Received: 12 January 2021 Revised: 1 March 2021 Accepted: 26 March 2021 IET Renewable Power Generation

DOI: 10.1049/rpg2.12182

ORIGINAL RESEARCH PAPER

Research on sub/super-synchronous oscillation suppression

method for direct-drive wind turbine based on energy

compensation

Jing Ma1 Min Zhang1 A. G. Phadke2

1 State Key Laboratory of Alternate Electrical PowerSystem with Renewable Energy Sources, NorthChina Electric Power University, Beijing 102206,China

2 Bradley Department of Electrical and ComputerEngineering, Virginia Polytechnic Institute and StateUniversity, Blacksburg, Virginia 24061, USA

Correspondence

Jing Ma, State Key Laboratory of Alternate ElectricalPower System with Renewable Energy Sources,North China Electric Power University, Beijing102206, China.Email: hdmajing@163.com

Funding information

National Natural Science Foundation of China,Grant/Award Number: 51777070

Abstract

A method to suppress sub/super-synchronous oscillation of direct-drive wind turbinesbased on energy compensation is proposed. First, the transient energy model of direct-drive wind turbine is built, and the negative damping energy terms that lead the oscillationof direct-drive wind turbine are extracted. On this basis, the expressions of voltage com-pensation terms corresponding to negative damping energy terms are derived by back-ward deduction, thus supplementary energy branches are constructed, and their impacton fundamental frequency characteristics of wind turbine is analyzed. And then, with thecompensation energy of supplementary branches reaching the maximum and the incre-ment of fundamental-frequency voltage being the minimum as the objective, and with thefrequency-domain characteristic and fundamental-frequency voltage characteristic of con-trol links being satisfied as constraints, a scheme to optimize the compensation coefficientsof multiple branches is established. Finally, the model of direct-drive wind turbine is builtin RT-LAB for hardware-in-the-loop tests. Simulation results verify that, the method canrealize fast frequency-dependent suppression of sub/super-synchronous oscillation in dif-ferent frequency bands concerning different grid strengths.

1 INTRODUCTION

As the percentage of permanent magnet synchronous gener-ators (PMSG) in the installed capacity of local areas rapidlyincreases, sub/super-synchronous oscillation caused by the inte-gration of PMSG to weak power grid via inverter occurs evermore frequently [1–4], greatly intimidating the safe and sta-ble operation of power grid. Currently, due to lack of effectivecontrol measures to suppress sub/super-synchronous oscilla-tion of wind turbines, passive measures such as generator trip-ping are often taken, which sacrifices a large amount of windpower output and causes huge economic loss. Therefore, it isurgent to study active control method to suppress sub/super-synchronous oscillation of direct-drive wind turbine.

In recent years, scholars worldwide have conducted extensiveresearch on measures to suppress sub/super-synchronous

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oscillation, and there are mainly three methods used—adjustingcontroller structure, adding damping device and optimizingcontroller parameters. The method of adjusting controllerstructure [5–9] is based on the existing inverter control links,and the dynamic characteristics of wind turbines are changed byimproving the control link structure of the wind turbine currentinner loop controller, DC voltage outer loop controller, andPLL controller. This method can achieve online oscillation sup-pression and has a good suppression effect for different typesof oscillations. However, this method needs to modify the con-trol system of the existing equipment, and the implementationprocess is more complicated. The method of adding dampingdevice [10–14] is to add an independent damping device to thewind power grid-connected system, and design the dampingcontrol branch based on the system’s observable/controllablecomprehensive geometric indicators to realize the online stable

2502 wileyonlinelibrary.com/iet-rpg IET Renew. Power Gener. 2021;15:2502–2514.

MA ET AL. 2503

control of the wind power system. This method has alreadyachieved a certain degree of engineering application, but itneeds to design and optimize damping parameters accordingto the actual grid characteristics. When the system oscillationfrequency drifts or the grid operation conditions change sig-nificantly, it is difficult to guarantee the suppression effectof the damping device. The method of optimizing controllerparameters [15–19] is to maximize the damping ratio of theinterconnected system by coordinating and optimizing the con-trol parameters of the wind turbine generator-side controller(MSC) and the grid-side controller (GSC), thereby changing theresonance point of the oscillation of the wind power systemand the grid interaction. This method can fundamentally reducethe risk of system instability. At present, it is only suitable foroffline stability analysis and research, and cannot realize onlineactive suppression of oscillation.

The above methods are mostly concerning single oscillationfrequency and do not consider the suppression effect at otheroscillation frequencies. Besides, the impact of variation of con-troller parameters on fundamental frequency characteristic anddynamic response characteristic of wind turbine is neglected.Compared with the existing sub/super-synchronous oscillationsuppression measures, the main contributions of the methodproposed in this paper are as follows. (1) It does not affect thedynamic characteristics of wind turbine during LVRT and canbe effectively compatible with fundamental-frequency responsecapability of wind turbine. (2) It can suppress sub/super-synchronous oscillation in power grid with different strengthswithin 0.2 s and has a good suppression effect. (3) It can adaptto multi-band sub/super-synchronous oscillation scenarios,and effectively suppress sub/super-synchronous oscillation infrequency bands of 5–40 Hz and 60–95 Hz.

The method to suppress sub/super-synchronous oscillationof direct-drive wind turbine based on energy compensation isput forward in this paper. First, the transient energy model ofdirect-drive wind turbine with grid-side converter control linksis built, and the transient energy characteristics of different con-trol links are analysed, thus the negative damping energy termsthat lead the oscillation of wind turbine are determined. On thisbasis, with the negative damping energy terms as compensationenergy terms, the corresponding voltage compensation termsare derived by backward deduction, and the supplementaryenergy branches are constructed. Further, the expressions ofcompensation energy and increment of fundamental-frequencyvoltage brought by each supplementary branch are derived.And then, define the ratio of compensation energy to incre-ment of fundamental-frequency voltage as the objective ofoptimization, and with the frequency-domain characteristic andfundamental-frequency voltage characteristic of control linksbeing satisfied as the constraints, a scheme to optimize thecompensation coefficients of multiple branches is established.The pattern search method is used to determine the optimalcompensation coefficients of supplementary branches. Finally,the model of system is built in RT-LAB for simulation tests,and simulation results verify the correctness and effectivenessof the proposed method.

2 TRANSIENT ENERGY MODELOF DIRECT-DRIVE WIND TURBINE

2.1 Transient energy model with grid-sideconverter control links

According to transient energy construction method based onnode voltage equation [20], the expression of transient energycan be obtained using the terminal and node information ofdirect-drive wind turbine:

WPMSG = ∫ Im(−I ∗G

dUG ) (1)

where UG is the bus voltage vector of direct-drive wind turbine.IG is the node injection current of direct-drive wind turbine. Immeans extracting the imaginary part of a complex.

Transform Equation (1) to dqc coordinate system of direct-drive wind turbine control system, so that the transient energyof direct-drive wind turbine can be expressed as:

WPMSG = ∫ (idcudc + iqcuqc )dΔ𝜃pll + ∫ idc d uqc − ∫ iqcd udc

(2)

where idc, iqc, udc and uqc are respectively d-axis and q-axis compo-nents of current and voltage at the terminal of direct-drive windturbine. Δθpll represents the dynamic angle of PLL generatedduring sub/super-synchronous oscillation.

Since the machine end portion of direct-drive wind turbine iselectrically decoupled from the grid, and the time scale of windspeed variation is much larger than the time scale of convertercontrol, when studying the transient energy at the machineend portion of direct-drive wind turbine during sub/super-synchronous oscillation, the impact of grid-side converter isemphasized. Besides, consider that in grid-side converter cas-cade control, voltage outer loop is dynamically decoupled fromcurrent inner loop, and the band width of voltage outer loopis smaller than the band width of current inner loop, thus thedynamic response of voltage outer loop is slow in sub/super-synchronous frequency band. Therefore, this paper is focusedon the impact of current inner loop and PLL on the transientenergy of direct-drive wind turbine grid-side converter.

The control system structure of the direct drive wind turbineas shown in Figure 1. In dqc coordinate system of direct-drivewind turbine control system, the control equations of grid-sideconverter are:

⎧⎪⎪⎨⎪⎪⎩udc =

(kp2 +

ki2

s

)(i∗

dc− idc ) − w2L2iqc + edc

uqc =

(kp2 +

ki2

s

)(i∗qc − iqc ) + w2L2idc + eqc

(3)

where kp2 and ki2 are proportion and integration coefficientsof current inner loop. i∗dc and i∗qc are d-axis and q-axis reference

2504 MA ET AL.

FIGURE 1 Control system structure of direct-drive wind turbine

values of current. w2 is the angular frequency of power grid. L2is the reactance of outlet line. edc and eqc are d-axis and q-axiscomponents of grid voltage in dqc coordinate system.

Combine Equations (2) and (3), and transform them todqs coordinate system of wind farm, so that the transientenergy of different control links in grid-side converter can beobtained:

WP = kp2 ∫[iqsd ids − idsd iqs

]+kp2 ∫ (ids + iqsΔ𝜃pll )i∗

dcdΔ𝜃pll

− kp2 ∫ (ids2 + iqs

2)Δ𝜃2pll

dΔ𝜃pll

= WP1 +WP2 +WP3 (4)

WI = ki2 ∫ i∗dc

t (ids + Δ𝜃pll iqs )dΔ𝜃pll

− ki2 ∫ (ids + Δ𝜃pll iqs )∫ (ids + Δ𝜃pll iqs )dt dΔ𝜃pll

− ki2 ∫ (iqs − Δ𝜃pll ids )∫ (iqs − Δ𝜃pll ids )dt dΔ𝜃pll

− ki2 ∫ (iqs − Δ𝜃pll ids )i∗dc

dt

= WI 1 +WI 2 +WI 3 +WI 4

(5)

WL = w2L2 ∫ (ids2 + iqs

2)Δ𝜃pll dΔ𝜃pll

+ w2L2 ∫(idsd ids + iqsd iqs

)= WL1 +WL2 (6)

where WP is the transient energy led by current-loop proportionlink. WI is the transient energy led by current-loop integrationlink. WL is the transient energy caused by the coupling betweend-axis and q-axis. ids and iqs are d-axis and q-axis measured cur-rents at the terminal of grid-side converter.

2.2 Transient energy characteristics ofdifferent control links in grid-side converter

According to Lyapunov’s second stability theorem, for a freedynamic system, if the variation rate of system overall energyW (W > 0) with time W(x) is constantly negative, system over-all energy will keep decreasing until it reaches the minimumvalue, when the system will be stable in an equilibrium state.Therefore, by analysing the accumulation and consumptiontrends of the overall energy of direct-drive wind turbine WPMSG,the stability of system can be identified. If ΔWPMSG keepsdecreasing, i.e. if ΔWPMSG is constantly negative, direct-drivewind turbine will absorb transient energy during sub/super-synchronous oscillation and exhibit positive damping character-istic. In this case, system oscillation will gradually converge andthe system will go stable. Otherwise, if ΔWPMSG is constantlypositive, direct-drive wind turbine will continuously generatetransient energy during oscillation and exhibit negative damp-ing characteristic, causing the system to become unstable.

In the transient energy model of direct-drive wind turbine,the damping characteristic of transient energy of differentcontrol links is the key factor that determines whether theoscillation of direct-drive wind turbine converges or not. Thus,screening out the control links that generate negative dampingenergy is key to suppressing oscillation and guaranteeing thestable operation of system. The transient energy characteristicsof different control links in grid-side converter are analysed asfollows.

During sub/super-synchronous oscillation, sub/super-synchronous frequency (w−/w+) current components can beexpressed as: {

�id s = Id e𝜆t cos(wst + 𝜑d )

�iqs = Iqe𝜆t sin(wst + 𝜑q )(7)

where Id, Iq,φd andφq are the amplitudes and initial phase anglesof d-axis and q-axis components of oscillation current. λ is theoscillation attenuation coefficient. ws is the frequency of oscilla-tion current, ws = w+−w2 = w2−w−.

Due to sub/super-synchronous frequency voltage compo-nents, PLL dynamic angle will be generated, which can beexpressed as:

Δ𝜃pll = −kp𝜃 ∫ Δuqsdt − ki𝜃 ∫ ∫ Δuqsdt dt

= 𝜃0 + Δ𝜃1e𝜆t sin (wst + 𝛽) (8)

where kpθ and kiθ are proportion and integration coefficientsof PLL. θ0 is the phase angle caused by outlet line reactance.Δθ1 and β are the oscillation amplitude and initial phase angleof PLL dynamic angle.

Apply Equations (7) and (8) to Equations (4), (5) and (6), sothat the variation rate of transient energy of each control link ingrid-side converter can be obtained:

ΔWP1 = −kp2WsId Iqe2𝜆t cos(𝜑d − 𝜑q ) (9)

MA ET AL. 2505

ΔWP2 =12

kp2Wsi∗dc

IdΔ𝜃1e2𝜆t cos(𝜑d − 𝛽) (10)

ΔWP3 = −kp2Wsids0Id𝜃1e2𝜆t cos(𝜑d − 𝛽) (11)

ΔWI 1 =12

ki2WsIdΔ𝜃1e2𝜆t cos(𝜑d − 𝛽)∫ i∗dc

dt (12)

ΔWI 2 =12

ki2Wsids0tIdΔ𝜃1e2𝜆t cos(𝜑d − 𝛽) (13)

ΔWI 3 =12

ki2ws𝜃0iqs0t IdΔ𝜃1e2𝜆t cos(𝜑d − 𝛽) (14)

ΔWI 4 = −12

ki2iqs0i∗dc

(15)

ΔWL1 = w2L2Wsids0𝜃0Δ𝜃1Id e2𝜆t cos(𝜑d − 𝛽) (16)

ΔWL2 =12𝜆(I 2d+ I 2

q

)e2𝜆t ≈ 0 (17)

where ids0 and iqs0 are d-axis and q-axis components of steady-state current at the terminal of grid-side converter.

The variation rates of transient energy of different controllinks ΔWPMSG characterize the accumulation and consumptiontrends of the overall energy of direct-drive wind turbine, andthe sign of ΔWPMSG (being positive or negative) directly deter-mines the stability of system. It can be seen from Equations (9)–(16) that, the sign of ΔWP1 is determined by cos(φd−φq), andthe signs of Equations (10)-(16) are determined by cos(φd−β).Angular differences φd−φq and φd−β have to do with the ini-tial phase angles of sub/super-synchronous frequency currentand voltage and PLL dynamic angle, which are analysed in detailbelow.

a. Initial phase angle of sub/super-synchronous frequency cur-rent and voltage

The initial phase angle of sub/super-synchronous frequencycurrent and voltage can be obtained by extending sub/super-synchronous frequency components:

cos(𝜑d − 𝜑q ) =1

Id Iq

(I+

2 − I−2)

(18)

cos(𝜑d − 𝜙q ) =

1IdUq

[I+U+ cos(𝛼+ − 𝜀+ ) + I−U+ cos(𝛼− − 𝜀+ )

−I+U− cos(𝛼+ − 𝜀− ) − I−U− cos(𝛼− − 𝜀− )

](19)

sin(𝜑d − 𝜙q ) =

1IdUq

[I+U+ sin(𝛼+ − 𝜀+ ) + I−U+ sin(𝛼− − 𝜀+ )

−I+U− sin(𝛼+ − 𝜀− ) − I−U− sin(𝛼− − 𝜀− )

](20)

where I−, I+, α− and α+ are the amplitudes and initial phaseangles of sub/super-synchronous frequency phase-A current.

U−, U+, ε− and ε+ are the amplitudes and initial phase angles ofsub/super-synchronous frequency phase-A voltage. Uq and ϕq

are the amplitude and initial phase angle of the q-axis oscillationvoltage.

When oscillation occurs in direct-drive wind turbine, super-synchronous frequency components are usually larger than sub-synchronous frequency components, thus Equation (18)>0,i.e. cos(𝜑d − 𝜑q) > 0. Meanwhile, φd−ϕq in Equations (19)and (20) can be approximated to the difference between initialphase angles of super-synchronous frequency current andsuper-synchronous frequency voltage. Since the reference valueof reactive power of outer-loop control is set to be 0, andthe reference value of active power is rated value, the outputpower is mainly active power. Thus, the difference betweeninitial phase angles of super-synchronous frequency current andsuper-synchronous frequency voltage is approximately 0, i.e.φd−ϕq ≈ 0. Therefore, the value of cos(φd−ϕq) in Equa-tions (19) is positive and much larger than sin(φd−ϕq) inEquation (20).

b. Initial phase angle of PLL dynamic angle

Detailed derivation of Equation (8) reveals that, the initialphase angle of PLL dynamic angle𝛽has to do with the ini-tial phase angle of q-axis sub/super-synchronous frequencyvoltage ϕq, i.e. β = ϕq + ϕ, where ϕ satisfies the followingequations:

⎧⎪⎪⎪⎨⎪⎪⎪⎩

sin𝜙 =kp𝜃

(ws

2 + 𝜆2)√

kp𝜃2(ws

2 + 𝜆2)2+ ki𝜃

2ws

2

cos𝜙 =ki𝜃ws√

kp𝜃2(ws

2 + 𝜆2)2+ ki𝜃

2ws

2

(21)

where cosϕ and sinϕ are both positive, and sinϕ is slightly largerthan cosϕ.

Apply β = ϕq + ϕ to cos(φd−β), so that

cos(𝜑d − 𝛽) = cos(𝜑d − 𝜙q )cos𝜙 + sin(𝜑d − 𝜙q )sin𝜙 (22)

Consider that the value of cos(φd−ϕq) in Equation (19)is positive and much larger than sin(φd−ϕq) in Equation(20),Equation (22) is constantly positive, i.e. cos(φd−β) > 0.

Therefore, Equations (9), (11), (13) and (15) are constantlynegative, Equation (17) is approximately 0,ΔWP1,ΔWP3,ΔWI2,ΔWI4 and ΔWL2 have positive damping effect on system oscil-lation and make for the converging of oscillation. Equations(10), (12), (14) and (16) are constantly positive, i.e. ΔWP2, ΔWI1,ΔWI3 and ΔWL1 are positive, thus they have negative damp-ing effect on system oscillation and make against the stability ofsystem. The amplitude of ΔWI3 is much smaller than the ampli-tudes of the other three terms, thus ΔWI3 can be neglected. Theenergy flow diagram of the direct-drive wind turbines is shownin Figure 2. The oscillation component is introduced throughthe PLL and the current loop. The d-axis current loop control

2506 MA ET AL.

FIGURE 2 The energy flow diagram of the direct-drive wind turbines

link, the q-axis current loop proportional link and the dq-axiscross coupling link through the PLL interact to generate nega-tive damping energy and increase the total energy of the system.The positive damping energy flows through the interaction ofthe PLL and the q-axis current loop integral link and the dq-axisproportional links of the current loop act independently to gen-erate positive damping energy and reduce the total energy of thesystem.

Based on the above analysis, WP2, WI1 and WL1 are the neg-ative damping energy terms that lead the oscillation of direct-drive wind turbine.

3 METHOD TO SUPPRESSSUB/SUPER-SYNCHRONOUSOSCILLATION OF DIRECT-DRIVE WINDTURBINE

During sub/super-synchronous oscillation, the negative damp-ing energy of direct-drive wind turbine is the key factor thataffects the stability of system. By reducing or compensat-ing for negative damping energy, the dissipation of systemenergy can be accelerated, thus sub/super-synchronous oscilla-tion can be suppressed. Thus, a method to suppress sub/super-synchronous oscillation of direct-drive wind turbine based onenergy compensation is put forward. With the negative dampingenergy as compensation energy, supplementary energy branchesare constructed, and in order for them to be compatible withfundamental frequency characteristic of direct-drive wind tur-bine, the supplementary energy branches are further optimized.

3.1 Design of supplementary energybranches

Backward deduction method is used to construct supplemen-tary energy branches. First, search for transient energy terms

in Equation (2), which are similar to negative damping energyterms. And then, eliminate the current terms in negative damp-ing energy terms which are the same as the similar terms, andthe rest part in negative damping energy terms are voltage com-pensation terms. Energy compensation can be converted tovoltage compensation, thus the voltage compensation terms canbe used to design supplementary energy branches.

Take negative damping energy WP2 for example, the detailedprocess of obtaining the corresponding voltage compensationterm is illustrated. First, transform WP2 in Equation (4) to dqc

coordinate system of direct-drive wind turbine control system:

WP2 = kp2 ∫ i∗dc

idc dΔ𝜃pll (23)

Compared with the expression of transient energy in Equa-tion (2), it can be seen that the expression of WP2 in Equation(23) is similar to the first term in Equation (2), i.e. ∫ idcudcdΔ𝜃pll ,both containing current term idc. Eliminate current term idc inWP2, so that the voltage compensation term can be obtained:

Δudc1 = −kp2i∗dc

(24)

Similarly, compare WI1 in Equation (5) and WL1 in Equation(6) with Equation (2), so that the corresponding voltage com-pensation terms can be extracted:

Δudc2 = −ki2 ∫ i∗dc

dt (25){�udc3 = −w2L2idc�𝜃pll

�uqc3 = −w2L2iqc�𝜃pll

(26)

For Equations (24) and (25), the input term is i∗dc, and the out-put terms are Δudc1 and Δudc2, which respectively represent pro-portion and integration control links, thus Equations (24) and(25) can form a PI controller. For Equation (26), the input termsare idc and iqc, and the output terms are Δudc3 and Δuqc3, whichrepresent proportion control links with equal d-axis and q-axisproportion coefficients. According to voltage compensationterms in Equations (24)–(26), supplementary energy branchesVP2, VI1 and VL1 are constructed, as shown in Figure 3.

Apply Equations (24)–(26) to Equation (2), so that the energyincrements brought by supplementary energy branches can beobtained:

WVP2 = 2kp2i∗dc ∫ idcΔ𝜃pll dΔ𝜃pll − kp2 ∫ i∗

dcidc dΔ𝜃pll

= We1 −WV 1 (27)

WVI 1 = ki2 ∫ iqc i∗dc

dt + 2ki2 ∫ i∗dc

t iqcΔ𝜃pll dΔ𝜃pll

− ki2 ∫ i∗dc

idctdΔ𝜃pll

= We2 −WV 2 (28)

MA ET AL. 2507

FIGURE 3 Supplementary energy branches

WVL1 = w2L2 ∫ Δ𝜃pll (iqc d idc − idc d iqc )

− w2L2 ∫ (idc2 + iqc

2)Δ𝜃pll dΔ𝜃pll

= We3 −WV 3 (29)

After energy branches VP2, VI1 and VL1 are added, theenergy increments contain two parts: WV1, WV2 and WV3 arenecessary compensation energy; We1, We2 and We3 are extraintroduced energy.

It can be seen from Equations (4)–(6), (9)–(17) and (27)–(29)that, WV1, WV2 and WV3 in dqc coordinate system are essen-tially negative damping energy WP2, WI1 and WL1 in dqs coor-dinate system. WP2, WI1 and WL1 contain the product term ofws (the difference between sub/super-synchronous frequencyand fundamental frequency), which corresponds to frequency-dependent compensation for the negative damping energy byeach supplementary branch. The bigger ws is, the larger thecompensated negative damping energy is, and the more evidentthe compensation effect of supplementary branch is. Mean-while, the impact of extra introduced energy We1, We2 andWe3 on system stability is analysed. The detailed expressionsof energy variation rate ΔWe1, ΔWe2 and ΔWe3 are shown inAppendix. It can be seen that, the components of ΔWe1, ΔWe2and ΔWe3 are mostly periodical, and the integration of ΔWe1,ΔWe2 and ΔWe2 in one oscillation period is approximately 0,thus extra introduced energy We1, We2 and We3 scarcely addto system energy, and their impact on system stability can beneglected.

The supplementary energy branches can realize frequency-dependent compensation for negative damping energy andimprove the stability of wind turbine during sub-synchronousoscillation. However, in fundamental-frequency normal opera-tion state, the introduction of supplementary energy brancheswill increase the output voltage of grid-side converter andmay change the fundamental frequency characteristic of windturbine. Therefore, the impact of each supplementary energy

branch on the fundamental frequency characteristic of wind tur-bine needs to be analysed.

Since PLL dynamic angle Δθpll is caused by supplementaryenergy branches and do not exist in fundamental frequency,when energy branches VP2, VI1 and VL1 are added, the incre-ments of fundamental-frequency voltage are:

Δu∗dc1 = −kp2i∗

dc(30)

Δu∗dc2 = −ki2 ∫ i∗

dcdt (31)

{�u∗

dc3 = 0

�u∗qc3 = 0

(32)

It can be seen from Equations (30)–(32) that, in fundamen-tal frequency, supplementary branches VP2 and VI1 mainlyaffect d-axis current inner-loop control, weakening PI steady-state error control of current inner loop, thus they will affect thefundamental-frequency voltage of wind turbine. The output ofsupplementary branch VL1 in fundamental frequency is 0, thusit does not affect the fundamental-frequency voltage of windturbine. In view of the compensation capability of differentsupplementary branches and their impact on the fundamental-frequency voltage, the control parameter of each supplementaryenergy branch should be appropriately set in order to realizeeffective suppression of oscillation.

3.2 Optimization of supplementary energybranches

In order to improve the compensation capability of supple-mentary energy branches without affecting the fundamental fre-quency characteristic of direct-drive wind turbine, a scheme tooptimize the supplementary energy branches is proposed. Withthe compensation energy of each branch being the maximumand the increment of fundamental-frequency voltage being theminimum as the objective, the compensation coefficient of eachsupplementary energy branch is optimized.

3.2.1 Objective function

The ratio of compensation energy to increment of fundamental-frequency voltage is defined as the objective of optimization, i.e.

max f =

|||∑n

i=1 kViWVi|||||||∑n

i=1 kViΔu∗d (q)c i

||||(33)

where kVi is the compensation coefficient of the ith supplemen-tary energy branch. WVi is the compensation energy of the ithsupplementary energy branch. Δu∗d(q)ci is the increment of d/q-axis fundamental-frequency voltage of the ith supplementary

2508 MA ET AL.

energy branch. n is the total number of supplementary energybranches, in this paper n = 3.

3.2.2 Constraints

Value range of compensation coefficientsConsider that supplementary branches VP2, VI1 and VL1 allaffect the control structure of current loop, to guarantee the sta-ble operation of control links after supplementary branches areadded, the parameter interval of compensation coefficient ofeach supplementary branch is designed referring to the stabilitycharacteristic of closed-loop system in the frequency domain.

Convert Equations (24)–(26) to the frequency domain andapply them to Equation (3), so that the transfer functions ofclosed-loop systems with supplementary energy branches canbe obtained:

TVPI (s) =

[1 − kV 1]

kp2s

L2+

[1 − kV 2] ki2

L2

s2 +[1 − kV 1]

kp2s

L2+

[1 − kV 2] ki2

L2

(34)

TVL1(s) =kV 3w2Δ𝜃pll

s + kV 3w2Δ𝜃pll

(35)

where Equation (34) is a typical second-order system with sup-plementary branches VP2 and VI1. Equation (35) is a typicalfirst-order system with d-axis branch of VL1. The system withq-axis branch of VL1 is similar to Equation (35) and is notrepeated here.

According to frequency-domain characteristics of closed-loop system, the compensation coefficient of each supplemen-tary branch can be calculated:

⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩

kV 1 =

1 − L2𝜔2PIc

(√1 + 4𝜉4

t − 2𝜉2t

)kp2

kV 2 =

1 − 2L2𝜔PIc

(√√1 + 4𝜉4

t − 2𝜉2t

)ki2

kV 3 =𝜔Lc

w2�𝜃pll

(36)

where ξt is the damping ratio of supplementary branches VP2and VI1. ωPIc = 2π*fPIc, where fPIc is the control bandwidth ofsupplementary branches VP2 and VL1. ωLc = 2π*fLc, where fLc

is the control bandwidth of supplementary branch VL1.It can be seen from Equation (36) that, the compensation

coefficient of each supplementary branch is determined by thedamping ratio or control bandwidth. To ensure the speed andsmoothness of supplementary branches, the damping ratio usu-ally satisfies: 0.4 ≤ ξt ≤ 0.8. Meanwhile, consider that the danger-ous frequency bands where sub/super-synchronous oscillationmay occur when direct-drive wind turbine is integrated to weak

power grid are 20–30 Hz and 70–80 Hz [21], fPIc and fLc canbe set as: 20 ≤ fPIc, fLc ≤ 30, 70 ≤ fPIc, fLc ≤ 80. According tothe value ranges of damping ratio and control bandwidth, theparameter intervals of compensation coefficients can be deter-mined:

⎧⎪⎨⎪⎩kV 1 ∈

[kV 1 min , kV 1 max]

kV 2 ∈[kV 2 min , kV 2 max]

kV 3 ∈[kV 3 min , kV 3 max]

(37)

where kV1min, kV1max, kV2min, kV2max, kV3min and kV3max canbe calculated according to Equation (36).

Constraints of fundamental-frequency voltageTo ensure the normal operation of direct-drive wind turbineafter supplementary energy branches are added, the incrementof fundamental-frequency voltage brought by supplementarybranches must not exceed the allowed range. According togeneral requirement on grid connection of wind turbine, theallowed voltage deviation in normal operation state is −10–10%, but consider the requirement of output and stability mar-gin, the voltage deviation is set to be between −5–5%, i.e. theincrement of fundamental-frequency voltage brought by sup-plementary branches should satisfy:√√√√ n∑

i=1

(kViΔu∗

d (q)c i

)2 ≤ 5%Un (38)

where Un is the rated voltage at the terminal of direct-drive windturbine, the per unit value of which is 1.

3.2.3 Optimization scheme

Concerning the above model to optimize the compensationcoefficients of supplementary energy branches, the patternsearch method is used to determine the optimal compensationcoefficients.

Step 1: Measure the data of voltage and current at theterminal of direct-drive wind turbine online, and cal-culate the compensation energy of each supplementarybranch according to Equations (27)–(29); calculate theincrement of fundamental-frequency voltage broughtby each supplementary branch according to Equations(30)–(32). And determine the parameter interval of eachcompensation coefficient according to Equations (36)and (37).

Step 2: Set the initial values of compensation coefficientskV1, kV2 and kV3. If a certain group of compensationcoefficients x1 satisfies the constraints in Equation (38),x1 is a feasible solution, i.e. the current optimal solution.Otherwise, set new initial values until any feasible solu-tion is found.

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FIGURE 4 Diagram of hardware-in-loop platform

TABLE 1 Parameters of direct-drive wind turbine

Symbol Parameter Value

Un Rated line voltage 0.69 kV

fn Rated frequency 50 Hz

Udc DC voltage 1.2 kV

L2 Filter inductance 2 mH

Lg Grid inductance 7 mH

fc Switching frequency 6 kHz

fs Sampling frequency 6 kHz

kp2, ki2 Parameters of current loop 0.0005, 0.1238

kpθ, kiθ Parameters of PLL 0.67, 38.2

Step 3: Based on the current optimal solution xi (i = 1, 2,3…), use the pattern search method to update the com-pensation coefficients. For new feasible solution xi+1that satisfies Equation (38), calculate the objective func-tion in Equation (33). If fi+1 > fi, xi+1 is the currentoptimal solution; otherwise, repeat Step 3.

Step 4: Repeat the search process until the number of iter-ations is satisfied. The current optimal solution is theoptimal compensation coefficient.

4 SIMULATION ANALYSIS

4.1 Test system

A model of power system integrated with direct-drive wind tur-bines is built in RTLAB for simulation tests, as shown in Fig-ure 4. Direct-drive wind turbines are collected to the bus via0.69/20kV field transformer and then connected to PCC (pointof common coupling) via 20/230kV transformer. The mainparameters of direct-drive wind turbine are shown in Table 1.

To verify the correctness and effectiveness of the proposedmethod, different sub/super-synchronous oscillation cases withdifferent power grid strengths are set in this paper, i.e. diverg-ing oscillation (Case 1), constant-amplitude oscillation (Case 2)and converging oscillation (Case 3). Concerning the three cases,the variation of transient energy of different control links ingrid-side converter and the suppression effect of supplementaryenergy branches are analysed.

FIGURE 5 Transient energy of different control links in grid-sideconverter in Case 1, Case 2 and Case 3(a) Case 1, (b) Case 2, (c) Case 3

4.2 Transient energy of different controllinks in grid-side converter

According to Equations (4)–(6), the transient energy of differ-ent control links in grid-side converter in Case 1, Case 2 andCase 3 is calculated (per unit values of variables are used in thecalculation and with 0 s as the oscillation start time). The simu-lation curves of transient energy are shown in Figure 5.

It can be seen from Figure 5(a,c) that, in Case 1, Case 2and Case 3, WP1, WP3, WI2 and WL2 are all negative, so aretheir variation rates, thus the corresponding control links exhibitpositive damping characteristic, they keep absorbing transientenergy, which makes for the stability of system. WI4 and its vari-ation rate is approximately 0, which basically has no effect onsystem stability. WP2, WI1, WI3 and WL1 are all positive, so aretheir variation rates, thus the corresponding control links exhibitnegative damping characteristic, they keep generating transientenergy, causing the system to go unstable. The amplitude ofWP1 is the largest, the amplitudes of WP2, WP3, WI1 and WI2

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FIGURE 6 Variation of compensation coefficients kV1 and kV2

are relatively large, while the amplitudes of WI3, WI4, WL1 andWL2 are relatively small, and the amplitude of WI3 and WL2are next to 0. The above simulation results verify the dampingcharacteristics of different control links in grid-side converteranalysed in Section 2.2. During sub/super-synchronous oscilla-tion, WP2, WI1 and WL1 are the negative damping energy termsthat lead the oscillation of direct-drive wind turbine. Thus, thecorresponding d-axis current loop control link and d-axis andq-axis cross-coupled control links have leading effect on systemoscillation, while q-axis current loop control link scarcely affectsthe oscillation.

4.3 Suppression effect of supplementaryenergy branches

Construct supplementary energy branches according to themethod proposed in Section 3.1, and combining the simulationdata of Case 1, the model to optimize the compensation coeffi-cients of multiple branches is built according to Equations (33)–(38). And then the pattern search method is used to determinethe optimal compensation coefficients. Since supplementarybranch VL1 does not generate any increment of fundamental-frequency voltage, its compensation coefficient kV3 is set torender its compensation energy the maximum. kV3 appliesthe maximum value in the parameter interval. Optimization ofcompensation coefficients of supplementary branches VP2 andVI1 is shown in Figure 6. It can be seen that, the bigger kV1is and the smaller kV2 is, the bigger the ratio of compensationenergy to increment of fundamental-frequency voltage is, andthe better compatible supplementary energy branches are withcompensation capability and impact on fundamental frequencycharacteristic. Therefore, the optimal compensation coefficientsare designed as: kV1 = 3.358, kV2 = 7.109 and kV3 = 0.0769.

To verify the effectiveness of the proposed supplemen-tary energy branches, the suppression effects of supplemen-tary energy branches corresponding to different grid strengthsand different oscillation frequencies are analysed. Besides, theimpact of supplementary energy branches on the fundamentalfrequency characteristic of wind turbine is verified.

4.3.1 Suppression effects of supplementaryenergy branches corresponding to different gridstrengths

Suppose the optimal supplementary energy branches are addedin Case 1, Case 2 and Case 3, and the variation curves ofoutput power of direct-drive wind turbine are shown in Fig-ure 7(a,c). By regulating the parameters of power grid, thesuppression effects of supplementary energy branches corre-sponding to different grid strengths can be obtained, shown inFigure 7(d).

It can be seen from Figure 7(a,c) that, after supplementaryenergy branches are added in Case 1, Case 2 and Case 3, theoscillation amplitude of output power of direct-drive wind tur-bine immediately drops, and the oscillation converges to stablestate within 0.2 s. According to Figure 7(d), for different gridstrengths, the dropping degree and converging trend of oscilla-tion amplitude are almost the same, and the oscillation can allbe effectively suppressed within 0.2 s.

4.3.2 Suppression effects of supplementaryenergy branches corresponding to differentoscillation frequencies

The oscillation in Case 1, Case 2 and Case 3 are all sub/super-synchronous oscillation with frequency of 28/72 Hz, where thesupplementary energy branches have relatively good suppres-sion effect. To verify the adaptability of supplementary energybranches to different oscillation frequency bands, forced oscilla-tion is used. Suppose 5–100 Hz harmonic current is injected tothe grid which causes oscillation to occur in the system, and thesuppression effect of supplementary energy branches is shownin Figure 8.

It can be seen from Figure 8(a,b) that, grid-side injected har-monic current causes forced oscillation to occur in the systemat t = 1 s. When the forced oscillation is in 40–60 Hz fre-quency band, which does not belong to the range of sub/super-synchronous frequency, the output power of direct-drive windturbine has no obvious variation after supplementary branchesare added, i.e. supplementary energy branches basically have nosuppression effect in this frequency band. According to Fig-ure 8(c,h), when the forced oscillation is in 5–40 Hz or 60–95 Hz frequency bands, the oscillation amplitude of outputpower obviously drops after supplementary energy branchesare added, i.e. the suppression effect of supplementary energybranches is relatively good in these frequency bands. How-ever, due to the existence of external disturbance, the oscilla-tion of wind turbine cannot converge. If the injected currentis removed, the oscillation will converge rapidly. Besides, thebigger the difference between oscillation frequency and fun-damental frequency is (i.e. the higher super-synchronous fre-quency is or the lower sub-synchronous frequency is), the largerthe negative damping energy compensated by supplementarybranches is, and the more obvious the oscillation suppressioneffect is.

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FIGURE 7 Variation of active power aftersupplementary energy(a) Supplementary energy branches are added inCase 1, (b) supplementary energy branches are addedin Case 2, (c) supplementary energy branches areadded in Case 3, (d) suppression effects ofsupplementary energy branches corresponding todifferent grid strengths

FIGURE 8 Suppression effects of supplementary energy branches corresponding to different oscillation frequencies(a) 45/55 Hz, (b) 40/60 Hz, (c) 35/65 Hz, (d) 30/70 Hz, (e) 25/75 Hz, (f) 20/80 Hz, (g) 10/90 Hz, (h) 5/95 Hz

2512 MA ET AL.

FIGURE 9 Impact of supplementary energy branches on fundamental-frequency voltage of wind turbine(a) The variation curves of d-axis voltage, (b) The variation curves of q-axis voltage

FIGURE 10 Variation of current and voltage of wind turbine aftersupplementary energy branches are added during LVRT(a) The variation curves of output d-axis current of wind turbine during LVRTwithout supplementary energy branches, (b) the variation curves of outputd-axis current of wind turbine during LVRT with supplementary energybranches, (c) the variation curves of output voltage of wind turbine duringLVRT without supplementary energy branches, (d) the variation curves ofoutput voltage of wind turbine during LVRT with supplementary energybranches

4.3.3 Impact of supplementary energy brancheson fundamental frequency characteristic ofdirect-drive wind turbine

Furthermore, the impact of supplementary energy branches onthe fundamental frequency characteristic of direct-drive windturbine is analysed. Suppose supplementary energy branches areadded at certain moment in normal operation state, the variationof fundamental-frequency voltage of wind turbine is shown inFigure 9. On this basis, LVRT simulation case is set to verifythe compatibility of supplementary energy branches with fun-damental frequency response of wind turbine. The variationcurves of output current and voltage of wind turbine duringLVRT are shown in Figure 10.

It can be seen from Figure 9(a,b) that, after supplementaryenergy branches are added, the output voltage of direct-drivewind turbine fluctuates, but the maximum fluctuation amplitudeis only 0.02p.u, thus the constraints of fundamental-frequencyvoltage in (38) are still satisfied, i.e. the impact of supplemen-tary branches on normal operation of direct-drive wind turbineis relatively small. It can be seen from Figure 10(a,b) that,when supplementary energy branches are added, the variationamplitude of current of wind turbine during LVRT is relativelysmall, thus system operation is not affected. According to Fig-ure 9(c,d), when supplementary energy branches are added, thevoltage of wind turbine scarcely changes, thus the LVRT charac-teristic of wind turbine is not affected. Therefore, the proposedsupplementary energy branches are proved to be compati-ble with fundamental frequency dynamic response of windturbine.

The above simulation results verify the correctness andeffectiveness of the proposed method to suppress sub/super-synchronous of direct-drive wind turbine based on energy com-pensation.

5 CONCLUSION

A method to suppress sub/super-synchronous oscillation ofdirect-drive wind turbine based on energy compensation is pro-posed in this paper, the correctness and feasibility of which areverified by theoretical analysis and simulation tests. The mainconclusions are as follows.

1. The positive damping energy and negative damping energyin system transient energy are key factors that characterizethe stability level of system. In the transient energy modelof direct-drive wind turbine, WP2, WI1 and WL1 are negativedamping energy terms which reflect the amount of energyaccumulated after the system is disturbed, thus they lead theoscillation and make against the stability of system.

2. Supplementary energy branches corresponding to the nega-tive damping energy terms are constructed, and a scheme tooptimize the compensation coefficients of multiple branchesis established based on the ratio of compensation energy toincrement of fundamental-frequency voltage. The optimized

MA ET AL. 2513

supplementary energy branches do not affect the dynamiccharacteristics of wind turbine during LVRT and are compat-ible with fundamental-frequency response capability of windturbine.

3. The proposed supplementary energy branches can effec-tively reduce the negative damping energy and improve thestability level of direct-drive wind turbine. They can suppresssub/super-synchronous oscillation in power grid with dif-ferent strengths within 0.2 s and can suppress sub/super-synchronous oscillation in frequency bands of 5–40 Hz and60–95 Hz.

ACKNOWLEDGMENT

This work was supported by National Natural Science Founda-tion of China (51777070).

NOMENCLATURE

UG voltage vector of direct-drive wind turbineIG injection current of direct-drive wind tur-

bineidc, iqc, udc, uqc d-axis and q-axis components of current and

voltage at the terminal of direct-drive windturbine

Δθpll dynamic angle of PLLkp2, ki2 proportion and integration coefficients of

current inner loopi∗dc, i∗qc d-axis and q-axis reference values of current

L2 reactance of outlet lineedc, eqc d-axis and q-axis components of grid volt-

age in dqc coordinate systemWP transient energy led by current-loop pro-

portion linkWI transient energy led by current-loop integra-

tion linkWL transient energy caused by the coupling

between d-axis and q-axisids, iqs d-axis and q-axis measured currents at the

terminal of grid-side converterId, Iq, φd, φq amplitudes and initial phase angles of d-axis

and q-axis components of oscillation cur-rent

λ oscillation attenuation coefficientws frequency of oscillation current

kpθ, kiθ proportion and integration coefficients ofPLL

θ0 phase angle caused by outlet line reactanceΔθ1, β oscillation amplitude and initial phase angle

of PLL dynamic angleids0, iqs0 d-axis and q-axis components of steady-

state current at the terminal of grid-sideconverter

I−, I+, α−, α+ amplitudes and initial phase angles ofsub/super-synchronous frequency phase-Acurrent

U−, U+, ε−, ε+ amplitudes and initial phase angles ofsub/super-synchronous frequency phase-Avoltage

Uq, ϕq amplitude and initial phase angle of q-axisoscillation voltage

VP2, VI1, VL1 supplementary energy branchesWV1, WV2, WV3 necessary compensation energy

We1, We2, We3 extra introduced energykVi compensation coefficient of the ith supple-

mentary energy branchWVi compensation energy of the ith supplemen-

tary energy branchΔu∗d(q)ci increment of d/q-axis fundamental-

frequency voltage of the ith supplementaryenergy branch

n total number of supplementary energybranches

ξt damping ratio of supplementary branchesVP2 and VI1

fPIc control bandwidth of supplementarybranches VP2 and VL1

fLc control bandwidth of supplementarybranch VL1

Un rated voltage at the terminal of direct-drivewind turbine

ORCID

Jing Ma https://orcid.org/0000-0002-8085-414X

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How to cite this article: Ma, J., Zhang, M., Phadke,A. G.: Research on sub/super-synchronous oscillationsuppression method for direct-drive wind turbine basedon energy compensation. IET Renew. Power Gener. 15,2502–2514 (2021). https://doi.org/10.1049/rpg2.12182

APPENDIX A

The variation rates of extra energy introduced by supplementaryenergy branches ΔWe1, ΔWe2 and ΔWe3 can be expressed as:

Δwe1= − 2kp2i∗dc

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

wsiqs0𝜃0Δ𝜃1e𝜆t cos(wst + 𝛽) − ws𝜃02ids0Δ𝜃1e𝜆t cos(wst + 𝛽)

+12

ws𝜃0IqΔ𝜃1e2𝜆t sin(wst + 𝜑q + 𝛽) +12

wsiqs0Δ𝜃12e2𝜆t sin(2wst + 2𝛽)

+12

ws𝜃0IqΔ𝜃1e2𝜆t sin(𝜑q − 𝛽) −12

wsids0𝜃0Δ𝜃12e2𝜆t sin(2wst + 2𝛽)

−12

ws𝜃02IdΔ𝜃1e2𝜆t cos(wst + 𝜑d + 𝛽) −

12

ws𝜃02IdΔ𝜃1e2𝜆t cos(𝜑d − 𝛽)

−12

wsids0𝜃0Δ𝜃12e2𝜆t sin(2wst + 2𝛽)

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(A.1)

ΔWe2 = −ki2i∗dc

⎡⎢⎢⎢⎢⎣iqs0 − ids0𝜃0 + e𝜆t Iq sin(wst + 𝜑q ) − ids0Δ𝜃1e𝜆t sin(wst + 𝛽)

−𝜃0e𝜆t Id cos(wst + 𝜑d ) + 2iqs0𝜃0Δ𝜃1e𝜆t sin(wst + 𝛽)

−𝜃0Δ𝜃1e2𝜆t Iq cos(2wst + 𝜑q + 𝛽) + 𝜃0Δ𝜃1e2𝜆t Iq cos(𝜑q − 𝛽)

⎤⎥⎥⎥⎥⎦− 2kp2i∗

dct

⎡⎢⎢⎢⎣wsiqs0𝜃0Δ𝜃1e𝜆t cos(wst + 𝛽) − ws𝜃0

2ids0Δ𝜃1e𝜆t cos(wst + 𝛽)

+12

ws𝜃0IqΔ𝜃1e2𝜆t sin(wst + 𝜑q + 𝛽) +12

ws𝜃0IqΔ𝜃1e2𝜆t sin(𝜑q − 𝛽)

⎤⎥⎥⎥⎦ (A.2)

ΔWe3 = w2L2

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣

wsId Iq (𝜃0 + 𝜃03)e2𝜆t cos(𝜑d − 𝜑q )

+wsiqs0(𝜃0 + 𝜃03)e𝜆t Id sin(wst + 𝜑d )

+wsids0(𝜃0 + 𝜃03)e𝜆t Iq cos(wst + 𝜑q )

−(i2ds0 + i2

qs0)(𝜃0 + 2𝜃03)wsΔ𝜃1e𝜆t cos(wst + 𝛽)

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦(A.3)