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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（ D 5 D 5 D_(5)\mathrm{D}_{5} 和 D 6 D 6 D_(6)\mathrm{D}_{6} ）组成，连接到输入侧电容分压器中点（2）的中性电网端子（图 6）。二极管 D 5 D 5 D_(5)\mathrm{D}_{5} 和 D 6 D 6 D_(6)\mathrm{D}_{6} ，也称为箝位二极管，限制开关 S 1 − S 4 S 1 − S 4 S_(1)-S_(4)S_{1}-S_{4} 所见电压为输入电压的一半。与半桥逆变器的情况一样，逆变器电感 L 1 L 1 L_(1)L_{1} 放置在线路端子中，而中性端子 ( L 2 = 0 ) L 2 = 0 (L_(2)=0)\left(L_{2}=0\right) 中没有放置电感。该拓扑的工作原理如下所述。
During the grid voltage positive half cycle, S 2 S 2 S_(2)\mathrm{S}_{2} remains on, whereas S 1 S 1 S_(1)S_{1} and S 3 S 3 S_(3)S_{3} commutate at the switching frequency in order to modulate the input voltage. In this case, when S 1 S 1 S_(1)\mathrm{S}_{1} is on and S 3 S 3 S_(3)\mathrm{S}_{3} is off, the voltage ν 12 = ν in − ν 2 N = ν in / 2 ν 12 = ν in  − ν 2 N = ν in / 2 nu_(12)=nu_("in ")-nu_(2N)=nu_(in)//2\nu_{12}=\nu_{\text {in }}-\nu_{2 N}=\nu_{\mathrm{in}} / 2, and the inductor current flowing through S 1 S 1 S_(1)\mathrm{S}_{1} and S 2 S 2 S_(2)\mathrm{S}_{2} increases. When S 1 S 1 S_(1)\mathrm{S}_{1} switches off and S 3 S 3 S_(3)S_{3} comes on, the current flows through D 5 D 5 D_(5)D_{5} and S 2 S 2 S_(2)\mathrm{S}_{2}. In this case, the voltage ν 12 ν 12 nu_(12)\nu_{12} is clamped to zero, and the current decreases.
在电网电压的正半周期， S 2 S 2 S_(2)\mathrm{S}_{2} 保持开启，而 S 1 S 1 S_(1)S_{1} 和 S 3 S 3 S_(3)S_{3} 以开关频率换相以调制输入电压。在这种情况下，当 S 1 S 1 S_(1)\mathrm{S}_{1} 开启而 S 3 S 3 S_(3)\mathrm{S}_{3} 关闭时，电压 ν 12 = ν in − ν 2 N = ν in / 2 ν 12 = ν in  − ν 2 N = ν in / 2 nu_(12)=nu_("in ")-nu_(2N)=nu_(in)//2\nu_{12}=\nu_{\text {in }}-\nu_{2 N}=\nu_{\mathrm{in}} / 2 ，流过 S 1 S 1 S_(1)\mathrm{S}_{1} 和 S 2 S 2 S_(2)\mathrm{S}_{2} 的电感电流增加。当 S 1 S 1 S_(1)\mathrm{S}_{1} 关闭而 S 3 S 3 S_(3)S_{3} 开启时，电流流过 D 5 D 5 D_(5)D_{5} 和 S 2 S 2 S_(2)\mathrm{S}_{2} 。在这种情况下，电压 ν 12 ν 12 nu_(12)\nu_{12} 被钳制为零，电流减少。
During the grid voltage negative half cycle, S 3 S 3 S_(3)\mathrm{S}_{3} remains on, whereas S 2 S 2 S_(2)S_{2} and S 4 S 4 S_(4)S_{4} commutate at the switching frequency. In this case, when S 4 S 4 S_(4)\mathrm{S}_{4} is on and S 2 S 2 S_(2)\mathrm{S}_{2} is off, the voltage ν 12 = ν 12 = nu_(12)=\nu_{12}= − ν 2 N = − ν in / 2 − ν 2 N = − ν in  / 2 -nu_(2N)=-nu_("in ")//2-\nu_{2 N}=-\nu_{\text {in }} / 2, and the current flowing through S 3 S 3 S_(3)\mathrm{S}_{3} and S 4 S 4 S_(4)\mathrm{S}_{4} decreases. When S 4 S 4 S_(4)\mathrm{S}_{4} switches off and S 2 S 2 S_(2)\mathrm{S}_{2} comes on, the current
在电网电压的负半周期中， S 3 S 3 S_(3)\mathrm{S}_{3} 保持开启，而 S 2 S 2 S_(2)S_{2} 和 S 4 S 4 S_(4)S_{4} 以开关频率换相。在这种情况下，当 S 4 S 4 S_(4)\mathrm{S}_{4} 开启而 S 2 S 2 S_(2)\mathrm{S}_{2} 关闭时，电压 ν 12 = ν 12 = nu_(12)=\nu_{12}= − ν 2 N = − ν in / 2 − ν 2 N = − ν in  / 2 -nu_(2N)=-nu_("in ")//2-\nu_{2 N}=-\nu_{\text {in }} / 2 ，流过 S 3 S 3 S_(3)\mathrm{S}_{3} 和 S 4 S 4 S_(4)\mathrm{S}_{4} 的电流减少。当 S 4 S 4 S_(4)\mathrm{S}_{4} 关闭而 S 2 S 2 S_(2)\mathrm{S}_{2} 开启时，电流
Fig. 7. Voltage ν 12 ν 12 nu_(12)\nu_{12} and inductor current in a single-phase three-level diodeclamped inverter. V in = 700 V , F sw = 5 kHz V in = 700 V , F sw = 5 kHz V_(in)=700V,F_(sw)=5kHzV_{\mathrm{in}}=700 \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 7. 单相三电平二极管箝位逆变器中的电压 ν 12 ν 12 nu_(12)\nu_{12} 和电感电流。 V in = 700 V , F sw = 5 kHz V in = 700 V , F sw = 5 kHz V_(in)=700V,F_(sw)=5kHzV_{\mathrm{in}}=700 \mathrm{~V}, F_{\mathrm{sw}}=5 \mathrm{kHz} ，和 L 1 = 3 mH L 1 = 3 mH L_(1)=3mHL_{1}=3 \mathrm{mH} 。
flows through S 3 S 3 S_(3)\mathrm{S}_{3} and D 6 D 6 D_(6)\mathrm{D}_{6}, and the voltage ν 12 ν 12 nu_(12)\nu_{12} is clamped to zero; thus, the coil current increases.
流经 S 3 S 3 S_(3)\mathrm{S}_{3} 和 D 6 D 6 D_(6)\mathrm{D}_{6} ，电压 ν 12 ν 12 nu_(12)\nu_{12} 被钳制为零；因此，线圈电流增加。
Fig. 7 shows the simulation results of the main electrical variables during a grid period. The input voltage, the switching frequency, and the inductance are the same as that used for the half-bridge simulation. Comparing the results shown in Fig. 5 with that in Fig. 7, it can be observed that the threelevel modulation ( ν in / 2 , 0 , − ν in / 2 ν in / 2 , 0 , − ν in / 2 nu_(in)//2,0,-nu_(in)//2\nu_{\mathrm{in}} / 2,0,-\nu_{\mathrm{in}} / 2 ) reduces the current ripple by half.
图 7 显示了在一个电网周期内主要电气变量的仿真结果。输入电压、开关频率和电感与半桥仿真中使用的相同。将图 5 中显示的结果与图 7 中的结果进行比较，可以观察到三电平调制（ ν in / 2 , 0 , − ν in / 2 ν in / 2 , 0 , − ν in / 2 nu_(in)//2,0,-nu_(in)//2\nu_{\mathrm{in}} / 2,0,-\nu_{\mathrm{in}} / 2 ）将电流波动减少了一半。
Following, and in accordance with, the working principle described earlier, the mean instantaneous value of the inverter differential-mode voltage ⟨ ν 12 ⟩ ν 12 (:nu_(12):)\left\langle\nu_{12}\right\rangle is defined. The term “mean instantaneous value” refers to the mean value calculated for the switching period T sw T sw T_(sw)T_{\mathrm{sw}}. The analysis has been made, supposing that the voltage ν 2 N ν 2 N nu_(2N)\nu_{2 N} equals ν in / 2 ν in  / 2 nu_("in ")//2\nu_{\text {in }} / 2.
根据之前描述的工作原理，定义了逆变器差模电压 ⟨ ν 12 ⟩ ν 12 (:nu_(12):)\left\langle\nu_{12}\right\rangle 的平均瞬时值。“平均瞬时值”一词是指在开关周期 T sw T sw T_(sw)T_{\mathrm{sw}} 内计算的平均值。分析假设电压 ν 2 N ν 2 N nu_(2N)\nu_{2 N} 等于 ν in / 2 ν in  / 2 nu_("in ")//2\nu_{\text {in }} / 2 。
During the grid voltage’s positive half cycle
在电网电压的正半周期期间
⟨ ν 12 ⟩ = ( ν in − ν 2 N ) ⋅ t on , S 1 T sw = ν in 2 ⋅ t on , S 1 T sw . ν 12 = ν in − ν 2 N ⋅ t on , S 1 T sw = ν in 2 ⋅ t on , S 1 T sw . (:nu_(12):)=(nu_(in)-nu_(2N))*(t_(on,S_(1)))/(T_(sw))=(nu_(in))/(2)*(t_(on,S_(1)))/(T_(sw)).\left\langle\nu_{12}\right\rangle=\left(\nu_{\mathrm{in}}-\nu_{2 N}\right) \cdot \frac{t_{\mathrm{on}, \mathrm{~S}_{1}}}{T_{\mathrm{sw}}}=\frac{\nu_{\mathrm{in}}}{2} \cdot \frac{t_{\mathrm{on}, \mathrm{~S}_{1}}}{T_{\mathrm{sw}}} .
During the grid voltage negative half cycle
在电网电压的负半周期间
⟨ ν 12 ⟩ = − ν 2 N ⋅ t on , S 4 T sw = − ν in 2 ⋅ t on , S 4 T sw . ν 12 = − ν 2 N ⋅ t on , S 4 T sw = − ν in 2 ⋅ t on , S 4 T sw . (:nu_(12):)=-nu_(2N)*(t_(on,S_(4)))/(T_(sw))=-(nu_(in))/(2)*(t_(on,S_(4)))/(T_(sw)).\left\langle\nu_{12}\right\rangle=-\nu_{2 N} \cdot \frac{t_{\mathrm{on}, \mathrm{~S}_{4}}}{T_{\mathrm{sw}}}=-\frac{\nu_{\mathrm{in}}}{2} \cdot \frac{t_{\mathrm{on}, \mathrm{~S}_{4}}}{T_{\mathrm{sw}}} .
Assuming that the mean instantaneous voltage of L 1 L 1 L_(1)L_{1} is negligible, it is obtained as
假设 L 1 L 1 L_(1)L_{1} 的平均瞬时电压可以忽略不计，则得到
⟨ ν 12 ⟩ = ν g = ν in 2 ⋅ m ν 12 = ν g = ν in 2 ⋅ m (:nu_(12):)=nu_(g)=(nu_(in))/(2)*m\left\langle\nu_{12}\right\rangle=\nu_{g}=\frac{\nu_{\mathrm{in}}}{2} \cdot m
where m m mm is the duty ratio defined as
其中 m m mm 是定义为的占空比
m = { t on , S 1 T Sw , if ν g ≥ 0 ( positive half cycle ) − t on , S 4 T sw , if ν g < 0 ( negative half cycle ) . m = t on , S 1 T Sw ,       if  ν g ≥ 0 (  positive half cycle  ) − t on , S 4 T sw ,       if  ν g < 0 (  negative half cycle  ) . m={[(t_(on,S_(1)))/(T_(Sw))","," if "nu_(g) >= 0(" positive half cycle ")],[-(t_(on,S_(4)))/(T_(sw))","," if "nu_(g) < 0(" negative half cycle ").]:}m= \begin{cases}\frac{t_{\mathrm{on}, \mathrm{~S}_{1}}}{T_{\mathrm{Sw}}}, & \text { if } \nu_{g} \geq 0(\text { positive half cycle }) \\ -\frac{t_{\mathrm{on}, \mathrm{~S}_{4}}}{T_{\mathrm{sw}}}, & \text { if } \nu_{g}<0(\text { negative half cycle }) .\end{cases}
The total common-mode voltage of the single-phase threelevel diode-clamped inverter, considering that L 2 = 0 L 2 = 0 L_(2)=0L_{2}=0, is
单相三电平二极管箝位逆变器的总共模电压，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 = ν tcm = ν cm + ν dm L 2 − L 1 2 L 1 + L 2 = ν 2 N = ν in 2 = nu_(tcm)=nu_(cm)+nu_(dm)(L_(2)-L_(1))/(2(L_(1)+L_(2)))=nu_(2N)=(nu_(in))/(2)=\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}= const.   ν tcm = ν cm + ν dm L 2 − L 1 2 ( L 1 + L 2 ) = ν 2 N = ν in 2 = ν tcm = ν cm + ν dm L 2 − L 1 2 L 1 + L 2 = ν 2 N = ν in 2 = nu_(tcm)=nu_(cm)+nu_(dm)(L_(2)-L_(1))/(2(L_(1)+L_(2)))=nu_(2N)=(nu_(in))/(2)=\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}= 常量。
Considering that the total common-mode voltage generated is constant, the topology guarantees the absence of ground currents.
考虑到产生的总共模电压是恒定的，该拓扑保证了没有接地电流。
With regard to dc, the connection of the diodes at the midpoint means that (5) is no longer applicable. The new relationship between the capacitor and grid currents depends on the configuration of the PV generator. In [6], the midpoint of the PV generator is connected to the capacitive midpoint (dotted line in Fig. 6). In this manner, the PV generator fixes the voltage ν 2 N ν 2 N nu_(2N)\nu_{2 N}, and the grid dc is proportional to the offsets of the measuring elements. Alternatively, this connection need not be made. In this case, the voltage ν 2 N ν 2 N nu_(2N)\nu_{2 N} must be controlled in a manner that is similar to that described for the half bridge. The grid current will then be given by
关于直流电，二极管在中点的连接意味着（5）不再适用。电容器和电网电流之间的新关系取决于光伏发电机的配置。在[6]中，光伏发电机的中点连接到电容中点（图 6 中的虚线）。通过这种方式，光伏发电机固定电压 ν 2 N ν 2 N nu_(2N)\nu_{2 N} ，而电网直流电与测量元件的偏移成正比。或者，这种连接也不必进行。在这种情况下，电压 ν 2 N ν 2 N nu_(2N)\nu_{2 N} 必须以类似于半桥所描述的方式进行控制。然后，电网电流将由
i g = i C 1 + i C 2 + i d = 2 ⋅ i C 2 + i d i g = i C 1 + i C 2 + i d = 2 ⋅ i C 2 + i d i_(g)=i_(C1)+i_(C2)+i_(d)=2*i_(C2)+i_(d)i_{g}=i_{\mathrm{C} 1}+i_{\mathrm{C} 2}+i_{\mathrm{d}}=2 \cdot i_{\mathrm{C} 2}+i_{\mathrm{d}}
Thus, the value of the dc injected into the grid will be
因此，注入电网的直流值将是
i g , dc ( T ) = 1 T ∫ 0 T i g ⋅ d t = 1 T ∫ 0 T ( 2 ⋅ i C 2 + i d ) ⋅ d t = 1 T ∫ 0 T 2 ⋅ i C 2 ⋅ d t + 1 T ∫ 0 T i d ⋅ d t i g , dc ( T ) = 1 T ∫ 0 T   i g ⋅ d t = 1 T ∫ 0 T   2 ⋅ i C 2 + i d ⋅ d t = 1 T ∫ 0 T   2 ⋅ i C 2 ⋅ d t + 1 T ∫ 0 T   i d ⋅ d t {:[i_(g,dc)(T)=(1)/(T)int_(0)^(T)i_(g)*dt=(1)/(T)int_(0)^(T)(2*i_(C2)+i_(d))*dt],[=(1)/(T)int_(0)^(T)2*i_(C2)*dt+(1)/(T)int_(0)^(T)i_(d)*dt]:}\begin{aligned} i_{g, \mathrm{dc}}(T) & =\frac{1}{T} \int_{0}^{T} i_{g} \cdot d t=\frac{1}{T} \int_{0}^{T}\left(2 \cdot i_{\mathrm{C} 2}+i_{\mathrm{d}}\right) \cdot d t \\ & =\frac{1}{T} \int_{0}^{T} 2 \cdot i_{\mathrm{C} 2} \cdot d t+\frac{1}{T} \int_{0}^{T} i_{\mathrm{d}} \cdot d t \end{aligned}
The voltage ν 2 N ν 2 N nu_(2N)\nu_{2 N} is kept constant during one grid cycle. Introducing (8) into (16), we obtain
在一个电网周期内，电压 ν 2 N ν 2 N nu_(2N)\nu_{2 N} 保持不变。将(8)代入(16)，我们得到
i g , dc ( T ) = 1 T ∫ 0 T i d ⋅ d t i g , dc ( T ) = 1 T ∫ 0 T   i d ⋅ d t i_(g,dc)(T)=(1)/(T)int_(0)^(T)i_(d)*dti_{g, \mathrm{dc}}(T)=\frac{1}{T} \int_{0}^{T} i_{\mathrm{d}} \cdot d t
The current flowing through the diodes i d i d i_(d)i_{\mathrm{d}} equals the grid current when D 5 D 5 D_(5)\mathrm{D}_{5} or D 6 D 6 D_(6)\mathrm{D}_{6} are conducting and is negligible if the diodes are switched off. According to (12) and (13), the diodes’ switching periods can be calculated as a function of the input and grid voltages.
通过二极管的电流 i d i d i_(d)i_{\mathrm{d}} 等于当 D 5 D 5 D_(5)\mathrm{D}_{5} 或 D 6 D 6 D_(6)\mathrm{D}_{6} 导通时的电网电流，如果二极管关闭则可以忽略不计。根据（12）和（13），二极管的开关周期可以作为输入和电网电压的函数进行计算。
During the grid voltage positive half cycle
在电网电压正半周期间
t on , D 5 T sw = 1 − t on , S 1 T sw = 1 − 2 ⋅ ν g ν in t on , D 5 T sw = 1 − t on , S 1 T sw = 1 − 2 ⋅ ν g ν in (t_(on,D_(5)))/(T_(sw))=1-(t_(on,S_(1)))/(T_(sw))=1-(2*nu_(g))/(nu_(in))\frac{t_{\mathrm{on}, \mathrm{D}_{5}}}{T_{\mathrm{sw}}}=1-\frac{t_{\mathrm{on}, \mathrm{~S}_{1}}}{T_{\mathrm{sw}}}=1-\frac{2 \cdot \nu_{g}}{\nu_{\mathrm{in}}}
During the grid voltage negative half cycle
在电网电压的负半周期间
t on , D 6 T sw = 1 − t on , S 4 T sw = 1 − 2 ⋅ ( − ν g ) ν in t on , D 6 T sw = 1 − t on , S 4 T sw = 1 − 2 ⋅ − ν g ν in (t_(on,D_(6)))/(T_(sw))=1-(t_(on,S_(4)))/(T_(sw))=1-(2*(-nu_(g)))/(nu_(in))\frac{t_{\mathrm{on}, \mathrm{D}_{6}}}{T_{\mathrm{sw}}}=1-\frac{t_{\mathrm{on}, \mathrm{~S}_{4}}}{T_{\mathrm{sw}}}=1-\frac{2 \cdot\left(-\nu_{g}\right)}{\nu_{\mathrm{in}}}
The mean instantaneous value of the current circulating through the diodes ⟨ i d ⟩ i d (:i_(d):)\left\langle i_{\mathrm{d}}\right\rangle (Fig. 8) is calculated according to (18) and (19)
通过公式（18）和（19）计算流经二极管 ⟨ i d ⟩ i d (:i_(d):)\left\langle i_{\mathrm{d}}\right\rangle （图 8）的电流的平均瞬时值。
⟨ i d ⟩ = 1 T sw ∫ 0 T sw i d ( t ) ⋅ d t = i g ⋅ d r i d = 1 T sw ∫ 0 T sw   i d ( t ) ⋅ d t = i g ⋅ d r (:i_(d):)=(1)/(T_(sw))int_(0)^(T_(sw))i_(d)(t)*dt=i_(g)*d_(r)\left\langle i_{\mathrm{d}}\right\rangle=\frac{1}{T_{\mathrm{sw}}} \int_{0}^{T_{\mathrm{sw}}} i_{\mathrm{d}}(t) \cdot d t=i_{g} \cdot d_{r}
where d r d r d_(r)d_{r} relates the grid and the input voltages so that
其中 d r d r d_(r)d_{r} 关联网格和输入电压，以便
d r = 1 − 2 ⋅ | ν g | ν in . d r = 1 − 2 ⋅ ν g ν in . d_(r)=1-(2*|nu_(g)|)/(nu_(in)).d_{r}=1-\frac{2 \cdot\left|\nu_{g}\right|}{\nu_{\mathrm{in}}} .
Fig. 8. Mean instantaneous value of current i d , ⟨ i d ⟩ . P = 5 kW , V g = i d , i d . P = 5 kW , V g = i_(d),(:i_(d):).P=5kW,V_(g)=i_{\mathrm{d}},\left\langle i_{\mathrm{d}}\right\rangle . P=5 \mathrm{~kW}, V_{g}= 230 V , and V in = 700 V V in  = 700 V V_("in ")=700VV_{\text {in }}=700 \mathrm{~V}.
图 8. 电流的平均瞬时值 i d , ⟨ i d ⟩ . P = 5 kW , V g = i d , i d . P = 5 kW , V g = i_(d),(:i_(d):).P=5kW,V_(g)=i_{\mathrm{d}},\left\langle i_{\mathrm{d}}\right\rangle . P=5 \mathrm{~kW}, V_{g}= 230 V 和 V in = 700 V V in  = 700 V V_("in ")=700VV_{\text {in }}=700 \mathrm{~V} 。
Fig. 9. (a) Factor d r d r d_(r)d_{r} over one grid period. V g = 230 V . V in = 700 V V g = 230 V . V in  = 700 V V_(g)=230V.V_("in ")=700VV_{g}=230 \mathrm{~V} . V_{\text {in }}=700 \mathrm{~V}. (b) Harmonic analysis of the factor d r d r d_(r)d_{r}.
图 9. (a) 因子 d r d r d_(r)d_{r} 在一个网格周期内。 V g = 230 V . V in = 700 V V g = 230 V . V in  = 700 V V_(g)=230V.V_("in ")=700VV_{g}=230 \mathrm{~V} . V_{\text {in }}=700 \mathrm{~V} 。(b) 因子 d r d r d_(r)d_{r} 的谐波分析。
As seen in Fig. 9(a), d r d r d_(r)d_{r} is a periodic wave with a frequency that is twice that of the grid. Considering that d r d r d_(r)d_{r} is a periodic signal, it can be expanded into a Fourier series. The series includes sine terms of frequencies that are the multiples of the fundamental repetition frequency ( 2 ω ) ( 2 ω ) (2omega)(2 \omega)
如图 9(a)所示， d r d r d_(r)d_{r} 是一个频率是网格频率两倍的周期波。考虑到 d r d r d_(r)d_{r} 是一个周期信号，它可以展开为傅里叶级数。该级数包括频率为基本重复频率 ( 2 ω ) ( 2 ω ) (2omega)(2 \omega) 的倍数的正弦项。
d r = d r , dc + ∑ n = 1 ∞ d r n ⋅ sin ⁡ ( n 2 ω t + β n ) d r = d r , dc + ∑ n = 1 ∞   d r n ⋅ sin ⁡ n 2 ω t + β n d_(r)=d_(r,dc)+sum_(n=1)^(oo)d_(rn)*sin(n2omega t+beta_(n))d_{r}=d_{r, \mathrm{dc}}+\sum_{n=1}^{\infty} d_{r n} \cdot \sin \left(n 2 \omega t+\beta_{n}\right)
Fig. 9(b) shows the harmonic decomposition of d r d r d_(r)d_{r}. These harmonics are multiples of 2 ω 2 ω 2omega2 \omega. In addition, this figure indicates
图 9(b)显示了 d r d r d_(r)d_{r} 的谐波分解。这些谐波是 2 ω 2 ω 2omega2 \omega 的倍数。此外，该图还指示
that the harmonic with the greatest amplitude is that which occurs at 2 ω 2 ω 2omega2 \omega.
在 2 ω 2 ω 2omega2 \omega 处出现的谐波具有最大的振幅。
The grid current i g i g i_(g)i_{g} is controlled to follow the reference current, i.e., a sine wave of the same frequency as the grid voltage ν g ν g nu_(g)\nu_{g}. However, in practice, this current will present a series of harmonics due to, among other reasons, the dead time between same branch switch commutations and the presence of harmonics in the grid voltage. The grid current might be written as
电网电流 i g i g i_(g)i_{g} 被控制为跟随参考电流，即与电网电压 ν g ν g nu_(g)\nu_{g} 频率相同的正弦波。然而，在实际中，由于同一支路开关切换之间的死区时间以及电网电压中存在的谐波等原因，这个电流会呈现出一系列谐波。电网电流可以写为
i g = ∑ n = 1 ∞ i g n ⋅ sin ⁡ ( n ω t + φ n ) i g = ∑ n = 1 ∞   i g n ⋅ sin ⁡ n ω t + φ n i_(g)=sum_(n=1)^(oo)i_(g_(n))*sin(n omega t+varphi_(n))i_{g}=\sum_{n=1}^{\infty} i_{g_{n}} \cdot \sin \left(n \omega t+\varphi_{n}\right)
From i g i g i_(g)i_{g} and d r d r d_(r)d_{r}, it is possible to calculate the dc injected into the grid during one grid cycle i g , dc ( T ) i g , dc ( T ) i_(g,dc)(T)i_{g, \mathrm{dc}}(\mathrm{T})
从 i g i g i_(g)i_{g} 和 d r d r d_(r)d_{r} ，可以计算在一个电网周期 i g , dc ( T ) i g , dc ( T ) i_(g,dc)(T)i_{g, \mathrm{dc}}(\mathrm{T}) 中注入电网的直流电
i g , dc ( T ) = 1 T ∫ 0 T i d ⋅ d t = 1 T ∫ 0 T i g ⋅ d r ⋅ d t = 1 T ∫ 0 T ( ∑ i = 1 ∞ i g i sin ⁡ ( i ω t + φ i ) ) × ( d r , dc + ∑ j = 1 ∞ d r j sin ⁡ ( 2 ⋅ j ω t + β j ) ) ⋅ d t i g , dc ( T ) = 1 T ∫ 0 T   i d ⋅ d t = 1 T ∫ 0 T   i g ⋅ d r ⋅ d t = 1 T ∫ 0 T   ∑ i = 1 ∞   i g i sin ⁡ i ω t + φ i × d r , dc + ∑ j = 1 ∞   d r j sin ⁡ 2 ⋅ j ω t + β j ⋅ d t {:[i_(g,dc)(T)=(1)/(T)int_(0)^(T)i_(d)*dt=(1)/(T)int_(0)^(T)i_(g)*d_(r)*dt],[=(1)/(T)int_(0)^(T)(sum_(i=1)^(oo)i_(g_(i))sin(i omega t+varphi_(i)))],[ xx(d_(r,dc)+sum_(j=1)^(oo)d_(rj)sin(2*j omega t+beta_(j)))*dt]:}\begin{aligned} i_{g, \mathrm{dc}}(T)= & \frac{1}{T} \int_{0}^{T} i_{\mathrm{d}} \cdot d t=\frac{1}{T} \int_{0}^{T} i_{g} \cdot d_{r} \cdot d t \\ = & \frac{1}{T} \int_{0}^{T}\left(\sum_{i=1}^{\infty} i_{g_{i}} \sin \left(i \omega t+\varphi_{i}\right)\right) \\ & \times\left(d_{r, \mathrm{dc}}+\sum_{j=1}^{\infty} d_{r j} \sin \left(2 \cdot j \omega t+\beta_{j}\right)\right) \cdot d t \end{aligned}
by applying  通过应用
∫ 0 T sin ⁡ ( i ω t + φ i ) ⋅ sin ⁡ ( j ω t + φ j ) ⋅ d t = 0 ∀ i ≠ j ∫ 0 T   sin ⁡ i ω t + φ i ⋅ sin ⁡ j ω t + φ j ⋅ d t = 0 ∀ i ≠ j int_(0)^(T)sin(i omega t+varphi_(i))*sin(j omega t+varphi_(j))*dt=0quad AA i!=j\int_{0}^{T} \sin \left(i \omega t+\varphi_{i}\right) \cdot \sin \left(j \omega t+\varphi_{j}\right) \cdot d t=0 \quad \forall i \neq j
This way, from (24) and (25), it is concluded that the grid current even harmonics can generate a direct component, which is even if the voltage ν 2 N ν 2 N nu_(2N)\nu_{2 N} remains constant during the cycle. The amplitude of the dc will depend on the order and amplitude of the even harmonics and the phase difference with respect to d r d r d_(r)d_{r}. Considering the harmonic spectrum of d r d r d_(r)d_{r} [Fig. 9(b)], the most troublesome even harmonic will be the second one. Fig. 10 shows the dc resulting from the second harmonic of the grid current. The dc is plotted as a function of the harmonic amplitude and its phase difference that is relative to the fundamental ( β n ) β n (beta_(n))\left(\beta_{n}\right). Calculations are based on 5 − kW 5 − kW 5-kW5-\mathrm{kW} power and an effective grid voltage of 230 V . The phase difference between the voltage and the fundamental is assumed to be zero ( φ 1 = 0 ) φ 1 = 0 (varphi_(1)=0)\left(\varphi_{1}=0\right) because, in general, PV inverters work with unity power factor. As shown in Fig. 10, the presence of a 2% second harmonic in the grid current, which is 90 ∘ 90 ∘ 90^(@)90^{\circ} out-of-phase with the fundamental, results in the injection of 120 mA of the dc to the grid.
通过（24）和（25），可以得出结论，电网电流的偶次谐波可以产生直流分量，即使电压 ν 2 N ν 2 N nu_(2N)\nu_{2 N} 在周期内保持不变。直流的幅度将取决于偶次谐波的阶数和幅度以及相对于 d r d r d_(r)d_{r} 的相位差。考虑到 d r d r d_(r)d_{r} 的谐波谱[图 9(b)]，最麻烦的偶次谐波将是第二个。图 10 显示了由电网电流的第二谐波产生的直流。直流作为谐波幅度及其相对于基波 ( β n ) β n (beta_(n))\left(\beta_{n}\right) 的相位差的函数绘制。计算基于 5 − kW 5 − kW 5-kW5-\mathrm{kW} 功率和 230 V 的有效电网电压。假设电压与基波之间的相位差为零 ( φ 1 = 0 ) φ 1 = 0 (varphi_(1)=0)\left(\varphi_{1}=0\right) ，因为一般来说，光伏逆变器以单位功率因数工作。如图 10 所示，电网电流中存在 2%的第二谐波，与基波 90 ∘ 90 ∘ 90^(@)90^{\circ} 相位相反，导致向电网注入 120 mA 的直流。

V. Proposed Topology  V. 提议的拓扑

The proposed topology is based on the single-phase threelevel diode-clamped inverter. The new topology adds a second capacitive divider to which the neutral grid terminal is connected (Fig. 11). This way, the voltage at the midpoint of the additional capacitive divider (MP2) is controlled and the
所提议的拓扑基于单相三电平二极管箝位逆变器。新的拓扑增加了一个第二个电容分压器，接入中性网终端（图 11）。这样，额外电容分压器的中点电压（MP2）得以控制，且
Fig. 10. DC injected into the grid i g , dc ( A ) i g , dc ( A ) i_(g,dc)(A)i_{g, \mathrm{dc}}(A) as a consequence of a second harmonic in the grid current.
图 10. 由于电网电流中的二次谐波，注入电网的直流电 i g , dc ( A ) i g , dc ( A ) i_(g,dc)(A)i_{g, \mathrm{dc}}(A) 。
Fig. 11. Proposed topology.
图 11. 提议的拓扑。
noninjection of the dc to the grid is topologically guaranteed. At the same time, the topology retains the positive characteristics of the single-phase three-level diode-clamped inverter; namely, the nongeneration of variable total common-mode voltage, the reduced current ripple, and the efficiency.
直流电源不注入到电网是拓扑上保证的。同时，该拓扑保留了单相三电平二极管箝位逆变器的积极特性；即不产生可变的总共模电压，降低了电流波动，并提高了效率。
Next, the differences between the single-phase three-level diode-clamped inverter and the proposed topology working principle are discussed. During the grid voltage positive half cycle, which is when S 1 S 1 S_(1)\mathrm{S}_{1} and S 2 S 2 S_(2)\mathrm{S}_{2} are on, the voltage ν 1 − MP 2 = ν 1 − MP 2 = nu_(1-MP2)=\nu_{1-\mathrm{MP} 2}= ν in − ν MP 2 ν in − ν MP 2 nu_(in)-nu_(MP2)\nu_{\mathrm{in}}-\nu_{\mathrm{MP} 2}. When S 2 S 2 S_(2)\mathrm{S}_{2} and D 5 D 5 D_(5)\mathrm{D}_{5} conduct, ν 1 − MP 2 = ν MP 1 − ν 1 − MP 2 = ν MP 1 − nu_(1-MP2)=nu_(MP1)-\nu_{1-\mathrm{MP} 2}=\nu_{\mathrm{MP} 1}- ν MP 2 ν MP 2 nu_(MP2)\nu_{\mathrm{MP} 2}. During the negative half-cycle, while S 3 S 3 S_(3)\mathrm{S}_{3} and S 4 S 4 S_(4)\mathrm{S}_{4} are on, ν 1 − MP 2 = ν MP 1 − ν in ν 1 − MP 2 = ν MP 1 − ν in nu_(1-MP2)=nu_(MP1)-nu_(in)\nu_{1-\mathrm{MP} 2}=\nu_{\mathrm{MP} 1}-\nu_{\mathrm{in}}. While S 3 S 3 S_(3)\mathrm{S}_{3} and D 6 D 6 D_(6)\mathrm{D}_{6} conduct, ν 1 − MP 2 = ν 1 − MP 2 = nu_(1-MP2)=\nu_{1-\mathrm{MP} 2}= ν MP 1 − ν MP 2 ν MP 1 − ν MP 2 nu_(MP1)-nu_(MP2)\nu_{\mathrm{MP} 1}-\nu_{\mathrm{MP} 2}.
接下来，讨论单相三电平二极管箝位逆变器与所提拓扑工作原理之间的差异。在电网电压的正半周期，即 S 1 S 1 S_(1)\mathrm{S}_{1} 和 S 2 S 2 S_(2)\mathrm{S}_{2} 导通时，电压 ν 1 − MP 2 = ν 1 − MP 2 = nu_(1-MP2)=\nu_{1-\mathrm{MP} 2}= ν in − ν MP 2 ν in − ν MP 2 nu_(in)-nu_(MP2)\nu_{\mathrm{in}}-\nu_{\mathrm{MP} 2} 。当 S 2 S 2 S_(2)\mathrm{S}_{2} 和 D 5 D 5 D_(5)\mathrm{D}_{5} 导通时， ν 1 − MP 2 = ν MP 1 − ν 1 − MP 2 = ν MP 1 − nu_(1-MP2)=nu_(MP1)-\nu_{1-\mathrm{MP} 2}=\nu_{\mathrm{MP} 1}- ν MP 2 ν MP 2 nu_(MP2)\nu_{\mathrm{MP} 2} 。在负半周期，当 S 3 S 3 S_(3)\mathrm{S}_{3} 和 S 4 S 4 S_(4)\mathrm{S}_{4} 导通时， ν 1 − MP 2 = ν MP 1 − ν in ν 1 − MP 2 = ν MP 1 − ν in nu_(1-MP2)=nu_(MP1)-nu_(in)\nu_{1-\mathrm{MP} 2}=\nu_{\mathrm{MP} 1}-\nu_{\mathrm{in}} 。当 S 3 S 3 S_(3)\mathrm{S}_{3} 和 D 6 D 6 D_(6)\mathrm{D}_{6} 导通时， ν 1 − MP 2 = ν 1 − MP 2 = nu_(1-MP2)=\nu_{1-\mathrm{MP} 2}= ν MP 1 − ν MP 2 ν MP 1 − ν MP 2 nu_(MP1)-nu_(MP2)\nu_{\mathrm{MP} 1}-\nu_{\mathrm{MP} 2} 。
The mean instantaneous value of the proposed inverter differential-mode voltage ⟨ ν 1 − MP 2 ⟩ ν 1 − MP 2 (:nu_(1-MP2):)\left\langle\nu_{1-\mathrm{MP} 2}\right\rangle during the positive half cycle is
所提议的逆变器差模电压 ⟨ ν 1 − MP 2 ⟩ ν 1 − MP 2 (:nu_(1-MP2):)\left\langle\nu_{1-\mathrm{MP} 2}\right\rangle 在正半周期的平均瞬时值是
⟨ ν 1 − MP 2 ⟩ = ( ν in − ν MP 2 ) ⋅ t on , S 1 + ( ν MP 1 − ν MP 2 ) ⋅ ( T sw − t on , S 1 ) T sw . ν 1 − MP 2 = ν in − ν MP 2 ⋅ t on , S 1 + ν MP 1 − ν MP 2 ⋅ T sw − t on , S 1 T sw . {:[(:nu_(1-MP2):)],[=((nu_(in)-nu_(MP2))*t_(on,S_(1))+(nu_(MP1)-nu_(MP2))*(T_(sw)-t_(on,S_(1))))/(T_(sw)).]:}\begin{aligned} & \left\langle\nu_{1-\mathrm{MP} 2}\right\rangle \\ & =\frac{\left(\nu_{\mathrm{in}}-\nu_{\mathrm{MP} 2}\right) \cdot t_{\mathrm{on}, \mathrm{~S}_{1}}+\left(\nu_{\mathrm{MP} 1}-\nu_{\mathrm{MP} 2}\right) \cdot\left(T_{\mathrm{sw}}-t_{\mathrm{on}, \mathrm{~S}_{1}}\right)}{T_{\mathrm{sw}}} . \end{aligned}
During the negative half cycle
在负半周期期间
⟨ ν 1 − MP 2 ⟩ = − ν MP 2 ⋅ t on , S 4 + ( ν MP 1 − ν MP 2 ) ⋅ ( T sw − t on , S 4 ) T sw ν 1 − MP 2 = − ν MP 2 ⋅ t on , S 4 + ν MP 1 − ν MP 2 ⋅ T sw − t on , S 4 T sw {:[(:nu_(1)-MP2:)],[=(-nu_(MP2)*t_(on,S_(4))+(nu_(MP1)-nu_(MP2))*(T_(sw)-t_(on,S_(4))))/(T_(sw))]:}\begin{aligned} & \left\langle\nu_{1}-\mathrm{MP} 2\right\rangle \\ & =\frac{-\nu_{\mathrm{MP} 2} \cdot t_{\mathrm{on}, \mathrm{~S}_{4}}+\left(\nu_{\mathrm{MP} 1}-\nu_{\mathrm{MP} 2}\right) \cdot\left(T_{\mathrm{sw}}-t_{\mathrm{on}, \mathrm{~S}_{4}}\right)}{T_{\mathrm{sw}}} \end{aligned}
Fig. 12. Voltage ν 12 ν 12 nu_(12)\nu_{12} and inductor current in the proposed topology. V in = V in  = V_("in ")=V_{\text {in }}= 800 V , V MP 1 = 350 V , V MP 2 = 400 V , F sw = 5 kHz 800 V , V MP 1 = 350 V , V MP 2 = 400 V , F sw = 5 kHz 800V,V_(MP1)=350V,V_(MP2)=400V,F_(sw)=5kHz800 \mathrm{~V}, V_{\mathrm{MP} 1}=350 \mathrm{~V}, V_{\mathrm{MP} 2}=400 \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 12. 提议拓扑中的电压 ν 12 ν 12 nu_(12)\nu_{12} 和电感电流。 V in = V in  = V_("in ")=V_{\text {in }}= 800 V , V MP 1 = 350 V , V MP 2 = 400 V , F sw = 5 kHz 800 V , V MP 1 = 350 V , V MP 2 = 400 V , F sw = 5 kHz 800V,V_(MP1)=350V,V_(MP2)=400V,F_(sw)=5kHz800 \mathrm{~V}, V_{\mathrm{MP} 1}=350 \mathrm{~V}, V_{\mathrm{MP} 2}=400 \mathrm{~V}, F_{\mathrm{sw}}=5 \mathrm{kHz} 和 L 1 = 3 mH L 1 = 3 mH L_(1)=3mHL_{1}=3 \mathrm{mH} 。
Ideally, if ν MP 2 ν MP 2 nu_(MP2)\nu_{\mathrm{MP} 2} equals ν MP 1 ν MP 1 nu_(MP1)\nu_{\mathrm{MP} 1}, the converter output voltage would be similar to the single-phase three-level diode-clamped inverter (12) and (13). However, asymmetries caused by partial shading, dirt, or panel manufacturing imperfections are often present on the PV generators. These asymmetries cause differences between the midpoint voltages ν MP 1 ν MP 1 nu_(MP1)\nu_{\mathrm{MP} 1} and ν MP 2 ν MP 2 nu_(MP2)\nu_{\mathrm{MP} 2}. This difference generates a perturbation on the output voltage ε ε epsi\varepsilon that is obtained from (12), (13), (26), and (27) as
理想情况下，如果 ν MP 2 ν MP 2 nu_(MP2)\nu_{\mathrm{MP} 2} 等于 ν MP 1 ν MP 1 nu_(MP1)\nu_{\mathrm{MP} 1} ，转换器输出电压将类似于单相三电平二极管箝位逆变器（12）和（13）。然而，光伏发电机上常常存在由于部分阴影、污垢或面板制造缺陷引起的不对称。这些不对称导致中点电压 ν MP 1 ν MP 1 nu_(MP1)\nu_{\mathrm{MP} 1} 和 ν MP 2 ν MP 2 nu_(MP2)\nu_{\mathrm{MP} 2} 之间的差异。这个差异在输出电压 ε ε epsi\varepsilon 上产生了扰动，该输出电压是从（12）、（13）、（26）和（27）获得的。
ε = ( ν MP 1 − ν MP 2 ) ⋅ ( 1 − | m | ) = ( ν MP 1 − ν MP 2 ) ⋅ ( 1 − | 2 ⋅ ν g ν in | ) . ε = ν MP 1 − ν MP 2 ⋅ ( 1 − | m | ) = ν MP 1 − ν MP 2 ⋅ 1 − 2 ⋅ ν g ν in . {:[epsi=(nu_(MP1)-nu_(MP2))*(1-|m|)],[=(nu_(MP1)-nu_(MP2))*(1-|(2*nu_(g))/(nu_(in))|).]:}\begin{aligned} \varepsilon & =\left(\nu_{\mathrm{MP} 1}-\nu_{\mathrm{MP} 2}\right) \cdot(1-|m|) \\ & =\left(\nu_{\mathrm{MP} 1}-\nu_{\mathrm{MP} 2}\right) \cdot\left(1-\left|\frac{2 \cdot \nu_{g}}{\nu_{\mathrm{in}}}\right|\right) . \end{aligned}
The amplitude of the perturbation is proportional to the voltage difference between its midpoints and its frequency to the grid ( 50 − 60 Hz ) ( 50 − 60 Hz ) (50-60Hz)(50-60 \mathrm{~Hz}). The current control loop compensates the perturbation. Fig. 12 shows the simulation results of the main electrical variables during a grid period when V in = 800 V V in = 800 V V_(in)=800VV_{\mathrm{in}}=800 \mathrm{~V}, V MP 1 = 350 V V MP 1 = 350 V V_(MP1)=350VV_{\mathrm{MP} 1}=350 \mathrm{~V}, and V MP 2 = 400 V V MP 2 = 400 V V_(MP2)=400VV_{\mathrm{MP} 2}=400 \mathrm{~V}.
扰动的幅度与其中点之间的电压差成正比，与其频率成正比 ( 50 − 60 Hz ) ( 50 − 60 Hz ) (50-60Hz)(50-60 \mathrm{~Hz}) 。电流控制回路补偿扰动。图 12 显示了在电网周期内主要电气变量的仿真结果，当 V in = 800 V V in = 800 V V_(in)=800VV_{\mathrm{in}}=800 \mathrm{~V} ， V MP 1 = 350 V V MP 1 = 350 V V_(MP1)=350VV_{\mathrm{MP} 1}=350 \mathrm{~V} ，和 V MP 2 = 400 V V MP 2 = 400 V V_(MP2)=400VV_{\mathrm{MP} 2}=400 \mathrm{~V} 。
As demonstrated for the half-bridge topology, which is shown in (5)-(9), the noninjection of a dc into the grid is guaranteed by connecting the neutral grid terminal to the midpoint of the second capacitive divider (MP2), which controls the average voltage of MP2.
如（5）-（9）所示的半桥拓扑所示，通过将中性电网端子连接到第二个电容分压器的中点（MP2），可以保证不向电网注入直流电，这控制了 MP2 的平均电压。
The efficiency of the proposed topology is similar to the single-phase three-level diode-clamped inverter, considering that the same semiconductors and operation are used.
所提议的拓扑的效率与单相三电平二极管箝位逆变器相似，考虑到使用了相同的半导体和操作。

VI. Control of THE Proposed TOPOlogy
VI. 对拟议拓扑的控制

The control of the new topology is based on cascading loops, as shown in Fig. 13.
新拓扑的控制基于级联环路，如图 13 所示。
A maximum power point tracking algorithm determines the reference input voltage that is necessary to maximize the PV generator output energy [20]-[23]. After this, a slow control loop of the input voltage calculates the effective value of the grid current fundamental. The fundamental thus obtained is multiplied by a sine wave in phase with the grid voltage in order to obtain a unity power factor.
最大功率点跟踪算法确定了最大化光伏发电机输出能量所需的参考输入电压[20]-[23]。之后，输入电压的慢控制回路计算电网电流基波的有效值。由此获得的基波与与电网电压同相的正弦波相乘，以获得单位功率因数。
Fig. 13. Control of the proposed topology.
图 13. 所提议拓扑的控制。
A second slow control loop is used to maintain ν MP2 ν MP2  nu_("MP2 ")\nu_{\text {MP2 }} that is equal to ν in / 2 ν in / 2 nu_(in)//2\nu_{\mathrm{in}} / 2; this control loop calculates the current that is necessary to assure this equivalence ( i dc ) i dc (i_(dc))\left(i_{\mathrm{dc}}\right). The i dc i dc i_(dc)i_{\mathrm{dc}} component is added to the reference current i g 1 ,ref i g 1 ,ref  i_(g1",ref ")i_{g 1 \text {,ref }} obtained by means of the control loop of the input voltage. Finally, a fast current control loop is used to make sure that the grid current trails the reference current i g , ref i g ,  ref  i_(g," ref ")i_{g, \text { ref }}.
第二个慢控制环路用于保持 ν MP2 ν MP2  nu_("MP2 ")\nu_{\text {MP2 }} 等于 ν in / 2 ν in / 2 nu_(in)//2\nu_{\mathrm{in}} / 2 ；该控制环路计算确保此等式成立所需的电流 ( i dc ) i dc (i_(dc))\left(i_{\mathrm{dc}}\right) 。 i dc i dc i_(dc)i_{\mathrm{dc}} 组件被添加到通过输入电压控制环路获得的参考电流 i g 1 ,ref i g 1 ,ref  i_(g1",ref ")i_{g 1 \text {,ref }} 中。最后，使用快速电流控制环路确保电网电流跟随参考电流 i g , ref i g ,  ref  i_(g," ref ")i_{g, \text { ref }} 。
In steady state, the component of the reference current calculated by the ν MP 2 ν MP 2 nu_(MP2)\nu_{\mathrm{MP} 2} control loop i dc i dc i_(dc)i_{\mathrm{dc}} corresponds to the offset introduced by the current measurement elements.
在稳态下，由 ν MP 2 ν MP 2 nu_(MP2)\nu_{\mathrm{MP} 2} 控制回路 i dc i dc i_(dc)i_{\mathrm{dc}} 计算的参考电流分量对应于电流测量元件引入的偏移。

VII. EXPERIMENTAl RESUlts
VII. 实验结果

To validate the operation and efficiency of the proposed topology, a prototype was built. The prototype specifications are an input voltage V PV V PV V_(PV)V_{\mathrm{PV}} between 700 and 1100 V , a grid voltage of 230 V , a rated power of 5 kW , a switching frequency of 16 kHz , and an inductance of 3 mH .
为了验证所提议拓扑的操作和效率，构建了一个原型。原型规格为输入电压 V PV V PV V_(PV)V_{\mathrm{PV}} 在 700 到 1100 V 之间，电网电压为 230 V，额定功率为 5 kW，开关频率为 16 kHz，电感为 3 mH。
International Rectifier’s IRG4PSC71UD 600-V fast insulated-gate bipolar transistors (IGBTs) were chosen for the switches, and IR HFA 25TB60 600-V diodes were selected for D 5 D 5 D_(5)D_{5} and D 6 D 6 D_(6)D_{6}. Optocoupled drivers, which are Concept 2SD106AI-17, were used to drive the IGBTs. The prototype is controlled by means of a DSP1104 from dSPACE. Fig. 14 shows the prototype.
国际整流器的 IRG4PSC71UD 600-V 快速绝缘栅双极晶体管（IGBT）被选为开关，IR HFA 25TB60 600-V 二极管被选用于 D 5 D 5 D_(5)D_{5} 和 D 6 D 6 D_(6)D_{6} 。使用了光耦合驱动器 Concept 2SD106AI-17 来驱动 IGBT。原型通过 dSPACE 的 DSP1104 进行控制。图 14 显示了原型。
As mentioned in Section III, the half bridge has similar characteristics to the proposed topology regarding the total common-mode voltage and noninjection of the dc to the grid. To compare the efficiency of the proposed topology and the half bridge, a second prototype (half bridge) has been constructed. This second prototype has similar specifications, namely, V PV = 700 − 1100 V , V g = 230 V , P = 5 kW , F sw = V PV = 700 − 1100 V , V g = 230 V , P = 5 kW , F sw = V_(PV)=700-1100V,V_(g)=230V,P=5kW,F_(sw)=V_{\mathrm{PV}}=700-1100 \mathrm{~V}, V_{g}=230 \mathrm{~V}, P=5 \mathrm{~kW}, F_{\mathrm{sw}}= 16 kHz , and L = 3 mH L = 3 mH L=3mHL=3 \mathrm{mH}. The IGBTs used were IRG4PSH71UD, which are of the same family as the IRG4PSC71UD, but of 1200 V .
如第三节所述，半桥在总共模电压和直流不注入电网方面与提议的拓扑具有相似特性。为了比较提议的拓扑和半桥的效率，构建了第二个原型（半桥）。这个第二个原型具有相似的规格，即 V PV = 700 − 1100 V , V g = 230 V , P = 5 kW , F sw = V PV = 700 − 1100 V , V g = 230 V , P = 5 kW , F sw = V_(PV)=700-1100V,V_(g)=230V,P=5kW,F_(sw)=V_{\mathrm{PV}}=700-1100 \mathrm{~V}, V_{g}=230 \mathrm{~V}, P=5 \mathrm{~kW}, F_{\mathrm{sw}}= 16 kHz 和 L = 3 mH L = 3 mH L=3mHL=3 \mathrm{mH} 。所使用的 IGBT 是 IRG4PSH71UD，属于与 IRG4PSC71UD 相同的系列，但额定电压为 1200 V。
Fig. 14. Implemented prototype.
图 14. 实现的原型。
Fig. 15. (a) Grid voltage ( 100 V / div 100 V / div 100V//div100 \mathrm{~V} / \mathrm{div} ) and output current ( 10 A / div 10 A / div 10A//div10 \mathrm{~A} / \mathrm{div} ) of the proposed topology. (b) DC injected into the grid by the proposed topology (5 mA/div).
图 15. (a) 所提拓扑的电网电压 ( 100 V / div 100 V / div 100V//div100 \mathrm{~V} / \mathrm{div} ) 和输出电流 ( 10 A / div 10 A / div 10A//div10 \mathrm{~A} / \mathrm{div} )。 (b) 所提拓扑注入电网的直流电 (5 mA/div)。
Fig. 14 shows the experimental results of the proposed inverter. Fig. 15(a) shows the grid voltage and current. Fig. 15(b) shows the dc injected into the grid over a 2-min period. As it is shown in Fig. 15(b), the level of dc does not exceed 7 mA at any instant.
图 14 显示了所提议的逆变器的实验结果。图 15(a)显示了电网电压和电流。图 15(b)显示了在 2 分钟内注入电网的直流电。如图 15(b)所示，任何时刻直流电的水平都不超过 7 毫安。
Fig. 16. Measured efficiency of the proposed topology and the half bridge. V in = 700 V V in  = 700 V V_("in ")=700VV_{\text {in }}=700 \mathrm{~V}.
图 16. 所提议拓扑和半桥的测量效率。 V in = 700 V V in  = 700 V V_("in ")=700VV_{\text {in }}=700 \mathrm{~V} 。
Fig. 16 shows the efficiency of the proposed topology and that of the half bridge as a function of the output power for an input voltage of 700 V . The maximum efficiency of the proposed topology is 98.16 % 98.16 % 98.16%98.16 \%, which is in comparison with 97.1 % 97.1 % 97.1%97.1 \% attained by the half bridge, which is an efficiency improvement of 1.06 % 1.06 % 1.06%1.06 \%.
图 16 显示了所提拓扑结构和半桥在 700 V 输入电压下输出功率的效率。所提拓扑结构的最大效率为 98.16 % 98.16 % 98.16%98.16 \% ，而半桥的效率为 97.1 % 97.1 % 97.1%97.1 \% ，这是一项 1.06 % 1.06 % 1.06%1.06 \% 的效率提升。

VIII. ConClusion  VIII. 结论

This paper proposes a new conversion topology designed for use in transformerless PV systems. The topology generates no varying total common-mode voltage, thus improving the behavior of the inverter in terms of electromagnetic interference, exhibits high efficiency, and guarantees that no dc is injected to the grid. The behavior of the proposed topology has been validated on a 5 − kW 5 − kW 5-kW5-\mathrm{kW} prototype. The maximum efficiency achieved by the topology is 98.16 % 98.16 % 98.16%98.16 \%. As a conclusion, the proposed topology represents a valuable power-conversion stage for transformerless grid-connected PV systems.
本文提出了一种新型转换拓扑，旨在用于无变压器光伏系统。该拓扑不产生变化的总共模电压，从而改善了逆变器在电磁干扰方面的表现，具有高效率，并确保不会向电网注入直流。所提议的拓扑的行为已在 5 − kW 5 − kW 5-kW5-\mathrm{kW} 原型上得到了验证。该拓扑实现的最大效率为 98.16 % 98.16 % 98.16%98.16 \% 。总之，所提议的拓扑代表了无变压器并网光伏系统中一个有价值的电力转换阶段。

REFERENCES  参考文献

[1] J. M. Carrasco, L. G. Franquelo, J. T. Bialasiewicz, E. Galván, R. C. Portillo Guisado, M. A. M. Prats, J. I. León, and N. Moreno-Alfonso, “Power-electronic systems for the grid integration of renewable energy sources: A survey,” IEEE Trans. Ind. Electron., vol. 53, no. 4, pp. 10021016, Jun. 2006.
[1] J. M. Carrasco, L. G. Franquelo, J. T. Bialasiewicz, E. Galván, R. C. Portillo Guisado, M. A. M. Prats, J. I. León, 和 N. Moreno-Alfonso, “用于可再生能源源网格集成的电力电子系统：一项调查,” IEEE Trans. Ind. Electron., vol. 53, no. 4, pp. 10021016, Jun. 2006.
[2] R. L. LaRocca, “Personnel protection devices for use on appliances,” IEEE Trans. Ind. Appl., vol. 28, no. 1, pp. 233-238, Jan./Feb. 1992.
[2] R. L. LaRocca, “用于电器的人员保护装置,” IEEE Trans. Ind. Appl., vol. 28, no. 1, pp. 233-238, 1992 年 1 月/2 月。
[3] W. Bower and J. Wiles, “Investigation of ground-fault protection devices for photovoltaic power system applications,” in Proc. 28th IEEE Conf. Rec. Photovolt. Spec., 2000, pp. 1378-1383.
[3] W. Bower 和 J. Wiles，“光伏电力系统应用的接地故障保护装置研究，”发表于第 28 届 IEEE 会议记录，光伏特性，2000 年，页码 1378-1383。
[4] E. Gubia, P. Sanchis, A. Ursúa, J. Lopez, and L. Marroyo, “Ground currents in single-phase transformerless photovoltaic systems,” Prog. Photovolt.: Res. Appl., vol. 15, no. 7, pp. 629-650, Nov. 2007.
[4] E. Gubia, P. Sanchis, A. Ursúa, J. Lopez, and L. Marroyo, “无变压器单相光伏系统中的接地电流,” Prog. Photovolt.: Res. Appl., vol. 15, no. 7, pp. 629-650, Nov. 2007.
[5] R. González, J. López, P. Sanchis, and L. Marroyo, “Transformerless inverter for single-phase photovoltaic systems,” IEEE Trans. Power Electron., vol. 22, no. 2, pp. 693-697, Mar. 2007.
[5] R. González, J. López, P. Sanchis, 和 L. Marroyo, “无变压器逆变器用于单相光伏系统,” IEEE Trans. Power Electron., vol. 22, no. 2, pp. 693-697, 2007 年 3 月。
[6] S. B. Kjaer, J. K. Pedersen, and F. Blaabjerg, “A review of single-phase grid-connected inverters for photovoltaic modules,” IEEE Trans. Ind. Appl., vol. 41, no. 5, pp. 1292-1306, Sep./Oct. 2005.
[7] IEEE Standard for Interconnecting Distributed Resources With Electric Power Systems, IEEE Dtd. 1547, 2003.
[7] IEEE 标准用于与电力系统互连的分布式资源，IEEE Dtd. 1547，2003。
[8] Characteristics of the Utility Interface for Photovoltaic (PV) Systems. IEC 61 727, 2004.
[8] 光伏（PV）系统的公用接口特性。IEC 61 727，2004。
[9] V Verband der Elektrotechnik, Elektronik und Informationstechnik (VDE), V 0126-1-1, Feb. 2006.
[9] V 德国电气工程、电子和信息技术协会 (VDE)，V 0126-1-1，2006 年 2 月。
[10] Recommendations for the connection of small-scale embedded generators in parallel with public low-voltage distribution networks, Energy Networks Assoc. Eng. Directorate. G38/1, 2004.
[10] 关于小型嵌入式发电机与公共低压配电网络并联连接的建议，能源网络协会工程局。G38/1，2004。
[11] J. M. A. Myrzik and M. Calais, “String and module integrated inverters for single-phase grid connected photovoltaic systems - A review,” in Proc. IEEE Power Tech. Conf., Bologna, Italy, Jun. 23-26, 2003, vol. 2, pp. 1-8.
[11] J. M. A. Myrzik 和 M. Calais，“用于单相并网光伏系统的串联和模块集成逆变器 - 综述，”在 IEEE 电力技术会议论文集中，意大利博洛尼亚，2003 年 6 月 23-26 日，第 2 卷，第 1-8 页。
[12] W. N. Mohan, T. Undeland, and W. P. Robbins, Power Electronics: Converters, Applications, and Design. Hoboken, NJ: Wiley, 2003.
[12] W. N. Mohan, T. Undeland, 和 W. P. Robbins, 《电力电子：转换器、应用与设计》。霍博肯，NJ：Wiley，2003。
[13] H. Schmidt, B. Burger, and C. Siedle, “Die heric wechselrichter topologie,” in Proc. 18th Symp. Photovoltaisch Sonnenergie, Bad Staffelstein, Germany, 2003.
[13] H. Schmidt, B. Burger, 和 C. Siedle, “Die heric wechselrichter topologie,” 在第 18 届光伏太阳能研讨会论文集中，德国巴德施塔夫尔斯坦，2003 年。
[14] D. Schekulin, Deutsches Patentamt, Patentschrift DE 19732218 C1, Mar. 1999.
[14] D. Schekulin, 德国专利局, 专利文献 DE 19732218 C1, 1999 年 3 月。
[15] T. Shimizu, O. Hashimoto, and G. Kimura, “A novel high-performance utility-interactive photovoltaic inverter system,” IEEE Trans. Power Electron., vol. 18, no. 2, pp. 704-711, Mar. 2003.
[15] T. Shimizu, O. Hashimoto, and G. Kimura, “一种新型高性能公用互动光伏逆变器系统，”IEEE Trans. Power Electron., vol. 18, no. 2, pp. 704-711, 2003 年 3 月。
[16] W. Tsai-Fu, N. Hung-Shou, H. Hui-Ming, and S. Chih-Lung, “PV power injection and active power filtering with amplitude-clamping and amplitude-scaling algorithms,” IEEE Trans. Ind. Appl., vol. 43, no. 3, pp. 731-741, May/Jun. 2007.
[16] W. Tsai-Fu, N. Hung-Shou, H. Hui-Ming, 和 S. Chih-Lung, “光伏功率注入和使用幅度限制和幅度缩放算法的有源功率滤波,” IEEE Trans. Ind. Appl., vol. 43, no. 3, pp. 731-741, 2007 年 5/6 月。
[17] M. Calais and V. G. Agelidis, “Multilevel converters for single-phase grid connected photovoltaic systems-An overview,” in Proc. IEEE Int. Symp. Ind. Electron., 1998, pp. 224-229.
[17] M. Calais 和 V. G. Agelidis, “用于单相并网光伏系统的多级变换器-概述,” 在 IEEE 国际工业电子学会会议论文集, 1998, 第 224-229 页。
[18] A. Nabae, H. Akagi, and I. Takahashi, “A new neutral-point-clamped PWM inverter,” IEEE Trans. Ind. Appl., vol. IA-17, no. 5, pp. 518-523, Sep./Oct. 1981.
[18] A. Nabae, H. Akagi, and I. Takahashi, “一种新的中性点钳位 PWM 逆变器,” IEEE Trans. Ind. Appl., vol. IA-17, no. 5, pp. 518-523, 1981 年 9 月/10 月。
[19] H. Schmidt, B. Burger, and C. Siedle, “Gefahrdungspotenzial transformatorloser Wechselrichter-Faktn und Gerüchte,” in Proc. 18th Symp. Photovoltaisch Sonnenergie, Bad Staffelstein, Germany, 2003.
[19] H. Schmidt, B. Burger, 和 C. Siedle, “无变压器逆变器的危险潜力——事实与谣言,” 在第 18 届光伏太阳能研讨会论文集中, 巴德施塔夫尔斯坦, 德国, 2003 年。
[20] J. Kwon, K. Nam, and B. Kwon, “Photovoltaic power conditioning system with line connection,” IEEE Trans. Ind. Electron., vol. 53, no. 4, pp. 10481054, Aug. 2006.
[20] J. Kwon, K. Nam, 和 B. Kwon, “光伏电源调节系统与线路连接,” IEEE Trans. Ind. Electron., vol. 53, no. 4, pp. 10481054, 2006 年 8 月。
[21] W. Xiao, M. G. J. Lind, W. G. Dunford, and A. Capel, “Real-time identification of optimal operating points in photovoltaic power systems,” IEEE Trans. Ind. Electron., vol. 53, no. 4, pp. 1017-1026, Aug. 2006.
[21] W. Xiao, M. G. J. Lind, W. G. Dunford, 和 A. Capel, “光伏电力系统中最佳运行点的实时识别,” IEEE Trans. Ind. Electron., vol. 53, no. 4, pp. 1017-1026, 2006 年 8 月。
[22] I. Kim, M. Kim, and M. Youn, “New maximum power point tracker using sliding-mode observer for estimation of solar array current in the gridconnected photovoltaic system,” IEEE Trans. Ind. Electron., vol. 53, no. 4, pp. 1027-1035, Aug. 2006.
[22] I. Kim, M. Kim, and M. Youn, “新型最大功率点跟踪器，利用滑模观测器估计并网光伏系统中的太阳能电池阵列电流，” IEEE Trans. Ind. Electron., vol. 53, no. 4, pp. 1027-1035, 2006 年 8 月。
[23] N. Mutoh, M. Ohno, and T. Inoue, “A method for MPPT control while searching for parameters corresponding to weather conditions for PV generation systems,” IEEE Trans. Ind. Electron., vol. 53, no. 4, pp. 10551065, Aug. 2006.
[23] N. Mutoh, M. Ohno, and T. Inoue, “一种在寻找与光伏发电系统天气条件相对应的参数时进行 MPPT 控制的方法，” IEEE Trans. Ind. Electron., vol. 53, no. 4, pp. 10551065, 2006 年 8 月。
Roberto González received the M.Sc. degree in industrial engineering from the Public University of Navarra (UPNA), Pamplona, Spain, in 2003.
罗伯托·冈萨雷斯于 2003 年获得西班牙潘普洛纳纳瓦拉公立大学（UPNA）工业工程硕士学位。
Since 2006, he has been with the Electrical and Electronic Department, UPNA, where he is an Assistant Professor and where he is currently involved in research projects with the Electrical Engineering, Power Electronics, and Renewable Energy research group (INGEPER). His research interests include power electronics and renewable energies, such as wind and photovoltaic plants.
自 2006 年以来，他一直在纳瓦拉大学电气与电子系担任助理教授，目前参与电气工程、电力电子和可再生能源研究小组（INGEPER）的研究项目。他的研究兴趣包括电力电子和可再生能源，如风能和光伏电站。
Eugenio Gubía (M’04) received the M.Sc. and Ph.D. degrees in industrial engineering from the Public University of Navarra (UPNA), Pamplona, Spain, in 1995 and 2003, respectively.
尤金尼奥·古比亚（M’04）于 1995 年和 2003 年分别获得西班牙潘普洛纳纳瓦拉公立大学（UPNA）工业工程硕士和博士学位。
Since 1996, he has been with the Electrical and Electronic Department, UPNA, where he is currently an Assistant Professor and where, in 2002, he joined the Electrical Engineering, Power Electronics, and Renewable Energy research group (INGEPER). He has been involved in several research projects that are mainly in cooperation with industries. His research interests are in the fields of power electronics, renewable energy systems, power system quality, and electromagnetic compatibility.
自 1996 年以来，他一直在纳瓦拉大学电气与电子系工作，目前担任助理教授，并于 2002 年加入电气工程、功率电子和可再生能源研究小组（INGEPER）。他参与了多个主要与工业合作的研究项目。他的研究兴趣包括功率电子、可再生能源系统、电力系统质量和电磁兼容性等领域。
Jesús López (M’05) received the M.Sc. degree in industrial engineering from the Public University of Navarra (UPNA), Pamplona, Spain, in 2000.
耶稣·洛佩斯（M’05）于 2000 年获得西班牙潘普洛纳纳瓦拉公立大学（UPNA）工业工程硕士学位。
Since 2001, he has been with the Electrical and Electronic Department, UPNA, where he is an Assistant Professor and where he is currently involved in research projects with the Electrical Engineering, Power Electronics, and Renewable Energy research group (INGEPER). His research interests include power electronics, power systems quality, and renewable energies, such as wind and photovoltaic plants.
自 2001 年以来，他一直在纳瓦拉大学电气与电子系担任助理教授，目前参与电气工程、电力电子和可再生能源研究小组（INGEPER）的研究项目。他的研究兴趣包括电力电子、电力系统质量以及可再生能源，如风能和光伏发电厂。
Luis Marroyo (M’04) received the M.Sc. degree in electrical engineering from the University of Tolouse, Tolouse, France, in 1993, the Ph.D. degree in electrical engineering from the Public University of Navarra (UPNA), Pamplona, Spain, in 1997, and the Ph.D. degree from the Laboratoire d’Electrotechnique et d’Electronique IndustrielleEcole Nationale Supérieure d’Electronique, d’Informatique, d’Hydraulique et des Télécommunications Institut National Polytechnique de Toulouse, Toulouse, France, in 1999.
路易斯·马罗约（M’04）于 1993 年获得法国图卢兹大学电气工程硕士学位，1997 年获得西班牙纳瓦拉公立大学（UPNA）电气工程博士学位，并于 1999 年获得法国图卢兹国立理工学院电气工程与工业电子实验室的博士学位。
From 1993 to 1998, he was an Assistant Professor with the Department of Electrical and Electronic Engineering, UPNA, where, since 1998, he has been an Associate Professor and where he is currently the Head of the Electrical Engineering, Power Electronics, and Renewable Energy research group (INGEPER). His research interests are in power electronics, grid quality, and renewable energy.
从 1993 年到 1998 年，他是纳瓦拉大学电气与电子工程系的助理教授，自 1998 年以来，他一直是副教授，并且目前是电气工程、电力电子和可再生能源研究小组（INGEPER）的负责人。他的研究兴趣包括电力电子、电网质量和可再生能源。
  1. Manuscript received November 12, 2007; revised March 21, 2008. This work was supported in part by the Spanish Ministry of Education and Science under Grant DPI2006-15627-C03-02.
    手稿于 2007 年 11 月 12 日收到；2008 年 3 月 21 日修订。此项工作部分得到了西班牙教育和科学部的支持，资助编号为 DPI2006-15627-C03-02。
    The authors are with the Department of Electrical and Electronic Engineering, Public University of Navarra, 31006 Pamplona, Spain.
    作者来自西班牙潘普洛纳公立大学电气与电子工程系，邮政编码 31006。
    Digital Object Identifier 10.1109/TIE.2008.924015