# Calculate Reactive Power of the Capacitor bank and Improve PF

**Dimensioning of the capacitor bank**

For the dimensioning of the capacitor bank to be installed in order to improve the power factor of a plant, it is necessary to calculate correctly the power factor according to the consumption or to the load cycle of the plant. This in order to avoid the intake of excess reactive energy, which is a condition normally forbidden by power supply authorities.

*" **To carry out distributed or group power factor correction, it is necessary to calculate the cosφ of the single load or of the group of loads (factory areas).*

**This can be carried out as follows:**

**Directly**– through direct measuring by means of a power factor meter**Indirectly**– through the reading of the active and reactive energy meters

**!!!** The ** power factor meter** is a measuring instrument able to display the power factor cosφ

**according to which the load is absorbing energy**. The reading of the instrument shall be carried out in different moments of the load cycle, so that an average power factor value can be obtained.

If the readings of the active and reactive energy absorbed by the load or by the whole of the loads constituting the factory areas during a work cycle are available, the ** average power factor** can be calculated as follows:

where:

EPi and EQi are the values of active and reactive energy read at the beginning of the work cycle

EPf and EQf are the values of active and reactive energy read at the end of the work cycle

**Calculation of the necessary reactive power**

Once the power factor (cosφ1) of the installation and the power factor to be obtained (cosφ2) are known, it is possible to calculate the reactive power of the capacitor bank necessary to improve the power factor.

**Indicating by:**

**P**– the installed active power**φ1**– the phase displacement angle before power factor correction**φ2**– the phase displacement angle to be obtained with**the power factor correction the power of the capacitor bank Qc is:**

Once the initial cosφ is known, Table 1 allows to calculate (in kvar per kW installed) the power of the capacitor bank necessary to obtain a defined power factor.

**I!!** In a three-phase system, the capacitor bank constituted by three capacitors having the same capacitance, **can be delta connected or star connected.**

When selecting the connection modality, it is necessary to keep into account that with delta connection, each capacitance is subject to the supply ** line-to-line voltage**, but, at the same level of generated reactive power, it has a value equal to 1/3 of the value it will have in case of star-connection:

In the low voltage field, where insulation problems are less important, the delta connection is usually preferred for the capacitor bank, since it allows a smaller sizing of the capacitances of each phase

Power factor correction table

**Example calculation**

In a plant with active power equal to **300 kW **at **400 V** and **cosφ= 0.75**, we want to increase the power factor up to **0.90**. In the table 1 above, at the intersection between the row “initial cosφ” 0.75 with the column “final cosφ” 0.9, **a value of 0.398 for the coefficient K is obtained.**

Therefore a capacitor bank is necessary with **power Qc **equal to:

Qc = K · P = 0.398 · 300 =** 119.4 kvar**

**The factor K can be determined also using the following nomograph:**

**Figure 1** – Nomograph for the calculation of the correction power

As shown in the figure, tracing a line segment from the value of the initial cosφ to the value to be obtained, the intersection of the line with the middle graduated scale, gives the value of K which, **multiplied by the active power P of the load, defines the necessary reactive power Qc.**

**Reference //** Power factor correction and harmonic filtering in electrical plants by ABB