I suspect the carbon price will have to be a fair bit higher than the one being mooted to advantage gas generation of electricity.
Some back of the envelope generalisations. Gas produces half the CO2 per MWhr/kWhr as does coal. Here in Qld it's close to 1t CO2/MWhr - black coal dominates the fuel mix. I'll assume coal-fired generation is $50/MWhr (a bit high compared to what AEMO is showing) and gas is $80/MWhr (prices I've seen quoted by various industry players). CO2 at $30/t sends coal to $80/MWhr and gas to $95/MWhr, which is certainly closer. On my assumptions we'd need a $60 carbon price before coal would become second choice to gas on generation costs alone.
For every $10/t of carbon price could see our (Qld) retail electricity price rise 1c/kWhr ($10/t(CO2)=1000c/t(CO2), 1t(CO2)/MWhr=1t(CO2)/1000kWhrs, -> 1000c/1000kWhrs -> 1c/kWhr). Simplistic but indicative.
Some other generalisations - generators from wind, like AGK and IFN, have spoken of wanting/needing $100-120+/MWhr for viability of windfarms but struggle to get that. Present technology PVs are supposedly in the $180-200/MWhr range, I've seen figures as low as $140 and as high as $340. A newspaper carried the story a few weeks ago of new generation PVs matching or bettering wind or gas within a few years.
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