Design of a Series–Parallel All-DC Power Generation System Based on a New DC Wind Turbine

Abstract

Wind energy is a good alternative to fossil fuels, as the use of fossil fuels has seriously exacerbated the emission of greenhouse gases such as carbon dioxide and has greatly affected the environment. Conventional AC wind farms and AC transmission systems inevitably face problems involving reactive currents and overvoltage in the context of large-scale, large-capacity, and long-distance transmission. However, the use of all-DC wind turbines, together with DC convergence and DC transmission systems, has obvious advantages over AC transmission in terms of transmission losses and expandability. Such technology does not require bulky frequency transformers and can well solve the aforementioned problems of reactive currents and overvoltage. This paper proposes a new series–parallel structure for an all-DC wind power generation system. The series end uses a DC/DC converter based on the Cuk circuit to solve the current consistency and power balancing problems of the series wind turbine through current control, whereas the parallel end uses a large-capacity DC/DC converter based on the capacity transfer principle, to solve the problem of voltage consistency at the grid-connected end. The series part is used to increase the voltage level of the system, which can reduce the huge construction costs of offshore platforms, and the parallel part is used to increase the capacity of the system, which enables its incorporation into large-scale wind farms to achieve the replacement of fossil fuel energy.

1. Introduction

Among renewable energy generation technologies, wind power is one of the most promising forms of power generation, with the potential for large-scale development. Among the forms of wind power generation, offshore wind power has the advantages of not occupying precious land resources and having a low impact on the natural environment. Offshore wind energy resources are abundant compared with those onshore, with high wind energy utilization hours [1].

The Xinjiang and Inner Mongolia regions of China are rich in wind energy resources, but the electricity load in China is concentrated in the eastern and southeastern coastal areas, which makes it difficult to consume the electricity generated by establishing large-scale wind farms in these two regions. The electricity has to be transmitted to the eastern or southeastern coastal areas through the power grid, which puts forward higher requirements for the stable operation of the power grid. This places higher demands on the stable operation of the grid and also brings huge transmission losses. Offshore wind farms are closer to China’s load concentration areas, which means that their generated power is easier to consume nearby and reduces the transmission distances. The high wind speeds and stability of the wind at sea also make offshore wind power more stable than onshore wind power [2,3].

Conventional AC wind farms and their transmission systems, in the face of long transmission distances due to their large scale, their large capacity, and the deep sea, inevitably face the problems of reactive currents and overvoltage, which are brought about by AC transmission. However, with the use of full-DC wind turbine units and DC convergence and DC transmission, a full-DC transmission system reduces transmission losses, improves scalability, reduces reactive power compensation, and removes the need for bulky transformers. It is also a good solution to the above-mentioned problems of reactive currents and overvoltage. In addition, conventional wind power generation requires the construction of large offshore platforms and high-power and high-ratio AC transformers, which can lead to huge construction costs [4,5].

Full-DC wind power systems can be divided into two main types according to the way in which the energy is pooled, namely series and parallel [6,7]. The parallel-type all-DC power generation systems include the machine-side boost type, the centralized boost type, the two-stage boost type, and three other types. The centralized and two-stage boost types require the construction of offshore boost stations and large offshore platforms [8,9]; the machine-side boost type requires a high-ratio boost within each DC wind turbine, which is difficult to achieve with isolated DC/DC converters due to the imperfect technology and manufacturing process of the medium- and high-frequency transformers in current usage [10]. The advantage of a series-connected all-DC power generation system is that the voltage level can be increased by connecting DC wind turbines in series, thus eliminating the need for a high-ratio step-up device [11,12,13]. In [14,15], it is suggested that the unit generating the highest power in a series-connected wind power FDC system is subjected to a high voltage to ground, which makes the insulation design of a DC wind power system more difficult, especially in wet offshore environments. The authors of [16] propose a series–parallel-type all-DC power generation system under voltage limiting for the power balancing problem of series wind turbines, but its control part is complicated and the amount of disturbance is high, which makes it difficult to apply practically. The authors of [17] propose a new topology for offshore DC tandem wind farms, in which the output current of each DC wind turbine is kept stable when the wind speed is uneven using a shunt circuit, but its structure is more complex and there is a loop current problem. The authors of [18] propose to boost the outlet voltage of each DC wind turbine through a DC collector, but this topology requires each DC wind turbine to be connected to a DC collector, which can greatly increase the consumption of cables and the cost of the power generation system.

The authors of [19] use two converters to control the DC wind turbine outlet current and the convergence-end outlet voltage, respectively, whereas the other converters control only the corresponding wind turbine DC voltage, and each wind turbine achieves its own maximum power tracking at the rated voltage. In [20], an all-DC series power generation system based on an H-bridge structure is proposed, but it is only suitable for small-capacity wind farms. The authors of [21] propose a new Cuk-based DC/DC converter that has improved efficiency and a lower rated voltage of the coupling capacitor. However, the above methods suffer from the weak speed regulation of individual wind turbines, complex control structures, the excessive use of power electronics, serious high-harmonics problems, high construction costs, and practical application difficulties.

In summary, the study of offshore full-DC wind power transmission systems is of great significance and has become a hotspot for research in industry and academia. The new topology and its operating characteristics are analyzed on the basis of the characteristics of series and parallel all-DC power generation systems, and the operating characteristics of the new power generation system under steady state, unstable wind speeds, and fault conditions are verified through simulation. The wind turbines are then connected in series and parallel to form a wind farm with DC convergence and DC transmission. This paper proposes a new series–parallel structure for an all-DC wind power generation system. The series part uses a DC/DC converter based on the Cuk circuit to solve the current consistency and power balancing problems of the series wind turbine through current control, whereas the parallel end uses a large-capacity DC/DC converter based on the capacity transfer principle to solve the problem of voltage consistency at the grid-connected end. The series part is used to increase the voltage level of the system, which can reduce the huge construction costs of offshore platforms, and the parallel part is used to increase the capacity of the system, which enables its incorporation into large-scale wind farms to achieve the replacement of fossil fuel energy.

2. Mathematical Model for DC Wind Power Systems

2.1. Mathematical Model for DC Wind Turbines

The equations of a permanent magnet synchronous motor in the coordinate system are transformed to obtain the equations in the rotating coordinate system:

$$\left[\begin{array}{l}{\psi }_{\mathrm{s}d}\\ {\psi }_{sq}\end{array}\right]=\left[\begin{array}{cc}{L}_{sd}& 0\\ 0& L_{sq}\end{array}\right]\left[\begin{array}{c}{i}_{sd}\\ i_{sq}\end{array}\right]+\left[\begin{array}{c}{\psi }_r\\ 0\end{array}\right]$$

(1)

In (1), $L_{sd}$ and $L_{sq}$ are the components of the inductance in the d and q axes, respectively; ${\psi }_r$ is the magnetic chains generated by the permanent magnets; $i_{sd}$ and $i_{sq}$ are the components of the stator current in the d and q axes, respectively.

In a rotating coordinate system based on the orientation of the rotor magnetic chain, the stator voltage equation can be written as follows:

$$\left[\begin{array}{l}{u}_{sd}\\ u_{sq}\end{array}\right]=\left[\begin{array}{cc}{R}_s& 0\\ 0& R_s\end{array}\right]\left[\begin{array}{l}{i}_{sd}\\ i_{sq}\end{array}\right]+\left[\begin{array}{cc}P& -{\omega }_r\\ {\omega }_r& P\end{array}\right]\left[\begin{array}{l}{\psi }_{sd}\\ {\psi }_{sq}\end{array}\right]$$

(2)

In (2), $u_{sd}$ and $u_{sq}$ are the components of the stator voltage in the d and q axes, respectively; $R_s$ is the stator resistance; ${\omega }_r$ is the angular velocity of rotation; $P$ is the differential operator.

The equation for the torque of the rotor chain of a permanent magnet synchronous motor in a rotating coordinate system can be expressed as follows:

$$T_{\mathrm{e}}=\frac{3}{2}\frac{n_p}{2}{\psi }_m{i}_{sq}$$

(3)

In (3), $n_p$ is the number of machine poles.

The equation of motion in a rotating coordinate system with the rotor’s magnetic chain oriented can be written as follows:

$$\frac{d{\omega }_m}{dt}=\frac{1}{J_m}\left(T_e-T_l-B_m{\omega }_m\right)$$

(4)

In (4), ${\omega }_m$ is the mechanical angular speed of the rotor of the PMG, i.e., the angular speed of rotation of the generator; $J_m$ is the rotational moment of inertia of the generator; $T_e$ and $T_l$ are the electromagnetic torque and the mechanical torque of the generator, respectively; $B_m$ is the damping factor of the generator [22,23].

2.2. Mathematical Model of the Rectifier

The mathematical model equation for the network-side rectifier in the three-phase stationary coordinate system can be expressed as follows:

$$\{\begin{array}{l}{e}_a-(s_a{u}_{dc}+u_{NO})=L\frac{d{i}_a}{dt}+R{i}_{sa}\\ e_b-(s_b{u}_{dc}+u_{NO})=L\frac{d{i}_b}{dt}+R{i}_{sb}\\ e_c-(s_c{u}_{dc}+u_{NO})=L\frac{d{i}_c}{dt}+R{i}_{sc}\\ C\frac{d{u}_{dc}}{dt}=s_a{i}_{sa}+s_b{i}_{sb}+s_c{i}_{sc}-\frac{u_{dc}-e_L}{R_L}\end{array}$$

(5)

In (5), $s_a$, $s_b$, and $s_c$ represent the switching functions of the three-phase bridge arms of the three-phase voltage source rectifier, respectively. $u_{NO}$ is the voltage between the negative pole n on the DC side and the neutral point o of the three-phase grid. Taking phase A as an example, when the upper arm is on, $s_a$ is 1, and when the lower arm is on, $s_a$ is 0. $i_a$, $i_b$, and $i_c$ are the three-phase current of the power grid; $i_{sa}$, $i_{sb}$, and $i_{sc}$ are the three-phase current of the power source.

The relationship between the three symmetrical system voltages and currents can be described as follows:

$$\{\begin{array}{l}{e}_a+e_b+e_c=0\\ i_{sa}+i_{sb}+i_{sc}=0\end{array}$$

(6)

Combining (5) and (6) leads to the following conclusion:

$$u_{NO}=-\frac{u_{dc}}{3}(s_a+s_b+s_c)$$

(7)

The mathematical model is then transformed from a three-phase symmetric abc stationary coordinate system via Clarke and Park to a dq coordinate system rotating synchronously at the base wave frequency of the grid [24]:

$$\begin{array}{l}L\frac{d{i}_d}{dt}=e_d-i_{d}R+\omega L{i}_q-{\nu }_d\\ L\frac{d{i}_q}{dt}=e_q-i_{q}R-\omega L{i}_d-{\nu }_q\\ c\frac{d{u}_{dc}}{dt}=s_d{i}_d+s_q{i}_q-i_{dc}\end{array}$$

(8)

In (8), $e_d$ and $e_q$ are the components of the grid voltage transformed to the d and q axes; $i_d$ and $i_q$ are the components of the grid-side current transformed to the d and q axes; $s_d$ and $s_q$ are the mapping of the switching function in the rotationally synchronous coordinate system; $v_d$ and $v_q$ are the components of the converter’s AC-side input voltage transformed to the d and q axes, respectively.

2.3. Mathematical Model of the DC/DC Converter

The new DC topology used in this paper requires the use of a DC/DC converter for the control of the series wind turbine current and for the isolation of the generator from the transmission voltage. There are currently three types of DC/DC converters that are widely used: voltage–source, current–source, and resonant. The most commonly used DC/DC converter is an isolated full-bridge circuit, where the output voltage amplitude is changed by varying the duty cycle of the fully controlled device, as shown in Figure 1.

In the diagram, $i_{in}$ and $i_{out}$ are the current input from the front-end rectifier and the current output from the back-end rectifier; $u_{in}$ and $u_{wt}$ are the voltage input from the front-end rectifier and the voltage output from the back-end rectifier. The diode, resistor, and capacitor form the buffer circuit; the filter inductor $L_v$ of the full-bridge circuit is placed on the input side to reduce the insulation requirements; the resistance $R_v$ is the equivalent resistance of the filter inductor; the capacitor connected in parallel with the power switching tubes $V_1$−$V_8$ acts as a buffer; and $C_{out}$ is the capacitor at the output of the rectifier.

In the DC/DC converter model, the state equations are described using continuous-state voltages and currents without considering the switching state of the converter. The dynamic model of the input current can be obtained from the relationship between itself and the filter inductor:

$$\frac{d{i}_{in}}{dt}=\frac{1}{L_v}(u_L-R_v{i}_{in})$$

(9)

Assuming that the transformer is an ideal transformer, the energy of the capacitance at the output can be expressed as follows:

$$\frac{1}{2}{C}_{out}\frac{d{u}_{wt}^2}{dt}=u_{in}{i}_{in}-u_{wt}{i}_{out}-\frac{1}{2}{L}_v\frac{d{i}_{in}^2}{dt}$$

(10)

2.4. New Series–Parallel Wind Turbine Topology for Grid Connection

The new DC/DC converter with a Cuk circuit and the topology of the high-voltage, high-power DC/DC converter based on the energy transfer principle proposed in this paper are shown in Figure 2.

3. Control of the DC/DC Converter Based on Cuk Circuit and Study of the Power Balancing Problem in Series Wind Turbines

In the new series–parallel topology, the series part is coupled, which results in the outlet current of the more powerful DC wind turbine generator systems (WTGs) being limited by the outlet current of the less powerful DC WTGs when the wind speed is uneven. The more powerful DC WTGs will therefore be subjected to higher voltages, and in order to prevent overvoltage in the higher-wind-speed DC WTGs, the pitch angle of the WTGs has to be adjusted to give up part of the wind energy so that the outlet voltage is maintained near the rated voltage of the WTGs. However, the outlet current of these WTGs is less than the rated current for the above reasons, so the output power does not reach the rated power, which is the reason for the unbalanced power of the tandem DC WTGs. Usually, there are two modes of operation for traditional tandem WTGs, i.e., normal mode and voltage-limiting mode. In normal mode, the outlet voltage and outlet current of the DC wind turbine are maintained near the rated voltage and rated current, the wind turbine outputs the rated power, and when the wind speed varies greatly, the voltage-limiting mode reduces the absorption of wind energy in order to prevent overvoltage, resulting in a power imbalance. For this reason, the authors of [25] suggest controlling the wind turbine output port current and the voltage of the parallel section by using a voltage–source converter at the output of each DC wind turbine and at the grid-connected end of the DC wind turbine. In [26], isolated DC/DC converters are used with a large number of power electronics at the outlet of each DC wind turbine in order to maintain the consistency of the current of the series-connected wind turbines, but their control is too complex, and the large amount of power electronics used exacerbates the impact of high harmonics on the power quality. In [27], phase control techniques are used on both the rectifier and inverter sides, setting the rectifier on the angle of the DC wind turbine with the highest wind speed in the series to 0. The other DC wind turbines in the same group determine their own angles based on the wind speed and compared with the wind speed of the largest DC wind turbine. In [28], a new non-isolated interleaved DC/DC converter is proposed to provide a high voltage conversion ratio in renewable energy systems. In [29], an isolated DC/DC converter with a full-bridge structure is added to the traditional series wind turbine power balancing solution. The authors of [30] present a novel high-gain CUK converter (HGCC) that uses voltage multiplier units.

However, the above methods have problems such as high costs, complex control, and severe high-order harmonics. In this section, a DC/DC converter based on the Cuk circuit is used to solve the problems of power balancing and current consistency in series-connected wind turbines. Only when the wind speed causes the output voltage to exceed the rated voltage of the WTGs is it necessary to operate the WTGs in voltage-limiting mode and reduce the pitch angle to reduce the wind energy absorption.

The topology of the new DC/DC converter studied in this paper is shown in Figure 3:

In this circuit, the capacitor C₁ is charged and discharged in one cycle in a balanced manner, i.e.,

$${\displaystyle \underset{0}{\overset{T}{\int }}{i}_{c}dt=0}$$

(11)

When the fully controlled device T is in the on state, the capacitive current and time product is $I_2{t}_{on}$. When the fully controlled device T is in the off state, the capacitive current and time product is $I_1{t}_{off}$. This leads to the following conclusion:

$$I_2{t}_{on}=I_1{t}_{off}$$

(12)

$$\frac{I_2}{I_1}=\frac{t_{off}}{t_{on}}=\frac{1-\alpha }{\alpha }$$

(13)

In the above equation, $\alpha$ is the turn-on time duty cycle.

When the fully controlled device is on, the circuit in which $i_1$ is located at this time is an RL series circuit, and the equation for the variation in $i_1$ with time can be obtained as follows:

$$i_1=i_L=\frac{u_i}{R}+\left[I_0-\frac{u_i}{R}\right]e^{-\frac{R}{L}t}$$

(14)

In the above equation, where $i_L$ is the inductance current and $R$ is the wire resistance (ignoring wire reactance), $t=t_{on}$, and it can be seen that the longer the conduction time, the larger $i_1$ becomes, and the maximum becomes $u_i/R$.

When the fully controlled device is switched off, the circuit in which $i_1$ is located at this time is an RLC series circuit, and the relationship between $i_1$ and the input voltage can be obtained as follows:

$$u_i=iR+L\frac{di}{dt}+\frac{1}{c}{\displaystyle \int idt}$$

(15)

The right-hand side of the above equation is divided into the voltages of the resistor, inductor, and capacitor, and the second-order differential equation is obtained by taking the derivative of both sides of the equation with respect to time as follows:

$$\frac{d^{2}i}{d{t}^2}+\frac{R}{L}\frac{di}{dt}+\frac{1}{LC}i=0$$

(16)

Solving this second-order constant coefficient chi-square differential equation yields the following equation:

$$i_1=c_1{e}^{-r_{1}t}+c_2{e}^{-r_{2}t}$$

(17)

In the above equation, $r_1=\frac{-R+\sqrt{\frac{R^{2}c-4L}{c}}}{2L}$; $r_2=\frac{-R-\sqrt{\frac{R^{2}c-4L}{c}}}{2L}$.

From the above equation, it can be seen that the longer the shutdown time of the fully controlled device, the smaller the current. The generation of the control signal for the fully controlled device is determined by the rated WTG current $I_{\mathrm{e}}$ and the Cuk circuit current $I_{\mathrm{cuk}}$, as shown in Figure 4.

In the event of a WTG fault, the DC/DC converter will block the full control device T to bypass the faulty WTG. Assuming an internal fault in the second WTG in Figure 5, the fault current flow path is shown as the dashed line in the figure when the full control device T is blocked.

The topology only needs to control one fully controlled device. The control structure is simple, and the Cuk circuit controls the busbar current to prevent the overvoltage of the wind turbine in the case of an uneven wind speed, which not only solves the power-balancing problem but also ensures the consistency of the series wind turbine current and ensures the reliable operation of the system.

4. Capacitive Energy Transfer DC/DC Converter

4.1. Topological Structure

This section proposes a capacitive energy transfer (CET) DC/DC converter based on the capacitive energy transfer principle, using thyristors and highly controllable half-bridge sub-modules to reduce costs and improve system reliability, and analyzes its operating principle and modulation method in detail.

The three topologies of a DC/DC converter based on the capacitive energy transfer principle are shown in Figure 6.

The three-phase topology is identical for each phase and consists of four sets of commutation valves (T_1j, T_2j, T_3j, T_4j) (j = a, b, c), an inductor L, and a capacitive energy storage bridge arm. The commutation valves are composed of thyristors connected in series to withstand high voltages, and the storage bridge arms are composed of half-bridge sub-modules of identical construction, connected in series to save costs and increase capacity.

The structure can realize the two-way flow of energy: when the power is transferred from the low-voltage side to the high-voltage side, the thyristor T_1j rate is turned on first, and the power flows from the low-voltage side to the energy storage bridge arm; then, T_1j is turned off and T_2j is turned on, and the power flows from the energy storage bridge arm to the high-voltage side. Similarly, when the power is transferred from the high-voltage side to the low-voltage side, the thyristors T_3j and T_4j are activated alternately. The phases of ABC three-phase conduction differ from each other by 120 degrees. $U_L$ and $i_L$ are the low-voltage-side voltage and current, and $U_H$ and $i_H$ are the high-voltage-side voltage and current.

The half-bridge sub-module consists of two IGBTs (S₁, S₂) and a capacitor (C). It has three operating states: when S₁ is on and S₂ is off, the sub-module is in the engaged state, and capacitor C can be charged and discharged. When S₁ is off and S₂ is on, the sub-module is in bypass, and capacitor C can neither be charged nor discharged; its voltage remains constant. When S₁ and S₂ are both off, the sub-module is in a blocked state.

4.2. Introduction to the Principle

The three-phase structure of the CET-type converter is the same; now, we take the first phase as an example to analyze its working principle. The principle is shown in Figure 7.

Figure 7a shows that when converter valve 1 is closed and converter valve 2 is opened, energy flows from the low-pressure side to the energy storage bridge arm. Figure 7b shows that when converter valve 1 is opened and converter valve 2 is closed, energy flows from the energy storage bridge arm to the high-pressure side.

Figure 7 shows the specific circuit structure diagram of the buck boost topology based on CET, which includes the same three-phase circuit, with each phase circuit containing a capacitive energy storage bridge arm and two converter valves. The current waveform of each phase circuit is the same, but the three-phase interleaving operates at 120 degrees, allowing the converter to ensure a continuous input and output DC current. Therefore, there is no need to use bulky AC transformers or filter inductors, and the volume and weight are small. The sub-modules in the arm can be commonly used as half-bridge sub-modules or other sub-modules that can reduce costs or achieve fault-blocking functions. When energy needs to flow from the low-voltage side to the high-voltage side, firstly, commutation valve 1 is turned on, the energy storage bridge arm is connected to the low-voltage side, the voltage of the low-voltage-side UL charges the energy storage bridge arm, and the charging method is stage rotation charging.

For example, if the energy storage bridge arm consists of 100 half-bridge sub-modules, and the voltage of the high-voltage side is two times the voltage of the low-voltage side, then the system will cause 50 of the sub-modules to connect to the circuit and, after charging is completed, the sum of the voltages of these 50 sub-modules will be the low-voltage-side voltage. Then, the fully charged sub-modules will be bypassed, so that the remaining 50 sub-modules will be connected to the circuit and start charging. After all sub-modules are fully charged, their voltages will be equal to two times the low-voltage-side voltage; then, commutation valve 1 will be switched off and commutation valve 2 will be switched on, and the voltage of the capacitive energy storage bridge arm will be supplied to the high-voltage side via commutation valve 2. Thus, the flow of energy from the low-voltage side to the high-voltage side is similar to the process described above and is achieved by controlling the number of sub-modules of the energy storage bridge arm connected to the circuit.

4.3. Parameter Design and Modulation Method

CET type converters use a three-phase staggered operation, with a phase difference of 120° between phases. In order to ensure that, after a short-circuit fault, the converter valve group can withstand the fault voltage without damage, it is necessary to alternately switch on the thyristor at 120°; at the same time, when one phase is running, the other two can be in charge and discharge states, to achieve a continuous flow of power. The on–off condition of the three-phase converter valve is shown in Figure 8.

The number of thyristors contained in the converter valve is related to the maximum fault voltage. Assuming a maximum fault voltage of $U_H$, the number of thyristors to be connected in series can be written as follows:

$$N_{\mathrm{thy}}=\frac{U_H}{{\lambda }_d{U}_B}$$

(18)

In the above equation, where $U_B$ is a thyristor-rated blocking voltage and ${\lambda }_d$ is the thyristor series voltage derating factor, ${\lambda }_d$ is usually 0.8–0.9.

In a CET-type converter, the series thyristor set operates in a zero-voltage on and zero-current off state; thus, the main losses are conduction losses, and the thyristor on-state voltage drop is lower than that of an IGBT. For example, under the condition of withstanding a 200kV DC voltage drop, the number of thyristors in series is 39, whereas the number of IGBTs is 56 (${\lambda }_d$ is 0.8). Therefore, the use of thyristors in series for the converter valve has a significant cost advantage over IGBTs. The average on-state currents of the converter valves T_1j and T_3j during steady-state operation can be written as follows:

$$I_{T1av}=I_{T3av}=\frac{1}{2\pi }{\displaystyle {\int }_0^{\frac{2\pi }{3}}{I}_{L}d\theta =\frac{I_L}{3}}$$

(19)

The average conduction currents for the same commutation valves, T_2j and T_4j, can be written as follows:

$$I_{T2av}=I_{T4av}=\frac{1}{2\pi }{\displaystyle {\int }_0^{\frac{2\pi }{3}}{I}_{H}d\theta =\frac{I_H}{3}}$$

(20)

The capacitance of the half-bridge sub-modules is critical to the energy balance of the energy storage bridge arm during a charge/discharge cycle. The energy of the bridge arm is stored in the capacitance of each half-bridge sub-module; thus, the capacitance voltage is bound to fluctuate during the flow of energy, and the smaller the range of capacitance voltage fluctuation, the better. It is therefore necessary to constrain the range of capacitance voltage fluctuation, and the sub-module capacitance is an important factor affecting the capacitance voltage fluctuation. The maximum value of the energy change in the time range [0, 0.5$T_h$] for the energy storage bridge arm can be expressed as follows:

$$\Delta E={\displaystyle {\int }_0^{0.5T_h}{u}_{pj}{i}_{pj}dt=\frac{U_L{I}_L{T}_h}{3}=\frac{P}{3f_h}}$$

(21)

In the above equation, $T_h$ is the cycle of operation, P is the power, $P=U_L{I}_L=U_H{I}_H$.

The energy of the bridge arm is stored in N sub-modules on average, which leads to the following conclusions:

$$\Delta E=\frac{P}{3f_h}=\frac{1}{2}NC(U_{C\max }^2-U_{C\min }^2)$$

(22)

In the above equation, $U_{C\max }$ is the maximum capacitor voltage and $U_{C\min }$ is the minimum capacitor voltage. Therefore, it can be concluded that the capacitance of the sub-module can be expressed as follows:

$$C=\frac{2P}{3N{f}_h(U_{C\max }^2-U_{C\min }^2)}$$

(23)

We can conclude from the above equation that the sub-module capacitance C is inversely proportional to the operating frequency $f_h$.

For CET converters, the modulation method greatly affects the output voltage’s harmonic characteristics, losses, and stability of operation. In this paper, we use the widely used and mature Nearest Level Control (NLC) scheme and optimize the NLC scheme by combining the working principle of the CET. NLC uses the round (x) function to calculate the required level number to approximate the reference signal [31], firstly using a rounding function and then using a step wave to approximate the required sine wave, and also considering the dynamic effect of the NLC. The output level of the NLC is updated every control cycle T_c. The output level of the nearest level modulation is updated every control period T_c. To ensure the stable operation of the CET and good quality of the output voltage waveform, the control frequency (fc = 1/T_c) should satisfy the following conditions:

$$\pi f\sqrt{2NM}\le f_c\le \pi fNM$$

(24)

In the above equation, $f$ is the AC output frequency, and M is the modulation ratio.

The number of half-bridge sub-modules is also related to the high-voltage-side voltage and the drive voltage. Without taking redundancy into account, the number of sub-modules required per energy storage bridge arm can be calculated as follows:

$$N=\frac{U_H+U_0}{U_C}$$

(25)

In the above equation, $U_H$ is the high-voltage-side voltage, and $U_0$ is the drive voltage. CET has a three-phase identical structure, and thus a total of 3N sub-modules are required, and the current stress required for the fully controlled device IGBT in the sub-module should be the maximum value of the bridge arm current $i_L$. The control block diagram of a CET-type converter is shown in Figure 9.

4.4. Number of Input Sub-Modules

The bridge arm voltage reference signal $u_{pj\_ref}$ is subjected to an upward rounding function to obtain the number of modules to be used for the nearest level modulation:

$$n_{NLC}=ceil(\frac{u_{pj\_ref}}{U_C})$$

(26)

The sub-module drop-cut logic is shown in Figure 10.

5. Simulation Validation and Conclusions

In order to verify the feasibility of the designed new DC/DC converter based on the Cuk circuit and the series–parallel wind farm system solution based on the energy transfer principle for high-voltage and high-power DC/DC converters, a series–parallel all-DC wind turbine generation system with a rated capacity of 24 MW is built based on the PSCAD/TMTDC simulation platform. In this new structure, three series groups, each containing four wind turbines, are selected and connected in parallel to form a series–parallel-type network.

In terms of system structure, the machine-side AC/DC converter of the all-DC wind power system adopts a three-phase, two-level voltage source rectifier; the machine-side DC/DC converter adopts a new DC/DC converter based on the Cuk circuit; and the grid-connected side adopts a high-voltage, high-capacity DC/DC converter based on the energy transfer principle. The whole simulation system is shown in Figure 11.

The selected parameter table for the permanent-magnet direct-drive wind turbine is shown in

Table 1. Main simulation parameters of the system.

Parameters	Value
Rated capacity of the DC wind farm Pwf (MW)	24
Number of DC wind turbines n	12
Rated capacity of DC wind turbine Pwt (MW)	2
The outlet voltage of the wind turbine VS (V)	690
Outlet voltage of the machine-side rectifier VH (kV)	3.3
Switching frequency of the machine-side rectifier fw (Hz)	2000
Switching frequency of the machine-side DC/DC fd (Hz)	10,000
Frequency of CET operation fc (Hz)	150
Bridge arm inductors for CETs Lc (mH)	10
CET sub-module capacitors Cc (mF)	4

.

5.1. Steady-State Operating Condition

Figure 12 shows the parameter waveforms of a series–parallel wind farm under rated steady-state operation. From top to bottom, they are the active power output of DC wind turbines, the outlet voltage of DC wind turbines, the total output voltage of series wind turbines, and the DC bus current.

The simulation results show that the system runs stably when the rated power output of the DC wind turbine is achieved. In order to facilitate the analysis of the operating characteristics of the system, the output characteristics of the DC wind turbine are represented by the DC component of the outlet voltage.

This paper adopts a new DC/DC converter based on the Cuk circuit for the control of the outlet current of a single wind turbine. The size of the output current is controlled by adjusting the duty cycle of the full control device of the new converter so that the output current is as close as possible to the rated current of the wind turbine. This prevents the current of this wind turbine from becoming lower than the rated value due to the small currents of other wind turbines in the same group, thus also preventing the output power of this wind turbine from becoming lower than the rated value under normal wind power. The DC/DC converter outlet current varies with the duty cycle, as shown in Figure 13.

The simulation results show that as the duty cycle rises, the outlet current of the new DC/DC converter also rises, but not in a simple linear relationship, which is consistent with the previous analysis. With the cooperation of the negative feedback mechanism, the outlet current can then be stabilized around the rated current of the wind turbine, thus ensuring that the wind turbine achieves the maximum power output.

5.2. Simulation Analysis of Series–Parallel Wind Turbines with Uneven Wind Speeds

5.2.1. Simulation of Series Wind Turbine with Uneven Wind Speed

The power of (2,1) of the simulated series wind turbines (1,1), (2,1), (3,1), and (4,1) was reduced from 2 MW to 1 MW, whereas the power of the other three wind turbines remained unchanged. The new DC/DC controller proposed in this paper was used for current control, and the measured waveforms are shown in Figure 14.

In Figure 14, the power of wind turbine (2,1), the outlet voltage of the rectifier, and the outlet current of the new DC/DC converter based on the Cuk circuit are shown from top to bottom, respectively. As can be seen from the simulation results, when the power of the series wind turbine (2,1) is reduced due to the wind speed, its voltage also decreases with the same amplitude, but the current remains stable after experiencing small fluctuations. From this, it can be seen that the Cuk circuit has played a role in maintaining the stability of the series wind turbine current, and only when the wind speed causes the output voltage to exceed the rated voltage of the WTGs is it necessary to operate the WTGs in voltage-limiting mode and reduce the pitch angle to reduce the wind energy absorption; therefore, the phenomenon of power below the rated power caused by voltage limiting has been solved.

5.2.2. Simulation of Parallel Wind Turbine with Uneven Wind Speed

The output voltage of the second row of parallel wind turbines (2,2) was simulated to decrease from 3.3 kV to 1.6 kV. We undertook a test as to whether the high-voltage and high-power DC/DC converter (CET) based on the principle of energy transfer could keep the voltage of the wind turbines in the second row consistent with that in the first and third columns. The waveform is shown in Figure 15. From top to bottom, it shows the outlet voltage of the DC/DC converter of the (2,2) wind turbine and the voltage after series of the second wind turbine.

In the figure above, the exit voltage of wind turbine (2,2) and the total voltage of the wind turbine in the second column are shown from top to bottom. As can be seen from the simulation results, after the power of the No. 2 wind turbine decreases for 1.5 s, the outlet voltage of the other three wind turbines in the same series circuit rises briefly and then recovers to the original value. The total voltage of the second-row wind turbine also recovers to its original value before falling after a short decline, indicating that CET has successfully restored the outlet voltage of the wind turbine to a stable state.

5.3. Faulty Operating Conditions

Figure 16 shows the system waveform diagram after wind turbine (3,1) is withdrawn from operation due to an internal fault and is put back into operation after fault or maintenance recovery.

As can be seen from the simulation results, when the internal fault in wind turbine (3,1) is removed, the full control device in the new DC/DC converter is locked, so that the outlet current of the rectifier is gradually attenuated to 0, and then the output power of the fan is attenuated to 0. The power of the other wind turbines does not fluctuate greatly but stabilizes around the original value after experiencing small fluctuations. After the fault in wind turbine (3,1) is repaired and put back into operation, the voltages of the other wind turbines above are also quickly stabilized at the rated operating state after slight fluctuations.

6. Conclusions

Due to the various drawbacks of traditional AC wind farms, this article proposes a new series–parallel structure for all-DC wind power generation systems with typical characteristics of DC convergence and DC transmission. Compared to general series DC wind farms, the topology proposed in this article incorporates a parallel part. The series part uses a DC/DC converter based on the Cuk circuit to solve the current consistency and power balance problems of the series wind turbine through current control, while the parallel end uses a large-capacity DC/DC converter based on the capacity transfer principle to solve the voltage consistency problem at the grid connection end. The series part is used to improve the voltage level of the system, which can reduce the huge construction costs of offshore platforms, while the parallel part is used to increase the capacity of the system.

To verify the effectiveness and feasibility of a new topology wind farm, a 24 MW series–parallel all-DC power generation system based on PSCAD/EMTDC was built for simulation verification. The theoretical analysis and simulation results show the following:

(1)

The series–parallel all-DC power generation system based on a new DC wind turbine proposed in this article can operate well in steady state, unstable wind speeds, and fault conditions and has good stability compared to traditional AC wind farms. It does not have problems of reactive currents and overvoltage, which are brought about by AC transmission, and has more capacity than a simple series DC wind farm.

(2)

The DC/DC converter based on the Cuk circuit proposed in this paper only needs to control one fully controlled device, and its control structure is simple. It can guarantee the stability of the series wind turbine outlet current and solve the power imbalance problem caused by the coupling between series wind turbines, but it also ensures the consistency of the series wind turbine current and ensures the reliable operation of the system.

(3)

The high-voltage, high-capacity DC/DC converter based on the energy transfer principle in this paper can effectively maintain the stability of the voltage at the grid-connected end, avoiding loop currents, and can also effectively guarantee the stable operation of the new power generation system.

The new series–parallel all-DC power generation system proposed in this paper is not only suitable for offshore large-capacity wind farms but also for onshore wind farms, which is conducive to the completion of all-DC wind power generation systems in the future.