Multilevel Middle Point Clamped (MMPC) Converter for DC Wind Power Applications

Abstract

This manuscript introduces a novel multilevel middle point clamped (MMPC) DC-DC converter and its associated switching scheme aimed at maintaining the desired medium-voltage DC (MVDC) collector grid within offshore all-DC wind farms. Building upon previous work by the authors, which proposed an all-DC structure serving as a benchmark system, this study explores the application of the MMPC DC-DC converter within this framework. Within the all-DC wind generation system, a 9-phase hybrid generator (HG) integrated into the wind turbine is linked to the MVDC collector grid through an AC-DC stage, which is a passive rectifier. This passive rectifier offers elevated voltage ratings and protection against back power flow. The conventional neutral point clamped (NPC) converter concept has been thoroughly investigated and expanded upon to develop the proposed MMPC DC-DC converter. The proposed MMPC DC-DC converter integrates boosting capabilities, facilitating the connection of the generator’s rectified voltage to the MVDC collector grid while regulating variable rectified voltage to a fixed MVDC collector grid voltage. The MVDC collector grid is further interconnected with high-voltage DC (HVDC) through a DC-DC converter situated in an offshore substation. This paper further provides a comprehensive overview of the proposed MMPC DC-DC converter, detailing its operational modes and corresponding switching schemes. Through an in-depth examination of operational modes, duty cycles for each switch and mode are defined, subsequently establishing the relationship between rectified input voltage and MVDC output voltage for the MMPC DC-DC converter. Utilizing the middle point clamped architecture, this innovative converter offers several advantages, including low ripple voltage, a modular structure, and reduced switching stress because of the multilevel voltage and the incorporation of a hard point, which also facilitates the capacitor voltage balancing. Finally, the effectiveness of the proposed converter is evaluated via simulation studies of a wind turbine conversion system utilizing two cascaded MMPC DC-DC converters operating under variable input voltage conditions. The simulations confirm its efficacy, supported by promising results, and validating its performance.

1. Introduction

Wind generation systems have seen increasing installations over the past decade, where the capacity of wind power grew to over 900 GW globally in 2022 [1,2,3,4]. Traditionally, the wind power systems use AC technologies for their collector and transmission grids. The high-voltage AC (HVAC) systems are well-established technologies; they are efficient over short distances, usually do not employ power electronics, and are well suited for AC grid integration. However, high-voltage DC (HVDC) systems have become popular for transmission grids, particularly in offshore farms, due to their flexibility, controllability, and improved performance, and the cost of high-voltage power electronics systems continuously reducing, which makes the DC system competitive with their AC counterpart [5,6,7,8,9]. There are different studies comparing HVDC and HVAC systems [10,11,12]: HVAC benefits from mature technology, efficiency over short distances, lower converter costs, and seamless integration into AC grids. However, its reliance on reactive power leads to higher transmission losses, necessitates substantial upgrades for renewable energy integration, and faces stability challenges over longer distances, contributing to higher carbon emissions. In contrast, HVDC offers advantages such as lower transmission losses, reduced carbon emissions, efficiency over longer distances, enhanced control capabilities, and the ability to interconnect asynchronous grids. Nevertheless, HVDC systems incur higher initial costs, require complex converter stations, are less economically viable for short-distance applications, and face limitations in equipment supply and specialized expertise.

Figure 1a illustrates the existing state-of-the-art wind turbine conversion system featuring a three-stage connection process for linking the wind turbine to the medium-voltage AC (MVAC) collector grid, which typically operates between 33 kV and 66 kV. Modern wind turbine conversion systems, as depicted in Figure 1a, utilize a direct drive mechanism, commonly incorporating a permanent magnet synchronous generator (PMSG) (rated at 400 V, 480 V, or 690 V) interfaced to two back-to-back voltage source converters (VSCs) (rated at 1000 V) that includes a machine side converter that controls the PMSG for maximum power point tracking, and a grid side converter that controls a fixed DC-link voltage and controls the active/reactive power flow. The output of the grid side converter is then stepped-up before connection to an MVAC collector grid (33 kV to 66 kV) [13,14,15,16,17]. An offshore substation collects the power from all wind turbines and sends the wind farm total power to the shore station via a transmission line, typically a high-voltage AC (HVAC) system ranging from 132 kV to 320 kV, or an HVDC link where most common systems are rated around 320 kV to 525 kV.

The authors in [30,31,32,33] present a comprehensive review of different architectures for wind power systems, concluding that the HVDC overcomes the major problems of the HVAC systems including reactive power, losses, and limited controls. In addition to transmission grids, there has recently been growing interest in using DC systems for the wind collector grids, which together with HVDC transmission grids, make the wind generation an ‘all-DC system’ [33,34,35,36,37]. An all-DC grid can be divided into three major DC parts: (i) a wind turbine with a DC output, (ii) a medium-voltage DC (MVDC) collector grid that collects the power from wind turbines and sends it to an offshore substation, and (iii) an HVDC transmission grid that transfers the power from the offshore substation to the shore before connection to the AC terrestrial grid [38,39,40,41,42].

The existing wind turbine conversion systems may be converted into a system suitable for connection to an MVDC collector grid by adding an AC-DC stage at the output of the transformer as shown in Figure 1b [18,19]. The challenges with the all-DC scheme in Figure 1b include the following: (i) This adds a fourth stage of conversion to the wind turbine, significantly reducing the overall efficiency of the wind turbine. (ii) As the power electronics switches are not available at high voltages and currents, the AC-DC stage (33 kV–66 kV AC to 40 kV–100 kV DC) will need to be constructed by a parallel/series connection of switches and in multilevel and/or modular configuration [43,44,45,46,47], which makes it bulky and costly [48,49,50]. Figure 1c shows a wind turbine conversion system where a DC-DC converter replaces the grid side converter in the existing scheme to step-up the wind turbine DC-link voltage [20,21,22,23]. In this scheme, to achieve suitable voltages, a number of wind turbines are connected in series before connection to an MVDC collector grid. Note, as the DC-DC converter topologies with a high step-up ratio are not suitable for confined space within the wind turbine, the series connection of wind turbines is necessary to achieve suitable voltages at the output of wind turbines in the scheme shown in Figure 1c. However, if one of the series connections fails, the power is shut from the entire group, hence making this scheme infeasible for practical applications. The existing wind turbines, Figure 1a–c, and the attempts in the literature to convert them to a system suitable for connection to an MVDC collector grid all use low-voltage conversion systems. In a fundamentally different approach, the authors in [24,25,26,27,51] have introduced a high-voltage wind turbine conversion system where a high-voltage PMSG is interfaced to an MVDC collector grid via a multilevel converter as shown in Figure 1d. The features of this system include the following: (i) Unlike conventional wind turbine generators, the machine in this topology must use high-voltage winding, where its per-phase voltage is suitable for connection to a 40 kV–100 kV MVDC collector grid. (ii) Due to limitations on the availability of high-voltage switches, a multilevel converter (3-level or 5-level) is used to support higher voltages. Note that in this scheme, as the number of converters is reduced, the degree of control is less. The multilevel converter controls the high-voltage PMSG for MPPT, while the MVDC voltage is controlled to be fixed via the offshore substation. This is essential for the correct operation of the multilevel converter [52,53].

Table 1. Rating of commercially easily available high-voltage switches.

Company Name	Module	Voltage (kV)	Current (A)	Package
MITSUBUSHI ELECTRIC	CMH1200DC-34S	1.7	1200	Dual IGBT
MITSUBUSHI ELECTRIC	CMH600DA-66X	3.3	600	Half-Bridge IGBT
MITSUBUSHI ELECTRIC	CM200HG-130H	6.5	200	Single IGBT
POWEREX	QID6508001	6.5	85	Half-Bridge IGBT
POWEREX	CM600HA-28H	1.4	600	Single IGBT
WOLFSPEED	CAB500M17HM3	1.7	500	Half-Bridge SiC

lists some of the commonly used commercially available switches. Although there are switches designed for higher voltages in limited numbers, the commercially available switches are limited to 6.5 kV that necessitates high-voltage converters to become multilevel and/or modular, which makes them bulky and costly. In an attempt to move away from these converters, the authors of [28,29,51,54,55,56] proposed a high-voltage wind turbine conversion system that uses a 9-phase hybrid generator (HG) interfaced to a 9-phase passive rectifier presented in Figure 1e. The HG uses a two-rotor topology, a PM rotor that is the primary rotor of the machine, and a wound field rotor that is mounted on the same shaft as the PM rotor. Since the passive rectifier is an uncontrolled device, the wind turbine MPPT control is shifted to the HG, which is achieved by controlling the wound field rotor via adjusting a DC current [51,57,58,59]. Although the proposed system in [28,29,51,54,55,56] simplifies the power electronics in a wind turbine, it poses the following challenges: (i) It adds complexity for the generator, as the HG uses a two-rotor topology. (ii) At low velocities, a large wound field current is required to maintain a desired power; this result is large-size wound field design that increases the HG volume and mass while reducing the overall HG efficiency, particularly at low speed. (iii) At each wind velocity, the MVDC voltage is required to match the rectified voltage of the wind turbine with the lowest velocity to avoid the turn-off of the rectifiers in parallel connected wind turbines. To enhance these aspects and provide an active control over the wind turbine output, this paper takes the 9-phase HG and rectifier scheme in [28,29,51,54,55,56] and proposes a modified middle point clamped (MMPC) converter as schematically shown in Figure 2. In this scheme, the output of the HG is interfaced to two parallel passive rectifiers, whose output is connected to two cascaded MMPC converters before interfacing to an MVDC collector grid. The contributions of this scheme include the following: (i) The control that was solely shifted to HG is now implemented by the MMPC converter, i.e., MPPT control as well as maintaining a fixed MVDC voltage at the output of the wind turbine. (ii) In this topology, the rectified voltage is allowed to vary since the modulation of the MMPC converter can be adjusted to take the variable voltage and control a fixed output voltage for the wind turbine. This reduces the requirements for the wound field of the HG, making it significantly smaller in volume and mass. (iii) The MMPC converter does not require a step-up transformer, and it utilizes off-the-shelf commercially available silicon carbide (SiC) switches. In this paper, the specification of a wind turbine and MVDC grid are adopted from [28,29,51,54,55,56] and listed in

Table 2. Specifications of HG.

Nominal power	3.6 MW
Rated speed	600 RPM
Phase RMS voltage	10.45 kV
Number of phases	9-phase
Number of poles	10
Efficiency	95%
Per-phase resistance	0.306 Ω
Per-phase inductance	75 mH

. As SiC devices with voltage ratings of 10 kV are developing and are available for specific applications [60,61,62,63,64], the proposed MMPC converter uses only two modules to meet the wind turbine ratings.

This paper is organized as follows: Section 1 presents the introduction, providing an overview of existing wind turbine conversion schemes. Section 2 details the proposed MMPC converter, explaining its topology development, operational modes, switching scheme construction, and mathematical derivations. Section 3 presents comprehensive simulation results and associated discussions regarding the voltage boosting capabilities of the MMPC converter. Finally, Section 4 offers concluding remarks.

2. Proposed MMPC Converter

2.1. Topology and Operational Modes

Figure 3 shows the circuit topology for the proposed DC-DC MMPC converter, which includes (i) two legs connected in parallel in a half-bridge topology and (ii) each leg contains five switches, being S₁, S₂, S_3(a,b), and S₄ for the first leg and S₅, S_6(a,b), S₇, and S₈ for the second leg; (iii) a middle point of each leg that is connected to two series diodes and clamped to the middle point of two DC-link capacitors; (iv) an inductor (L_b) that is in series with a leg, an output diode (D_b), and a capacitor (C_b) at the output terminals. The inductor acts as a temporary energy storage providing the MMPC converter with boosting capabilities. Placing L_b only on leg one gives boost capability, and it also seems and behaves like a conventional boost converter, which can be easily analyzed from operational modes for charging and discharging of the inductor depicted in Figure 4. It is worthwhile to note that it is possible to include two inductors, one per leg, but it is not required here as it complicates the analyses as well as overall cost and size of the proposed converter.

Compared to a conventional half-bridge, the proposed MMPC converter has two distinct features: (i) The output voltage has a 3-level waveshape, enabling a move towards higher-voltage applications. (ii) The middle of the two clamping diodes is tied to the middle of the DC-link capacitor, point ‘O’ in Figure 3. This provides a hard-point neutral for the converter and hence facilitates capacitor voltage balancing, an issue that is exacerbated in low-speed wind turbine operation [52,65,66]. Because of the hard-point “O”, the voltage stress on switches in MMPC topology is half as compared to half-bridge topology. The input to the proposed MMPC converter is the rectified output voltage of the wind turbine passive rectifier denoted as V_rdc, Figure 2, while its output cascaded with a second MMPC converter forms the wind turbine output voltage, V_MVDC. Note that in the proposed topology, switches S₃ and S₆ are formed by the series connection of two switches (S_3a and S_3b, and S_6a and S_6b, respectively, as shown in Figure 3). This is to ensure that the voltage stress across all the switches will be equal to half of the DC-link voltage analyzed in [59]. There are four modes of operations for the proposed MMPC converter detailed below, while

Table 3. Inductor voltage, duty cycle, and switching strategy for each operational mode.

Inductor Voltage States	S1	S2	S3	S4	S5	S6	S7	S8	Duty Cycle
$V_L=V_{rdc}$	1	1	1	1	0	0	0	0	$d_1$
$V_L={\displaystyle \frac{V_{rdc}}{2}}-V_{MVDC}$	1	1	0	0	0	1	1	0	$d_2={\displaystyle \frac{1-d_1}{3}}$
$V_L=V_{rdc}-V_{MVDC}$	1	1	0	0	0	0	1	1	$d_3={\displaystyle \frac{1-d_1}{3}}$
$V_L={\displaystyle \frac{V_{rdc}}{2}}-V_{MVDC}$	0	1	0	0	0	0	1	1	$d_4={\displaystyle \frac{1-d_1}{3}}$
Switching Strategy
Duty Cycle	Switching Group					Complementary			Mode
$d_1$	S1, S2, S3, S4					S5, S6, S7, S8			I
$d_2$	S1, S2, S6, S7					S3, S4, S5, S8			II
$d_3$	S1, S2, S7, S8					S3, S4, S5, S6			III
$d_4$	S2, S7, S8					S1, S3, S4, S5, S6			IV

lists the switching states and respective mode duty cycles.

• Mode I: Figure 4a—Switches S₁, S₂, S₃, and S₄ turn ON, while S₅, S₆, S₇, and S₈ turn OFF. The energy will be stored in the inductor (L_b). Therefore, the input voltage ($V_{rdc}$) will appear across the inductor as

$$V_L=V_{rdc}={\displaystyle \frac{Ld{i}_{L\left(ON\right)1}}{dt}}$$

(1)

where $i_{L\left(ON\right)1}$ is the inductor current during the ON state of switches S₁, S₂, S₃, and S₄, which can be expressed as

$$d{i}_{L\left(ON\right)1}={\displaystyle \frac{dt}{L}}{V}_{rdc}$$

(2)

• Mode II: Figure 4b—S₁, S₂, and S₇ turn ON while the rest of the switches turn OFF. The energy will be delivered to the load, i.e., MVDC grid, through the capacitor (C₁), and diode (D_b). In this mode, the inductor voltage and current are expressed as

$$V_L=-\left({\displaystyle \frac{V_{rdc}}{2}}-V_{MVDC}\right)$$

(3)

$${\displaystyle \frac{Ld{i}_{L\left(OFF\right)2}}{dt}}=-\left({\displaystyle \frac{V_{rdc}}{2}}-V_{MVDC}\right)$$

(4)

where $d{i}_{L\left(OFF\right)2}$ is the inductor current during the ON state of switches S₁, S₂, and S₇. The negative sign in (4) shows that the slope of the current waveform is negative; i.e., the inductor current is decreasing and hence depleting the energy in the inductor.

• Mode III: Figure 4c—S₁, S₂, S₇, and S₈ will turn ON while the rest of the switches turn OFF. The energy will be delivered to the load through capacitors (C₁, C₂), and the diode (D_b). In this mode, the inductor voltage and current are expressed as

$$V_L=V_{rdc}-V_{MVDC}$$

(5)

$${\displaystyle \frac{Ld{i}_{L\left(OFF\right)3}}{dt}}=V_{rdc}-V_{MVDC}$$

(6)

where $d{i}_{L\left(OFF\right)3}$ is the inductor current during the ON state of switches S₁, S₂, S₇, and S₈.

• Mode IV: Figure 4d—S₂, S₇, and S₈ turn ON while the rest of the switches turn OFF. The energy will be delivered to the load through the capacitor (C₂), and diodes (D₁, D_b). In this mode, the voltage across the inductor is the same as Mode II, i.e., (3)–(4), except the switching scheme is different. Hence,

$${\displaystyle \frac{Ld{i}_{L\left(OFF\right)4}}{dt}}=-\left({\displaystyle \frac{V_{rdc}}{2}}-V_{MVDC}\right)$$

(7)

2.2. Mathematical Models

Figure 5a shows the generation of switching signals for the MMPC converter, where the triangular waveform, denoted as (V_tri), represents the carrier signal in pulse width modulation (PWM), while the control signal (V_c) represents the desired MVDC output voltage of the MMPC converter. Note that to ensure generic applicability, the signals are normalized. The time period of V_tri is denoted by T_s, which is further divided into turn ON (T_ON) and turn OFF (T_OFF) times. T_ON is the time when V_c is greater than V_tri: during this interval, all the switches in leg 1, i.e., S₁, S₂, S₃, and S₄, are ON while leg two switches S₅, S₆, S₇, and S₈ are OFF. This period defined earlier is characterized as Mode I, wherein the inductor is fully charged as the source terminals are shorted via the inductor. Consequently, the duty cycle of switches S₁, S₂, S₃, and S₄ in this mode is represented by d₁:

$$T_S=T_{ON}+T_{OFF}$$

(8)

$$d_1={\displaystyle \frac{T_{ON}}{T_S}}$$

(9)

Similarly, T_OFF represents the duration when V_c is less than V_tri. Given the proposed MMPC topology, which features a middle point clamped configuration comprising two input capacitors C₁ and C₂, there exist three potential methods to utilize the T_OFF: (i) utilizing exclusively the voltage across C₁ to produce the output voltage V_MVDC when switches S₁, S₂, and S₇ turn ON, i.e., Mode II, with the corresponding duty cycle denoted as d₂; (ii) employing both capacitor C₁ and C₂ voltages collectively to generate the output voltage V_MVDC when switches S₁, S₂, S₇, and S₈ turn ON, i.e., Mode III, with the respective duty cycle denoted as d₃; (iii) solely utilizing the voltage across C₂ to produce the output voltage V_MVDC, designated as Mode IV, with the corresponding duty cycle denoted as d₄. Consequently, for each of the three distinct modes, T_OFF is divided into three equal periods (T_OFF/3) to facilitate the utilization of each mode. The duty cycles are expressed as

$$d_2=d_3=d_4={\displaystyle \frac{T_{OFF}/3}{T_S}}$$

(10)

Using (8), (10) can be rewritten as

$$d_2=d_3=d_4={\displaystyle \frac{(T_S-T_{ON})/3}{T_S}}$$

(11)

$$d_2=d_3=d_4={\displaystyle \frac{1-d_1}{3}}$$

(12)

It is important to note that switch S₂ is employed across all modes, signifying its continuous ON state, while switches S₅ and S₆ remain OFF throughout, ensuring a positive output voltage. Conversely, these switches can be engaged when a negative output voltage is needed. Furthermore, a single switch may be activated across multiple modes; thus, it is important to not confuse the duty cycle of each switch with the duty cycle of each mode, as they may or may not be the same.

Figure 5b illustrates the switching signal for switch S₁, with its duty cycle represented as d_S1. To compute d_S1 in terms of duty cycle d₁, which is defined for Mode I, the following is derived based on Figure 5b:

$$d_{S1}={\displaystyle \frac{(T_S-\frac{T_{OFF}}{3})}{T_S}}={\displaystyle \frac{(T_S-\frac{T_S-T_{ON}}{3})}{T_S}}$$

(13)

Using (11) and (12), (13) becomes

$$d_{S1}=1-\left({\displaystyle \frac{1-d_1}{3}}\right)={\displaystyle \frac{2+d_1}{3}}$$

(14)

The duty cycle of switches S₃ and S₄ denoted by d_S3–S4 in Figure 5c is the same as duty cycle d₁ computed in (9) since they exclusively turn ON during Mode I:

$$d_1={\displaystyle \frac{T_{ON}}{T_S}}=d_{S3-S4}$$

(15)

Figure 5d displays the switching signal of switch S₇, which is the complement of the switching signal of switches S₃ and S₄. Consequently, the duty cycle of S₇, denoted as d_S7, will be the complement of d_S3–S4 expressed as

$$d_{S7}=1-d_1$$

(16)

Figure 5e illustrates the switching signal of switch S₈, with its duty cycle denoted as d_S8 and described as

$$d_{S8}={\displaystyle \frac{\left(\frac{T_{OFF}}{3}+\frac{T_{OFF}}{3}\right)}{T_S}}={\displaystyle \frac{{2\times T}_{OFF}}{3\times T_S}}$$

(17)

$$d_{S8}={\displaystyle \frac{{2\times (T_S-T}_{ON})}{3\times T_S}}$$

(18)

Based on (11) and (12), (18) can be further simplified as

$$d_{S8}={\displaystyle \frac{{2\times (1-d}_1)}{3}}$$

(19)

To establish the correlation between the input voltage V_rdc and output voltage V_MVDC in terms of d₁, Figure 5f,g are referenced. These figures, respectively, depict the inductor voltage and inductor currents in each operational mode. Referring to Figure 4a when switches S₁, S₂, S₃, and S₄ are ON, which is Mode I, the voltage across the inductor is equal to the MMPC converter input voltage, i.e., $V_L=V_{rdc}$, and the inductor current increases to a maximum $I_{L\left(max\right)}$. However, in Mode II, switches S₁, S₂, and S₇ are ON to discharge capacitor C₁, leading to a decrease in the inductor current as it discharges into a load via D_b and C_b, as illustrated in Figure 5g. The corresponding inductor voltage is depicted in Figure 6f.

Similarly, in Mode III, switches S₁, S₂, S₇, and S₈ are ON, causing both capacitors C₁ and C₂ to discharge, gradually charging the inductor with a slight slope, as shown in Figure 5g. The corresponding voltage is illustrated in Figure 6f. Likewise, in Mode IV, switches S₂, S₇, and S₈ are ON to discharge capacitor C₂, leading to a decrease in the inductor current as it discharges into a load via D_b and C_b, reaching its minimum value $I_{L\left(min\right)}$, as depicted in Figure 5g, and the respective inductor voltage is shown in Figure 6f.

Considering T_S as the switching period and d₁, d₂, d₃, and d₄ as the duty cycles in Mode I, Mode II, Mode III, and Mode IV, respectively, the current across the inductor in each mode can be calculated from Equations (2), (4), (6), and (7). For Mode I, the inductor current $d{i}_{L\left(OFF\right)1}$ from (2) is

$$d{i}_{L\left(ON\right)1}={\displaystyle \frac{d_1{T}_S}{L}}{V}_{rdc}$$

(20)

For Mode II, the inductor current $d{i}_{L\left(OFF\right)2}$ from (4) is

$$d{i}_{L\left(OFF\right)2}=-\left({\displaystyle \frac{V_{rdc}}{2}}-V_{MVDC}\right)\times {\displaystyle \frac{d_2{T}_s}{L}}$$

(21)

For Mode III, the inductor current $d{i}_{L\left(OFF\right)3}$ from (6) is

$$i_{L\left(OFF\right)3}=\left(V_{rdc}-V_{MVDC}\right)\times {\displaystyle \frac{d_3{T}_s}{L}}$$

(22)

For Mode III, the inductor current $d{i}_{L\left(OFF\right)4}$ from (7) is

$$d{i}_{L\left(OFF\right)4}=-\left({\displaystyle \frac{V_{rdc}}{2}}-V_{MVDC}\right)\times {\displaystyle \frac{d_4{T}_s}{L}}$$

(23)

Using the inherent property of an inductor, which resists changes in the current passing through it, the change in current flow through the inductor before and after turning ON of the switches should be the same, as expressed by

$$d{i}_{L\left(ON\right)}=d{i}_{L\left(OFF\right)1}+d{i}_{L\left(OFF\right)2}+d{i}_{L\left(OFF\right)3},$$

(24)

By substituting all changes in currents in each mode into (24), given d₂ = d₃ = d₄ = (1 − d₁)/3, and subsequently simplifying, the following equation results:

$${\displaystyle \frac{V_{MVDC}}{V_{rdc}}}={\displaystyle \frac{3\times d_1}{1-d_1}}$$

(25)

Therefore, (25) provides the duty cycle equation necessary for computing the output voltage of the proposed converter. When $V_{rdc}=V_{MVDC}$, then (25) becomes

$${\displaystyle \frac{3\times d_1}{1-d_1}}=1$$

(26)

$$d_1=0.25$$

Thus, the proposed converter will function as a boost converter for $d_1>0.25$ and as a buck converter for $d_1<0.25$. To compute the minimum inductance required for continuous conduction mode (CCM) operation, assuming a resistive load R, one can equate the ideal DC-DC converter input power P_in to the output power P_out, expressed as

$$P_{in}=P_{out}$$

$$V_{rdc}{I}_L=V_{MVDC}\times I_{MVDC}$$

(27)

$${\displaystyle \frac{I_L}{I_{MVDC}}}={\displaystyle \frac{V_{MVDC}}{V_{rdc}}}$$

(28)

where $I_L$ is the inductor current, the same as input current, and $I_{MVDC}$ is the output current. Substituting (25) into (28) results in

$${\displaystyle \frac{I_L}{I_{MVDC}}}={\displaystyle \frac{V_{MVDC}}{V_{rdc}}}={\displaystyle \frac{3\times d_1}{1-d_1}}$$

(29)

Substituting $I_{MVDC}={\displaystyle \frac{V_{MVDC}}{R}}$ into (29) results in

$$I_L={\displaystyle \frac{V_{MVDC}\times I_{MVDC}}{V_{rdc}}}={\displaystyle \frac{V_{MVDC}\times V_{MVDC}}{V_{rdc}\times R}}$$

(30)

Substituting $V_{MVDC}$ from (25) into (30) gives

$$I_L={\displaystyle \frac{{V_{MVDC}}^2}{V_{rdc}\times R}}={\left({\displaystyle \frac{3\times d_1}{1-d_1}}\times V_{rdc}\right)}^2\times {\displaystyle \frac{1}{V_{rdc}\ast R}}$$

(31)

$$I_L={\left({\displaystyle \frac{3\ast d_1}{1-d_1}}\right)}^2\times {\displaystyle \frac{V_{rdc}}{R}}$$

(32)

To compute minimum inductance $L_{min}$ for the converter to operate in CCM, it can be expressed as

$$I_L-{\displaystyle \frac{{\Delta I}_L}{2}}=0$$

(33)

Substituting ${\Delta I}_L=d{i}_{L\left(ON\right)}={\displaystyle \frac{d_1{T}_s}{L}}{V}_{rdc}$ and $I_L$ from (32) into (33) gives

$${\left({\displaystyle \frac{3\times d_1}{1-d_1}}\right)}^2\times {\displaystyle \frac{V_{rdc}}{R}}-{\displaystyle \frac{d_1{T}_s}{2\times L}}{V}_{rdc}=0$$

(34)

$$L_{min}={\displaystyle \frac{R\times T_s\times {(1-d_1)}^2}{18\times d_1}}$$

(35)

$$L_{min}={\displaystyle \frac{R{(1-d_1)}^2}{18\times d_1{\times f}_s}}$$

(36)

3. Simulation Studies

To validate the functionality of the proposed MMPC DC-DC boost converter and assess its efficiency, a simulation platform is developed using Matlab R2022a Simulink, replicating the wind turbine generation system depicted in Figure 2. The simulation spanned 10 s with a sampling frequency of 1 kHz, and the results are analyzed based on the simulation results presented in Figure 6.

Table 4. Specifications of Proposed MMPC DC-DC Converter.

Parameters	Variables	Values
Nominal Power		3.6 MW
Rectified Input Voltage	Vrdc	Cases	Voltage	Simulation Time (s)
		1	18.5 kV	0–2, 8–10
		2	12.5 kV	2–4, 6–8
		3	6.5 kV	4–6
Output MVDC Voltage	VMVDC	37 kV
Output MVDC Current	IMVDC	97.3 A
Input Capacitors	C1, C2	10 μF, 10 μF
Inductor	Lb	3.3 mH
Output Capacitor	Cb	2200 μF

provides all the components and respective characteristics of the proposed MMPC DC-DC converter developed for simulation.

The variability (6.5 kV to 18.5 kV) of rectified input voltage to the proposed MMPC DC-DC converter is presented in Table 4 with the respective simulation times, which in turn shows the variable output voltage of the passive rectifier connected to HG based on cut-in and cut-out wind velocities of 4 m/s and 25 m/s, respectively. This variability is based on wind speed characteristics vs. turbine power for the Siemens SWT-3.6-107 turbine, as detailed in [56], where the MPPT power is tracked from cut-in speed of 3–4 m/s to around 15 m/s. From wind velocity of 15 m/s to cut-out wind velocity of 25 m/s, the turbine speed is controlled to maintain a fixed output power of 3.6 MW. The detailed mathematical relationship between wind velocity v, turbine power P_t, and rectified voltage V_rdc is presented by the authors of [51]. The turbine power is related to turbine power coefficient C_p and C_p itself is a function of two parameters: blade pitch angle $\beta$ and blade tip speed ratio λ. The respective relationships between P_t, C_p, $\beta$, and λ are given below as

$$\lambda ={\displaystyle \frac{u}{v}}={\displaystyle \frac{R\omega }{v}}$$

(37)

where u is the tangential velocity of the blade tip and R is the rotor radius.

$$C_p\left(\lambda ,\beta \right)=c_1\left(c_2-c_3\beta -c_4{\beta }^x-c_5\right)e^{-c6}+c_7\lambda$$

(38)

For further details, a look at [48] provides exact values of C_p parameters.

The turbine power and wind velocity relationship is mathematically given as

$$P_t=\left\{\begin{array}{c}0 v\le v_{cut-in}\\ {\displaystyle \frac{1}{2}}\rho \pi R^5{\omega }^3{C}_p\left(\lambda ,\beta \right) { v}_{cut-in}\le v\le v_{rated} \\ P_{nominal} { v}_{rated}\le v\le v_{cut-out}\\ 0 v\ge v_{cut-out}\end{array}\right.$$

(39)

To reflect the same variability, three distinct scenarios are considered during simulation: (i) a rectified input voltage V_rdc of 18.5 kV during periods 0–2 s and 8–10 s, corresponding to the cut-out wind velocity of 25 m/s; (ii) a V_rdc of 12.5 kV during periods 2–4 s and 6–8 s, representing a wind velocity of 15 m/s where constant power output from the HG begins; and (iii) a V_rdc of 6.5 kV during period 4–6 s, reflecting a cut-in wind velocity of 4 m/s. In the proposed system shown in Figure 2, the MVDC bus voltage is maintained at 37 kV, while the output from each rectifier varies between 6.5 kV and 18.5 kV. Consequently, the cascaded MMPC converter ensures a stable MVDC interconnection by regulating the output voltage to 37 kV across all input variabilities. The output MVDC current is expected to remain fixed around 97.3 A for the considered 3.6 MW nominally rated wind power system.

The proposed cascaded MMPC DC-DC converters are designed with two independent inputs as depicted in Figure 2, accommodating the output of the two-port hybrid generator. Each output from the HG is connected to an independent 9-phase rectifier, with each rectifier’s variable output V_rdc feeding into the two independent inputs of the cascaded MMPC converters for MVDC interconnection. The results of the implemented simulation model are illustrated in Figure 6, depicting the variable input voltage and corresponding duty cycle for each variability, along with the output from each MMPC module. These outputs from each module collectively contribute to the total V_MVDC and I_MVDC outputs. Figure 6b illustrates the variable rectified input V_rdc ranging from 6.5 kV to 18.5 kV across each MMPC module. Since the proposed MMPC topology employs a middle point clamped architecture, the voltage distribution across each input capacitor within a module is half of the rectified input voltage, i.e., V_rdc/2, as depicted in Figure 3. These input capacitors discharge based on the defined operational modes outlined in Figure 4. For the fixed V_MVDC, the output from each module of the proposed cascaded MMPC converter must be 18.5 kV irrespective of the input variability to ensure a total output of 37 kV for stable MVDC collector grid connection. As the input voltage to the proposed MMPC converter is variable, the duty cycle d₁, as per Equation (25), varies for each case to output the fixed V_MVDC. Figure 6a zooms in on the d₁ of 0.25, 0.33, and 0.48 for each case, respectively. During the duration of 0–2 s, with V_rdc at 18.5 kV, the d₁ should be 0.25 to maintain a fixed V_MVDC of 18.5 kV across each module. For the duration of 2–4 s, with V_rdc at 12.5 kV, the d₁ should be 0.33 to maintain a fixed V_MVDC of 18.5 kV across each module. Also, for the duration of 4–6 s, with V_rdc at 6.5 kV, the d₁ should be 0.48 to maintain a fixed V_MVDC of 18.5 kV across each module. Similarly, throughout the simulation duration of 6–10 s, the same variations in input V_rdc are repeated, leading to corresponding adjustments in d₁. This adjustment of d₁ is depicted in Figure 6a based on input V_rdc variability in Figure 6b. Consequently, Figure 6c,d show constant output voltages V_M1 and V_M2 of 18.5 kV from each module of the proposed MMPC DC-DC converter, summing up to a total output voltage V_MVDC of 37 kV for stable MVDC collector grid connection. Hence, Figure 6e illustrates a fixed V_MVDC of 37 kV, meeting the requirements of the considered wind power system with a rating of 3.6 MW. Finally, Figure 6f demonstrates a constant MVDC current I_MVDC of approximately 97.3 A, aligning with the system’s specifications. The variability of V_rdc and the respective adjustment of d₁ for each simulated case to output fixed V_MVDC and fixed I_MVDC are tabulated in

Table 5. Variable Input voltage and the respective duty cycles for fixed V_MVDC and I_MVDC.

Input Voltage Vrdc (kV)	Duty Cycle d1	Output Voltage VMVDC (kV)	Output Current IMVDC (A)
18.5	0.25	37	97.3
12.5	0.33
9.5	0.48

.

Hence, results of Figure 6 show that the proposed converter addresses issues in the latest topology as depicted in Figure 1e. The identified issues associated with the topology in Figure 1e are outlined as follows: (i) The output voltage exhibits variability corresponding to wind velocity. (ii) At lower wind velocities, adjustment of the output voltage to its rated values necessitates increasing the wound field current, thereby augmenting the overall dimensions of the HG. (iii) For MVDC collection interconnection, a fixed MVDC voltage is recommended over variable MVDC voltage. Consequently, the proposed topology incorporates boosting capability and effectively mitigates the aforementioned issues by ensuring a consistent output voltage. One of its key advantages lies in its modular structure, facilitating scalability to accommodate higher-voltage applications in the future.

4. Conclusions

This paper is focused on an attempt to interconnect wind turbine generator variable output to an MVDC grid through a proposed wind turbine conversion system. Initially, the shortcomings and challenges of existing MVAC collector grid-based wind conversion systems are outlined, paving the way for discussions on transitioning to MVDC collector grid-based systems within the framework of an all-DC wind generation approach. The transition from an MVAC collector grid to MVDC collector grid and the respective wind turbine conversion systems are presented following the concept of an all-DC wind generation system. However, this transition increases the number of conversion stages in MVDC collector grid-based systems, which poses efficiency and switching rating limitations, necessitating the use of MMC modules. Therefore, this study explores high-voltage generator- and HG-based wind turbine conversion systems from the existing literature, where a single conversion stage suffices for connecting wind turbines to MVDC collector grids. Contrasting the simplicity and reliability of HG-based passive rectifiers’ conversion system with the complexity of a high-voltage generator-based multilevel converter conversion system, the passive rectifier-based conversion system using HG is more effective and practical. The HG-based conversion system gives variable output based on cut-in and cut-out speed; however, the voltage is fixed in modern MVDC collector grids. Moreover, in all-DC wind generation systems employing HG-based turbines, significant wound field current is required at low speeds, leading to bulkier turbines and voltage mismatch in parallel rectifiers in parallelly connected wind turbines. To address these challenges, this paper proposed a cascaded MMPC DC-DC converter that adapts variable voltage outputs from wind turbine rectifiers to the fixed-voltage MVDC collector grid. Unlike simple two-level DC-DC converters with limitations in ripple factors and voltage/current ratings, the proposed MMPC boost converter topology utilizes modular design and off-the-shelf semiconductors to achieve high-voltage, high-power conversion while minimizing waveform distortion and ripple effects. By enabling the direct connection of wind turbines to MVDC collector grids, the proposed boost converter streamlines the conversion process, thereby reducing the number of conversion stages and enhancing overall system efficiency and stability. The proposed MMPC DC-DC converter enables an all-DC wind generation system by eliminating the need for multiple conversion stages required to interface with a fixed-voltage MVDC bus. Further research is necessary to adapt the MMPC DC-DC converter for integration with a fixed-voltage HVDC bus to support HVDC transmission systems.