5), (3) can berewritten as

ER =12√

6

πNTRUF −

√2/3XTR

NTR (1 + cos µ)

PF

UF

= kUEUF − kIEPF

UF,

(6)

where ER is the estimated average direct voltage, XTR is theestimated DR transformer leakage reactance, and µ is the es-timated DR commutation overlap angle. Equation (6) impliesthat the offshore terminal direct voltage, ER, can be estimatedfrom measurements local to the OWF, UF, PF, and knowledgeor offline estimation of the parameters corresponding to theDR platform, NTRXTR , µ. The parameter values used in thiswork are given in Table III.

If the frequency of the offshore ac network is only allowedto vary within a narrow range around its nominal value (toreduce the size of the filters in the DR platform) [7], the

4

Q∗

T,k

QT,k

ω0

−

+

kQ,k+

+

Reactive Power

Control

ωk

+

−

kω,k

Frequency

Control

UTq,k

UTd,k

ωk

Id,k

Iq,k

+

−

+

−

kUp,k +kUi,k

s

PI

kUp,k +kUi,k

s

PI

++

+

++

−

b

b

Ck

Ck

×

×

×

×

b

Voltage Control

P ∗

T,k

PT,k

U0

kPp,k +kPi,k

s

+

−

+

+

Active Power Control

ITq,k

ITd,k

ωk

UTd,k

UTq,k

+

−

+

−

kIp,k +kIi,k

s

PI

kIp,k +kIi,k

s

PI

++

+

++

−

b

b

Lk

Lk

×

×

×

×

b

Current Control

UT,k

θk

U∗

W,k ≈ UW,k

UTd,kabc

dq

dq

abc

ω0

kLp,k +kLi,k

s

PI

+

+

1

sb

Phase-Locked Loop

Ik IT,k

Id,k

Iq,k

ITd,k

ITq,k

abcdq

abcdq

b

UTq,k

θkωk

U∗

Td,k I∗Td,k

ω∗

k

U∗

Tq,k I∗Tq,k U∗

Wq,k

U∗

Wd,k

Fig. 3. kth wind turbine front-end (grid-/line-side) converter controls; parameter values and limits given in Table IV

nominal value of the DR transformer leakage reactance, XnomTR

,can be used in (6), i.e.

XTR = XnomTR

. (7)

Using (5), (4) can be rewritten as

cosµ ≈ −1 +π

2√

6NTR

IR,ac

IR,dccosφ

≈ −1 +π

6√

6NTR

PF

UFIdc.

(8)

Using (8), cosµ can be estimated from measurements fordifferent operating points. µ can then be calculated as

µ = arccos (cosµ) , (9)

where cosµ is the mean of the estimated values for cosµ.

C. Wind Turbine Front-End Converter Controls

The front-end (grid-/line-side) network of the kth windturbine(s), WTk, is shown in Fig. 1b. The grid-forming WTfront-end (grid-/line-side) converter (FEC) controls, shown inFig. 3, are based on those proposed in [6] and are implementedon a rotating reference frame oriented on the voltage at thefilter capacitor, UT,k.

In each WT front-end network, the filter capacitor voltagedirect (d) and quadrature (q) axis components are regulated bythe FEC lower/inner control loops to follow the correspondingreferences, U∗

Td,k, U∗Tq,k, respectively. U∗

Td,k consists of twocomponents: the offshore ac network voltage set point, U0,common to all WTs, and a component individual to eachWT, which is altered to control the FEC active power output,PT,k. In an additional control loop based on the FEC phase-locked loop (PLL), a proportional regulator manipulates U∗

Tq,kto control the offshore ac network (angular) frequency, ω.The reference to such additional loop also consists of twocomponents: the offshore ac network (angular) frequency set

point, ω0, common to all WTs, and a component individual toeach WT, which is altered to control the FEC reactive poweroutput, QT,k.

When the WF is exporting power, the FEC upper/outercontrol loops in each WT regulate PT,k and QT,k as follows. Aproportional-integral (PI) regulator controls PT,k to follow thecorresponding reference, P ∗

T,k, whereas QT,k is controlled by aproportional regulator (reactive-power-frequency droop) witha given reference, Q∗

T,k, so that reactive power is shared amongthe WT FECs (avoiding overcurrents and reactive currentcirculation). Values for the control parameters and limits aregiven in Table IV.

D. Wind Farm Active Power Controls

To study the capability of such a WF to provide FS toan onshore ac network, the model is extended to includethe supervisory active power controls at plant level shown inFig. 4, based on those used in [11], [12], [16]. Values for theparameters and limits are given Table V.

On the right side of Fig. 4, a proportional-integral (PI) reg-ulator controls the WF active power output, PF, by altering theWF active power dispatch, P ∗. A first-order LPF is applied tothe corresponding measurement signal. Hardware and controllimits are modelled by means of corresponding restrictions onthe regulator’s output value and its rate of change. ProportionalWF generation dispatch is used. In doing so, P ∗ is dividedby the overall aerodynamic power available from the wind,Pava, to generate the OWF active power dispatch coefficient,κdisp. The active power set point of each WT FEC is thenset as the product of the corresponding aerodynamic poweravailable from the wind, Pava,k, and the active power dispatchcoefficient, i.e.

P ∗T,k = κdispPava,k . (10)

When providing FS to the onshore ac network, the baseactive power reference, P ∗

F , is modified by means of an

5

UF

E∗

R

b

÷

×

kIE

kUE+

−

−

+

kEf

1

1 + sTfP

LPF

fP

−fP

Deadband

kfP

Onshore Frequency Support

P ∗

F

PF

Pava

b

+

+

+

−

1

1 + sTF

LPF

kFp +kFi

s

PI

×

÷

κdispP P ∗

∆ER ∆fon

ER

∆PFS

Fig. 4. Wind farm active power controls with Method 1 for providing communication-less frequency support; parameter values and limits given in Table V

additional active power reference, ∆PFS, based on an onshorefrequency deviation signal, ∆fon, i.e.

P = P ∗F + ∆PFS(∆fon) . (11)

PFR is implemented by making ∆PFS proportional to ∆fon (towhich a first-order LPF and a deadband can also be applied),using a given droop.

When providing CLFS, ∆fon is determined by applying agiven droop to the offshore (terminal) direct voltage deviationsignal, ∆ER. Assuming perfect knowledge of the offshoreterminal direct voltage, ∆ER ≈ ∆ER,

∆fon = kEf∆ER ≈ kEf∆ER . (12)

Equations (2) and (12) can be combined as:

∆fon ≈ kEfkfE∆fon = ∆fon ⇐⇒ kEfkfE = 1 , (13)

which implies that the onshore frequency deviation signal,∆fon, can be estimated in the WF active power control schemewithout any need for long-distance communication. The choiceof values for kEf and kfE must ensure that the direct voltagevariations due to onshore frequency deviations are sufficientlylarge to be distinguishable from normal voltage drifts andmeasurement and estimation uncertainty, but sufficiently smallto lie within the allowable operating range. By applyingthe corresponding deadbands, the controls can ignore smalldeviations in onshore frequency or offshore terminal directvoltage.

Two different methods are proposed for implementing CLFSin the WF active power controls. In Method 1 (CLFS1), shownin Fig. 4, the estimated offshore terminal direct voltage (6),ER, is used for computing ∆ER. In Method 2 (CLFS2), theactual offshore terminal direct voltage measurement, ER, isused instead of ER.

III. SIMULATION RESULTS

Results of the EMT simulations performed in PSCAD arepresented in Figs. 5–10. The results illustrated in Figs. 5–8,discussed in Section III-A, correspond to the closed-loop testsconducted to assess the dynamic performance of the proposedCLFS methods and compare it to that of CBFS. Figs. 9 and 10,discussed in Section III-B, correspond to the parametric sen-sitivity study conducted to asses the proposed CLFS methods’accuracy and sensitivity to parameter estimation errors.

Onshore frequency events have been simulated by meansof a 0.075 pu load step change (i.e. 60 MW/800 MW) att = 0.5 s for different wind speed scenarios over the wholeOWF’s operating range. Wind speed (and the aerodynamicpower available from it) has been considered constant in eachsimulation. All (equivalent) WT front-end networks (Fig. 1b)and corresponding grid-forming converter controls (Fig. 3)have the same per-unit (pu) parameters and limits (given inTables I and IV). Moreover, U0 = 0.86 pu, ω0 = 1 pu, andQ∗

T,k = 0 in all such controls, and f∗on = 1 pu = E∗R in the

controls depicted in Figs. 2 and 4. A maximum allowablevariation of 0.06 pu (2 % of the HVdc link’s rated voltage)has been assumed for ER.

A. Closed-Loop PerformanceResults of the closed-loop tests are shown in Figs. 5–8. Each

fig. includes base case responses, corresponding to no FS fromthe OWF to the onshore ac network (i.e. the FS consistingsolely of that of the SM). The (light) grey signals in eachfig. represent the base case, while the (dark) red and blacktraces illustrate the cases in which the OWF provides CBFSand CLFS, respectively. In the case with CBFS, ∆fon has beenassumed to be communicated continuously to the OWF witha delay of 100 ms. Method 1 (CLFS1) has been employed inthe case with CLFS. The dynamic performance of the caseusing CLFS2 is almost identical to that of the case employingCLFS1 and is thus omitted.

High, medium and low wind speed scenarios have beenconsidered in these tests. As with those in [12], the consideredindividual WT operating points in each scenario take into ac-count the wind speed deficit due to the aerodynamic interactionbetween WTs. In principle, Pava,k decreases along the string inthe wind speed direction.WF production is curtailed to provideactive power reserves of 0.1 pu, i.e. P ∗

F = Pava − 0.1 pu .WF responses to an onshore underfrequency event at high

and low wind speeds are depicted in Figs. 5 and 6, respectively.Similar results have been obtained in the medium wind speedscenario. The offshore ac network (angular) frequency, ω, andWF reactive power output, QF, are only presented in Fig. 5b,corresponding to the high wind speed scenario. However,similar results have also been obtained in the other wind speedscenarios.

WT responses to an onshore underfrequency event atmedium and low wind speeds are illustrated by Figs. 7 and

6

Onsh

ore

freq

uen

cy,

fo

n[p

u]

Base Case CBFS CLFSO

ffsh

ore

term

inal

dir

ect

volt

age,

ER

[pu]

Time, t [s]

OW

Fact

ive

pow

eroutp

ut,

PF

[pu]

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 60.88

0.9

0.92

0.94

0.96

0.98

0.94

0.96

0.98

1

1.02

0.975

0.98

0.985

0.99

0.995

1

(a)

OW

Ffr

equen

cy,

ω[p

u]

Base Case CBFS CLFS

Time, t [s]

OW

Fre

act

ive

pow

eroutp

ut,

QF

[pu]

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6-0.15

-0.1

-0.05

0

0.05

0.1

0.999

1

1.001

1.002

1.003

1.004

(b)

Fig. 5. Wind farm response to an onshore underfrequency event at high windspeed

Onsh

ore

freq

uen

cy,

fo

n[p

u]

Base Case CBFS CLFS

Off

shore

term

inal

dir

ect

volt

age,

ER

[pu]

Time, t [s]

OW

Fact

ive

pow

eroutp

ut,

PF

[pu]

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 60

0.02

0.04

0.06

0.08

0.1

0.94

0.96

0.98

1

1.02

0.975

0.98

0.985

0.99

0.995

1

Fig. 6. Wind farm response to an onshore underfrequency event at low windspeed

WT

kte

rmin

al

rms

volt

age,

Uk

[pu]

Base Case CBFS CLFS

WT

kact

ive

pow

eroutp

ut,

Pk

[pu]

Time, t [s]

WT

kre

act

ive

pow

eroutp

ut,

Qk

[pu]

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

0.2

0.4

0.6

0.8

1

0.87

0.89

0.91

0.93

0.95

Fig. 7. kth wind turbine response to an onshore underfrequency event atmedium-low wind speed – Solid: k = 1, Dashed: k = 9

WT

kte

rmin

al

rms

volt

age,

Uk

[pu]

Base Case CBFS CLFS

WT

kact

ive

pow

eroutp

ut,

Pk

[pu]

Time, t [s]

WT

kre

act

ive

pow

eroutp

ut,

Qk

[pu]

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6-0.35

-0.3

-0.25

-0.2

-0.15

-0.4

-0.2

0

0.2

0.4

0.6

0.85

0.87

0.89

0.91

0.93

Fig. 8. kth wind turbine response to an onshore underfrequency event at lowwind speed – Solid: k = 1, Dashed: k = 9

8, respectively. Solid and dashed traces—superimposed in thecase of the WT terminal rms voltages, Uk—represent theresponses of WTs 1 and 9, respectively, corresponding to theturbines at both ends of the string that is represented in detail.Similar results have been obtained in the high wind speedscenario.

The responses in Figs. 5–8 reflect characteristics of DR-connected OWFs observed in literature, such as:

• Active and reactive power flows through the DRs are notdecoupled.

• Physical coupling between active power and voltagemagnitude in the ac networks of such OWFs arisesfrom the fact that active power flow through the DRsis determined by the voltage difference between their acand dc terminals.

• As a result, most grid-forming control schemes proposedfor WT FECs in DR-connected OWFs manipulate the

7

magnitude of the alternating voltage to control the activepower flow, and manipulate its frequency to control thereactive power flow.

As can be seen in Figs. 5a and 6 by comparing the basecase responses to those of the case with CBFS, the onshorefrequency response can be improved by having the OWFprovide FS to the onshore ac network. By drawing on theactive power reserves and increasing PF, the OWF increasesfon and maintains it at a higher value for as long as thewind allows. The increase in current results in an increasein the DR reactive power consumption. This is reflected in theincreases in QF and ω in Fig. 5b. However, such changes areone and three orders of magnitude smaller than that in PF,respectively, while ω is kept close to 1 pu. That is the resultof every grid-forming WT FEC contributing autonomouslyto controlling ω by means of its corresponding PLL-basedproportional regulator, while sharing the reactive power withthe other grid-forming WT FECs by means of its reactive-power-frequency droop (proportional regulator) with constantreference Q∗

T,k = 0.The WT active power outputs, Pk, in Figs. 7 and 8 reflect

the assumed distributions of Pava,k and the changes in P ∗ andκdisp when FS is provided. In all wind speed scenarios, theincrease in PF in response to the onshore underfrequency eventis achieved by an increase in Uk that is one order of magnitudesmaller, keeping them within their normal operating range, asdepicted in both figs. As shown also in both figs., the WTsshare the reactive power consumption (negative values of Qk)according to their power rating and their active power output,Pk.

The overall performance of the case with CLFS is verysimilar to that of the case with CBFS, as evidenced by thetraces of fon and PF in Figs. 5a and 6. A similar amount ofenergy is injected in both cases, but it is injected at differentrates. The dynamic performance of the case with CLFS isslightly better immediately after the event, as the onshoreterminal extracts active power from the HVdc link to lower itsvoltage, and slightly worse after the frequency nadir, as someof the OWF active power output is used to raise such voltage.Such behaviour is, in general, preferable, as the faster responseimmediately after the event assists in limiting the nadir, whilethe slower response occurs after the most critical stage of theevent has passed.

For similar values of Pk, the decrease in Uk when providingCLFS results in currents higher than those when providingCBFS, as evidenced by the greater values of Qk in Figs. 7and 8. Higher currents result in increased DR reactive powerconsumption, which is reflected in the higher values of ω andQF in Fig. 5b for the case with CLFS. The slightly worsestatic performance (i.e. smaller steady-state values of fon andPF in Figs. 5a and 6) can be attributed mainly to the error inthe estimation of ER.

Unique features of the provision of CLFS from OWFsconnected to HVdc via DRs are illustrated by the traces ofω and Uk in Figs. 5b, 7 and 8:

• Since the DRs clamp the magnitude of the alternatingvoltage in the offshore ac network to the offshore terminaldirect voltage, changes in the latter are naturally reflected

OWF active power output, PF [pu]

Off

shore

dir

ect

volt

age

esti

mati

on

erro

r,ǫ E

R=

[

ER

(∞)

−E

R(∞

)]

/E

∗ R[%

]

Base0.9µ1.1µ0.9XTR

1.1XTR

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Fig. 9. Parametric sensitivity analysis of the offshore direct voltage estimation

in the former, without the need of an additional controlloop.

• The onshore frequency is not mirrored in the offshore acnetwork, but its deviation is reflected in the magnitude ofthe alternating voltage in the offshore ac network.

• The OWF active power controls can use the magnitudeof the alternating voltage in the offshore ac network—instead of its frequency—to estimate the active powerimbalance in the onshore ac network.

• Since the voltage drop over the DRs varies with theoperating point, an accurate provision of CLFS over thewhole operating range of the OWF requires knowledgeof either the offshore terminal direct voltage or theOWF operating point (e.g. OWF active power or currentoutput).

As illustrated by Fig. 5, the consumption/production ofreactive power, necessary to control the offshore ac network(angular) frequency, ω, can reduce the active power headroomof the corresponding grid-forming WTs. Lowering the voltagein response to an onshore underfrequency event may thusrequire a greater WT FEC current headroom to providethe necessary additional active power at high wind speeds.Moreover, there is a trade-off at low wind speeds betweenthe maximum allowable variation of ER and the minimumallowable WT terminal rms voltage, Uk, as can be observedin Fig. 8. For example, increasing the variation of ER mayresult in values of Uk below 0.85 pu.

B. Accuracy and Sensitivity to Parameter Estimation Errors

To assess the impact of parameter estimation errors (i.e. inthe estimation of Rdc in both methods, plus µ and XTR inCLFS1) on the provision of CLFS, a parametric sensitivitystudy has been performed, with the results shown in Figs.9 and 10. The study has consisted of open-loop tests, inwhich the onshore terminal modulates the HVdc link voltagein proportion to the onshore frequency deviation (1), but theOWF does not provide FS to the onshore ac network, i.e. theOWF active power output, PF, remains constant. The same

8

OWF active power output, PF [pu]

Onsh

ore

freq

uen

cydev

iati

on

esti

mati

on

erro

r,

ǫ ∆f

on

=[

∆f o

n(∞

)−

∆f o

n(∞

)]

/f

∗ on

[%]

CLFS1: BaseCLFS1: 0.9µCLFS1: 1.1µCLFS1: 0.9XTR

CLFS1: 1.1XTR

CLFS1: 0.9Rdc

CLFS1: 1.1Rdc

CLFS2: BaseCLFS2: 0.9Rdc

CLFS2: 1.1Rdc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Fig. 10. Parametric sensitivity analysis of the onshore frequency deviationestimation

aerodynamic power available from the wind has been consid-ered for all WTs. Moreover, no active power reserves frompreventively curtailed OWF production have been considered,i.e. P ∗

F = Pava .

The plots represent the steady-state values of different quan-tities from the dynamic simulations of onshore underfrequencyevents similar to those in Section III-A, for different operatingpoints (i.e. OWF active power output, PF) in the OWF oper-ating range. Moreover, they include base cases, correspondingto Rdc ≈ Rdc and the recommended estimation of XTR and µ,(7), (9). The corresponding values are given in Tables II andIII. The onshore underfrequency events have been arranged sothat the steady-state value of the onshore frequency deviationsignal, ∆fon(∞), has a magnitude of about 0.0136 pu (e.g.0.68 Hz for f∗on = 50 Hz) in every simulation. However,similar results can be expected over the assumed ranges foronshore frequency deviation signal and offshore direct voltage,∆fon ∈ [−0.02, 0.02] pu , ER ∈ [0.94, 1.06] pu .

Fig. 9 illustrates the accuracy of the offshore terminal directvoltage estimation (6), ER, used in CLFS1, and its sensitivityto errors in the estimation of XTR and µ. This is done byrepresenting the error of ER, εER

= (ER − ER)/E∗R , for the

base case parameter values and variations of ±10 %. Variationsin Rdc have a negligible effect on εER

(i.e. they are reflectedin both terms of the subtraction) and are thus omitted.

Fig. 10 depicts the accuracy of the onshore frequencydeviation estimation (12), ∆fon, and its sensitivity to errorsin the estimation of Rdc, XTR and µ for both CLFS methods.This is done by representing the error of ∆fon, ε∆fon

=

(∆fon−∆fon)/f∗on , for the base case parameter values and forvariations of ±10 %. The solid traces represent the cases withCLFS1, while the dashed traces correspond to the cases withCLFS2. Variations in XTR and µ are only relevant to CLFS1

and are thus omitted for CLFS2.As evidenced by the cyan (base case) trace in Fig. 9, the

results indicate that the proposed method (6) for estimatingER can be expected to have an error, εER

, of around 0.03 %in magnitude (i.e. 64 V for E∗

R ≈ 213 kV), which may be

inherent to any estimation of ER. As a consequence, ε∆foncan

be expected to be around 0.01 percentage points (e.g. 5 mHzfor f∗on = 50 Hz) greater when using CLFS1, as illustrated bythe cyan and black (base case) curves in Fig. 10. Variationsin Rdc, XTR and µ impact the estimations of offshore directvoltage and onshore frequency deviation in a manner that isdirectly proportional to PF, as can be seen in both figs. Thisreflects the role of such parameters in the estimation of thecorresponding voltage drops in the DR platform and HVdclink, which are directly proportional to PF. The maximumvalues of εER

and ε∆fonthus correspond to PF = 1 pu.

When using CLFS1, an error of ±10 % in the estimationof µ can result in greater magnitudes of εER

and ε∆fon, as

depicted by the magenta and brown traces in Figs. 9 and10, respectively. Such magnitudes can be as high as 0.06 %and 0.02 %, respectively. Likewise, an error of ±10 % in theestimation of XTR can result in magnitudes of εER

and ε∆fon

as high as 0.52 % and 0.17 %, respectively, as illustrated bythe orange and yellow curves in Figs. 9 and 10, respectively.

An error of ±10 % in the estimation of Rdc can result inmagnitudes of ε∆fon

as high as 0.12 %, which indicates thatε∆fon

is more sensitive to errors in the estimation of Rdc thanto errors in the estimation of µ, but is even more sensitive toerrors in the estimation of XTR . As illustrated by the red andblue curves, the ±10 % error in the estimation of Rdc has asimilar effect on ε∆fon

when using CLFS2. Moreover, similaraccuracy and sensitivity to errors in the estimation of Rdc canbe expected when VSC-connected OWFs provide CLFS.

In OWFs, transformers are typically purpose-built, meaningthat the uncertainty in the estimation of XTR can be reducedsignificantly by measuring their impedance during acceptancetests. The uncertainty in the estimation of Rdc can be reducedby the distributed temperature sensing systems typically em-ployed in large OWFs. Since the corresponding thermal timeconstants are much greater, corrections in Rdc can be done ata lower frequency, e.g. every 10 minutes. Moreover, adaptiveestimators can also be used to correct the values of µ, XTR

and Rdc at similar frequencies.

IV. CONCLUSIONS

The simulation results indicate that the new connectionconcept using DRs (and corresponding changes in WT control)does not impact the capability of OWFs to provide CLFS bymeans of plant-level active power control strategies similarto those developed for OWFs connected to HVdc via VSCs.The onshore frequency is not mirrored in the offshore acnetwork, but its deviation is reflected in the magnitude ofthe alternating voltage in the offshore ac network, while theoffshore frequency varies relatively little. The proposed OWFactive power controls can use the magnitude of the alternatingvoltage in the offshore ac network—instead of its frequency—to estimate the active power imbalance in the onshore acnetwork. In this way, DR-connected OWFs respond to onshorefrequency events, while their grid-forming WTs share thereactive power consumption/production and keep the offshorefrequency and voltages within their normal operating ranges.

The overall performance of the case with CLFS is similarto that of the case with CBFS. The dynamic performance

9

is slightly better immediately after the event, as the onshoreterminal extracts active power from the HVdc link to lower itsvoltage, and slightly worse after the frequency nadir, as someof the OWF active power output is used to raise such voltage.Such behaviour is, in general, preferable, as the faster responseimmediately after the event assists in limiting the nadir, whilethe slower response occurs after the most critical stage of theevent has passed.

APPENDIX

TABLE IPARAMETERS OF THE STUDIED SYSTEM

Component Parameter(s) Value(s)

Rated power 1200 MWHVdc Rated pole-to-ground voltage ±320 kV

link Nominal power 400 MW

Nominal pole-to-pole voltage 213 kV

Rated apparent power 400 MVARated rms line-to-line voltage 133 kV

Inertia time constant 1.5 s

Synchronous Water starting time 0.01 smachine Penstock head loss coefficient 0.1 pu

+ Turbine damping constant 3 pu

turbine Governor permanent droop 1 × 10−3 pu+ Governor proportional gain 10 pu

governor Governor integral gain 0

Governor derivative gain 0Pilot servomotor time constant 0.01 s

Gate servo(motor) time constants 0

Onshore Equivalent capacitance 131 µFHVdc Arm inductance 206 mH/phase

terminal Arm resistance 586 mΩ/phase

DR transformer (Y/Y/∆) rated66/43.4/43.4 kV

Diode rms line-to-line voltagesrectifier DR transformer leakage reactance, Xnom

TR1.41 Ω/phase

platform Equivalent dc smoothing reactor 33.3 H/pole

Shunt compensation inductance 1.77 H/phase

Rated apparent power 8 MVATransformer (Y/∆) rated

0.69/66 kVWind rms line-to-line voltages

turbine Transformer leakage inductance 0.1 pu/phase(front-end Transformer resistance 0.01 pu/phase

network) Filter capacitance, Ck 0.05 pu/phaseFilter inductance, Lk 0.1 pu/phase

Filter resistance, Rk 0

TABLE IIONSHORE TERMINAL OUTER CONTROL LOOP PARAMETERS AND LIMITS

Par. Value Par. Value

fE 5 × 10−4 pu Rdc 3.05 × 10−2 pukfE 3 pu TfE 10 ms

Limits: −0.06 pu ≤ ∆E ≤ 0.06 pu

TABLE IIIOFFSHORE TERMINAL DIRECT VOLTAGE ESTIMATION PARAMETERS

Par. Value Par. Value Par. Value

µ 22.3 NTR 43.37/66 XTR 1.41 Ω/phase

TABLE IVkTH WIND TURBINE FRONT-END (GRID-/LINE-SIDE) CONVERTER

CONTROL PARAMETERS AND LIMITS

Par. Value Par. Value Par. Value

Ck 0.05 pu kLp,k 0.16 pu kQ,k 0.01 pu

kIi,k 0.04 pu/s kω,k 50 pu kUi,k 40 pu/s

kIp,k 0.4 pu kPi,k 40 pu/s kUp,k 4 pu

kLi,k 1.6 × 10−4 pu/s kPp,k 4 pu Lk 0.1 pu

Limits: 0 ≤ I∗T,k ≤ 1.1 pu , 0 ≤ U∗W,k ≤ 1.1 pu

TABLE VWIND FARM ACTIVE POWER CONTROL PARAMETERS AND LIMITS

Par. Value Par. Value Par. Value

fP 0 kFp 1 × 10−3 pu kUE 1.10 pu

kEf 0.333 pu kFi 5 pu/s TF 10 ms

kfP −5 pu kIE 4.48 × 10−2 pu TfP 10 ms

Limits:1 × 10−3 pu ≤ UF , 1 × 10−3 pu ≤ Pava ,

−0.1 pu ≤ ∆PFS ≤ 0.1 pu ,0.025 pu ≤ P ∗ ≤ 1.1 pu , −1 pu/s ≤ dP ∗/dt ≤ 1 pu/s

ACKNOWLEDGEMENT

The authors gratefully acknowledge the contributions ofPoul E. Sørensen to the discussions leading up to this work.

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Oscar Saborío-Romano (S’12) received the BSc(Hons) degree in Electrical Engineering from theUniversity of Costa Rica in 2013. In 2015, hereceived the MSc degrees in Electrical Engineeringand Wind Energy from Delft University of Technol-ogy and the Norwegian University of Science andTechnology, respectively. He joined the Departmentof Wind Energy at the Technical University ofDenmark in 2016, where he has pursued a PhD. Hisresearch interests include power system control andstability, integration of renewable energy sources,

modelling and control of wind power, HVdc transmission, and microgrids.

Ali Bidadfar (M’14) worked as a power systemresearcher at KTH Royal Institute of Technologyfrom 2013 to 2016. He has been a PhD researcherat the Technical University of Denmark since 2016.During his PhD, he has focused on frequency sup-port provision from offshore HVdc grids. In August2019, he joined Ørsted, Denmark, as a power sys-tem engineer. His research interests include HVdccontrol and operation, offshore wind generation andtransmission technologies, control and stability ofpower systems.

Jayachandra N. Sakamuri received the MTechdegree in Electrical Engineering from the Indian In-stitute of Technology in 2009, after spending a yearas an exchange student at the Technical Universityof Berlin in 2008. He obtained his PhD degree fromthe Department of Wind Energy at the TechnicalUniversity of Denmark, where his work focusedon coordinated control of wind farms in offshoreHVdc grids. Before the PhD, he worked for GridSystem R&D, ABB on HVdc System Design forthree years and also at Crompton Greaves Ltd. on

HV switchgear design. His research interests include HVdc, offshore windfarm integration and control, and HV switchgear design.

Lorenzo Zeni (S’13–M’16) is with Ørsted Offshore,Denmark. He holds BSc and MSc degrees in Elec-trical Engineering from the University of Padua, aswell as a MSc degree in Sustainable Energy from theTechnical University of Denmark. He conducted anindustrially-driven PhD study on HVdc connectionof wind farms with the Technical University ofDenmark and DONG Energy (now Ørsted). He isinvolved in electrical design and grid connectionactivities for offshore wind farms as well as R&Dtasks, with special focus on application of FACTS

and HVdc to offshore wind farms.

Ömer Göksu received the BSc and MSc degreesin Electrical and Electronics Engineering from theMiddle East Technical University in 2004 and 2008,respectively, and was employed in Aselsan Inc. from2004 to 2009. He obtained his PhD degree from theDepartment of Energy Technology at Aalborg Uni-versityin 2012, under the Vestas Power Programme.In 2013, he was a research associate at the Universityof Manchester. Since 2013 he is a researcher at theDepartment of Wind Energy, Technical University ofDenmark. His research is focused on ac and HVdc

connected wind turbine and wind farm control and modelling, and integrationof power electronics to power systems.

Nicolaos A. Cutululis (SM’18) received the MScand PhD degrees, both in Automatic Control, in1998 and 2005, respectively. Currently, he is a pro-fessor at the Department of Wind Energy, TechnicalUniversity of Denmark. His main research interestsare integration of wind power, with a special focuson offshore wind power, and grids.