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Transformerless Single-Phase Multilevel-Based Photovoltaic Inverter
无变压器单相多级光伏逆变器

Roberto González, Eugenio Gubía, Member, IEEE, Jesús López, Member, IEEE, and Luis Marroyo, Member, IEEE
罗伯托·冈萨雷斯，尤金尼奥·古比亚，IEEE 会员，耶稣·洛佩斯，IEEE 会员，路易斯·马罗约，IEEE 会员

Abstract  摘要

The elimination of the output transformer from gridconnected photovoltaic (PV) systems not only reduces the cost, size, and weight of the conversion stage but also increases the system overall efficiency. However, if the transformer is removed, the galvanic isolation between the PV generator and the grid is lost. This may cause safety hazards in the event of ground faults. In addition, the circulation of leakage currents (common-mode currents) through the stray capacitance between the PV array and the ground would be enabled. Furthermore, when no transformer is used, the inverter could inject direct current (dc) to the grid, causing the saturation of the transformers along the distribution network. While safety requirements in transformerless systems can be met by means of external elements, leakage currents and the injection of dc into the grid must be guaranteed topologically or by the inverter’s control system. This paper proposes a new high-efficiency topology for transformerless systems, which does not generate common-mode currents and topologically guarantees that no dc is injected into the grid. The proposed topology has been verified in a 5 − kW 5 − kW 5-kW5-\mathrm{kW} prototype with satisfactory results.
从并网光伏（PV）系统中消除输出变压器不仅降低了转换阶段的成本、体积和重量，还提高了系统的整体效率。然而，如果去掉变压器，光伏发电机与电网之间的电气隔离就会丧失。这可能在接地故障发生时造成安全隐患。此外，光伏阵列与地面之间的杂散电容会导致漏电流（共模电流）的循环。此外，当不使用变压器时，逆变器可能会向电网注入直流电（dc），导致配电网络中变压器的饱和。虽然无变压器系统的安全要求可以通过外部元件来满足，但漏电流和向电网注入直流电必须通过拓扑结构或逆变器的控制系统来保证。本文提出了一种新的高效拓扑结构，用于无变压器系统，该结构不产生共模电流，并在拓扑上保证不向电网注入直流电。 所提议的拓扑已在一个 5 − kW 5 − kW 5-kW5-\mathrm{kW} 原型中得到了验证，结果令人满意。

Index Terms-Direct current (dc)-alternating current (ac) power conversion, half bridge, photovoltaic (PV) systems, single-phase three-level diode-clamped inverter, transformerless inverter.
索引词-直流（dc）-交流（ac）电力转换，半桥，光伏（PV）系统，单相三电平二极管箝位逆变器，无变压器逆变器。

I. Introduction  一. 引言

GRID-CONNECTED photovoltaic (PV) systems often include a line transformer between the conversion stage and the grid. The transformer guarantees galvanic isolation between the grid and the PV system, thus fulfilling safety standards. Furthermore, it significantly reduces leakage currents between the PV system and the ground and ensures that no direct current (dc) is injected into the grid. However, because of its low frequency ( 50 − 60 Hz 50 − 60 Hz 50-60Hz50-60 \mathrm{~Hz} ), the transformer is big, heavy, and expensive. More to the point, it reduces the overall efficiency of the conversion stage. Because of the cost and size reduction and overall efficiency improvement, the interest on transformerless conversion topologies is growing [1].
并网光伏（PV）系统通常在转换阶段和电网之间包括一个线路变压器。变压器保证了电网与光伏系统之间的电气隔离，从而满足安全标准。此外，它显著减少了光伏系统与地面之间的漏电流，并确保没有直流（dc）注入电网。然而，由于其低频率（ 50 − 60 Hz 50 − 60 Hz 50-60Hz50-60 \mathrm{~Hz} ），变压器体积大、重量重且价格昂贵。更重要的是，它降低了转换阶段的整体效率。由于成本和体积的减少以及整体效率的提高，对无变压器转换拓扑的兴趣正在增长[1]。
In order to keep the system’s features in transformerless PV systems, the inverter must cover the purpose of the transformer.
为了保持无变压器光伏系统的特性，逆变器必须承担变压器的功能。
Safety requirements can be fulfilled by including a ground fault detector in the inverter. A ground fault detector is a simple but reliable device that disconnects the inverter upon the detection of an isolation fault in the installation [2], [3].
安全要求可以通过在逆变器中包含接地故障检测器来满足。接地故障检测器是一种简单但可靠的设备，在检测到安装中的绝缘故障时会断开逆变器。
Fig. 1. Common-mode currents in a transformerless conversion stage.
图 1. 无变压器转换阶段的共模电流。
The galvanic connection between the grid and the PV array results in the appearance of a common-mode resonant circuit consisting, on the stray capacitance, of the PV generator to ground and the filtering elements (Fig. 1) [4], [5]. If the common-mode voltage generated by the inverter includes frequencies close to that of the circuit’s resonance, large commonmode currents will appear. These common-mode currents might cause severe (conducted and radiated) electromagnetic interferences, grid current distortion, and additional losses in the system. To avoid the circulation of these leakage currents in transformerless PV systems, it is necessary to use conversion topologies, which do not generate variable common-mode voltages [4].
光伏阵列与电网之间的电 galvanic 连接导致出现一个共模谐振电路，该电路由光伏发电机到地的杂散电容和滤波元件组成（图 1）[4]，[5]。如果逆变器产生的共模电压包含接近电路谐振频率的频率，将会出现大共模电流。这些共模电流可能导致严重的（传导和辐射）电磁干扰、电网电流失真以及系统中的额外损耗。为了避免在无变压器光伏系统中这些漏电流的循环，有必要使用不产生可变共模电压的转换拓扑[4]。
The injection of dc into the grid is a matter of great concern for electric utility companies because it might cause the saturation of the distribution transformers along the grid [6]. Consequently, limitation standards range from several hundred milliamps in the most lenient countries [7]-[9] down to 20 mA in England [10]. Usually, the grid current is controlled by means of a PI regulator. This type of regulator eliminates the error in the permanent regime, i.e., it guarantees that the error will not have a direct component. However, the current measurement elements (current sensor, operational amplifiers for signal conditioning, and an analog-to-digital converter if the control is digitally implemented) can offset the measurements, resulting in the appearance of a direct component in the grid current. The magnitude of this dc is equal to the sum of all the measuring element offsets. Complying with the most lenient regulations is easily accomplished by means of the control system. However, to attain levels of dc current under 20 mA , measurement devices with very low offsets would be required ( 20 mA in a 3.6 − kW 3.6 − kW 3.6-kW3.6-\mathrm{kW} inverter supposes a total offset of less than 0.125 % 0.125 % 0.125%0.125 \% ), significantly increasing the cost of the hardware. An alternative to the use of such low-offset elements
将直流注入电网是电力公司非常关注的问题，因为这可能导致电网沿线配电变压器的饱和。因此，限制标准在最宽松的国家范围内从几百毫安到英国的 20 毫安不等。通常，电网电流是通过 PI 调节器来控制的。这种类型的调节器消除了稳态下的误差，即它保证误差不会有直接分量。然而，电流测量元件（电流传感器、用于信号调理的运算放大器，以及如果控制是数字实现的则需要模拟到数字转换器）可能会抵消测量，导致电网电流中出现直接分量。这个直流的大小等于所有测量元件偏移的总和。通过控制系统，遵守最宽松的规定是很容易实现的。 然而，要达到低于 20 毫安的直流电流，需要具有非常低偏移的测量设备（在 3.6 − kW 3.6 − kW 3.6-kW3.6-\mathrm{kW} 逆变器中，20 毫安假设总偏移小于 0.125 % 0.125 % 0.125%0.125 \% ），这将显著增加硬件的成本。使用此类低偏移元件的替代方案
is to implement conversion topologies, which ensures no dc injection into the grid.
是实现转换拓扑，以确保不会向电网注入直流。
Several conversion topologies that do not generate variable common-mode voltages have been proposed for use in transformerless PV systems. One of these topologies is the full bridge with bipolar pulsewidth modulation [5], [11], [12]. However, bipolar modulation causes large current ripple and high switching losses, reducing the overall efficiency of the inverter. Furthermore, this topology would not prevent the injection of dc current into the grid. References [5], [13], and [14] are proposals for two modifications of the full-bridge topology, which reduce the current ripple and improve the efficiency of the full-bridge topology. However, these topologies do not resolve the dc problem.
已经提出了几种不产生可变共模电压的转换拓扑，用于无变压器光伏系统。其中一种拓扑是采用双极脉宽调制的全桥拓扑[5]，[11]，[12]。然而，双极调制会导致较大的电流波动和高开关损耗，从而降低逆变器的整体效率。此外，这种拓扑无法防止直流电流注入电网。参考文献[5]，[13]和[14]是对全桥拓扑的两种改进提案，旨在减少电流波动并提高全桥拓扑的效率。然而，这些拓扑并未解决直流问题。
Another topology proposed for transformerless PV systems is the half-bridge inverter [1], [6], [15], [16]. This topology, which besides not generating variable common-mode voltage, guarantees the noninjection of dc current by connecting one of the grid terminals to the midpoint of a capacity divider. However, the half-bridge inverter causes a large current ripple and high switching losses, thus reducing the efficiency of the inverter. In order to improve the efficiency and reduce the current ripple, the use of a single-phase three-level diodeclamped inverter has been proposed [6], [17]-[19]. In this case, the connection of the clamping diodes to the capacity midpoint enables the dc to get to the grid.
另一种为无变压器光伏系统提出的拓扑结构是半桥逆变器[1]，[6]，[15]，[16]。这种拓扑结构除了不产生可变的共模电压外，还通过将电网端子之一连接到电容分压器的中点来保证不注入直流电流。然而，半桥逆变器会导致较大的电流波动和高开关损耗，从而降低逆变器的效率。为了提高效率并减少电流波动，提出了使用单相三电平二极管箝位逆变器[6]，[17]-[19]。在这种情况下，箝位二极管与电容中点的连接使直流电能够进入电网。
This paper proposes a modification of the single-phase threelevel diode-clamped inverter. The resulting conversion topology adds to the advantages of the traditional single-phase three-level diode-clamped inverter, the topological guarantee of the noninjection of dc into the grid. The functioning of the inverter and a proposed control strategy are described later. The results obtained by simulation have been verified in a 5 − kW 5 − kW 5-kW5-\mathrm{kW} prototype.
本文提出了一种单相三电平二极管箝位逆变器的改进。所得到的转换拓扑增加了传统单相三电平二极管箝位逆变器的优点，即对直流电注入电网的拓扑保证。逆变器的工作原理和提出的控制策略将在后文中描述。通过仿真获得的结果已在 5 − kW 5 − kW 5-kW5-\mathrm{kW} 原型中得到了验证。

II. Common-Mode System DESCRIPTION
II. 共模系统描述

When no transformer is used, a galvanic connection between the ground of the grid and the PV array exists. Under these conditions and because of the high stray capacitance between the PV generator and the ground, large ground leakage currents can appear. The amplitude of these currents can exceed the legal norms [9]. In [4], a model is proposed for the analysis of the common-mode system behavior. This model determines the effect, on ground currents, of the conversion topology and the arrangement of its elements.
当不使用变压器时，电网的接地与光伏阵列之间存在电 galvanic 连接。在这些条件下，由于光伏发电机与接地之间的高漏电容，可能会出现大规模的接地漏电流。这些电流的幅度可能超过法律规范 [9]。在 [4] 中，提出了一种用于分析共模系统行为的模型。该模型确定了转换拓扑和其元件排列对接地电流的影响。
Fig. 1 shows a detailed scheme of a transformerless PV system, including the most important stray elements influencing ground current dynamics, which are the stray capacitance between the PV array and the ground C PVg C PVg C_(PVg)C_{\mathrm{PVg}} and the series impedance between the ground connection points of the inverter and the grid Z GcGg Z GcGg  Z_("GcGg ")Z_{\text {GcGg }}. Fig. 1 also shows the inverter inductor (split in two parts L 1 L 1 L_(1)L_{1} and L 2 L 2 L_(2)L_{2}, which are between the line and the neutral), the differential-mode filter capacitor C dm C dm C_(dm)C_{\mathrm{dm}}, and the common-mode filter elements ( L cm L cm L_(cm)L_{\mathrm{cm}} and C cm C cm C_(cm)C_{\mathrm{cm}} ). The effect of the stray capacitances between the inverter outputs and the ground have been disregarded because of their low value relative to that of the PV generator, which, in
图 1 显示了一个无变压器光伏系统的详细方案，包括影响接地电流动态的最重要的杂散元件，即光伏阵列与地面之间的杂散电容 C PVg C PVg C_(PVg)C_{\mathrm{PVg}} 和逆变器与电网接地连接点之间的串联阻抗 Z GcGg Z GcGg  Z_("GcGg ")Z_{\text {GcGg }} 。图 1 还显示了逆变器电感（分为两部分 L 1 L 1 L_(1)L_{1} 和 L 2 L 2 L_(2)L_{2} ，位于相线和中性线之间）、差模滤波电容 C dm C dm C_(dm)C_{\mathrm{dm}} 以及共模滤波元件（ L cm L cm L_(cm)L_{\mathrm{cm}} 和 C cm C cm C_(cm)C_{\mathrm{cm}} ）。由于逆变器输出与地面之间的杂散电容相对于光伏发电机的值较低，因此被忽略。
Fig. 2. PV system model in terms of the converter differential and commonmode voltages.
图 2. 以转换器差模和共模电压为基础的光伏系统模型。
damp environments or on rainy days, can exceed 200 nF / kWp 200 nF / kWp 200nF//kWp200 \mathrm{nF} / \mathrm{kWp} [11], [17].
潮湿环境或雨天，可能超过 200 nF / kWp 200 nF / kWp 200nF//kWp200 \mathrm{nF} / \mathrm{kWp} [11], [17]。
To study the leakage current into the ground, it is useful to describe the system behavior with the help of the common- and differential-mode concepts. The common-mode output voltage of any circuit is the average value of the voltages between the outputs and a common reference. In our case, it is convenient to use the negative terminal of the dc input, which is point N N NN, as the common reference. Therefore, the common-mode voltage of the converter ν cm ν cm nu_(cm)\nu_{\mathrm{cm}} is
为了研究漏电流进入地面，使用共模和差模概念描述系统行为是有用的。任何电路的共模输出电压是输出与共参考之间电压的平均值。在我们的情况下，使用直流输入的负端，即点 N N NN ，作为共参考是方便的。因此，转换器 ν cm ν cm nu_(cm)\nu_{\mathrm{cm}} 的共模电压是
ν cm = ν 1 N + ν 2 N 2 ν cm = ν 1 N + ν 2 N 2 nu_(cm)=(nu_(1N)+nu_(2N))/(2)\nu_{\mathrm{cm}}=\frac{\nu_{1 N}+\nu_{2 N}}{2}
The differential-mode output voltage ν dm ν dm nu_(dm)\nu_{\mathrm{dm}} is defined as the voltage between both converter outputs
差模输出电压 ν dm ν dm nu_(dm)\nu_{\mathrm{dm}} 定义为两个转换器输出之间的电压
ν dm = ν 1 N − ν 2 N = ν 12 ν dm = ν 1 N − ν 2 N = ν 12 nu_(dm)=nu_(1N)-nu_(2N)=nu_(12)\nu_{\mathrm{dm}}=\nu_{1 N}-\nu_{2 N}=\nu_{12}
In real PV systems, there are stray capacitances that provide electrical paths for the ground current, known as the commonmode current i cm i cm i_(cm)i_{\mathrm{cm}}. The value of the common-mode current is a function of the common-mode voltage. However, the value of i cm i cm i_(cm)i_{\mathrm{cm}} cannot be directly deduced from the value of ν cm ν cm nu_(cm)\nu_{\mathrm{cm}} because i cm i cm i_(cm)i_{\mathrm{cm}} is also affected by other voltage sources and by elements such as the system parasitic elements.
在实际的光伏系统中，存在提供接地电流电气路径的杂散电容，称为共模电流 i cm i cm i_(cm)i_{\mathrm{cm}} 。共模电流的值是共模电压的函数。然而， i cm i cm i_(cm)i_{\mathrm{cm}} 的值不能直接从 ν cm ν cm nu_(cm)\nu_{\mathrm{cm}} 的值推导出来，因为 i cm i cm i_(cm)i_{\mathrm{cm}} 也受到其他电压源和系统寄生元件等因素的影响。
The voltages between the outputs of the converter and point N N NN, which are ν 1 N ν 1 N nu_(1N)\nu_{1 N} and ν 2 N ν 2 N nu_(2N)\nu_{2 N}, are determined by the switching modulation sequence. Therefore, both outputs can be studied as controlled voltage sources connected to the negative terminal of the dc input (point N N NN ).
转换器输出与点 N N NN 之间的电压为 ν 1 N ν 1 N nu_(1N)\nu_{1 N} 和 ν 2 N ν 2 N nu_(2N)\nu_{2 N} ，由开关调制序列决定。因此，两个输出可以视为连接到直流输入负端（点 N N NN ）的受控电压源。
By redrawing Fig. 1 and expressing voltages ν 1 N ν 1 N nu_(1N)\nu_{1 N} and ν 2 N ν 2 N nu_(2N)\nu_{2 N} as the functions of ν cm ν cm nu_(cm)\nu_{\mathrm{cm}} and ν dm ν dm nu_(dm)\nu_{\mathrm{dm}}, the model shown in Fig. 2 is obtained.
通过重新绘制图 1，并将电压 ν 1 N ν 1 N nu_(1N)\nu_{1 N} 和 ν 2 N ν 2 N nu_(2N)\nu_{2 N} 表示为 ν cm ν cm nu_(cm)\nu_{\mathrm{cm}} 和 ν dm ν dm nu_(dm)\nu_{\mathrm{dm}} 的函数，得到图 2 所示的模型。
The grid affects the voltage across the stray capacitance between the PV generator and the ground. Considering that the grid is a low-frequency voltage source ( 50 Hz − 60 Hz 50 Hz − 60 Hz 50Hz-60Hz50 \mathrm{~Hz}-60 \mathrm{~Hz} ), its influence on the common-mode current will be hereby ignored. Moreover, the capacitance C dm C dm C_(dm)C_{\mathrm{dm}} does not affect the commonmode current. Fig. 3 results from introducing the equivalent
电网影响光伏发电机与地面之间的漏电容上的电压。考虑到电网是一个低频电压源（ 50 Hz − 60 Hz 50 Hz − 60 Hz 50Hz-60Hz50 \mathrm{~Hz}-60 \mathrm{~Hz} ），因此将忽略其对共模电流的影响。此外，电容 C dm C dm C_(dm)C_{\mathrm{dm}} 不影响共模电流。图 3 是引入等效后得到的结果。
Fig. 3. Model of the common-mode.
图 3. 共模模型。
Fig. 4. Half-bridge inverter.
图 4. 半桥逆变器。
circuits between points A A AA and B B BB in the model of Fig. 2. This model is only applicable to the common-mode analysis.
图 2 中模型中点 A A AA 和 B B BB 之间的电路。该模型仅适用于共模分析。
Besides the voltage source ν cm ν cm nu_(cm)\nu_{\mathrm{cm}}, the model includes the additional voltage source ν s 1 ν s 1 nu_(s1)\nu_{\mathrm{s} 1} due to differential-mode impedance asymmetries, i.e., in the inverter inductors. Therefore, although an inverter does not generate any common-mode voltage, it is possible to have common-mode currents if there are asymmetries in the value of the aforementioned impedances. For this reason, it is convenient to introduce the concept of the total common-mode voltage ν tcm ν tcm  nu_("tcm ")\nu_{\text {tcm }} in order to study the development of ground currents
除了电压源 ν cm ν cm nu_(cm)\nu_{\mathrm{cm}} ，该模型还包括由于差模阻抗不对称而产生的额外电压源 ν s 1 ν s 1 nu_(s1)\nu_{\mathrm{s} 1} ，即在逆变器电感中。因此，尽管逆变器不产生任何共模电压，但如果上述阻抗的值存在不对称，就可能会产生共模电流。因此，引入总共模电压 ν tcm ν tcm  nu_("tcm ")\nu_{\text {tcm }} 的概念是方便的，以便研究接地电流的发展。
ν tcm = ν cm + ν dm L 2 − L 1 2 ( L 1 + L 2 ) ν tcm = ν cm + ν dm L 2 − L 1 2 L 1 + L 2 nu_(tcm)=nu_(cm)+nu_(dm)(L_(2)-L_(1))/(2(L_(1)+L_(2)))\nu_{\mathrm{tcm}}=\nu_{\mathrm{cm}}+\nu_{\mathrm{dm}} \frac{L_{2}-L_{1}}{2\left(L_{1}+L_{2}\right)}
An immediate conclusion is that if the voltage ν tcm ν tcm nu_(tcm)\nu_{\mathrm{tcm}} does not vary, no common-mode current flows through the circuit. This is because the capacitance C PVg C PVg C_(PVg)C_{\mathrm{PVg}} remains charged at voltage ν tcm ν tcm nu_(tcm)\nu_{\mathrm{tcm}}.
一个直接的结论是，如果电压 ν tcm ν tcm nu_(tcm)\nu_{\mathrm{tcm}} 不变化，则没有共模电流流过电路。这是因为电容 C PVg C PVg C_(PVg)C_{\mathrm{PVg}} 在电压 ν tcm ν tcm nu_(tcm)\nu_{\mathrm{tcm}} 下保持充电。

III. Half-BRIDGE InVERTER
III. 半桥逆变器

One of the conversion topologies proposed for PV applications is the half-bridge inverter [1], [6], [15], [16]. The basic elements of this topology, shown in Fig. 4, are comprised of two switches ( S 1 S 1 S_(1)\mathrm{S}_{1} and S 2 S 2 S_(2)\mathrm{S}_{2} ), the inverter inductor L 1 L 1 L_(1)L_{1}, and an input-side capacity divider with its midpoint (2) connected to the neutral terminal of the grid. Characteristically, with this topology, the inverter inductor is connected to a single grid terminal ( L 2 = 0 ) L 2 = 0 (L_(2)=0)\left(L_{2}=0\right), obtaining a constant total common-mode voltage [4].
为光伏应用提出的转换拓扑之一是半桥逆变器[1]，[6]，[15]，[16]。该拓扑的基本元件，如图 4 所示，由两个开关（ S 1 S 1 S_(1)\mathrm{S}_{1} 和 S 2 S 2 S_(2)\mathrm{S}_{2} ）、逆变器电感 L 1 L 1 L_(1)L_{1} 以及一个输入侧电容分压器组成，其中点（2）连接到电网的中性端子。该拓扑的特点是，逆变器电感连接到单个电网端子 ( L 2 = 0 ) L 2 = 0 (L_(2)=0)\left(L_{2}=0\right) ，获得恒定的总共模电压[4]。
Taking into account that the gate signals to turn the switches S 1 S 1 S_(1)S_{1} and S 2 S 2 S_(2)S_{2} on and off must be complementary in order to avoid a short-circuit of the input voltage, the working principle of this topology is straightforward. If S 1 S 1 S_(1)S_{1} is on, the voltage ν 12 = ν in / 2 ν 12 = ν in  / 2 nu_(12)=nu_("in ")//2\nu_{12}=\nu_{\text {in }} / 2, whereas if S 2 S 2 S_(2)\mathrm{S}_{2} is on, the voltage ν 12 = − ν in / 2 ν 12 = − ν in  / 2 nu_(12)=-nu_("in ")//2\nu_{12}=-\nu_{\text {in }} / 2.
考虑到控制开关 S 1 S 1 S_(1)S_{1} 和 S 2 S 2 S_(2)S_{2} 的门信号必须是互补的，以避免输入电压短路，这种拓扑的工作原理很简单。如果 S 1 S 1 S_(1)S_{1} 开启，则电压为 ν 12 = ν in / 2 ν 12 = ν in  / 2 nu_(12)=nu_("in ")//2\nu_{12}=\nu_{\text {in }} / 2 ，而如果 S 2 S 2 S_(2)\mathrm{S}_{2} 开启，则电压为 ν 12 = − ν in / 2 ν 12 = − ν in  / 2 nu_(12)=-nu_("in ")//2\nu_{12}=-\nu_{\text {in }} / 2 。
Fig. 5. Voltage ν 12 ν 12 nu_(12)\nu_{12} and inductor current in a half-bridge inverter. V PV = V PV = V_(PV)=V_{\mathrm{PV}}= 700 V , F sw = 5 kHz 700 V , F sw = 5 kHz 700V,F_(sw)=5kHz700 \mathrm{~V}, F_{\mathrm{sw}}=5 \mathrm{kHz}, and L 1 = 3 mH L 1 = 3 mH L_(1)=3mHL_{1}=3 \mathrm{mH}.
图 5. 半桥逆变器中的电压 ν 12 ν 12 nu_(12)\nu_{12} 和电感电流。 V PV = V PV = V_(PV)=V_{\mathrm{PV}}= 700 V , F sw = 5 kHz 700 V , F sw = 5 kHz 700V,F_(sw)=5kHz700 \mathrm{~V}, F_{\mathrm{sw}}=5 \mathrm{kHz} ，和 L 1 = 3 mH L 1 = 3 mH L_(1)=3mHL_{1}=3 \mathrm{mH} 。
For the correct functioning of the topology, the input voltage must be at least twice the maximum grid voltage. Fig. 5 shows the simulation results of the main electrical variables during a grid period.
为了拓扑的正确运行，输入电压必须至少是最大电网电压的两倍。图 5 显示了在一个电网周期内主要电气变量的仿真结果。
The total common-mode voltage of the half bridge, considering that L 2 = 0 L 2 = 0 L_(2)=0L_{2}=0, is
半桥的总共模电压，考虑到 L 2 = 0 L 2 = 0 L_(2)=0L_{2}=0 ，是
ν tcm = ν cm + ν dm L 2 − L 1 2 ( L 1 + L 2 ) = ν 2 N = ν in 2 = const. ν tcm = ν cm + ν dm L 2 − L 1 2 L 1 + L 2 = ν 2 N = ν in 2 =  const.  nu_(tcm)=nu_(cm)+nu_(dm)(L_(2)-L_(1))/(2(L_(1)+L_(2)))=nu_(2N)=(nu_(in))/(2)=" const. "\nu_{\mathrm{tcm}}=\nu_{\mathrm{cm}}+\nu_{\mathrm{dm}} \frac{L_{2}-L_{1}}{2\left(L_{1}+L_{2}\right)}=\nu_{2 N}=\frac{\nu_{\mathrm{in}}}{2}=\text { const. }
By generating a constant total common-mode voltage, the half bridge guarantees the absence of ground currents.
通过产生恒定的总共模电压，半桥保证了没有接地电流。
For the correct functioning of the half bridge, the voltage ν 2 N ν 2 N nu_(2N)\nu_{2 N} must be kept constant and equal to ν in / 2 ν in / 2 nu_(in)//2\nu_{\mathrm{in}} / 2. This is achieved by implementing a PI to control ν 2 N ν 2 N nu_(2N)\nu_{2 N}, adding a direct component to the grid current reference. The grid current can be expressed as a function of the capacitors C 1 and C 2
为了半桥的正确运行，电压 ν 2 N ν 2 N nu_(2N)\nu_{2 N} 必须保持恒定并等于 ν in / 2 ν in / 2 nu_(in)//2\nu_{\mathrm{in}} / 2 。这通过实施 PI 控制 ν 2 N ν 2 N nu_(2N)\nu_{2 N} 来实现，向电网电流参考添加一个直接分量。电网电流可以表示为电容器 C1 和 C2 的函数。
i g = i C 1 + i C 2 i g = i C 1 + i C 2 i_(g)=i_(C1)+i_(C2)i_{g}=i_{\mathrm{C} 1}+i_{\mathrm{C} 2}
If the capacitors are equal, the current through each capacitor will be the same
如果电容器相等，则每个电容器中的电流将是相同的
i g = i C 1 + i C 2 = 2 ⋅ i C 2 i g = i C 1 + i C 2 = 2 ⋅ i C 2 i_(g)=i_(C1)+i_(C2)=2*i_(C2)i_{g}=i_{\mathrm{C} 1}+i_{\mathrm{C} 2}=2 \cdot i_{\mathrm{C} 2}
The dc injected into the grid by the inverter during one grid cycle i g , dc ( T ) i g , dc ( T ) i_(g,dc)(T)i_{g, \mathrm{dc}}(\mathrm{T}) can be expressed in terms of the grid current
在一个电网周期 i g , dc ( T ) i g , dc ( T ) i_(g,dc)(T)i_{g, \mathrm{dc}}(\mathrm{T}) 中，逆变器注入到电网中的直流电可以用电网电流来表示
i g , dc ( T ) = 1 T ∫ 0 T i g ⋅ d t = 1 T ∫ 0 T 2 ⋅ i C 2 ⋅ d t i g , dc ( T ) = 1 T ∫ 0 T   i g ⋅ d t = 1 T ∫ 0 T   2 ⋅ i C 2 ⋅ d t i_(g,dc)(T)=(1)/(T)int_(0)^(T)i_(g)*dt=(1)/(T)int_(0)^(T)2*i_(C2)*dti_{g, \mathrm{dc}}(T)=\frac{1}{T} \int_{0}^{T} i_{g} \cdot d t=\frac{1}{T} \int_{0}^{T} 2 \cdot i_{\mathrm{C} 2} \cdot d t
If the voltage ν 2 N ν 2 N nu_(2N)\nu_{2 N} is controlled so that its change over one grid cycle is negligible, we obtain
如果电压 ν 2 N ν 2 N nu_(2N)\nu_{2 N} 被控制，使其在一个网格周期内的变化可以忽略不计，我们得到
Δ V 2 N ( T ) = 0 ⇒ ∫ 0 T i C 2 ⋅ d t = 0 Δ V 2 N ( T ) = 0 ⇒ ∫ 0 T   i C 2 ⋅ d t = 0 DeltaV_(2N)(T)=0=>int_(0)^(T)i_(C2)*dt=0\Delta V_{2 N}(T)=0 \Rightarrow \int_{0}^{T} i_{\mathrm{C} 2} \cdot d t=0
Fig. 6. Single-phase three-level diode-clamped inverter.
图 6. 单相三电平二极管箝位逆变器。
Therefore  因此
i g , dc ( T ) = 1 T ∫ 0 T i g ⋅ d t = 1 T ∫ 0 T 2 ⋅ i C 2 ⋅ d t = 0 i g , dc ( T ) = 1 T ∫ 0 T   i g ⋅ d t = 1 T ∫ 0 T   2 ⋅ i C 2 ⋅ d t = 0 i_(g,dc)(T)=(1)/(T)int_(0)^(T)i_(g)*dt=(1)/(T)int_(0)^(T)2*i_(C2)*dt=0i_{g, \mathrm{dc}}(T)=\frac{1}{T} \int_{0}^{T} i_{g} \cdot d t=\frac{1}{T} \int_{0}^{T} 2 \cdot i_{\mathrm{C} 2} \cdot d t=0
From (9), it can be deduced that if ν 2 N ν 2 N nu_(2N)\nu_{2 N} is controlled such that its change over one grid cycle is negligible, then no dc is injected into the grid. This noninjection is independent of the current measurement offsets. More precisely, the offsets of the elements in the current measurement sequence are compensated by the integral part of the regulator of voltage ν 2 N ν 2 N nu_(2N)\nu_{2 N}.
从（9）可以推断，如果 ν 2 N ν 2 N nu_(2N)\nu_{2 N} 被控制，使其在一个网格周期内的变化可以忽略不计，则不会向电网注入直流电。这种非注入与电流测量偏差无关。更准确地说，电流测量序列中元素的偏差由电压 ν 2 N ν 2 N nu_(2N)\nu_{2 N} 的调节器的积分部分进行补偿。
However, the half-bridge inverter has two relevant disadvantages. First, the output voltage ν 12 ν 12 nu_(12)\nu_{12} is modulated between ν in / 2 ν in / 2 nu_(in)//2\nu_{\mathrm{in}} / 2 and − ν in / 2 − ν in / 2 -nu_(in)//2-\nu_{\mathrm{in}} / 2, generating a considerable current ripple. Second, the semiconductors switch with the whole input voltage, which reduces the efficiency of the inverter.
然而，半桥逆变器有两个相关的缺点。首先，输出电压 ν 12 ν 12 nu_(12)\nu_{12} 在 ν in / 2 ν in / 2 nu_(in)//2\nu_{\mathrm{in}} / 2 和 − ν in / 2 − ν in / 2 -nu_(in)//2-\nu_{\mathrm{in}} / 2 之间调制，产生了相当大的电流波动。其次，半导体在整个输入电压下切换，这降低了逆变器的效率。

IV. Single-Phase Three-LeVel DIODE-ClampED INVERTER
IV. 单相三电平二极管箝位逆变器

To improve the efficiency of the half bridge and reduce its current ripple, the use of a single-phase three-level diodeclamped inverter has been proposed [6], [17]-[19]. This topology consists of four switches ( S 1 − S 4 ) S 1 − S 4 (S_(1)-S_(4))\left(\mathrm{S}_{1}-\mathrm{S}_{4}\right) and two diodes ( D 5 D 5 D_(5)\mathrm{D}_{5} and D 6 D 6 D_(6)\mathrm{D}_{6} ) connected to the neutral grid terminal at the midpoint (2) of the input-side capacitive divider (Fig. 6). The diodes D 5 D 5 D_(5)\mathrm{D}_{5} and D 6 D 6 D_(6)\mathrm{D}_{6}, which are also referred to as clamping diodes, limit the voltage seen by the switches S 1 − S 4 S 1 − S 4 S_(1)-S_(4)S_{1}-S_{4} to half the input voltage. As in the case of the half-bridge inverter, the inverter inductor L 1 L 1 L_(1)L_{1} is placed in the line terminal, and no inductor is placed in the neutral terminal ( L 2 = 0 ) L 2 = 0 (L_(2)=0)\left(L_{2}=0\right). The working principle of the topology is described in the following.
为了提高半桥的效率并减少其电流波动，提出了使用单相三电平二极管箝位逆变器的方案[6]，[17]-[19]。该拓扑由四个开关 ( S 1 − S 4 ) S 1 − S 4 (S_(1)-S_(4))\left(\mathrm{S}_{1}-\mathrm{S}_{4}\right) 和两个二极管（