Scientific Methodology & Engineering Physics
WattMatrix does not use marketing rules-of-thumb or generic installer estimates. Every simulation on this platform is computed from first-principles thermodynamic physics, non-linear electromechanical models, empirical discharge testing, and statutory Irish & European grid standards.
Thermodynamic Hot Water Storage & Standing Loss Equations
Heating a domestic hot water cylinder requires energy strictly bounded by the isobaric specific heat capacity of water. For a cylinder of volume V (litres), with cold water mains inlet temperature T_cold and setpoint temperature T_hot:
// Cylinder Thermal Energy Demand
E_tank (kWh) = V_litres × c_water × (T_hot - T_cold) + E_standing_loss
// Thermodynamic Constant:
c_water = 4.184 kJ/(kg·°C) = 0.00116222 kWh/(L·°C)
// Standing Jacket Heat Loss (BS 1566 / ErP Standard):
E_standing_loss (kWh/day) = 1.10 kWh (Factory Foam) to 2.40 kWh (Uninsulated Copper)
When evaluating immersion diverters (e.g. Myenergi Eddi) against grid export via the Clean Export Guarantee (CEG), the effective cost of alternative heating fuels must incorporate statutory seasonal boiler efficiency η_seasonal:
// Effective Useful Fuel Cost
Cost_effective (€/kWh_th) = Tariff_fuel / η_seasonal
// Baseline Calibration: Kerosene @ €0.11/kWh (η=88% condensing) → €0.125/kWh_th
// Clean Export Guarantee (CEG): 15.0c to 20.0c/kWh cash credit
ESB Networks NC6 6.0 kVA Export Limit & Single-Phase Inverter Clipping
Under ESB Networks Conditions of Connection (Specification NC6 / EN 50549-1), microgeneration installations on standard domestic single-phase 230V supplies are capped at a maximum apparent inverter power rating of 6.0 kVA (26.1 A).
// Statutory Inverter Export Ceiling
P_export_max = 6,000 VA = 6.0 kW (at unity power factor cos φ = 1.0)
// Curtailed Generation Instantaneous Balance:
P_clipped = max(0, P_solar(t) - P_house(t) - P_batt_charge(t) - 6.0 kW)
Oversized arrays (e.g. 8.0 kWp to 10.0 kWp) generate surplus peak power during high insolation midday hours. If the domestic home battery is fully charged (or restricted by its max continuous charge rate, typically 5.0 kW for hybrid inverters), excess power above 6.0 kW is curtailed by the inverter's maximum power point tracker (MPPT).
Inverter Efficiency Curves & Quiescent Tare Losses
No power conversion is 100% efficient. Inverters suffer from fixed internal quiescent tare power P_tare (cooling fans, microcontrollers, gate drives, display telemetry) plus resistive I²R copper and switching semiconductor losses:
// Non-Linear Inverter Efficiency Model
P_dc_draw = P_tare + (P_ac_load / η(P_ac)) + k_switching × (P_ac_load)²
// Typical Tare Benchmarks:
• Portable Power Stations: 15W to 35W constant idle draw
• Hybrid Residential ESS Inverters: 25W to 65W round-the-clock draw
EV On-Board Charger (OBC) Tare & IEC 61851 6A Minimum Threshold
Charging an EV at low currents from rooftop solar suffers dramatic efficiency penalties. Modern electric vehicles wake their battery thermal management systems, coolant pumps, and high-voltage computers during AC charging, consuming 280W to 320W of auxiliary tare power regardless of charge speed.
// Charging Efficiency Derating
η_effective(I) = (V × I × cos φ - P_aux_tare) / (V × I × cos φ) × η_conversion
// Minimum Standard Cutoff (IEC 61851-1):
I_min = 6 Amperes → P_min = 230V × 6A = 1,380 W (Solar surplus below 1.4 kW cannot charge EV)
Heat Loss Indicator (HLI) & SEAI Grant Eligibility Thresholds
To qualify for the SEAI €6,500 domestic heat pump grant, an independent technical assessment must confirm that the home achieves a Heat Loss Indicator of ≤ 2.0 W/K/m². Homes exceeding 2.0 must undergo fabric-first insulation upgrades before heat pump installation.
// Building Heat Loss Indicator
HLI (W/K/m²) = Total Specific Fabric & Infiltration Heat Loss (W/K) / Total Floor Area (m²)
// SEAI Statutory Rules:
• HLI ≤ 2.0 W/K/m²: Eligible for immediate heat pump capital grant (-€6,500)
• HLI 2.0–2.3 W/K/m²: Marginal; requires specific radiator flow temperature verification
• HLI > 2.3 W/K/m²: Requires fabric deep-retrofit (wall insulation, triple glazing)
Arrhenius Fuel Oxidation Kinetics (ASTM D525)
Emergency backup generators depend on stored fuel. Unleaded gasoline oxidizes over time into gummy polymers and varnish. The degradation rate doubles for every 10°C rise in ambient temperature, modeled via the Arrhenius equation:
// Arrhenius Oxidation Rate
k(T) = A × exp(-E_a / (R × T))
// Shelf-Life Benchmarks:
• Untreated E10 Gasoline @ 20°C: 90 days before phase separation & gum formation
• Stabilized Fuel (ASTM D525 anti-oxidant): 365 to 730 days
• HD-5 Liquefied Petroleum Gas (Propane): Indefinite chemical shelf-life (zero peroxide gumming)