Active and reactive
power
Renewables Summer Course
17.7.2014
Eetu Ahonen
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Contents
• Power
• Apparent power
• Active power
• Reactive power
• Creation of reactive power
• Consumption of reactive power
•
•
•
•
Power factor
Transmission line impedance
Reactive power & renewables
Summary
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Apparent power (näennäisteho)
• Power that is
transferred by the
conductors
• 𝑆 = 𝑈𝐼 (Joule’s law)
• Measured in voltamperes
• Transmission lines
”see” only apparent
power
• 𝑆 2 = 𝑃2 + 𝑄 2
Relation of apparent power S, active power P and reactive
power Q. Figure from wikipedia.
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Active power (pätöteho)
• Real part of apparent power
• Transfers real energy, does work
• Measured in watts (W)
• In a resistive circuit:
• 𝑆 = 𝑉rms 𝐼rms > 0 ∀ 𝑡
• Current and voltage in phase
• Energy is dissipated at power 𝑆 = 𝑃.
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Reactive power (loisteho)
• Deadweight, foam of the beer
• Reactive power does not do work
• Result of current transferring no energy
• Measured in VArs (volt-ampere reactive)
• Imaginary part of apparent power
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Creation of reactive power
• In a capacitive circuit
• Current leads the
voltage by 90 degrees
• 𝑆 = 𝑉rms 𝐼rms < 0 ∃ 𝑡
• 𝑃=0
• Capacitive load
creates reactive
power
Voltage and current in a capacitive circuit
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Consumption of reactive power
• In an inductive circuit
• Current lags the
voltage by 90 degrees
• 𝑆 = 𝑉rms 𝐼rms < 0 ∃ 𝑡
• 𝑃=0
• Capacitive load
consume reactive
power
Voltage and current in an inductive circuit
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Power factor
• Ratio of active power to apparent power
• cos 𝜙 =
𝑃
𝑆
=
𝑉𝑅
𝑉𝑍
=
𝑅
𝑍
∈ [−1,1]
• Low power factor
• More demands for conductors
• Higher reactive and apparent power
• More distribution losses
• Example: Power factor of 0.2 (really low), active power
demand 1 kW
• Needed apparent power 5 kVA
• Can be compensated with capacitors
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Transmission line impedance
• Transmission lines have
resistance and reactance
• Resistance from the metal
• Reactance from the
capacitive and inductive
properties of the circuit
Simplified model of a transmission line. 𝐺spec stands for
shunt resistance
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Transmission line impedance
• Transmission lines have
significant impedance
• Restricts the amount of
power transferred
• Voltage can drop or rise(!)
over the line
• Less than 10% voltage drop
acceptable
Voltage drop over a typical 200 km 100 kV transmission line
as a function of active power demand for different values of
load power factor
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Reactive power & renewables
• Renewable sources do not provide reactive power
• High renewable production
• Only few large power stations online
• Reactive power transferred over great distances
• Voltage collapse due to insufficient line capacity
• Large plants cannot be used for power control
• Smaller modular generating units near the loads are needed
• Other mitigating methods
• Capacitors
• Synchronised generators
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Summary
• Power
• Apparent power seen by the conductors
• Active power transfer energy
• Reactive power
• Does not transfer energy
• Created by capacitive loads
• Consumed by inductive loads
• Power factor, measure of a load ”goodness”
• Reactive power demands have to be taken into account in
network design
• Especially in networks with high penetration of renewables
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