Volcanic eruptions effectively inject large quantities of aerosols in the upper layers of the atmosphere, increasing Earth's albedo and reducing the intensity of the solar radiation reaching the surface. Such reduction would indeed lower the solar energy available to solar panels.
These effects of volcanic eruptions have been studied by Gao et al. (2008) and Crowley and Unterman (2013). Both studies were combined by the IPCC Working Group I during the assessment report 5 (2013), and summarized on the figure 8.18 (Chapter 8), together with other climatic forcings:
You can see that the largest drop in effective radiative forcing happens in 1815 as a consequence of the Tambora eruption.
Unfortunately, that event goes out the scale of the plot. However, the data is available on Table AII.1.2 of Annex II, were we can see that the minimum value indeed happens in 1815 and reaches –11.629 W/m².
Considering the typical amount of energy received from the Sun under clear skies at seal level is roughly 1,000 W/m², the irradiation drop produced by Tambora would represent a drop of about 1% on the energy reaching the Earth's surface. Of course, much larger local effects could be observed due to transient and more localized dense ash clouds.
Therefore, at a global scale, if a new "year without summer" where to happen, photovoltaic energy output would drop by ~1%.
Of course, larger effects would take place if the eruption happens to be close to the most important areas for photovoltaic energy production.