  This paper evaluates market equilibrium under different pricing mechanisms in
a two-settlement 100%-renewables electricity market. Given general probability
distributions of renewable energy, we establish game-theoretical models to
analyze equilibrium bidding strategies, market prices, and profits under
uniform pricing (UP) and pay-as-bid pricing (PAB). We prove that UP can
incentivize suppliers to withhold bidding quantities and lead to price spikes.
PAB can reduce the market price, but it may lead to a mixed-strategy price
equilibrium. Then, we present a regulated uniform pricing scheme (RUP) based on
suppliers' marginal costs that include penalty costs for real-time deviations.
We show that RUP can achieve lower yet positive prices and profits compared
with PAB in a duopoly market, which approximates the least-cost system outcome.
Simulations with synthetic and real data find that under PAB and RUP, higher
uncertainty of renewables and real-time shortage penalty prices can increase
the market price by encouraging lower bidding quantities, thereby increasing
suppliers' profits.
