Harmonic Susceptibility Study of DC Collection Network Based on Frequency Scan and Discrete Time-Domain Modelling Approach

.e equivalent model of offshore DC power collection network for the harmonic susceptibility study is proposed based on the discrete time-domain modelling technique and frequency scan approach in the frequency domain..e proposedmethodology for modelling a power converter and a DC collection system in the frequency domain can satisfy harmonic studies of any configuration of wind farm network and thereby find suitable design of power components and array network. .e methodology is intended to allow studies on any configuration of the wind power collection, regardless of choice of converter topology, array cable configuration, and control design. To facilitate harmonic susceptibility study, modelling DC collection network includes creating the harmonic model of the DC turbine converter and modelling the array network. .e current harmonics within the DC collection network are obtained in the frequency domain to identify the resonance frequency of the array network and potential voltage amplification issues, where the harmonic model of the turbine converter is verified by the comparison of the converter switching model in the PLECSTM circuit simulation tool and laboratory test bench, and show a good agreement.


Introduction
Offshore wind power is becoming an important energy resource in Europe. However, electrical power losses are always a concern in the operation of wind farm with longrange power transmission. To reduce losses, researchers look to replace AC with DC in the entire path from the wind turbine, through power collection and transmission to shore. Medium-voltage DC (MVDC) collection of wind power is an attractive solution to reduce overall losses and installation cost [1,2]. e article [2] addresses cost-efficient solution to form the multiterminals of DC grid with the diode rectifier unit (DRU). However, the solution of DRU can produce a considerable harmonic current within the array network if the 6-pulse DRU topology is used. Figure 1 illustrates a DC collection network of radial type of offshore wind farm with the HVDC transmission. is general configuration in Figure 1 supports any choice of MVDC collector voltage level as well as converter topology and the number of wind power plant (WPP) clusters. For example, the turbine and offshore substation can employ any DC/DC converter topology with multiple degrees of freedom: uni-vs bidirectional power flow; modular (parallel/ series connection) vs monolithic; topology (single active bridge, dual active bridge, and more [3][4][5]). Figures 1 and 2 illustrate the details of wind farm configuration including wind turbine DC/DC converters, offshore substation converters, and onshore substation converters. e offshore wind farm is designed to generated and deliver 700 MW power from offshore to onshore [1]. e series resonant converter (SRC#) is selected as the turbine DC/DC converter based on the converter efficiency, high-voltage transfer ratio, scale of converter, and galvanic isolation property. Considering the existing converter topology and its power rating in high-power applications, the modular multilevel converter (MMC) with the galvanic isolation and unidirectional power flow control is selected to serve as the offshore substation converter to deliver the   offshore wind power to the onshore grid via the HVDC transmission line. e onshore substation captures the power from the offshore wind farm by the onshore MMC with a grid-connected 50/60 Hz transformer. e onshore substation is designed to match with onshore AC grid voltage (utility) and deliver the offshore power to the onshore AC transmission network and alleviate the influence from the grid fault.
In this study, a series resonant converter topology (named SRC#) shown in Figure 3 is selected as the candidate for DC power conversion via ±50 kV DC MVDC array network. With the series resonant converter, the DC turbine converter can take advantages of high efficiency, highvoltage transformation ratio, and galvanic fault isolation for different ratings of turbine generator [6][7][8][9]. A series resonant converter SRC# with the resonant tank on the secondary side and governed by the phase shift and a frequency-depended power flow control technique is here considered [10,11].
To synthesize the DC-connected wind turbine converter and the MVDC gird, the wind turbine converter has to meet the following requirements: (1) Control of the LVDC bus (2) High-voltage transformation from the LVDC to MVDC (3) Galvanic isolation (4) Roust and compact design Large amount of possible topology of converter topologies for a DC turbine is investigated. However, all of existing converter designs are immature technology, thus selecting an optimal topology is not a straightforward solution for converter design [12]. e turbine converter is designed to deliver the captured wind energy produced by the generator to the MVDC gird and then control the LVDC bus. Regarding power rating, number of components, and the possible solution of the turbine converter topologies in the early DC wind farm design, the hard-switched fullbridge power converter is selected as preferred topology [4,[13][14][15][16][17]. erefore, the proposed series resonant converter # (SRC#) combined with the medium-frequency transformer (MF transformer) which serves as the DC turbine converter is selected to boot the low-voltage DC (LVDC) to high-voltage DC (MVDC-side of SRC#) with a high-voltage transferring ratio and provides a galvanic isolation to make sure that the line is immune from line faults [4,18,19]. e concept of SRC is widely used in the traction applications, which is usually operated at constant frequency and subresonant mode to archive a roust and compact design target in high-voltage specifications [20][21][22][23][24]. One of famous modulation techniques (or topologies) is the half-cycle discontinuous-conduction-mode series resonant converter (HC-DCM-SRC). Under the traction applications, the DC/DC converter is tied between two DC voltages with a fixed voltage transfer ratio and the openloop control. Relying on the pulse removal technique, the bulky transformer in the classic SRC can be voided in the proposed SRC#, and thus the compact convert design can be archived [25]. More details of operation principle of SRC# is addressed Section 2.
To archive the study of harmonic susceptibility in offshore wind farm with the selected turbine converter, the analysis of array network in wind farm includes modelling the selected turbine converter (SRC#), array cable, and substation converter, where the substation converter in this study is considered as an ideal voltage source to produce DC component of MVDC and harmonic components. e objective of the study is to investigate how the harmonic affects the turbine converter and array networks. In the power collection system, the wind turbines and substation are connected together by medium-voltage DC cables. However, there are no standards or guidelines for such DC array network design, and thus some studies are still made by simply selecting commercially available medium-voltage AC submarine cables without giving any additional consideration in the cable's properties such as insulation [26].
Modelling of the array cables is an essential task for evaluating results of cable sizing by computer simulation. e complexity of modelling is dependent on the phenomenon, which will be conducted in the study case. For example, the travelling waves (voltage and current) with a finite propagation speed cause reflections. is phenomenon has to be represented on the cable model when study cases are intended to conduct the overvoltage or switching transient issues. Typically, three types of cable models, Pi Model, Bergeron model, and frequency-dependent models, which are available in the electromagnetic transient simulation program PSCAD ™ (EMTDC) for studying AC and DC power collection systems are used [27][28][29][30]. To adequately represent the cable parameters for the harmonic susceptibility studies over different frequency ranges, the frequencydependent array cable models are generated from geometric cable data based on the method [31] and recommendations proposed by the articles [32] and verified by the generated cable model in PSCAD ™ .
Although these DC alternatives promise lower electrical losses and lower bill-of-material, it is still an immature technology. As the many existing AC wind power plants, the harmonic pollution is an important issue since wind power collection systems serve by large amount of turbine converters [33][34][35][36]. Depending on the configuration of the wind power plant, every power collection system has its own inherent resonance behavior. e network, which is rich in the harmonic current, can increase the power losses and the stress of power components and cause unpredicted equipment trip. e resonance behavior inside the collection network is affected by properties of the array cable, filter designs, converter topologies, and PWM schemes. erefore, the objective of this paper is to develop a methodology to identify potential harmonic resonant problems in the DC collection network. For example, the phenomenon of harmonic amplification relates to grid contingencies, variation of load flow, cable length, and uncertainties of network [33,37]. e article [38] focuses on the stability issues of DC grid related to the travel waves on the transmission line and harmonic content of converters. e paper identifies the travelling wave in the long submarine array cable and resonant problem between the cable length and the switching action of the substation converter. According to the practical cases, the DC wind farm topologies for the case study mainly focus on the offshore wind farm with a short DC power transmission path.
Reviewing the common techniques for wind farm analysis, the frequency scan techniques are usually used for identifying harmonic voltage distortion of specific harmonic component in wind farms [34,39,40]. In this case, the wind turbines are represented for a specific frequency with an admittance equivalent circuit. e array cable model is selected according to the cable length and interesting frequency ranges of harmonic analysis. To adequately represent the cable parameters in the study, both equivalent PI section and frequency-dependent phase model are generally used to consider the frequency dependence of the cable parameters [28,31,41]. Additionally, the wind farm configuration could be changed via the operation of disconnectors or circuit breakers due to maintenance or forced outages of fault. erefore, the harmonic study of wind farm must include all agreed switching configuration [39].

Review of Operation Principle of Series
Resonant Converter # e circuit topology of series resonant converter # (SRC#) with the medium-frequency transformer is depicted in Figure 3, and the topology comprises a full-bridge inverter, a medium-frequency transformer, resonant LC tank, and medium-voltage output diode rectifier. e switch pairs T 1 (leading leg) and T 2 and T 3 (lagging leg) and T 4 operate at a 50% duty cycle as in Figure 4(e). Commutation of switches on the leading leg (T 1 , and T 2 ) is shifted by an angle of δ, which is respect to the conduction of the switches on the lagging leg (T 3 , and T 4 ). e duration of phase shift equals to half cycle of the L r C r tank resonant period, resulting in a quasisquare excitation voltage as seen in Figure 4(a), and then, the voltage passes through the medium-frequency transformer and excites L r C r resonant tank where the resonant tank current i r is given in Figure 4(b). Via the diode rectifier and the output filter, the current (or power) is delivered to the medium-voltage network, V MVDC . Up to this point, there is no difference in the operation compared to a constant frequency and phase-shift control of classical SRC, which is usually operated in the super resonant mode, to achieve ZVS at turn on.
Considering the switching losses with IGTB applications, the subresonant mode is preferred in SRC# which allows ZCS or a low current at turnoff ( Figure 5(a)); regardless of switching frequency, a full-resonant current pulse is delivered to the load [12]. e control law of SRC# is also allowed ZVS at turnon and ZCS at turnoff for the diode rectifier, as shown in Figure 5(b). It should be noted that the output power has a positive relation with the switching frequency, which means that the output power depends how much energy (current pulse) transfers to the output stage. SRC# operated in a low frequency means lower output power, while high-frequency operation will deliver a higher output power.

Linearized Model and Closed-Loop Control of Series Resonant Converter
e objective of the study is to understand the harmonics distribution of offshore DC wind farm and how the DC wind turbines are affected by harmonics from the MVDC gird. Figure 6 summarizes the derivation of the plant model of the DC wind turbine based on the discrete timedomain modelling approach (Steps 1-8) [42], the transfer function of the output LC filter (Step 9), and SRC#'s control design (Steps 10-12). e details of the derivation (or equations) are address in Appendices A, B, and C which can help reader to reach the harmonic model of the DC wind turbine and then conduct harmonic susceptibility study of the DC wind farm. e following discussion including the flow chart only shows most important conclusions (or equations) of the derivation due to the limitation of page length. e ideal of the harmonic model of the DC wind turbine converter is developed based on the harmonic model of the AC wind turbine and linearized model of the series resonant converter (SRC#) with discrete timedomain modelling approach [42,43]. A linearized statespace model of SRC# in subresonant mode is reported in (1) and in (A.37) in Appendix:  Journal of Electrical and Computer Engineering where x 1 � I r and x 2 � v cr . It is enough to recall here that the duty cycle is fixed to 50%, and one event is defined as a whole time interval in which the IGBT T 1 is pulsed or not, lasting half of the switching period [10]. e state variables are meaningful of the tank current and resonant capacitor voltage at the beginning of one event, while the rectified output current is averaged over one event.
e average output current is regulated by the proper action of the switching frequency. Transfer functions between converter output current and input variables are  . e transfer function between output current and input variables (i.e., g 1 (s), g 2 (s), and g 3 (s)) can be obtained via where ose transfer functions describe how the averaged output current of the converter, before the output LC filter, is influenced by input disturbances. Regarding the voltage harmonics in the array network (MVDC network), the transfer function g 3 (s) can be used to evaluate the effect of the voltage harmonics on the converter output current. Detailed derivation of the linearized state-space model for SRC# from (1) order to have constant power delivered to the MVDC grid and attenuate high frequency harmonics, around twice the switching frequency. Based on the plant model of SRC#, the transfer function of the compensator (or controller) g c (s) in the control block shown in Figure 7 for a specific operating point (OP) is set as e transfer function g c in (5) is designed based on predetermined specifications, such as the ability to reach its reference output current with least ringing, overshoot, and fastest dynamic during perturbations in input variables. e compensator is composed by an integrator to minimize the steady-state error, a pole around the resonant frequency of the filter to lower the resonant magnitude peak influence (ω p ), and finally a gain K, necessary to set a proper crossover frequency, which in this case needs to be lower than the resonant frequency of the filter to avoid instability. Control deign of SRC# is revealed in Appendix, and the parameters of the controller are described in Section 6 that operates in the working conditions specified in Table 1 are shown in Table 2. Figure 8 demonstrates the transfer function g c (s) at the operation point (ω p � −250 rad/s, K � 50.8 dB, and P out � 12.7 MW). e result shows that the gain margin G M is Step 12 Step 10 Step 11 Step 5 Step 6 Step 7 Step 8 Step 1 Step 2 Step 3 Step 4 Step 9 Derive the output LC filter infinite (>0 dB) and the phase margin Φ M is around 78.7 deg. at 49.8 rad/s which represents that the controller is stable. e design criterion has been implemented to select the parameters for the different operation points (different output powers of the DC wind turbine), which have enough gain margin and the phase margin to deal with the parameter uncertainty and variation.

Modelling of DC Wind Turbine Converter for Harmonic Susceptibility Study
To identify the harmonic model of the DC wind turbine converter for the harmonic susceptibility study, the voltage harmonics within the MVDC network are considered as a perturbation on the steady-state operation point. According to the control block diagram of the SRC# given in Figure 7, the harmonic components (disturbance component I turb ) on the output current are dominated by the disturbance on the power reference signal P REF , the disturbance in the lowvoltage DC network V g , and the disturbance in the output terminal voltage of diode rectifier V turb . Without the disturbance component in the power reference signal P REF and in the low voltage DC network V g (P REF � 0 and V g � 0), therefore, the harmonic model of WTG (wind turbine generator) considering the output LC filter (L f and C f ) can be represented by an admittance equivalent Y eq in (6) as given in Figure 9, where the harmonic admittance Y eq is affected by the circuit parameters of DC wind turbine converter topology (plant model), the control design, and the output LC filter: where the admittance of the converter without considering the output filter can be represented by the following equation: Equation (6) describes satisfactorily the variation of the converter current delivered to the grid in response to grid voltage disturbances where the transfer functions g 1 and g 3 in (6) and (7) (the details of expression is in (3)) describe how the output current I o,Rec is influenced by the disturbances in the control input signal f s and the output voltage V o (∝ voltage V MVDC ), respectively. In practical applications, the output LC filter contains a tiny amount of the parasitic resistances which can alleviate the peak value of admittance magnitude Y eq at the resonances frequency, as done in the following sections for the study case described in Section 6. Figure 10(a) shows the variation of admittance magnitude |Y eq | of the converter with/without the output LC filter. It also represents the magnitude |Y c | of the converter without the output LC filter to observe the filter's influence on the equivalent admittance of the converter. Admittance magnitude of the converter with the output filter is high as it approaches the natural frequency of the output LC filter (f f ≈ 100 Hz), while the magnitude of admittance of the converter itself (without output filter) is low in the whole spectrum and reaches a constant value at low frequencies. Regarding the phase angle of the admittance equivalent, the behavior of the converter with output filter changes from inductive, at low frequencies, to capacitive, at the natural frequency of the filter as shown in Figure 10

Harmonic Susceptibility Study of DC Collection Network
In this section, the harmonic susceptibility study of DC collection network is revealed based on the harmonic model of the turbine converter developed previously and compared      to a switching model implemented in PLECS ™ . According to Figure 9, a radial-type cluster of seven wind turbines of an offshore wind power plant (OWPP) is given. It will represent the study case for the comparison of the harmonic model and switching model. e parameters for the turbine converter and operating point of the plant model with controller are given in Section 6. Since different configurations of collection network and wind turbine converter topologies could generate different harmonic spectra, background harmonics of the DC grid (correction/array network) from the offshore substation DC/DC converter and DC wind turbine generator (DC WTG) can cause undesirable resonant phenomena and raise stability issues. One of the major tasks of the harmonic susceptibility study is to identify resonance frequencies of network and investigate potential voltage amplification issues.

Cable Model.
Array cables in the following study cases are modelled as a pi-equivalent model with longitudinal admittance parallel branches in order to consider the frequency dependency of distributed cable parameters and represent correctly the behavior in the frequency ranging from 0 to 10 kHz [31,44]. In the study, the electromagnetic transient program PSCAD is usefully employed to extract the longitudinal admittance and the shunt capacitance from the geometric data of array cable [41]. e values of resistance, inductance, and capacitance to use at each frequency are calculated by the software individually.
According to the cable model in PSCAD, the capacitance is not varying within the range of interesting frequency. Instead, as the frequency rises, the resistance keeps increasing, due to the skin effect, and the inductance decreases its value due to the eddy currents in the outer conductors. For the considered study case, eight RL series branches are used to approximate the longitudinal impedance.
e PSCAD generates the admittance date (i.e., matrix [Z PSCAD ] and [Y PSCAD ]) from the geometrical data of the marine cable (in frequency-dependent (phase) model) in certain operational frequency to form "pi-equivalent cable model" [45]. An equivalent pi-equivalent model is built based on the cable model, which can fit the admittance date (matrix [Z PSCAD ] and [Y PSCAD ]) from the geometrical data of the submarine cable (implemented in frequencydependent (phase) model in PSCAD) to make sure that the adequate cable model is implemented in the array cable network. Actually, the frequency-dependent phase model in PSCAD is also regarded as a most numerically accurate cable model thus far. e formulation of models has been proved that the bandwidths of the model can be up to 1 MHz, which can satisfy most of transient studies and harmonics studies [41,45].

Frequency Scan Approach.
e WPP cluster consists of seven turbines with seven MVDC cable segments, where the offshore substation converter is represented by an ideal harmonic voltage source. According to the frequency scan approach for network analysis addressed in Figure 11, the harmonic voltage source (disturbance component) in the output DC voltage of the offshore substation converter is activated and injects harmonic voltage component into the MVDC grid with 0.5% (�0.005 p.u) of voltage magnitude (|V MVDC,h,n | � 500 V) and the frequency of injected harmonic voltage raises until 300 Hz, by steps of 20 Hz. e output voltage and output current traces of each wind turbine model in each frequency step are extracted for FFT analysis after the steady-state condition is reached. is approach allows an arbitrary choice of frequency and magnitude of the disturbance in the offshore substation. erefore, it does not intend to represent only a specific range of harmonics in the DC collection network. Eventually, models of the DC collection system (or network) could be established for different frequencies of the injected disturbances. As an example, for the harmonic model, the wind turbine converter can be described by a particular RL or RC series branch for disturbance frequency.
Based on the harmonic model of DC collection network in Figure 9, Figure 11 gives a flow chart of frequency scan approach for the DC collection system in the harmonic susceptibility study. e process includes the identification of the harmonic model of the DC wind turbine for certain frequency of the injected disturbance (harmonic) and the establishment of the harmonic model of DC collection network. e DC collection network in Figure 9 is set as an example to explain the sequence of frequency scan illustrated in Figure 11.
Step 1: the harmonic voltage source in the offshore substation (V MVDC ) is connected to the network and injects a 20 Hz harmonic disturbance into the MVDC network with a specific voltage magnitude |V MVDC |. e harmonic model of the DC wind turbine generator (WTG) under 20 Hz perturbation (harmonic frequency) in MVDC network is identified by connecting to the MVDC network at t � t 1 .
Step 2: the voltage and current within network are extracted for FFT analysis after the voltage and current have reached the steady-state condition.
Step 3: at t � t 2 , the frequency for which the harmonic model of the DC wind turbine is evaluated and is increased by 20 Hz, as the frequency of the injected disturbance. e algorithm turns back to Step 2. Eventually, the frequency sweep continues until 300 Hz (at t � t n−1 ), which depends on the control bandwidth of the DC wind turbine converter and interesting frequency range in the harmonic susceptibility study.

Verification
Based on the DC collection network in Figure 9 and the converter control design addressed in (5), Tables 1 and 2 give the parameters used in the study of the DC collection grid, where the geometric parameters of cables are shown in Figure 12 which is implemented in the created equivalent PI section according to the frequency-dependent (phase) model in PSCAD. For the turbine harmonic model, all the turbines are considered operating in the same operating point, described in Table 2  is 4.04 kV, while the voltage drops across cables are responsible for different voltages at the output terminal of the wind turbines. e controller of each turbine regulates the switching frequency in order to control the output power to follow its reference. In particular, the frequencies are higher as wind turbines move further away from the offshore substation, to compensate the lower voltage difference on the two sides of the converter. According to the frequency scan approach illustrated in Figure 11, additionally, a perturbation with a specific sequence of frequency in the range of 20 to 300 Hz is applied to the corresponding harmonic model of turbine converter and the results are given in Figure 13 for a single wind turbine. Figure 13 gives a verification of the turbine harmonic model (equivalent admittance) by comparing the harmonic spectrum of output current with the results generated by the corresponding switching model of the turbine converter in PLECS ™ . e current spectrum shows that the derived harmonic model and converter switching model are very close up to 300 Hz.
e magnitude of output current spectrum is reduced as the frequency of the harmonic component is far from the natural frequency of the output LC filter, where the mismatch between the harmonic model and its switching model in PLECS ™ becomes higher. Furthermore, the turbine output current trace shows that the harmonic component of output current is amplified, while the frequency of MVDC harmonic voltage (V MVDC,h,n ) approaches to the natural frequency of output LC filter of the turbine converter. e results of network (array network) simulation in Figure 14 between both models (harmonic model and the corresponding switching model) show a good agreement. However, some mismatch coming from the harmonic model developed can be seen in all turbines in cluster. Furthermore, as observed along the cluster, last wind turbines (shown in Figures 14(f) and 14(g)) have second-and third-order current harmonics due to nonlinear behavior considered by the turbine converter switching model. is is because the proposed harmonic model cannot predict these higher order harmonics since the modelling approach for the turbine converter in MVDC network are linear. Figure 15 gives a comparison of the harmonic spectrum of output current for wind turbines at different locations to study the error of the harmonic model. While in the closest WTG to the offshore substation, a sinusoidal wave is observed (WTG11); in the last ones, sinusoidal waves have a considerable amount of harmonic components at multiples of the injected disturbance frequency (WTG17). Furthermore, the amplitudes of the fundamental current harmonics decrease along the cluster, approaching the farthest wind turbine from the offshore substation. is phenomenon is related to the rising amplitude of higher order harmonics as depicted in Figure 15. Additionally, it is worth mentioning that, in the switching model, there are current harmonics around 1600 Hz, twice of the switching frequency of converter, as the filter at the output of each converter cannot cancel completely these current harmonics. e harmonic current spectrum at natural frequency of the output LC filter (≈100 Hz) was not shown in the grid simulation in Figure 14 because it was in the equivalent turbine model (admittance equivalent), since it was "ideal" current source (linear model), the parameters were really high and were not matching the switching model at al. Probably the filter damping is too small which results in very high current (approx. 500 A) at resonance of the output LC filter for a single turbine in grid simulation (equivalent model). However, the results of grid simulation still shows that the admittance equivalent follows results from the switching model for a single turbine in all frequencies; at natural frequency of the turbine output LC filter, the admittance equivalent is clearly not well represented.
In the verification of modelling of the array cable with equivalent PI-cable section based on the method proposed by Beerten et al. [31], the values of resistance and inductance of each branch are calculated in order to fit the behavior of the longitudinal admittance in the frequency domain calculated by PSCAD's cable model (frequency-dependent (phase) model). Figure 16 shows a good matching of the fitted values of the admittance by the eight parallel branches (N � 8) and the values calculated by software (PSCAD's cable). e error on the magnitude of the admittance between two models is less than 1.0%, within the range of 0.001 Hz-10000 Hz. e error in phase is always less than 1.7°, in the range of interesting frequency.
Since the calculation of the admittance date from the frequency-dependent (phase) model in PSCAD is not straightforward and is extremely complicate, there are some articles which are useful to conduct the calculation of admittance date from the geometry date of the cable model [28,30,45].

Laboratory Test
A laboratory test is performed to prove the validity of the proposed harmonic model of the turbine converter. A schematic of the setup of the DC wind turbine converter for SRC# is depicted in Figure 17. e down-scale prototype circuit with 216 V DC (V LVDC ) to 400 V DC (V MVDC ) DC wind turbine converter is built to verify the harmonic distribution of the turbine converter. e wind turbine converters, whatever AC or DC turbines, are the boost structures in order to increase the efficiency of power transmission. erefore, the down-scale prototype circuit is designed to match with this character (boost the low-voltage DC, V LVDC , from the generator) to match with the DC grid voltage (medium-voltage DC, V MVDC ) from the offshore substation. Although only a single turbine converter is implemented in the test bench, the harmonic signatures of the wind turbine converter (in the test bench) in the interesting frequency range have been confirmed which match with the simulation model as in the following results.
A programmable AC source is used to emulate the harmonic voltage source (V MVDC,h ) with sinusoidal waves at different frequencies on the output terminal of the converter. A module of resistors R load and a diode D Aux are placed on the output side of the converter to simulate the character of unidirectional power flow of MVDC network. Table 3    Journal of Electrical and Computer Engineering  Figure 14: Output current spectrum of individual turbines in the operating point described in Tables 1 and 2, being WTG11 the closest to the offshore substation and WTG17 the furthest. Harmonic current amplitude and phase angle are represented for a switching model of the DC wind turbine converter (|I turb,sw,WTGxx |∠θ turb,sw,WTGxx ) and for the admittance equivalent model (harmonic model) (|I turb,eq,WTGxx |∠θ turb,eq,WTGxx ).   Figure 18. e results show that there is a good agreement with the proposed DC turbine harmonic model. However, there is a mismatch in the amplitudes (Figure 18(a)) when the injected frequencies approach the natural frequency of the output LC filter. As given in Section 4, the admittance of the DC turbine harmonic model is heavily influenced by the output LC filter. e behavior of the converter changes from inductive to capacitive at the natural frequency of the filter as in Figure 18(b). It should be noted that there is no standard for selecting the medium-voltage DC (MVDC) grid. e MVDC of 400 V DC is chosen as output voltage of the down-scale prototype circuit of SRC# from the available test equipment in the laboratory for simulating the MVDC gird (controllable DC power source). In practical applications, the selection of MVDC is based on the electromagnetic transient (EMT) simulation of the grid and existing offshore wind farm technologies such as power converters, protection devices, available offshore platform, and array cables [1].

Conclusion
A model-based methodology in conducting the harmonic susceptibility study is revealed based on the discrete timedomain modelling technique and the frequency scan approach in the frequency domain. e developed harmonic model in the paper can be used to perform a harmonic susceptibility study of power collection network in an early stage of a wind farm project because of its simplicity and low computational cost compared to a switching model. In the later stage, the proposed method is recommended to consider the switching model of the converters in order to be closer to reality. e process of harmonic susceptibility study contains identification of the harmonic model of the turbine converter and the establishment of array network in the frequency domain. e validation of the harmonic model of the turbine converter is given in Sections 6 and 7 via computer simulation implemented in PLECS ™ and the laboratory tests, respectively. Additionally, the distribution of current harmonics within DC collection network is investigated including the identification of possible resonance frequency within array network. Moreover, analytical data from simulation and the laboratory tests give indications to set a proper design and natural frequency for the output LC filter of the DC turbine converter and a matched switching frequency for the converter placed in the offshore substation.

Appendix
According to the flow chart of mathematical derivation in Figure 6 in Section 3, firstly, the circuit topology of the turbine converter and mode of operations are decided as shown in Figures 3 and 19, and then the equivalent circuit based on the switching sequence of transistors is created as shown in Figure 20. In Figure 20, the large-signal model of the converter is generated (Step 4) and then the interesting state variables (Step 5) are defined to create the small-signal equations. Steps 6 and 7 establish the space model of the plant. Finally, the converter plant mode is established based on the discrete time-domain modelling approach proposed in (Step 8) [42,46]. Step 9 gives a set of interesting transfer function of the output LC filter. Eventually, Steps 10 to 12 focus on the control design for SRC#.

A. Derivation of the Plant Model
Steps 1-3. Decide the circuit topology of DC turbine converter, resonant tank waveform, and equivalent circuit.
Steps 1-3 describe how to obtain the large-signal model and the corresponding equivalent circuit in subresonant CCM in Figure 20 from the circuit topology of SRC#, which is operated in subresonant CCM as in Figures 3 and 20, respectively. e waveform in Figure 19 is divided by different time zones (different switching sequences) based on the discrete time-domain modelling approach. e figures are eventually used to generate the large-signal model of SRC#.  Step 4. Large-signal model.
In the large-signal model, the final value of interesting state variables in each switching interval is represented by the initial values of states. According to discrete time-domain modelling approach, the procedure is only valid when the variations in MVDC grid voltage v o (t) (output terminal voltage) and LVDC voltage v g (t) (input terminal voltage) in the event (switching) are relatively small than their initial and final values [42]. According to Figures 19 and 20 For At time t � t 1(k) , the tank current i r reaches the point of zero crossing, commutating the IGBT switches T 1 and T 4 turnoff and turning on body-diode D 1 , and IGBT switch T 3 . erefore, the resonant inductor current i r (t) can be expressed by where · cos ω rs β K + I r,0(k) Z r · sin ω rs β K − V o,0(k) .

A.1. Steady-State Solution of Large-Signal Model.
e following equation expresses the conditions for obtaining steady-state solution (at certain operating points of CCM) of the discrete state equation of the large-signal model: By substituting (A.15) into (A.12) and (A.13), the steadystate solution of I r,0(k) and V Cr,0(k) can be written in term of V o,0(k) , V g,0(k) , β k , and α k : I r � I r,0(k) � f V o,0(k) , V g,0(k) , β K , α k , V Cr � V Cr,0(k) � f V o,0(k) , V g,0(k) , β K , α k , (A. 16) where the overbar used in equations is to indicate the steadystate value of the interesting state variables. For simplifying the derivation of the plant model, the output LC filter of SRC# (i.e., L f and C f ) is neglected due to a very slow dynamics in voltage and current comparing with the dynamics in the resonant inductor current i r (t) and resonant capacitor voltage 18 Journal of Electrical and Computer Engineering v Cr (t). erefore, only the DC component of the output current diode rectifier i out,Rec is considered as an output variable which is expressed by i o . Eventually, the output current equation delivered by the SRC# during the K th event is express as ω rs sin ω rs β k + 1 ω rs sin ω rs β K · 1 − cos ω rs α k · I r,0(k) + 1 c k · − 1 ω rs 1 Z r 1 − cos ω rs β k + 1 ω rs 1 Z r cos · ω rs β K · 1 − cos ω rs α k · V Cr,0(k) It should be noted that the initial value of inductor current is represented by I r,0(k) , V Cr,0(k) is the initial value of capacitor voltage, the initial value of rectifier output voltage is written as V o,0(k) , and V g,0(k) is then the initial value of input voltage of SRC#. Characteristic impedance Z r is defined by the parameter of resonant tanks (� ���� L r C r ), α k is the transistor and diode conduction angle during the switching interval event k, and the switching frequency of the converter is represented by θ s (�ω s ·t). Finally, the steady-state solution of the discretestate equation for the output variable i o can be obtained by substituting the steady-state condition into (A.17) as I o � i o β k �β,α k �α,c k �c,I r,0(k) �I r ,V Cr,0(k) �V cr ,V o,0(k) �V o ,V g,0(k) �V g . (A.19) Step 5. Define state variable.
Control design technique based on the linear control theory cannot directly be applied for, mainly because of the high nonlinearity in the discrete large-signal state equations in (A.12), (A.13), and (A.17). erefore, the linearization of the above large-signal equations is necessary. Equation (A.20) shows the definitions of interesting state variables in both k th switching event (t 0(k) ≤ t ≤ t 2(k) ) and (k + 1) th switching event (t 2(k) ≤ t ≤ t 2(k+1) ) which is used in the linearization process. Eventually, the following equations of approximation of derivative are applied for converting the discrete large-signal model into the continuous time: x 1(k) � I r,0(k) , x 2(k) � V Cr,0(k) , I r,2(k) � −x 1(k+1) , V Cr,2(k) � −x 2(k+1) , where c k � ω s t 2(k) − t 0(k) � ω s t 0(k+1) − t 0(k) . Switching frequency of the series resonant converter defined by � ω s /2π ω r : Natural resonant frequency of the tank defined by ω r � 1/ ���� L r C r .

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.