Active and reactive power Introduction Renewables Summer Course 17.7.2014 Eetu Ahonen

Contents Power Power factor Transmission line impedance Apparent power Active power Reactive power Creation of reactive power Consumption of reactive power Power factor Transmission line impedance Reactive power & renewables Summary Firstly… secondly…

Apparent power (näennäisteho) Power that is transferred by the conductors 𝑆=𝑈𝐼 (Joule’s law) Measured in volt-amperes Transmission lines ”see” only apparent power 𝑆 2 = 𝑃 2 + 𝑄 2 Relation of apparent power S, active power P and reactive power Q. Figure from wikipedia. AC circuits

Active power (pätöteho) Real part of apparent power Transfers real energy, does work Measured in watts (W) In a resistive circuit: 𝑆= 𝑉 rms 𝐼 rms >0 ∀ 𝑡 Current and voltage in phase Energy is dissipated at power 𝑆=𝑃. Electric heater

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 Loisteho = parasitic power

Creation of reactive power In a capacitive circuit Current leads the voltage by 90 degrees 𝑆= 𝑉 rms 𝐼 rms <0 ∃ 𝑡 𝑃=0 Capacitive load creates reactive power Capacitive circuit = only capacitor Voltage and current in a capacitive circuit

Consumption of reactive power In an inductive circuit Current lags the voltage by 90 degrees 𝑆= 𝑉 rms 𝐼 rms <0 ∃ 𝑡 𝑃=0 Capacitive load consume reactive power Inductive = only a coil Voltage and current in an inductive circuit

Power factor Ratio of active power to apparent power cos 𝜙 = 𝑃 𝑆 = 𝑉 𝑅 𝑉 𝑍 = 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 Phi = phase difference of voltage and current Example: Electric motor, fluorescent lamp ballast etc.

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. 𝐺 spec stands for shunt resistance Shunt resistance = some connection between ground (earth) and the transmission line exist.

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 Voltage rise: Capacitive load, typical inductive transmission line (overhead)

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

Summary Power Power factor, measure of a load ”goodness” 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 To summarise