# What is cosine phi and reactive power?

Not all power flowing through cables in a plant is also consumed by machines. With an AC connection, you often have to deal with reactive power and the cosine phi. Reactive power is power that flows through cables, causes heat and energy loss, but is not consumed by machines. The magnitude of the reactive power is determined by the cosine phi. How exactly does this work? Sensorfact’s experts explain.

## What is reactive power?

So reactive power is power that passes through cables but cannot be consumed by machines. Because it passes through the cables, it takes up some of the capacity of these power cables. Thus, with high reactive power, the same cable can provide less useful power. In addition, reactive power (just like active power) generates heat as it flows through the cable. This causes more energy loss during transmission.

Reactive power does not directly increase consumption in equipment, but it does lead to higher costs and energy loss in transmission for grid operators. Therefore, grid operators may charge extra costs for reactive power of large consumers.

## Active and reactive power

The part of the power that does actually get consumed is the active power. You will see this on your energy bill as your “normal” energy consumption. The reactive power is what you, as a large consumer, will find on your utility bill as reactive power. In a lot of countries the cosine phi is explicitly mentioned on the energy bill.

Reactive power is a consequence of an alternating current (AC) connection. The power grid and a lot of factories in Europe use an AC connection. In such a connection, the voltage (V) and current (I) fluctuate between positive and negative values like a wave. The actual power (P) flowing through the connection is then given by P = V * I.

Ideally, the voltage and current are exactly synchronous (or in phase), so that they are always either both positive or both negative. This is because then, the power is positive at all times. In this case, there is only active power and no reactive power.

In practice, the waves for voltage and current do not always switch signs at the same time. This can be due to a variety of equipment, such as transformers or electromagnets. As a result, the power becomes negative at some moments. These moments make up the reactive power.

## What is cosine phi (cos φ)?

The power you expect at an AC connection where the voltage and current are perfectly synchronized is called the total or apparent power. The ratio of active power to apparent power is called the power factor and is expressed by cosine phi. The cosine phi is a number between 0 and 1 and is thus a measure of how far the voltage and current lag behind each other (the phase shift). If the cosine phi is 1, the active power is equal to the apparent power and thus there is no reactive power.

A cosine phi of 0.9 indicates that active power is equal to 0.9 * apparent power. With a higher cosine phi, more of the total power passing through the power lines can actually be consumed by machines. As a result, less transmission capacity is needed (both at the plant and on the power grid) and there is less energy loss during transmission. In addition, grid operators often charge large consumers at cosine phi of 0.85 and below.

### Apparent equity and active equity

Apparent power, active power and reactive power are related according to the following formula:

(Apparent Power)² = (Actual Power)² + (Reactive Power)²

Based on this relationship, we can also find the formulas for actual and blind power expressed in apparent power:

Actual power = Apparent power * cos φ

Reactive power = Apparent power * sin φ

### Beer glass comparison

To clarify the relationship between apparent power and actual power, a comparison is often made with a beer glass. The beer glass symbolizes the power system. The beer is the active power, the foam is the reactive power.

Both too high active power and too high reactive power can cause the beer glass to overflow. At that point, therefore, the power network becomes overloaded. A decrease in reactive power (the foam) can allow more room for active power (the beer), without needing a larger glass (more connection capacity). Thus, more power can be used usefully without overflowing the glass.

## A bad cosine phi (power factor)

If the cosine phi is too low, the grid operator incurs additional costs because it has to transmit reactive power. Depending on your location, grid operators might therefore use a lower limit for the cosinus phi of 0.85. A lower cosinus phi causes more wear and tear and a higher load on the power grid. Network operators can therefore serve fewer companies with the same connections. Larger transformers and more copper are needed.

For consumed reactive power with a cosinus phi lower than 0.85, grid operators in countries such as the Netherlands often charge an extra fee. So you pay a penalty if your cosinus phi is too low and the grid operator has to transport a lot of reactive power. In this way, grid operators hope to encourage industrial companies to take measures when the cosinus phi gets too low. It is therefore advantageous to make sure you keep your cos phi as close to 1 as possible. That way you can increase your consumption capacity yourself without a new connection and you don’t risk a fine.

In some regions like in Flanders, the grid operator uses a lower limit for the cosine phi. This limit is higher than in the Netherlands; starting from a cos phi of about 0.95 extra costs can already be charged to large consumers. At a cosinus phi lower than 0.72, those costs go up even more. In addition, in Flanders, at times when consumption is low (less than 10% of peak power over the past 12 months, measured per 15 minutes) a minimum amount of reactive power is charged for. Therefore, if your energy consumption fluctuates a lot, you may be faced with extra costs for reactive power, depending on your country. One more reason to keep your cos phi as high as possible.

## Disadvantages of reactive power or a low cosine phi

Besides a penalty, there are other disadvantages of a low cos phi or too high reactive power:

• More energy loss in power lines.
• Increased plant loads, which can cause devices to overheat and even fail.
• Business processes can then be disrupted and bottlenecks can occur.
• Running into the maximum capacity of the connection faster, requiring it to be expanded.

## Causes of reactive power

Reactive power is often caused by machines that create magnetic fields. Transformers, electromagnets, electric motors, lighting and computers can all affect the cosine phi. Industrial locations often have more machines with strong magnetic fields. Therefore, these locations are more likely to have lower cosine phi. Connections at home and for commercial properties are less likely to suffer from too low a cosine phi. For this reason, only large consumers have to pay when the cosine phi is too low.

## Phase shift

The divergence of the voltage and current waves is also called a phase shift. With a perfect cosine phi of 1, the two waves run exactly in phase; with a low cosine phi, there is a phase shift. That phase shift is usually due to the magnetic fields generated by the machines. In particular, large consumers with strong magnetic fields suffer from phase shift.

## Types of phase shifts

Not every device provides the same type of phase shift. We can divide reactive power into two types: inductive (or positive) reactive power provides a forward phase shift, while capacitive (or negative) reactive power provides a backward phase shift.

### Inductive reactive power

In inductive reactive power, in order for devices to work, power is needed to magnetize the coils. This happens, for example, in electric motors and transformers. This power is called inductive reactive power. In this case, the current lags behind the voltage.

### Capacitive reactive power

Capacitive reactive power arises from capacitive loads, such as capacitors. Examples of devices that can cause capacitive reactive power are lighting and computer components. In capacitive reactive power, the current runs ahead of the voltage.

Inductive and capacitive reactive power actually have opposite effects. Thus, they can be used to cancel each other out. The size and type of reactive power of an entire commercial building is ultimately a sum of all types of reactive current in the building. Industrial premises are mostly affected by inductive reactive current.

### Harmonic reactive power

In addition to phase shift, there can also be harmonic reactive power. This is due to devices that create nonlinear loads on the power grid. These devices use power not in a uniform sine wave, but in irregular pulses. As a result, they distort the voltage waves in the power grid. This is called harmonic pollution and also causes reactive power. Examples of these devices include LED lighting, HVAC systems and computers.

So in total, reactive power consists of three different types of reactive power: inductive, capacitive and harmonic.

## Reduce phase shift with a capacitor bank

Inductive reactive power can be compensated for using a capacitor bank (or capacitor battery). A capacitor bank compensates for the phase shift caused by magnetizing coils, for example.

A capacitor bank provides capacitive reactive power, which locally compensates for the phase shift of the inductive reactive power. Thus, this reactive power no longer needs to be transmitted by the grid operator. As a result, the cosine phi of the connection goes up and the costs for the grid operator go down.

The advantages of a capacitor bank at a glance:

• Avoiding a cos phi penalty by the grid operator
• Less load on the power grid
• Less energy loss while transporting power
• Less overloading of installations, thus longer service life and lower life cycle costs
• More capacity on the same power grid, so more opportunities to expand

## Reduce phase shift with a static VAR generator

A static VAR generator prevents phase shift by “injecting” current. The VAR generator detects the cosine phi and whether we are dealing with inductive or capacitive reactive power. Because the VAR generator injects current at the right time, it works against both inductive and capacitive reactive power.

## Improve your energy efficiency with expert energy advice

Sensorfact’s energy consultants utilize smart software to identify opportunities for increasing your cosine phi and your energy efficiency in general. So far, our customers have saved up to 10-15% on energy bills. Considering current gas and electricity prices, this often results in over €100,000 of potential annual savings!

Curious about how this can work for your plant? Request a demo today, free of any obligations.