Control method for improving conversion efficiency of a multi-channel MPPT inverter

Abstract

The present disclosure provides a control method for improving conversion efficiency of a multi-channel MPPT input inverter, which implements high efficient operation of the inverter.

Description

FIELD

The present disclosure relates to a control method of a multi-channel MPPT inverter, and more particularly, to a control method for improving conversion efficiency of a multi-channel MPPT inverter.

BACKGROUND

A photovoltaic power generation system is usually composed of three parts: a photovoltaic panel array, a direct-current boost converter and a grid-connected power converter. The direct-current boost converter and the grid-connected power converter are interconnected and isolated by an intermediate direct-current bus, and are usually as a whole, called a photovoltaic inverter. The main working principle is that the direct-current boost converter boosts low-voltage direct current output by the photovoltaic panel array to high-voltage stable direct current for converting into alternating current by the back stage grid-connected power converter and then feeding into the power grid. With the increase in grid-connected power of photovoltaic power generation systems and the dropping of the maximum power point (MPP) of photovoltaic panels (PVs), single-channel direct-current boost circuits are difficult to take account of application scenarios of both high power and high boost ratio. Thus use of a multi-channel MPPT input to improve grid-connected power generation of photovoltaic inverters is a research hotspot of various manufacturers.

Without loss of generality, using the more applied dual-channel MPPT input photovoltaic inverter as an example, the existing multi-channel MPPT control logic is described. FIG. 1 shows a structural diagram of a dual-channel PV input photovoltaic inverter system 10 comprising photovoltaic panels PV1, PV2, input capacitors C1, C2, input boost circuit boost112, boost214, a direct-current bus capacitor Cdo, an H-bridge inverter 16 and a controller DSC 18. Outputs of the boost circuit boost112 and boost214 are connected to a common direct-current bus 20, and power is fed into the power grid 22 through the bus capacitor Cdo and the H-bridge inverter 16. PWM1 and PWM2 are drive signals of the boost circuits boost112 and boost214, respectively. The controller DSC 18 generally implements dual-channel MPPT control using a digital signal processor (DSP) by acquisition of information of PV input voltages v_PV1 and v_PV2 in two channels, PV input currents i_PV1 and i_PV2 in the two channels and a direct-current bus voltage v_bus, a brief control flow chart 40 is shown in FIG. 2. In FIG. 2, v_PV1*, v_PV2* and v_bus* are reference signals of the PV voltages in the two channels and direct-current bus voltage, respectively, Δv_PV is the difference between the PV voltages in the two channels, Δv_PV=v_PV1−v_PV2; V_TH is a judging threshold of the difference between the PV voltages in the two channels. The controller DSC obtains PV input power signals P_PV1 and P_PV2 in the two channels by sampling the PV input voltages v_PV1, and v_PV2 in the two channels at 44 and the PV input currents i_PV1 and i_PV2 in the two channels at 42, and obtains the PV voltage reference signals v_PV1* and v_PV2* through their respective MPPT module operation. At the same time, the controller DSC calculates the difference Δv_PV between the PV voltages in the two channels at 46, and substitutes it into a boost start and stop control logic to compare with the preset threshold V_TH. There are three cases:

Δv_PV≥V_TH (Y at 48), the controller DSC turns off a boost1 controller, blocks the drive signal PWM1 of the boost1 circuit, turns off the boost1 circuit at 50, enables a boost2 controller and obtains the drive signal PWM2 of the boost2 circuit, and the direct-current bus voltage reference signal v_bus*=v_PV1* at 52.

Δv_PV≤V_TH (Y at 54), the controller DSC turns off the boost2 controller, blocks the drive signal PWM2 of the boost2 circuit, turns off the boost2 circuit at 56, enables the boost2 controller and obtains the drive signal PWM1 of the boost1 circuit, and the direct-current bus voltage reference signal v_bus*=v_PV2* at 58.

V_TH≥Δv_PV≥−V_TH, (N at 54) the controller DSC enables both the boost1 and boost2 controllers and obtains the drive signals PWM1 and PWM2 of the boost1 and boost2 circuits at 60, and the direct-current bus voltage reference signal v_bus* uses the maximum of the two PV voltage reference signals, i.e., v_bus*=max(v_PV1*, v_PV2*) at 62

In the practical application, comprehensively considering thermal balance of a direct-current boost circuit of the inverter, conversion efficiency of the whole inverter and the service life of components, for the multi-channel MPPT input inverter, photovoltaic panels in all channels are usually configured almost uniformly, thus a PV curve of each input of the inverter is approximately the same. It can be seen from FIG. 2, using the existing multi-channel MPPT control method, each boost circuit is in a working state at a steady operating point, the conversion efficiency of the inverter is low, and the grid-connected power generation is small.

SUMMARY

An object of the present disclosure is to solve shortcomings and problems existing in the prior art, and propose a control method which can improve conversion efficiency of a multi-channel MPPT input inverter. By constructing a new boost start and stop control logic and virtual local maximum power point (VLMPP), a voltage difference between input PV voltages in multiple channels and the VLMPP is detected in real time and processed according to a certain logical relationship, and then turn-off and turn-on of a PV input boost circuit in each channel is controlled, to implement high efficient operation of the invertor.

The technical scheme adopted by the present disclosure according to one embodiment is as follows.

A control method for improving conversion efficiency of a multi-channel MPPT inverter comprises at act S1: collecting an input voltage v_PVm of a photovoltaic panel in each channel, an input current i_PVm of the photovoltaic panel in each channel and a direct-current bus voltage v_bus, obtaining an input power P_PVm of the photovoltaic panel in each channel, and using input voltages of at least two channels to obtain a voltage difference Δv_PV, wherein m=1, 2, . . . , M, M is a number of input channels of the photovoltaic inverter MPPT. At act S2, the method comprises comparing the voltage difference Δv_PV with a preset on-off control judging threshold to obtain a start and stop state of a boost circuit in each channel, a voltage reference signal v_PVm* in each channel and a direct-current bus voltage reference signal v_bus*. The boost start and stop state is determined as follows: at act S21, when |Δv_PV|≥V_THb, turning off a boost circuit in a channel corresponding to a maximum input voltage v_{PV_max}, activating boost circuits in the remaining channels, wherein V_THb is a boost on-off control judging threshold 1, and maximizing the input power P_PVm by an MPPT module in each channel to obtain the voltage reference signal v_PVm* in each channel, the direct-current bus voltage reference signal v_bus* using a maximum voltage reference signal v_{PV_max}*. At act S22, when V_THb≥|Δv_PV|≥V_THs, activating all boost circuits, wherein V_THs is a boost on-off control judging threshold 2, and V_THs<V_THb; and maximizing the input power v_PVm by the MPPT module in each channel to obtain the voltage reference signal v_PVm* in each channel, the direct-current bus voltage reference signal v_bus* using the maximum voltage reference signal v_{PV_max}*. At act S23, when V_THs≥|Δv_PV|≥0, when the act is performed for a first time, obtaining a voltage V_VLMPP at a virtual local maximum power point (VLMPP), turning off all the boost circuits, maximizing a total input power P_{PV_sum} of the inverter by an MPPT module based on the direct-current bus voltage v_bus to obtain the direct-current bus voltage reference signal v_bus*, monitoring a voltage difference between the direct-current bus voltage v_bus and V_VLMPP, and activating all the boost circuits when the voltage difference exceeds V_THb.

In one embodiment, at act S1, using the maximum input voltage v_{PV_max}, a PV input voltage v_{PV_Smax} slightly less than v_{PV_max} and a minimum PV input voltage v_{PV_min} to obtain a voltage difference Δv_{PV_max} between v_{PV_max} and v_{P_min} and a voltage difference Δv_{PV_MS} between v_{PV_max} and v_{PV_Smax}. At act S2, comparing the voltage differences Δv_{PV_max} and Δv_{PV_MS} with the preset on-off control judging threshold to obtain the start and stop state of the boost circuit in each channel. The boost start and stop state is determined as follows: at act S21, Δv_PV|≥V_THb, turning off the boost circuit in the channel corresponding to the maximum input voltage v_{PV_max}, and activating the boost circuits in remaining channels. At act S22, V_THb≥|Δv_PV|≥V_THs, activating all the boost circuits. At act S23, V_THs≥|Δv_PV|≥0, when the step is performed for the first time, obtaining the voltage V_VLMPP at the VLMPP point, turning off all the boost circuits, monitoring the voltage difference between v_bus and V_VLMPP, and activating all the boost circuits when the voltage difference exceeds V_THb.

In one embodiment, act S23 further comprises: at act S231, when V_THb≥|v_bus−V_VLMPP|≥0, turning off all the boost circuits, and maximizing the total input power P_{PV_sum} of the inverter by the MPPT module based on v_bus to obtain the direct-current bus voltage reference signal v_bus*. At act S232, when V_THb≥|v_bus−V_VLMPP|≥0, activating all the boost circuits, and maximizing the input power P_PVm by the MPPT module in each channel to obtain the voltage reference signal in each channel, the direct-current bus voltage reference signal v_bus* using the maximum voltage reference signal v_{PV_max}*.

In one embodiment, at act S23, the voltage V_VLMPP at the VLMPP point is obtained by following formula:

$V_{\mathrm{VLMPP}}=\frac{\mathrm{SUM}\left(v_{\mathrm{PV}1},v_{\mathrm{PV}2},\dots ,v_{\mathrm{PVM}}\right)}{M}.$

In one embodiment, at act S1, at least use a voltage difference between the maximum input voltage and the minimum input voltage of all input channels.

In one embodiment, at act S1, use the maximum input voltage and the minimum input voltage to obtain the voltage difference of all input channels.

In one embodiment, the following acts comprise: at act S1, a controller DSC collecting a PV input voltage v_PVm in each channel, a PV input current i_PVm in each channel and a direct-current bus voltage v_bus, calculating and obtaining an input power P_PVm in each channel and a total input power P_{PV_sum} of an inverter, calculating and obtaining a maximum PV input voltage v_{PV_max}, a PV input voltage v_{PV_Smax} slightly less than v_{PV_max} and a minimum PV input voltage v_{PV_min}, and calculating and obtaining a voltage difference Δv_{PV_max} between v_{PV_max} and v_{PV_min} and a voltage difference Δv_{PV_MS} between v_{PV_max} and v_{PV_Smax}; wherein m=1, 2, . . . , M, M is the number of input channels of the photovoltaic inverter MPPT, Δv_{PV_max}=v_{PV_max}−v_{PV_min}, and Δv_{PV_MS}=v_{PV_max}−v_{PV_Smax}. At act S2, comparing the voltage differences Δv_{PV_max} and Δv_{PV_MS} to obtain a start and stop state of a boost circuit in each channel, a PV voltage reference signal v_PVm* in each channel and a direct-current bus voltage reference signal v_bus*, specifically comprising: at act S21, when |Δv_{PV_MS}|≥V_THb, the controller DSC turning off a boost controller in a channel with the maximum PV input voltage v_{PV_max}, blocking a drive signal in the channel, turning off the boost circuit in the channel, enabling boost controllers in remaining channels and obtaining drive signals PWMm in the channels, and at a same time the controller DSC maximizing an input power P_PVm by an MPPT module in each channel to obtain a PV voltage reference signal v_PVm* in each channel, the direct-current bus voltage reference signal using the maximum PV input voltage reference signal v_{PV_max}*, i.e., v_bus*=v_{PV_max}, and wherein V_THb in the formula is a boost on-off control judging threshold 1. At act S22, when V_THb≥|Δv_{PV_MS}|≥V_THs, the controller DSC enabling the boost controller in each channel and obtaining the drive signal PWMM of the boost circuit in each channel, and at the same time the controller DSC substituting the input power P_PVm in each channel into the MPPT module in each channel to obtain the PV voltage reference signal v_PVm* in each channel, the direct-current bus voltage reference signal v_bus* using the maximum value v_{PV_max}* of PV voltage reference signals, i.e., v_bus*=v_{PV_max}*, and wherein V_THs in the formula is a boost on-off control judging threshold 2, wherein V_THs<V_THb. At act S23: when V_THs≥|Δv_{PV_max}|≥0, the controller DSC constructing VLMPP point voltage information, turning off all the boost circuits, blocking the drive signal PWMm of the boost circuit in each channel, maximizing a total input power P_{PV_sum} of the inverter by an MPPT module based on v_bus to obtain the direct-current bus voltage reference signal v_bus*.

At act S23, the controller DSC monitoring a voltage difference between v_bus and V_VLMPP in real time, when the voltage difference between v_bus and V_VLMPP exceeds V_THb, activates the boost controller in each channel mandatorily and starting all the boost circuits; at the same time the controller DSC maximizes the input power P_PVm by the MPPT module in each channel to obtain the PV voltage reference signal v_PVm* in each channel, the DC bus voltage reference signal v_bus* using a maximum value v_{PV_max}* of PV voltage reference signals, i.e., v_bus*=v_{PV_max}*; wherein if M=2, that is, in a two-channel MPPT inverter, the PV input voltage v_{PV_Smax} slightly less than v_{PV_max} and the minimum PV input voltage V_{PV_min} are the same value, Δv_{PV_max}=Δv_{V_MS}.

Compared to the prior art, the present disclosure has the following advantages using the scheme described above: a new boost start and stop control logic and a virtual local maximum power point (VLMPP) are constructed, a voltage difference between input PV voltages in multiple channels and the VLMPP is detected in real time and processed according to a certain logical relationship, and then turn-off and turn-on of a PV input boost circuit in each channel is controlled, thereby reducing the power loss in a steady state of the inverter, improving the conversion efficiency of the inverter, and implementing the economic and efficient operation of the inverter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a structural diagram of a control system of a dual-channel MPPT photovoltaic inverter;

FIG. 2 is a control flow chart of a dual-channel MPPT photovoltaic inverter in prior art; and

FIG. 3 is a control flow chart of a dual-channel MPPT photovoltaic inverter according to the present disclosure.

DETAILED DESCRIPTION

Various embodiments of the present disclosure will be described in detail in conjunction with the accompanying drawings so that advantages and features of the present disclosure will be more readily understood by those skilled in the art.

Without loss of generality, using the more applied dual-channel MPPT input photovoltaic inverter as an example, a multi-channel MPPT control logic and control method according to the present invent are described.

A hardware circuit used by the present disclosure as shown in FIG. 1 may be employed, and comprises photovoltaic panels PV1, PV2, input capacitors C1, C2, input boost circuit boost112, boost214, a direct-current bus capacitor Cdo, an H-bridge inverter 16 and a controller DSC 18. Outputs of the boost circuit boost112 and boost214 are connected to a common direct-current bus 20, and power is fed into the power grid 22 through the bus capacitor Cdo and the H-bridge inverter 16. PWM1 and PWM2 are drive signals of the boost circuits boost112 and boost214, respectively. A digital signal processor (DSP) is adopted in one embodiment to implement the controller DSC by corresponding hardware signal processing and acquisition of information of PV input voltages v_PV1 and v_PV2 in two channels, PV input currents i_PV1 and i_PV2 in the two channels and a direct-current bus voltage v_bus.

Compared with the existing two-channel MPPT control method 40 of FIG. 2, the control method according to the present disclosure redesigns a start and stop control logic of the dual-channel PV input boost circuit, and constructs a virtual local maximum power point (VLMMP) for judgment in restart of the double-channel boost circuit. Using the control method according to the present disclosure, the power loss in a steady state of the inverter can be reduced, the conversion efficiency of the inverter is improved, and the economic operation of the inverter is implemented.

The control method 80 according to the present disclosure as shown in FIG. 3 comprises various acts. At act S1, a controller DSC collecting and obtaining information of PV input voltages v_PV1 and v_PV2 in two channels, PV input current i_PV1 and i_PV2 in the two channels and a direct-current bus voltage v_bus at 82; a PV1 input power P_PV1, a PV2 input power P_PV2 and a total input power P_{PV_sum} of the inverter are calculated and obtained at 84, while a voltage difference a Δv_PV between the two PV input voltages is obtained at 86, and the expressions are as below:P_PV1=v_PV1*i_PV1  IP_PV2=v_PV2*i_PV2  IIP_{PV_sum}=P_PV1+P_PV1  IIIΔv_PV=v_PV1−v_PV2  IVAt act S2, voltage differences Δv_{PV_max} and Δv_{PV_MS} are compared to obtain a start and stop state of a boost circuit in each channel, a PV voltage reference signal v_PVm*in each channel and a direct-current bus voltage reference signal v_bus*, which specifically comprises: at act S21, when Δv_PV≥V_THb (Y at 88), the controller DSC turns off a boost1 controller, blocks a drive signal PWM1 of the boost1 circuit, turns off the boost1 circuit at 92, enables a boost2 controller and obtains a drive signal PWM2 of the boost2 circuit at 94, and at the same time the controller DSC maximizes the PV1 input power P_PV1 and the PV2 input power P_PV2 by an MPPT modules to obtain PV voltage reference signals v_PV1* and v_PV2* in the two channels at 90, a direct-current bus voltage reference signal v_bus* is given by the PV1 input voltage reference signal, i.e., v_bus*=v_PV1*. When Δv_PV≤−V_THb (Y at 96), the controller DSC turns off the boost2 controller, blocks the drive signal PWM2 of the boost2 circuit, turns off the boost2 circuit at 100, enables the boost1 controller and obtaining the drive signal PWM1 of the boost1 circuit at 102, and at the same time the controller DSC maximizes the PV1 input power P_PV1 and the PV2 input power P_PV2 by the MPPT modules to obtain PV voltage reference signals v_PV1* and v_PV2* in the two channels at 98, the direct-current bus voltage reference signal v_bus* is given by the PV2 input voltage reference signal, i.e., v_bus*=v_PV2*. At act S22, when V_THb≥|Δv_{PV_MS}|≥V_THs (Y at 104), the controller DSC enables both the boost1 and boost2 controllers and obtains the drive signals PWM1 and PWM2 of the boost1 and boost2 circuits at 108, and at the same time the controller DSC maximizing the PV1 input power P_PV1 and the PV2 input power P_PV2 by the MPPT modules to obtain the PV voltage reference signals v_PV1* and v_PV2* in the two channels at 106, the direct-current bus voltage reference signal v_bus* is a maximum value of PV voltage reference signals in the two channels, i.e., v_bus*=max(v_PV1*, v_PV2*) at 110. At act S23, when V_THs≥|Δv_PV|≥0 (N at 104), when the controller DSC enters this mode for the first time, the controller DSC constructs a VLMPP voltage at 112 based on formula V and the collected information of the direct-current bus voltage v_bus, which comprises the follow two acts: at act S231, when V_THb≥|v_bus−V_VLMPP|≥0 (Y at 114), the controller DSC turns off both the boost1 and boost2 controllers, blocks the drive signals PWM1 and PWM2 of the boost1 and boost2 circuits at 116 and maximizes the total input power P_{PV_sum} of the inverter by the MPPT module based on v_bus to obtain the direct-current bus voltage reference signal v_bus* at 118, at which point the PV voltage reference signals v_PV1* and v_PV2* in the two channels will not work. At act S232, when |v_bus−V_VLMPP|≥V_THb (N at 114), the controller DSC enables both the boost1 and boost2 controllers mandatorily, obtains the drive signals PWM1 and PWM2 of the boost1 and boost2 circuits at 120 and maximizes the PV1 input power P_PV1 and the PV2 input power P_PV2 by the MPPT module to obtain the PV voltage reference signals v_PV1* and v_PV2* in the two channels at 122, the direct-current bus voltage reference signal v_bus* is a maximum value of PV voltage reference signals in the two channels, i.e., v_bus*=max(v_PV1*, v_PV2*) at 124.

$\begin{array}{cc}{V}_{\mathrm{VLMPP}}=\frac{v_{\mathrm{PV}1+v_{\mathrm{PV}2}}}{2}& V\end{array}$

The disclosure mainly performs logic control on the multi-channel MPPT. In specific implementation, the expected result can only be achieved in conjunction with a boost voltage, current double closed-loop controller, the existing single-channel MPPT controller, etc. At the same time, in order to reduce power sampling and calculation errors, the controller DSC will calculate power using voltage and current sampling averages within 0.2 s; an operational cycle of the MPPT module is 1 s to reduce the phenomenon of misjudgment.

The embodiment described above is merely illustrative of the technical concept and features of the present disclosure and is one example embodiment so as to enable those skilled in the art to understand the content of the present disclosure and practice it accordingly, and is not intended to limit the protection scope of the present disclosure. Any equivalent alteration or modification made in accordance with the spirit of the present disclosure should be included in the protection scope of the present disclosure.

Claims

1. A control method for improving conversion efficiency of a multi-channel Maximum Power Point Tracking (MPPT) inverter, comprising: collecting an input voltage (vPVm) of a photovoltaic panel in each channel, an input current (iPVm) of the photovoltaic panel in each channel and a direct-current bus voltage (vbus), obtaining an input power (PPVm) of the photovoltaic panel in each channel, and using input voltages of at least two channels to obtain a voltage difference (ΔvPV), wherein m=1, 2, . . . , M, and M is a number of input channels of the photovoltaic inverter MPPT;comparing the voltage difference (ΔvPV) with a preset on-off control judging threshold to obtain a start state and a stop state of a boost circuit in each channel, a voltage reference signal (v*PVm) in each channel and a direct-current bus voltage reference signal (v*bus) wherein the boost start state and the stop state is determined by: when |ΔvPV|≥VTHb, turning off a boost circuit in a channel corresponding to a maximum input voltage (vPV_max), activating the boost circuits in remaining channels, wherein VTHb is a first boost on-off control judging threshold, and maximizing the input power (PPVm) by an MPPT module in each channel to obtain the voltage reference signal (v*PVm) in each channel, the direct-current bus voltage reference signal (v*bus) using a maximum voltage reference signal (v*PV_max);when VTHb≥|ΔvPV|≥VTHs, activating all boost circuits, wherein VTHs is a second boost on-off control judging threshold, wherein VTHs<VTHb; and maximizing the input power (PPVm) by the MPPT module in each channel to obtain the voltage reference signal (v*PVm) in each channel, the direct-current bus voltage reference signal (v*bus) using the maximum voltage reference signal (v*PV_max); andwhen VTHs≥|ΔvPV|≥0, obtaining a voltage (VVLMPP) at a virtual local maximum power point (VLMPP), turning off all the boost circuits, maximizing a total input power (PPV_sum) of the inverter by an MPPT module based on the direct-current bus voltage (vbus) to obtain the direct-current bus voltage reference signal (v*bus), monitoring a voltage difference between the direct-current bus voltage (vbus) and the voltage at the virtual local maximum power point (VVLMPP), and activating all the boost circuits when the voltage difference between the direct-current bus voltage (vbus) and the voltage at the virtual local maximum power point (VVLMPP) exceeds the boost on-off control judging threshold (VTHb).

2. The control method according to claim 1, wherein: when collecting the input voltage (vPVm) using the maximum input voltage (vPV_max), a photovoltaic (PV) input voltage (vPV_Smax) less than vPV_max and a minimum PV input voltage (vPV_min) to obtain a voltage difference (ΔvPV_max) between vPV_max and vPV_min and a voltage difference (ΔvPV_MS) between vPV_max and vPV_Smax;when comparing, comparing the voltage differences ΔvPV_max and ΔvPV_MS with the preset on-off control judging threshold to obtain the start state and the stop state of the boost circuit in each channel, wherein a boost start and stop control logic is as follows: when |ΔvPV|≥VTHb, turning off the boost circuit in the channel corresponding to the maximum input voltage (vPV_max), and activating the boost circuits in the remaining channels;when VTHb≥|ΔvPV|≥VTHs, activating all the boost circuits; andwhen VTHs≥|ΔvPV|≥0, obtaining the voltage (VVLMPP) at the VLMPP, turning off all the boost circuits, monitoring the voltage difference between vbus and VVLMPP, and activating all the boost circuits when the voltage difference between vbus and VVLMPP exceeds VTHb.

3. The control method according to claim 2, wherein obtaining the voltage (VVLMPP) further comprises: when VTHb≥|vbus−VVLMPP|≥0, turning off all the boost circuits, and maximizing the total input power (PPV_sum) of the inverter by the MPPT module based on vbus to obtain the direct-current bus voltage reference signal (v*bus); andwhen VTHb≥vbus−VVLMPP≥0, activating all the boost circuits, and maximizing the input power (PPVm) by the MPPT module in each channel to obtain the voltage reference signal (v*PVm) in each channel, the direct-current bus voltage reference signal (v*bus) using the maximum voltage reference signal (v*PV_max).

4. The control method according to claim 2, wherein the voltage (VVLMPP) at the VLMPP is obtained by the following formula:

5. The control method according to claim 1, wherein when collecting the input voltage (vPVm), at least using a voltage difference between the maximum input voltage and the minimum input voltage of all input channels.

6. The control method according to claim 1, wherein when collecting the input voltage (vPVm), using the maximum input voltage (vPV_max) and vPV_Smax less than vPV_max to obtain a voltage difference (ΔvPV_MS) between vPV_max and vPV_Smax.