Engineering Formula Library

Electrical Machines
Generator Efficiency
\eta_{gen}\% = (P_{electrical} / P_{mechanical}) \times 100
Electrical Machines
Turbine Efficiency
\eta_{turbine}\% = (P_{shaft} / P_{water}) \times 100
Electrical Machines
Turbine Specific Speed
N_s = N\sqrt{P} / H^{5/4}
Hydropower
Annual Energy Generation
AEG = P_{rated} \times CF \times 8760
Hydropower
Hydraulic (Water) Power Input
P_{water} = \rho \times g \times Q \times H
Hydropower
Hydropower Output Power
P = (\rho \times g \times Q \times H \times \eta) / 1000
Hydropower
Net Head
H_{net} = H_{gross} - H_{losses}
Hydropower
Overall Hydropower Plant Efficiency
\eta_{plant} = \eta_{turbine} \times \eta_{generator} \times \eta_{transformer}
Hydropower
Penstock Flow Velocity
V = Q / (\pi D^2 / 4)
Hydropower
Penstock Friction Head Loss (Darcy-Weisbach)
h_f = f \times (L/D) \times (V^2 / 2g)
Motor
Motor Full Load Current
I = P/(√3 × V × PF × η)
Motor
Motor Slip
Slip = ((Ns - Nr)/Ns) × 100
Power System
Power Factor Correction
Qc = P × (tanφ1 - tanφ2)
Power System
Single Phase Current
I = P / (V \times PF)
Power System
Three Phase Current
I = P / (\sqrt{3} \times V \times PF)
Power System Utilization
Annual Load Factor
ALF\% = (Total\ Annual\ Energy / (Peak\ Demand \times 8760)) \times 100
Power System Utilization
Diversity Factor (Definition)
DvF = \Sigma(Individual\ Max\ Demands) / System\ Max\ Demand
Power System Utilization
Levelized Cost per Unit Generated
Cost_{kWh} = Total\ Annual\ Cost / Annual\ Energy\ Generated
Power System Utilization
Load Factor
LF\% = (Average\ Load / Peak\ Load) \times 100
Power System Utilization
Loss Load Factor
LLF = 0.3 \times LF + 0.7 \times LF^2
Power System Utilization
Per-Unit (p.u.) System Value
Value_{pu} = Actual\ Value / Base\ Value
Power System Utilization
Plant Capacity Factor
CF\% = (Actual\ Energy / (Rated\ Capacity \times Hours)) \times 100
Power System Utilization
Plant Use Factor
UF\% = (Actual\ Energy / (Rated\ Capacity \times Hours\ Operated)) \times 100
Power System Utilization
Reserve Margin
RM\% = ((Available\ Capacity - Peak\ Demand) / Peak\ Demand) \times 100
Power System Utilization
Transmission & Distribution System Loss
Loss\% = ((Generation - Delivered) / Generation) \times 100
Protection
Cable Size
A = I / J
Protection
Voltage Drop Single Phase
VD = 2 imes I imes L imes R
Protection
Voltage Drop Three Phase
VD = sqrt{3} imes I imes L imes R
Transformer
Transformer Full Load Current
I = (kVA × 1000)/(√3 × V)
Transformer
Transformer kVA
kVA = (√3 × V × I)/1000