= Solution
At fixed spectrum and <temperature>, photocurrent is approximately proportional to <irradiance>, so the magnitude of <short-circuit current> increases nearly linearly. In the ideal model,
$$
V_{\rm oc}=n\frac{k_BT}{q}\ln\!\left(1+\frac{I_{\rm ph}}{I_0}\right),
$$
so <open-circuit voltage> rises only logarithmically with <irradiance>. More incident optical <power> generally raises the maximum electrical <power>, within the device's thermal and resistive limits.
Increasing <temperature> strongly increases the dark saturation <electric current>. In <silicon> this normally reduces <open-circuit voltage> and maximum <power>, despite a small increase in <short-circuit current> associated with the <temperature> dependence of absorption and <band gap>. The thermal-voltage factor alone is insufficient to predict the sign; the <temperature> dependence of $I_0$ matters.
\b[<maximum power point tracking> adjusts the load seen by the cell] as <irradiance> and <temperature> change. A controlled DC–DC converter can transform the external load so that operation stays near the changing maximum of $-VI$, instead of at the generally suboptimal intersection with a fixed load. It matches operating conditions and cannot generate additional <energy> beyond the photovoltaic output.
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