1.) Electrical Power (DC Circuits)
P = V x I
Where:
P = Power (in watts)
V = Voltage (in volts)
I = Current (in amperes)
2.) Electrical Power (AC Circuit, Single Phase)
P = V x I x cos Ɵ
Where:
Ɵ = is the phase angle between voltage and current (power factor)
3.) Electrical Power (AC circuit, Three Phase)
P = √3 x V x I x cos Ɵ
Where:
V = line voltage (in volts)
I = line current (in amperes)
cos Ɵ = power factor
4.) Efficiency of Power Generation System
Eff. = (P out / P in) X 100
Where:
Eff. = efficiency (Percentage)
P out = output power (in watts)
P in = input power (in watts)
5.) Mechanical Power Output of a Turbine
P = T x ῶ
Where:
ῶ = angular velocity (in radians per second)
6.) Thermal Efficiency of Heat Engines (Carnot Efficiency)
ἡ carnot = 1 – (T cold / T hot)
Where:
T cold = temperature of the cold reservoir (in kelvins)
T hot = temperature of hot reservoir (in kelvins)
7.) Heat Rate (Energy Efficiency of a Power Plant)
Heat Rate = Fuel Energy Input (Btu per hour) / Electricity Output ((kWh)
• Lower heat rate means higher efficiency.
8.) Energy Generated by a Wind Turbine
P = ½ ῤ A v^3 C p
Where:
ῤ = air density (in kg/m^3)
A = swept area of the turbine blades (in m^2)
V = wind speed (in m/s)
C p = power coefficient (depends on the turbine)
9.) Hydroelectric Power Generation
P = ἡ ῤ g h Q
Where:
ἡ = turbine efficiency
ῤ = water density (in kg/m^3)
g = acceleration due to gravity (9.81 m/s^2)
h = height of the waterfall (in meters)
Q = water flow rate (in cubic meters per second)
10.) Steam Power Generation (Rankine Cycle Efficiency)
ἡ rankine = W turbine – W pump / Q in
Where:
W turbine = work done by the turbine (in joules)
W pump = work required to pump the fluid (in joules)
Q in = heat energy added (in joules)
11.) Photovoltaic Power Output (Solar Panels)
P = A x E x ἡ
Where:
P = power output (in watts)
A = area of the panel (in square meters)
E = solar irradiance (in watts per square meter)
ἡ = panel efficiency
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