**1. Introduction**

The aim of decreasing the emission of greenhouse gas to minimize the impact on the environment has given a tremendous push to power plants based on renewable energy sources. Solar power is abundantly available and many countries have pledged to use 100% renewable energy by 2050 [1]. The large share of energy consumption from renewable sources will be contributed by solar power in the near future. As the extraction of solar power is highly weather-dependent, efficient power converters are necessary that can harvest the available power at all weather conditions.

Modular PV power plants are preferred in locations where energy yield is impacted due to varying weather conditions. Furthermore, modular PV power plants are preferred for commercial installation where partial shading of the panel is a concern. The modular power converters decrease the effects of PV panel mismatch as compared to central power converters where the PV panels are connected to form an array. The modularity of such converters can be a panel, string, or array level. However, in most of the cases the modularity is achieved at the cost of additional *dc–dc* converters [2].

The PV power plant using Cascaded H-Bridge (CHB) converter is studied in [3,4], it operates at high efficiency and increases energy yield due to increase in number of Maximum Power Point Tracking (MPPT). The Modular Multilevel Converter (MMC) proposed in [5] increases the number of MPPT for the same number of switches compared to the CHB converter. The MMC topology, its

variants, and applications are discussed in [6,7]. In [3,8,9], MMC is proposed as an inverter for PV plant. The detailed discussion on topology and control methods for the MMC are presented in [10]. The Figure 1a shows a three-phase double star MMC with Half-Bridge (HB) sub-modules. Each phase of the MMC can be divided into sub-units referred to as upper and lower arm, respectively. Each arm of the MMC has series-connected power electronic blocks referred to as "sub-modules" and an inductor referred to as "arm inductor". The sub-modules can be identical or a combination of different power converter topologies [11]. Typically used sub-modules are half-bridge or full-bridge converters.

Three distinct variants of the topology for connecting the PV panels to the sub-modules are shown in Figure 1b–d. In [12,13], the PV panels are directly connected to the sub-module of the MMC as shown in Figure 1b. The overall efficiency of the PV plant is considerably high as the MMC efficiency is in the range of 99% [14]. Such a system is comparable to the central PV power plant with the additional benefit of an increased number of independent MPPT algorithms, which in this case is equal to the number of sub-modules. This results in higher energy yield and better efficiency than the central PV power plant. In [15], the authors show that the Levelized Cost of Energy (LCOE) for the MMC-based PV plant can be brought lower than that of the central PV plant. The PV panels connected to the sub-modules using the *dc–dc* converters is shown in Figure 1c,d. The use of a *dc-dc* converter allows the decoupling of the PV control and the MMC control. The advantage is that the sub-module capacitor voltages across the MMC are equal; therefore, no modification is necessary in the MMC control. However, in this configuration the overall efficiency is lower compared to PV plant without *dc-dc* converters. In cases where the isolated converters are used, the *dc*-link voltage can be scaled to Medium Voltage (MV) facilitating direct connection of the MMC PV plant to the distribution grid. Thereby, avoiding the need for a step-up transformer typically used for connection to the MV grid.

In [16], the control method for the MMC uses individual Pulse Width Modulators (PWM) for each of the sub-modules. In [17], the method presented in [16] is further extended to control the MMC with the energy sources connected to the sub-modules. The energy in each of the sub-module is locally controlled, which effectively provides the possibility of distributing the control between the main and local controllers. It uses phase-shifted PWM and additional sub-modules are necessary as energy buffers to avoid: (1) large variation of capacitor voltage in the sub-module with an energy source and (2) to avoid very high switching frequency of the sub-module. In [18,19] the non-carrier based approach is used for controlling the MMC when the energy sources are connected to the sub-modules. The non-carrier based control method relies on calculating the fundamental positive and negative sequence circulating current references required to balance the energy between the upper and lower arms of the MMC. In [12], a cost function is presented to optimize the calculation of fundamental circulating current references for extracting the maximum power from the PV and injection of balanced power to the grid. Calculating weights for the cost function is not straight forward and is usually obtained from trial-and-error or extensive simulation cases. In [13], arm power control of MMC is presented, the control system is distributed such that each arm of the MMC is controlled independently. This method also avoids the mathematical computation of the fundamental circulating current references.

Using arm power control the MMC is controlled such that maximum power is extracted from the PV panels and a balanced power is injected to the *ac* grid. The sum of sub-module capacitor voltages in an arm of the MMC is allowed to be different across the upper and lower arms of the MMC. However, within the arm of the MMC, all capacitor voltages are maintained to be equal. This is achieved with the help of sorting and tracking algorithm. The variation of the irradiance is assumed at arm-level for the three-phase MMC leading to six independent MPPT. Such an assumption is viable in large power plants were the effects of shading is minimal. In the case of residential and commercial PV plants, the consequence of shading between the sub-modules cannot be neglected. The shading of PV panels will result in a decrease of power extracted as the MMC is only capable of MPPT at arm-level. This will reduce the yield ratio and LCOE compared to the module-level power converters.

The MMC with arm power control can enable MPPT at the sub-module level. This is achieved by providing individual sub-module capacitor voltage references obtained from the MPPT algorithm. As a result, the sub-module capacitor voltages within the arm of the MMC will not be equal to its average value. Therefore, the voltage inserted by each arm of the MMC will not be equal. As the output voltage in a phase of the MMC is the difference of the upper and the lower arm voltages, the unequal arm voltages will result in a residual voltage at the output terminal. A high deviation in the magnitude of the sub-module capacitor voltages in the arm of the MMC might result in higher residual voltage. This will result in undesired current harmonics and unbalance current components.

In this paper, the effect of unequal sub-module capacitor voltages in the arm of the MMC using arm power control is investigated. A modified sorting and balancing algorithm is proposed that allows the MMC-based PV plant with arm power control to track the MPPT at the sub-module level and inject balanced power to the *ac* grid. The effect of phase current THD is analyzed in the case of uneven irradiance on the sub-modules. The modified sorting and tracking algorithm mitigates the residual voltage between the converter and grid voltages thereby reducing the THD in the phase currents. As a consequence of lower residual voltage the unbalance in the phase current is mitigated. The modified algorithm ensures balanced power injection to the *ac* grid despite extreme unbalance in power generation. The proposed solution makes the arm power control for the MMC suitable for PV applications which are prone to uneven irradiance.

**Figure 1.** The Modular Multilevel Converter (MMC) and sub-modules with photovoltaic (PV) panels. (**a**) Three-phase MMC indicating the upper and lower arms and the sub-module, (**b**) the HB sub-module with direct connection of the PV panel, (**c**) the PV is connected to the sub-module using a non-isolated *dc-dc* converter, and (**d**) the PV is connected to the sub-module using a isolated converter.

#### **2. Direct Connection of PV Panels to the MMC**

To utilize the modularity, increase efficiency, and reliability of the MMC, either a group or individual PV panels is connected directly to the sub-modules of the MMC. Such a configuration inherits the advantages of the MMC such as redundancy, fault-tolerant operation, improved harmonic performance, and hot-swap.

The topology of the MMC with the direct connection of PV panels to the sub-module is shown in Figure 2. Two PV panels are connected in series to form a string which is connected to the sub-module with a series diode to avoid power flow into the PV string. The number of PV panels connected in series or parallel depends on the sizing of the PV plant. Such a configuration is versatile and can have "6 *N*" independent MPPT algorithms. The MPPT granularity is defined as the number of independent MPPT. The MMC can be controlled such that MPPT is performed either at sub-module, arm, or MMC level depending on the irradiance pattern. This will ensure high energy yield under different operating conditions.

**Figure 2.** The PV string, two PV panels in series, is connected to the *i*th sub-module. A diode is included to avoid the power flow into PV string.

The sub-module is said to be inserted when the capacitor is included in the arm of the MMC, i.e., when insertion index *nxyi* = 1. When the capacitor is not included in the arm of the MMC, the corresponding sub-module is said to be bypassed, i.e, when insertion index is *nxyi* = 0. When the sub-module is inserted the output voltage of the sub-module is *vxyi* = *nxyi* · *vcxyi* . Therefore, the voltage across the arm of the MMC is sum of the individual sub-module output voltages expressed as

$$\upsilon\_{\mathbf{x}} = \sum\_{i=1}^{N} n\_{x\_{yi}} \cdot \upsilon\_{\mathcal{C}x\_{yi}} \tag{1}$$

The current through the sub-module capacitor voltage is expressed as

$$\mathbb{C}\frac{d}{dt}\left(v\_{cx\_{yi}}\right) = i\_{px\_{yi}} + n\_{x\_{yi}} \cdot i\_{x\_{y}} \tag{2}$$

The current from the PV string, *ipxyi* , depends on the irradiance level, temperature, and the capacitor sub-module voltage. To track the maximum power on each sub-module, the capacitor voltage is varied and retained at an operating point where the maximum power is extracted from the PV string. When the sub-module is inserted the magnitude of the capacitor voltage changes based on the net current through the capacitor. In this configuration, the PV string current always has a positive average value, however, the arm current alternates sinusoidally. Therefore, the sub-modules in the arm of the MMC have to be selectively inserted or bypassed to reduce the error between the capacitor voltage and the Maximum Power Point (MPP) voltage.

The fundamental sub-module capacitor ripple voltage also influences the power extracted from the PV string. In [20], the effective power loss per panel is studied concerning the sub-module capacitor voltage ripple. For a fixed switching frequency, irradiance of 1000 W/m2, and at a constant temperature, it is shown that the decrease of sub-module capacitor voltage ripple from 10% to 5% results in a decrease of effective loss of power extracted from PV panel, i.e., from 2.47% to 0.56%, respectively.

In Figure 3a, the voltage across the sub-module capacitor is shown for capacitance between 20 mF to 100 mF incremented in steps of 10 mF. The data from the Canadian Solar CS6K-285M-FG PV panel is used for the analysis. The maximum allowed sub-module capacitor voltage is 75 V. The switching frequency is selected to be 10 kHz, the irradiance is maintained at 1000 W/m2. Figure 3 shows the capacitance of the sub-module against the capacitor voltage ripple, to keep the fundamental ripple voltage within 5% of the rated sub-module capacitor voltage the capacitance has to be greater than 50 mF. This capacitance is easily attainable as the sub-module operates at low voltage in the order of few tens of volts.

**Figure 3.** (**a**) Sub-module capacitor voltages for different value of capacitance ranging from 20 mF to 100 mF in steps of 10 mF. (**b**) Sub-module capacitance as a function of ripple voltage at maximum rated capacity of the plant operating with 10 kHz switching frequency.

#### **3. Arm Power Control of MMC Based PV Plant**

The block diagram of arm power control proposed in [13] is shown in Figure 4. The power in each arm of the MMC is independently controlled such that (1) each phase of the MMC delivers the same balanced power to the grid, and the (2) maximum power from the PV is extracted in each arm of the MMC. Such a control method leads to MPPT granularity of six.

**Figure 4.** The block diagram of arm power control method of the MMC for PV application proposed in [13].

The MPPT Algorithm provides the individual voltage references for the sub-modules in arm of the MMC as a vector, *vcxy* [1 × N]. These voltage references are added to obtain the desired sum-capacitor voltage reference for individual arm of the MMC, i.e., *v*Σ- *cxy* = ∑*Ni*=<sup>1</sup> *vcxyi* . A Proportional-Integral (PI) controller is used to generate the power reference such that the voltage error between *v*Σ- *cxy* and *vdc* is driven to zero as 

$$P\_{x\_y}^{\star}(s) = \left[\upsilon\_{cx\_y}^{\Sigma \star}(s) - \upsilon\_{dc}(s)\right] \cdot \left(k\_{p\_{dc}} + \frac{k\_{i\_{dc}}}{s}\right) \tag{3}$$

The *ac* current reference for the arm of the MMC is calculated using the power reference (*Pxy* ) and the grid voltage at the point of common coupling. The *dc* current reference for the arm of the MMC is obtained with a PI controller to drive the error between the arm power reference and the average arm power to zero. The average arm power is the mean of power extracted from the PV in each arm of the MMC, defined as in (4).

$$P\_{\text{avg}} = \frac{1}{6} \left( \sum\_{y=a, b, c} \left[ \sum\_{x=u, l} \left\{ \sum\_{i=1}^{N} w\_{cx\_{yi}} \cdot i\_{px\_{yi}} \right\} \right] \right) \tag{4}$$

The desired voltage reference for each arm of the MMC is obtained as sum of outputs from "output voltage reference generation" and the "*dc* voltage reference generation" blocks, respectively. In the *dc* voltage reference generation, a separate Proportional Resonant (PR) controller is used to suppress the second harmonic circulating current. The insertion index for the arm is calculated as (5) using the arm voltage reference, *vxy*.

$$m\_{\mathbf{x}\_{\mathcal{Y}}} = \frac{\upsilon\_{\mathbf{x}\_{\mathcal{Y}}}^{\*}}{\upsilon\_{dc}} = \frac{\sum\_{i=1}^{N} n\_{\mathbf{x}\_{\mathcal{Y}}} \cdot \upsilon\_{c\mathbf{x}\_{\mathcal{Y}}}}{\upsilon\_{dc}} \tag{5}$$

The number of sub-module inserted in a switching period is positive integer value of *Nxy* , i.e., *Nxy* = *nxy* · *N*. The "Sorting and Tracking Algorithm" is shown in Figure 5, the sub-modules are referred as SM in the algorithm. It enables the insertion and bypass of the sub-module in a switching period such that the sub-module voltages in an arm of the MMC are maintained to their desired values. However, in [13], all the sub-module capacitor voltages in an arm of the MMC are maintained equal. The scenario of the uneven irradiance within the arm of the MMC has not been considered. Such an uneven irradiance within the arm of the MMC will result in different sub-module capacitor voltage references from the MPPT algorithm. The algorithm provides the provision to address unequal irradiance between the sub-modules in an arm of the MMC. The list *L*1 contains all the sub-modules with voltage less than their MPPT references, and *L*2 contains all the sub-modules with voltage greater than their MPPT references. Based on the polarity of the arm current and the magnitude of the sub-module capacitor voltages, the sub-modules are either inserted or bypassed to maintain the voltage within a threshold . The only limitation is that all the sub-module capacitor voltage references are identical for an arm of the MMC, i.e., ∀ *i* = 1 *to N*, *vcxyi*= *vcx*.

For this study, the parameters of the MMC are identical to the case considered in [13], as tabulated in Table A1. The PI- and PR-controller parameters are shown in Table A2.
