# How to determine the optimum level of compensation?

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## General method

### Listing of reactive power demands at the design stage

This listing can be made in the same way (and at the same time) as that for the power loading described in General rules of electrical installation design. The levels of active and reactive power loading, at each level of the installation (generally at points of distribution and sub-distribution of circuits) can then be determined.

### Technical-economic optimization for an existing installation

The optimum rating of compensation capacitors for an existing installation can be determined from the following principal considerations:

• Electricity bills prior to the installation of capacitors
• Future electricity bills anticipated following the installation of capacitors
• Costs of:
• Purchase of capacitors and control equipment (contactors, relaying, cabinets, etc.)
• Installation and maintenance costs
• Cost of dielectric heating losses in the capacitors, versus reduced losses in cables, transformer, etc., following the installation of capacitors

Several simplified methods applied to typical tariffs (common in Europe) are shown in Method based on the avoidance of tariff penalties and Method based on reduction of declared maximum apparent power (kVA).

## Simplified method

### General principle

An approximate calculation is generally adequate for most practical cases, and may be based on the assumption of a power factor of 0.8 (lagging) before compensation. In order to improve the power factor to a value sufficient to avoid tariff penalties (this depends on local tariff structures, but is assumed here to be 0.93) and to reduce losses, volt-drops, etc. in the installation, reference can be made to Figure L16.

From the figure, it can be seen that, to raise the power factor of the installation from 0.8 to 0.93 will require 0.355 kvar per kW of load. The rating of a bank of capacitors at the busbars of the main distribution board of the installation would be

Q (kvar) = 0.355 x P (kW).

This simple approach allows a rapid determination of the compensation capacitors required, albeit in the global, partial or independent mode.

### Example

It is required to improve the power factor of a 666 kVA installation from 0.75 to 0.928. The active power demand is 666 x 0.75 = 500 kW.

In Figure L16, the intersection of the row cos φ = 0.75 (before correction) with the column cos φ = 0.93 (after correction) indicates a value of 0.487 kvar of compensation per kW of load.

For a load of 500 kW, therefore, 500 x 0.487 = 244 kvar of capacitive compensation is required.

Note: this method is valid for any voltage level, i.e. is independent of voltage.

Fig. L16 – kvar to be installed per kW of load, to improve the power factor of an installation
Before compensation kvar rating of capacitor bank to install per kW of load, to improve cos φ (the power factor) or tan φ, to a given value
tan φ 0.75 0.59 0.48 0.46 0.43 0.40 0.36 0.33 0.29 0.25 0.20 0.14 0.0
tan φ cos φ cos φ 0.80 0.86 0.90 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1
2.29 0.40 1.557 1.691 1.805 1.832 1.861 1.895 1.924 1.959 1.998 2.037 2.085 2.146 2.288
2.22 0.41 1.474 1.625 1.742 1.769 1.798 1.831 1.840 1.896 1.935 1.973 2.021 2.082 2.225
2.16 0.42 1.413 1.561 1.681 1.709 1.738 1.771 1.800 1.836 1.874 1.913 1.961 2.022 2.164
2.10 0.43 1.356 1.499 1.624 1.651 1.680 1.713 1.742 1.778 1.816 1.855 1.903 1.964 2.107
2.04 0.44 1.290 1.441 1.558 1.585 1.614 1.647 1.677 1.712 1.751 1.790 1.837 1.899 2.041
1.98 0.45 1.230 1.384 1.501 1.532 1.561 1.592 1.628 1.659 1.695 1.737 1.784 1.846 1.988
1.93 0.46 1.179 1.330 1.446 1.473 1.502 1.533 1.567 1.600 1.636 1.677 1.725 1.786 1.929
1.88 0.47 1.130 1.278 1.397 1.425 1.454 1.485 1.519 1.532 1.588 1.629 1.677 1.758 1.881
1.83 0.48 1.076 1.228 1.343 1.370 1.400 1.430 1.464 1.497 1.534 1.575 1.623 1.684 1.826
1.78 0.49 1.030 1.179 1.297 1.326 1.355 1.386 1.420 1.453 1.489 1.530 1.578 1.639 1.782
1.73 0.50 0.982 1.232 1.248 1.276 1303 1.337 1.369 1.403 1.441 1.481 1.529 1.590 1.732
1.69 0.51 0.936 1.087 1.202 1.230 1.257 1.291 1.323 1.357 1.395 1.435 1.483 1.544 1.686
1.64 0.52 0.894 1.043 1.160 1.188 1.215 1.249 1.281 1.315 1.353 1.393 1.441 1.502 1.644
1.60 0.53 0.850 1.000 1.116 1.144 1.171 1.205 1.237 1.271 1.309 1.349 1.397 1.458 1.600
1.56 0.54 0.809 0.959 1.075 1.103 1.130 1.164 1.196 1.230 1.268 1.308 1.356 1.417 1.559
1.52 0.55 0.769 0.918 1.035 1.063 1.090 1.124 1.156 1.190 1.228 1.268 1.316 1.377 1.519
1.48 0.56 0.730 0.879 0.996 1.024 1.051 1.085 1.117 1.151 1.189 1.229 1.277 1.338 1.480
1.44 0.57 0.692 0.841 0.958 0.986 1.013 1.047 1.079 1.113 1.151 1.191 1.239 1.300 1.442
1.40 0.58 0.665 0.805 0.921 0.949 0.976 1.010 1.042 1.076 1.114 1.154 1.202 1.263 1.405
1.37 0.59 0.618 0.768 0.884 0.912 0.939 0.973 1.005 1.039 1.077 1.117 1.165 1.226 1.368
1.33 0.60 0.584 0.733 0.849 0.878 0.905 0.939 0.971 1.005 1.043 1.083 1.131 1.192 1.334
1.30 0.61 0.549 0.699 0.815 0.843 0.870 0.904 0.936 0.970 1.008 1.048 1.096 1.157 1.299
1.27 0.62 0.515 0.665 0.781 0.809 0.836 0.870 0.902 0.936 0.974 1.014 1.062 1.123 1.265
1.23 0.63 0.483 0.633 0.749 0.777 0.804 0.838 0.870 0.904 0.942 0.982 1.030 1.091 1.233
1.20 0.64 0.450 0.601 0.716 0.744 0.771 0.805 0.837 0.871 0.909 0.949 0.997 1.058 1.200
1.17 0.65 0.419 0.569 0.685 0.713 0.740 0.774 0.806 0.840 0.878 0.918 0.966 1.007 1.169
1.14 0.66 0.388 0.538 0.654 0.682 0.709 0.743 0.775 0.809 0.847 0.887 0.935 0.996 1.138
1.11 0.67 0.358 0.508 0.624 0.652 0.679 0.713 0.745 0.779 0.817 0.857 0.905 0.966 1.108
1.08 0.68 0.329 0.478 0.595 0.623 0.650 0.684 0.716 0.750 0.788 0.828 0.876 0.937 1.079
1.05 0.69 0.299 0.499 0.565 0.593 0.620 0.654 0.686 0.720 0.758 0.798 0.840 0.907 1.049
1.02 0.70 0.270 0.420 0.536 0.564 0.591 0.625 0.657 0.691 0.729 0.769 0.811 0.878 1.020
0.99 0.71 0.242 0.392 0.508 0.536 0.563 0.597 0.629 0.663 0.701 0.741 0.783 0.850 0.992
0.96 0.72 0.213 0.364 0.479 0.507 0.534 0.568 0.600 0.634 0.672 0.712 0.754 0.821 0.963
0.94 0.73 0.186 0.336 0.452 0.480 0.507 0.541 0.573 0.607 0.645 0.685 0.727 0.794 0.936
0.91 0.74 0.159 0.309 0.425 0.453 0.480 0.514 0.546 0.580 0.618 0.658 0.700 0.767 0.909
0.88 0.75 0.132 0.82 0.398 0.426 0.453 0.487 0.519 0.553 0.591 0.631 0.673 0.740 0.882
0.86 0.76 0.105 0.255 0.371 0.399 0.426 0.460 0.492 0.526 0.564 0.604 0.652 0.713 0.855
0.83 0.77 0.079 0.229 0.345 0.373 0.400 0.434 0.466 0.500 0.538 0.578 0.620 0.687 0.829
0.80 0.78 0.053 0.202 0.319 0.347 0.374 0.408 0.440 0.474 0.512 0.552 0.594 0.661 0.803
0.78 0.79 0.026 0.176 0.292 0.320 0.347 0.381 0.413 0.447 0.485 0.525 0.567 0.634 0.776
0.75 0.80 0.150 0.266 0.294 0.321 0.355 0.387 0.421 0.459 0.499 0.541 0.608 0.750
0.72 0.81 0.124 0.240 0.268 0.295 0.329 0.361 0.395 0.433 0.473 0.515 0.582 0.724
0.70 0.82 0.098 0.214 0.242 0.269 0.303 0.335 0.369 0.407 0.447 0.489 0.556 0.698
0.67 0.83 0.072 0.188 0.216 0.243 0.277 0.309 0.343 0.381 0.421 0.463 0.530 0.672
0.65 0.84 0.046 0.162 0.190 0.217 0.251 0.283 0.317 0.355 0.395 0.437 0.504 0.645
0.62 0.85 0.020 0.136 0.164 0.191 0.225 0.257 0.291 0.329 0.369 0.417 0.478 0.620
0.59 0.86 0.109 0.140 0.167 0.198 0.230 0.264 0.301 0.343 0.390 0.450 0.593
0.57 0.87 0.083 0.114 0.141 0.172 0.204 0.238 0.275 0.317 0.364 0.424 0.567
0.54 0.88 0.054 0.085 0.112 0.143 0.175 0.209 0.246 0.288 0.335 0.395 0.538
0.51 0.89 0.028 0.059 0.086 0.117 0.149 0.183 0.230 0.262 0.309 0.369 0.512
0.48 0.90 0.031 0.058 0.089 0.121 0.155 0.192 0.234 0.281 0.341 0.484
 Value selected as an example on Simplified method Value selected as an example on Method based on the avoidance of tariff penalties

## Method based on the avoidance of tariff penalties

In the case of certain (common) types of tariff, an examination of several bills covering the most heavily-loaded period of the year allows determination of the kvar level of compensation required to avoid kvarh (reactive-energy) charges. The pay-back period of a bank of power-factor-correction capacitors and associated equipment is generally about 18 months

The following method allows calculation of the rating of a proposed capacitor bank, based on billing details, where the tariff structure corresponds with (or is similar to) the one described in Reduction in the cost of electricity.

The method determines the minimum compensation required to avoid these charges which are based on kvarh consumption.

The procedure is as follows:

• Refer to the bills covering consumption for the 5 months of winter (in France these are November to March inclusive).
Note: in tropical climates the summer months may constitute the period of heaviest loading and highest peaks (owing to extensive air conditioning loads) so that a consequent variation of high-tariff periods is necessary in this case. The remainder of this example will assume Winter conditions in France.
• Identify the line on the bills referring to “reactive-energy consumed” and “kvarh to be charged”. Choose the bill which shows the highest charge for kvarh (after checking that this was not due to some exceptional situation).

For example: 15,966 kvarh in January.

• Evaluate the total period of loaded operation of the installation for that month, for instance: 220 hours (22 days x 10 hours). The hours which must be counted are those occurring during the heaviest load and the highest peak loads occurring on the power system. These are given in the tariff documents, and are (commonly) during a 16-hour period each day, either from 06.00 h to 22.00 h or from 07.00 h to 23.00 h according to the region. Outside these periods, no charge is made for kvarh consumption.
• The necessary value of compensation in kvar = kvarh billed/number of hours of operation[1] = Qc

The rating of the installed capacitor bank is generally chosen to be slightly larger than that calculated.

Certain manufacturers can provide “slide rules” especially designed to facilitate these kinds of calculation, according to particular tariffs. These devices and accompanying documentation advice on suitable equipment and control schemes, as well as drawing attention to constraints imposed by harmonic voltages on the power system. Such voltages require either over dimensioned capacitors (in terms of heat-dissipation, voltage and current ratings) and/or harmonic-suppression inductors or filters.

## Method based on reduction of declared maximum apparent power (kVA)

For 2-part tariffs based partly on a declared value of kVA, Figure L18 allows determination of the kvar of compensation required to reduce the value of kVA declared, and to avoid exceeding it

For consumers whose tariffs are based on a fixed charge per kVA declared, plus a charge per kWh consumed, it is evident that a reduction in declared kVA would be beneficial. The diagram of Figure L17 shows that as the power factor improves, the kVA value diminishes for a given value of kW (P). The improvement of the power factor is aimed at (apart from other advantages previously mentioned) reducing the declared level and never exceeding it, thereby avoiding the payment of an excessive price per kVA during the periods of excess, and/or tripping of the the main circuit-breaker. Figure L16 indicates the value of kvar of compensation per kW of load, required to improve from one value of power factor to another.

Example:

A supermarket has a declared load of 122 kVA at a power factor of 0.7 lagging, i.e.an active-power load of 85.4 kW. The particular contract for this consumer was based on stepped values of declared kVA (in steps of 6 kVA up to 108 kVA, and 12 kVA steps above that value, this is a common feature in many types of two-part tariff). In the case being considered, the consumer was billed on the basis of 132 kVA. Referring to Figure L16, it can be seen that a 60 kvar bank of capacitors will improve the power factor of the load from 0.7 to 0.95 (0.691 x 85.4 = 59 kvar in the figure). The declared value of kVA will then be $\displaystyle{ \frac{85.4}{0.95}=90kVA }$, i.e. an improvement of 30%.

Fig. L17 – Reduction of declared maximum kVA by power-factor improvement

## Notes

1. ^ In the billing period, during the hours for which reactive energy is charged for the case considered above: $\displaystyle{ Qc = \frac {15,996\, kvarh}{220\, h} = 73\, kvar }$