How to determine the optimum level of compensation?

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 chapter A. 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 sub-clauses 5.3 and 5.4.

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 L15.
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 L15, 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.

 

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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	1.740	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	1.36	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	1010	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			0.06	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 section 5.2
	Value selected as an example on section 5.4

        

Fig. L15 : kvar to be installed per kW of load, to improve the power factor of an installation

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