# Renewables and reactive power

Unfortunately, reactive power is often poorly explained, but is actually pretty simple.

By definition, ‘apparent power’ equals ‘real power’ plus ‘reactive power’. The idea of ‘real power’ is straightforward and intuitive, but the concept of ‘reactive power’ is not. I’ve seen many analogies, such as the beer glass, but the problem with these are that they are simply metaphors and do not capture what is actually going on.

In direct current (DC), the voltage and current are constant. The only three variables of interest are voltage, current, and resistance, where Ohm’s Law states that –

voltage = current x resistance

At this point it can be useful to compare the mechanical relation of –

force = velocity x friction

Electrical power equals voltage x current. Mechanical power equals force x velocity. Both are expressed in watts.

But in alternating current (AC) circuits, it gets a bit more interesting. There are two additional

*variables*– the rate of change of voltage, and the rate of change of current – and two additional

*properties*– capacitance and inductance. A capacitor connected

*across*a voltage resists a change in voltage, and inductors connected

*in series*with a current resist a change in current.

If there are only resistive elements in an AC circuit, the voltage (measured across) and current (measured in series) are exactly in phase. But when there are capacitive and/or inductive elements, the voltage and current waveforms are no longer in phase. The reason can be described mathematically, but in simple terms, these reactive elements respond to rates of change.

*Power factor*is equal to the ratio of ‘real power’ and ‘apparent power’, or can be calculated as the cosine of the phase difference. Hence, in-phase waveforms corespond to a power factor of one, and real power equals apparent power.

Assume that a capacitor is connected directly across 230 volts AC (don’t try this at home!). The capacitor will fully charge then fully discharge each AC cycle, but the capacitor itself won’t consume any ‘real’ power over the full cycle. However, measured instantaneously, the capacitor is in fact sinking, then sourcing ‘real’ current.

In an AC system, a capacitor is doing the same as a clock pendulum. As a pendulum rises, it converts kinetic energy to potential energy, and vice-versa as it falls. A clock only needs winding every few days because very little ‘real’ energy is being consumed, even though ‘real’ energy transfer is occurring each cycle. It’s just that that the energy lost and gained each cycle is nearly the same so the average power over a full cycle is zero. In fact, an electrical-mechanical analogy can be used to aid complex circuit analysis by converting between electrical and mechanical representations. As already noted, the analogous property of electrical capacitors in mechanics is moving masses. In a capacitor, the current through the capacitor is equal to (capacitance x the rate of change of voltage across the capacitor). Likewise, force is equal to the (mass x the rate of change of velocity). Furthermore, the energy stored in a capacitor is equal to (0.5 x capacitance x voltage^2), and the energy stored in a moving mass is equal to (0.5 x mass x velocity^2).

So we have a simple definition of reactive power – it is simply the energy circulating back and forth between the source (e.g. generator and/or transmission system) and the load (e.g. motor). In practice, most reactive loads are motors, which are inductive. In motors, the electrical current is converted into a magnetic field, some of which returns an electrical current on the next part of the cycle as the magnetic field reverses. The portion that is not returned has been converted to torque in the motor and is termed the ‘real power’. The portion that is not actually consumed and returned to the source is termed ‘reactive power’.

The reason that reactive power should be minimised is that the transfer of current through the whole transmission system adds to the transmission load, creates actual losses, and leads to voltage instability. Reactive power is very ‘real’, but doesn’t relate to any actual work being consumed. Reactive power can be addressed at a facility level, local, transmission, or at the generator. For example, installing power factor correction locally, such as a capacitor bank, means that the reactive power is only circulating locally.

Part of the reason for confusion is that reactive power is sometimes referred to as the ‘imaginary’ part of AC power. The expression ‘imaginary’ comes from the use of complex numbers to perform AC circuit analysis. A complex number is a number that can be expressed in the form

*a + bj*, where

*a*and

*b*are real numbers, and

*j*is a solution of the equation x^2 = −1. The

*a*is the ‘real’ part and the

*b*the ‘imaginary’. Since there is no real number that satisfies this equation (the square root of negative 1), it is called an imaginary number. It just works out that complex numbers work really well for AC analyses. There is nothing ‘imaginary’ going on in AC circuits – j originally emerged in the sixteenth century as a way to solve quadratic equations. It tuned out that using the square root of negative 1 as an intermediate step, which became -1 when squared, turned out to be a powerful way to solve quadratics and cubics. Euler and others expanded on this simple idea to build a suite of powerful mathematical tools.

The issue in relation to renewables is that reactive power is readily supplied by synchronous generators, but non-synchronous generators have not traditionally provided this functionality to a great extent. However, modern power electronics now provide the capability to provide reactive support, but only where it is specifically designed, required, and implemented. Regardless, reactive power is as much a transmission and distribution network issue, and not just related to generation. With greater penetration of non-synchronous generators, there will be additional costs associated with reactive power, such as the use of synchronous condensers, but the costs are likely to be modest in relation to overall costs.

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