# Mastering Reactive Power and Power Factor in AC Networks

Navigating the Complexities of Reactive Power and Power Factor in Electrical Systems

*This article was originally published on Star Delta Power and has been adapted and updated for EasyCableSizing to provide a global perspective.*

An important and largely misunderstood part of every AC electrical network is **reactive power** and the relationship between this power and other types of power, known as **power factor**. Having a sound understanding of how this relationship works will aid in realising the full potential of an installation.

## § Electrical characteristics of components

A network is built up of lots of components which may include: cables, motors, generators, power electronic devices, capacitors, lighting, etc. All these components include a combination of 3 important electrical characteristics: **resistance**, **inductance** and **capacitance**.

**Resistance ®** is determined by the type of material and its cross sectional area used to conduct electricity.

Inductance is created by coils of a conductor. High levels of inductance can be found in transformers, reactors and motors as these are predominantly made up of coils.

Capacitance can be found where conductors pass closely but not touching, like between insulated cables positioned next to each other, or even between the conductors used to make a coil (winding) in a transformer.

Both capacitance and inductance can be converted to **reactance (X)**. Inductive reactance and capacitive reactance are opposites, and can negate each other.

**Impedance (Z)** is a function of R and X, and can be expressed by *Z² = R² + X²*.

### § How do these characteristics affect power flow?

Depending on the components present on an AC network, the current and voltage waves will cross 0 at the same time or offset from one another.

In a network which only has resistive components, current and voltage waves cross 0 at the same time. Once *inductive* and *capacitive* components are introduced to the network, this begins to change.

An *inductor* causes the current to cross 0 after the voltage, meaning the current *lags* the voltage. A *capacitor* causes the current to cross 0 before the voltage, meaning the current *leads* the voltage.

The time that the current *leads* or *lags* the voltage is measured in degrees, where a full cycle is 360 degrees. This is the **phase angle (phi or φ)**.

When the phase angle is 0 degrees, power can be determined simply using *P = VI*. This power is **active power (P), measured in watts (W)**. This is the type of power which is desired by **Transmission System Operators (TSOs)** and **Distribution Network Operators (DNOs)** as it is the most usable.

When the phase angle isn’t 0 degrees, there is another type of power - **reactive power (Q), measured in volt-amperes reactive (VAr)** - which is produced or consumed depending on whether the network is *lagging* or *leading*. An inductive *lagging* network consumes reactive power, whereas a capacitive *leading* network produces reactive power.

**Apparent power (S), measured in volt-amperes (VA)**, is the overall power in a network and is expressed by *S² = P² + Q²*. This relationship is often demonstrated by and known as the **power triangle**.

## § Power factor

*Power factor (pf)* is directly related to the phase angle. It can be expressed by *pf = Cos(φ)*. This way of representing the phase angle is more commonly used.

A pf of 1 - known as **unity power factor** - equates to a φ of 0 degrees, meaning the network is purely resistive. A pf of 0 equates to a φ of 90 degrees, meaning the network is purely reactive, whether it be inductive or capacitive.

TSOs and DNOs establish a window in which their network and any attached equipment or private networks should function between. This may be between 0.9 lagging, to unity, to 0.9 leading; or 0.95 to 0.95; or any value they specify in their policies.

## § How does power factor affect a network?

A low power factor, and in turn reactive power, can be both damaging to equipment and costly.

A load which requires 1MVA at unity power factor - 1MW and 0MVAr of active power and reactive power respectively - will require a generation source on the network to be produce a minimum of 1MW to meet the load’s demands.

But what happens when the network contains a lot of reactance? For example a transformer - which is inductive - consumes reactive power. We can assume that the transformer consumes 300kVAr for this example.

The generator will aim to compensate for the consumption of reactive power by producing a similar amount, alongside the required 1MW of power. 1MW and 0.3MVAr equates to a power factor of 0.958, and a total apparent power of 1.044MVA. Generating 1.044MVA of power rather than 1MVA of power will be more costly over a sustained duration, not only financially, but in the case of a synchronous or asynchronous generator, environmentally too, as more fuel is required.

According to the UK *Department for Business, Energy & Industrial Strategy* , the UK used approximately 300 TWh of power in 2018 (source). If the network were running at a lagging power factor of 0.95, a massive 98.6 TVAr would additionally be required. The ongoing running cost of generation required to try and compensate for this reactive power must be astronomical.

### § How can a network be made more efficient?

Looking at our example, we can make the installation more efficient by providing **power factor correction (PFC)** via other means.

We have already seen that generation is able to compensate for the reactive power on the network as much as the equipment allows. We have also seen how this is costly and requires fuel.

Another way to compensate for the reactive power consumption in this instance could be to install capacitors, a passive type of compensation. These capacitors would be a low maintenance and come without a running cost. By installing correctly sized capacitors, the power factor could be improved to around unity. This would mean the generator would be producing the power required by the load only, and not producing extra power to compensate for network equipment.

The example given here has been to use capacitors to compensate for inductive reactance.

To compensate for capacitive reactance on a network, which may be required local to extensive cabling networks, inductance would be required. Reactors are often used for this purpose.

## § Should you make your generation installation more efficient?

It’s important to note that each country may have different reactive power requirements and grid codes that govern the operation and efficiency of electrical installations. Any entity which is intending on exporting the Registered Capacity (Pmax) that they have specified should aim to reduce the reactive power on their local network to both minimize costs of generation and use their equipment to its full potential.

In the UK, and based on ENA G99 or Grid Code, **Power Park Module (PPM)** installation with an installed capacity of 20 MVA, is required to operate through a power factor range of 0.95 lagging to 0.95 leading while maintaining it’s registered capacity. Based on the power triangle formula, this PPM would therefore be able to have a Pmax of 19 MW.

If this 19 MW PPM consists of components which consume or produce reactance, this also must be taken into consideration. For example, an additional reactive power consumption of 3 MVAr would vastly change the Pmax of the site, and reduce it to 17.73 MW. an export reduction, and in turn, profit reduction of approximately 6.7%.

By reducing or compensating for this 3 MVAr reactive power consumption, the Pmax of the installation could be increased to or towards 19 MW, and therefore maximising profit.

The overall reactive power of an installation should definitely be taken into consideration, and will likely increase the installation efficiency and profit making abilities.

### § Practical Application in Solar PV Systems

In a recent project, we aimed to optimize the number of MV inverter strings in a photovoltaic (PV) plant to reduce cable costs. However, this optimization presented an unexpected challenge. By reducing the number of circuits, we inadvertently decreased the system’s capacitance. This reduction in capacitance meant that the inductance provided by the power transformer was no longer sufficiently offset by the cable capacitance. The resulting imbalance posed a significant issue in maintaining an efficient power factor.

Faced with this dilemma, we explored several options: adding more inverters, implementing Power Factor Correction (PFC), or maintaining a higher number of circuits than initially planned. Each solution had its trade-offs in terms of cost, efficiency, and system complexity. This scenario exemplifies the intricate balance required in system design, where changes in one aspect, like cable configuration, can have cascading effects on overall system performance, particularly in terms of reactive power management.

For further reading on related topics, consider exploring our articles on Tackling Voltage Drop in Electrical Cables and Understanding the IEC 60502 Sizing System.