A working map of the course for a BESS modeller: ten modules, two bridge tracks, twelve weeks. Pairs with the written Study Companion — this page is the navigator, that document is the depth.
Technology is fixed at a point in time, but how it is used — and how it evolves — depends entirely on the incentives participants face. Market design is the deliberate engineering of those incentives, constrained by physics and by law.
| Residual demand | DR_i(p) = D(p) − Σ_{j≠i} S_j(p) |
| One-step best reply (DR = a − bp, MC = c) | p* = a/2b + c/2 ; q = (a − bc)/2 |
| Ability | η(p) = −(1/100) · DR(p)/DR′(p) ; markup = 100·η(p*) in the linear case |
| Profit with a CfD | Π(p) = (P_C − c)·Q_C + [DR(p) − Q_C]·(p − c) |
| Incentive | η^C(p) = η(p) · [DR(p) − (Q_R + Q_C)] / DR(p) — sign = net exposure |
| Pivotal / net pivotal | DR(p̄) > 0 ; DR(p̄) − (Q_R + Q_C) > 0 |
| Thermal vs storage MC | HeatRate·P_fuel + VOM (+ e·P_CO₂) ; storage: opportunity cost θ + degradation φ |
| Flows via shift factors | F_ℓ = Σ_k SF_ℓk · NetInj_k ; i→j of Q: F_ℓ = Q·(SF_ℓi − SF_ℓj) |
| LMP | LMP_k = λ − Σ_ℓ SF_ℓk · (μ_ℓ^UB − μ_ℓ^LB) (+ marginal-loss term) |
| Losses | L ≈ αQ² ⇒ marginal ≈ 2 × average |
| INC / DEC rents | DEC keeps (P* − P^DEC)·ΔQ ; INC earns (P^INC − MC)·ΔQ |
| Italy conduct (GQW) | Δoffer ≈ +8 €/MWh per +0.1 P(INC) ; ≈ −16 €/MWh per +0.1 P(DEC) |
| Nodal-switch effects | CAISO: −2.5% energy, −2.1% VC, +0.18 starts/h · ERCOT: −3.8% VC (~$300m/yr), +5.8% CO₂ |
| Virtual bid | payoff = ±(P^DA − P^RT) ; equilibrium P^DA → E[P^RT | info] |
| Storage FOCs | discharge iff p ≥ θ/η_dis + φ_dis ; charge iff p ≤ η_ch·θ − φ_ch ; θ = SOC dual (water value) |
| Storage equilibrium scale | CA: first 5 GWh ≈ −5.6% prices ; 25→50 GWh ≈ −2.6% (BDG 2025) |