Power Calculations
Electrical Power Electric power is the rate at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second. Electric power is usually produced by electric generators, but can also be supplied by sources such as electric batteries.
Common electrical units used in formulas and equations are: Volt - unit of electrical potential or motive force - potential is required to send one ampere of current through one ohm of resistance Ohm - unit of resistance - one ohm is the resistance offered to the passage of one ampere when impelled by one volt Ampere - units of current - one ampere is the current which one volt can send through a resistance of one ohm Watt - unit of electrical energy or power - one watt is the product of one ampere and one volt - one ampere of current flowing under the force of one volt gives one watt of energy Volt Ampere - product of volts and amperes as shown by a voltmeter and ammeter - in direct current systems the volt ampere is the same as watts or the energy delivered - in alternating current systems - the volts and amperes may or may not be 100% synchronous - when synchronous the volt amperes equals the watts on a wattmeter - when not synchronous volt amperes exceed watts - reactive power Kilovolt Ampere - one kilovolt ampere - KVA - is equal to 1,000 volt amperes
Electric Power Formulas P = V I P = R I2 P = V2/ R where P = power (watts, W) V = voltage (volts, V) I = current (amperes, A) R = resistance (ohms, Ω)
I = V / R I = P / V R = V / I R = V2/ P R = P / I2 V = R I V = P / I
Power Factor It is common to define the Power Factor - PF - as the cosine of the phase angle between voltage and current - or the "cosφ". PF = cosφ where PF = power factor φ = phase angle between voltage and current
The power factor defined by IEEE and IEC is the ratio between the applied active (true) power - and theapparent power, and can in general be expressed as: PF = P / S (1) Where PF = power factor P = active (true or real) power (Watts) S = apparent power (VA, volts amps)
Power factor is an important measurement in electrical AC systems because an overall power factor less than 1 indicates that the electricity supplier need to provide more generating capacity than actually required the current waveform distortion that contributes to reduced power factor is caused by voltage waveform distortion and overheating in the neutral cables of three-phase systems
Example - Power Factor A industrial plant draws 200 A at 400 V and the supply transformer and backup UPS is rated 200 A 400 V = 80 kva. If the power factor - PF - of the loads is only 0.7 - only 80 kva 0.7 = 56 kw of real power is consumed by the system. If the power factor is close to 1 (purely resistive circuit) the supply system with transformers, cables, switchgear and UPS could be made considerably smaller.
"Leading" or "Lagging" Power Factors Power factors are usually stated as "leading" or "lagging" to show the sign of the phase angle. With a purely resistive load current and voltage changes polarity in step and the power factor will be 1. Electrical energy flows in a single direction across the network in each cycle. Inductive loads - transformers, motors and wound coils - consumes reactive power with current waveform lagging the voltage. Capacitive loads - capacitor banks or buried cables - generates reactive power with current phase leading the voltage.
Power Loss Calculations A small power station transmits 1MW into the grid. The nominal voltage is 32kV. The resistance of the power lines is measured at 10ohms. What is the power lost on the line?
Power Loss Calculations The 1 MW power plant has purchased a transformer to transmit the power on the 10ohms power lines until it feeds the grid. The transmission voltage is 400kV. What is the power loss? Note the difference between the 32kV and 400kV transmission.
Solve the Problem A kettle has a power rating of 2.5kW You have to choose a extension lead to connect the kettle. The leads have the following power rating: - 13A very expensive - 10A Cheaper - 5A very cheap - 3A very cheap - Choose the best cable for the kettle at the best price!
Problem: What is the maximum power dissipation allowed for a 13Amp plug?
An Electric heater has a power rating of 2kW choose the appropriate fuse: 13A 10A 7A 5A 3A
kwh 1 kwh means that an item consuming 1kW is running for one hour. The cost of 1kWh in the UK is about 10 pence. If a security light with a 500W bulb is running for 2 hours it would cost 0.10
Calculating Power Consumption A computer use 180Watts. It is turned on all day. Calculate how much power is consumed in 1 hour. How much would it cost to keep the computer running for the full day (16hrs), week, month and year.
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