Power factor improvement has always been a crucial area of concern for all industrial plants and big office spaces incurring large electricity cost. According to government norms, these type of consumers are to be supplied through HT line and billed on KVAh instead of Kwh. Where Kwh means total active energy delivered and KVAh is vector sum of both active and reactive energy. Supply at HT line of 11kv or 33kv has increased the effects of low power factor on the billing amount of the users. Although capacitor banks are already installed at every facility for power factor correction, confusion still remains about the ideal point of sensing and correction to minimize the overall losses.
To get the ideal point of compensation, we need to analyze the ways in which low power factor affects the total electricity cost.

#### Type of losses due to low Power Factor-

For all the users which are being supplied at HT, low power factor affects the billing by two ways. One component is the difference of KVAh and Kwh, which accounts for direct per unit billing and the other is of the copper losses in the transmission and distribution losses due to the extra current.

• #### Direct losses-

Considering the example data to quantify this type of losses. For a 1000KVA connection (contract demand), if the user is consuming a constant load of 800kw at 0.9 power factor on day1 and at 0.95 on day2.

For day1- Energy consumed= (800/0.9)*24= 21333KVAh

For day2- Energy consumed= (800/0.95)*24= 20210KVAh
This shows an additional 1123 units in one day for which the consumer will be charged for a power factor of 0.9 as compared with 0.95.

• #### Copper losses –

Considering the same situation as for direct losses, current flowing in the conductors will be higher on day1; when the power factor is low. So there will be additional heating losses in the conductors for both transmission and distribution side. As the current on HT lines are low as compare to LT, this type of losses are very less on HT conductors. But on LT line, as the voltage is 430V, current flowing will be-

For day1- ((800/0.9)*1000)/430= 1192 amperes

For day2- ((800/0.95)*1000)/430=1130 amperes
Copper losses are directly proportional to square of current and resistance of the conductors. As cables used for distribution are generally 4 core copper armored cables and they are of different sizes according to load distribution and have different resistances.

For a rough estimation, consider the conductor resistance as 0.19 ohm/km (based on data in Table.1) and length of conductor as 200meter for distribution. Copper losses will be-

For day1- ((1192)^2*(0.19/5))/1000= 54kw; for 24 hours- 54*24=1296kwh

For day2- ((1130)^2*(0.19/5))/1000=48kw; for 24 hour- 48*24=1152kwh

This indicates the additional loss of 144 units in one day.

Ideal Point of correction-

The decision about the point of capacitor connection and APFC relay sensing is to be decided while keeping in mind the utility’s billing design and copper losses in the power cables. Along with cables, the reactive current flowing in the transformer decreases its efficiency and results in poor voltage regulation. 

Different approaches to the problem are presented below, along with their benefits and shortcomings. CASE1: Capacitor Bank and APFC connected at Point B-

Refer to figure.1 and consider line-1 and line-2 connected under this condition, the power factor on the distribution is low (without compensation) but it is corrected at the HT panel, there will be no penalty from the utility but the copper losses in the distribution will be high. In this situation, there will be reactive current flowing in the transformer as well, reducing its efficiency and operational life. As the sensing of APFC is at point B, control on the power factor of point B will be better.

CASE2: Capacitor Bank and APFC connected at Point A-

Consider Line-3 and Line-4 as connecting lines in fig.1, in this case, the relay and capacitor arrangement will increase the power factor at point A. Consider PF to be 0.99 at point A. But in this condition relay has no data about the power factor at point A, it is the point at which the utility will bill the consumer. It will fall below setpoint due to the inductive nature of the transformer and the power cables. Thus this arrangement will reduce the copper losses at distribution but the relay will have poor control over the power factor at which the utility is billing.

CASE3: Capacitor Bank at point A and APFC relay at Point B-

Consider line-2 and line-3 connected, as the APFC is connected at point B and Capacitor at point A, the relay will always sense the power factor at HT meter. Under this situation, the power factor of the distribution side is high and capacitor switching is governed by the power factor at the HT meter. Thus, this arrangement gives the high PF at the distribution side and also better control over the PF at HT meter and is considered as the ideal situation of working.

Sizing of Capacitor Banks-

For attaining proper control over the power factor through APFC, capacitor banks are to be sized properly otherwise frequent switching of power contactors will damage the capacitor and power feeder as well.

For illustration, consider a distribution circuit where 250KVAr of reactive power is required and the capacitor banks are of 50KVAr each. If this arrangement will put on AUTO mode of APFC control, relay will switch ON 5 Capacitor Banks and power factor will be close to unity but it will not be able to respond to small changes in KVAr demand. If the KVAr demand is shifted from 250 to 225, the relay will not be able to maintain a unity PF. To maintain a power factor close to unity, the rating of different capacitor banks is dependent upon the analysis on the reactive power requirement. Based on demand analysis, this compensation requirement should be divided into fixed and variable parts. For a production plant, minimum load and thus minimum KVAr load can be calculated. And the remaining KVAr is to be compensated based on the variable requirements. Consider the similar situation of 250KVAr requirement; calculation for minimum reactive power requirement can be done based on stored data for months. Let’s assume that the minimum requirement comes out to be 150KVAr; that means a single capacitor bank of 150 ratings is to be used. Along with this, rest of the demand is to be compensated in steps. Thus, ideal compensation should have one 150KVAr, 3*25KVAr capacitors and 3*10 capacitors. As one APFC relay can control the switching of up to 12 capacitor banks, all the arrangement can be controlled by one relay. (Other than this, APFC relay are available for 3, 5, 7 and 8 capacitor control too.  ) In this distribution scheme, relay will sense the change in reactive compensation and switch ON/OFF the capacitor bank which gives the best result.

By the analysis of the data collected by Zenatix’s software, we help clients to figure out the ideal number of Capacitor Banks and their sizes at different points of distribution network. Other than the size of capacitor bank, optimum number of APFC relay required and number of capacitor banks to be controlled by it can be determined by the same data.

Figure and Table Detail-

Fig.1-Power distribution scheme of a consumer with HT incomer along with capacitor banks

Table.1-Resistance of 4 core armored copper cables with their specific current rating

Table-2-Pros and cons of different power factor improvement schemes