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Table 1 Parameters involved in our model

From: Intraday renewable electricity trading: advanced modeling and numerical optimal control

Wind energy \(D_{t}\)

\(\sigma_{D}\)

Volatility

\(D_{0}\)

Initial value

Conventional units

n

Number of agent’s conventional units

\(c_{i}\)

Marginal costs of conventional units, i = 1,…,n

\(\kappa^{\min}_{i}\), \(\kappa^{\max}_{i}\)

Minimal/maximal capacity of units i = 1,…,n

Prices \(Y_{t}\), \(P_{t}\)

Payoff g

Profit f

Value function V

\(\mu_{Y}\)

Drift of permanently impacted mid price

\(\sigma_{Y}\)

Volatility of permanently impacted mid price

ψ

Permanent price impact of agent’s trading

\(Y_{0}\)

Initial value

h

Half-spread function

φ

Execution cost function

α

Penalty function