The PV source has a PMT impedance of \$Vpmt/Ipmt = Zpmt\$. The job of the PMT controller to track this rising impedance as solarity declines. Vpmt~82% Voc at the full sun then drops to ~70%Voc which as current reduces Zpmt rises. MPT occurs when the PV impedances are matched at the interface.
The combination of PV and battery energy capacity and available Solarity must exceed the max load energy demand over a long period of many days with cloud cover to avoid dropout. A cost tradeoff calculation is required for both PV vs Battery energy capacity per week to achieve the best economical choice.
The job of the battery is to have adequate Wh energy storage capacity for a given load of W and duration in h to sustain a Vmin to continue without UVLO (under-voltage lockout) near 10% SOC (state of charge).
The job of the GTI is to exceed the W output demand load and input voltage range so that output Vac is within tolerance while not overloading the PV and result in loss of PV max efficiency. (MPPT)
Thus if the GTI has output regulation as well as input MPT regulation, it's job is to present an impedance that never goes lower than Zmpt of the PV panel so it's output voltage does not drop below optimal efficiency. This may not guarantee that the PV can have adequate power to supply the load and charge the battery so all 3 components (PV, GTI, load) must be sized such that stage 1 and 2 meet the load demand at all times.