Offshore Wind Farm Sizing in the North Sea

Case Study 1: Offshore Wind Farm Sizing in the North Sea

Scenario A utility-scale offshore wind project off the coast of Denmark (Horns Rev 3 site) requires preliminary turbine sizing to meet a 25 MW annual energy yield per turbine. Constraints include strict marine spatial planning limits (max rotor diameter ≤ 180 m), seabed foundation compatibility, and higher-than-continental air density due to maritime conditions. Turbine selection must align with certified offshore models (e.g., Vestas V174-9.5 MW or Siemens Gamesa SG 14-222).

Given Data

• Air density: 1.25 kg/m³ (measured at hub height, 100 m, over North Sea)
• Average wind speed: 9.2 m/s (long-term met mast data, 10-min averaged, Weibull k = 2.1)
• Power coefficient: 0.42 (manufacturer-specified for high-efficiency offshore blades)
• Capacity factor: 0.44 (validated against nearby operational farms and IEC 61400-12-1 power curve extrapolation)
• Target AEP: 42,000,000 kWh/year (equivalent to ~4.8 MW average power × 8760 h × 0.44 CF)

Calculation The Wind Turbine Sizing Tool uses the fundamental AEP relationship:

AEP = 0.5 × ρ × v³ × Cp × A × CF × 8760

Solving for rotor swept area A:

A = AEP / (0.5 × ρ × v³ × Cp × CF × 8760)

Substituting values:

• AEP = 42,000,000 kWh/yr = 42,000,000 × 1000 Wh/yr
• ρ = 1.25 kg/m³
• v = 9.2 m/s → v³ = 9.2³ = 778.688
• Cp = 0.42
• CF = 0.44
• 8760 h/yr

Numerator: 42,000,000,000 Wh/yr
Denominator: 0.5 × 1.25 × 778.688 × 0.42 × 0.44 × 8760 ≈ 0.5 × 1.25 × 778.688 × 0.42 × 0.44 × 8760 = 742,312.5

A = 42,000,000,000 / 742,312.5 ≈ 56,580 m²

Rounded to two decimals per tool spec: 56,580.00 m²

Verifying rotor diameter: A = π × (D/2)² → D = 2 × √(A/π) = 2 × √(56,580/3.1416) ≈ 2 × √18,010 ≈ 2 × 134.2 ≈ 268.4 m — exceeds constraint.

Re-evaluation: Since 268 m is infeasible, engineers iterated using the tool’s sensitivity feature—reducing target AEP to 38,500,000 kWh/yr (to fit within 180 m rotor limit). At D = 180 m → A = π × 90² = 25,447 m². Back-calculating feasible AEP confirms 38.5 GWh/yr is achievable with CF = 0.44 and site winds.

Result and Decision Selected Siemens Gamesa SG 14-222 (rotor diameter 222 m, A = 38,700 m²), which yields ~41.2 GWh/yr at site conditions—meeting target with 7% margin and complying with foundation and grid interconnection constraints. Final layout optimized for wake loss using PARK model.

Lesson Rotor swept area derived from AEP is a starting point—not a final specification; physical, logistical, and regulatory constraints often govern turbine selection more than theoretical energy demand. Always cross-check calculated A against commercially available offshore platforms before locking in site layout.