Applications of Power Capacitors in Electrical Distribution Systems (Part I)

Shunt and series reactive compensation using capacitors has been a widely recognized and powerful method to combat the problems of voltage drops, power losses and voltage flicker in power distribution networks. The importance of compensation schemes has gone up in recent years due to the increased awareness on energy conservation and quality of supply on the part of the Power Utility as well as power consumers. This article (in two parts) amplifies on the advantages that accrue from using shunt and series capacitor compensation. It also tries to answer the twin questions of how much to compensate and where to locate the compensation capacitors.

1. Why Use Shunt Capacitor compensation in Distribution systems?

Fig. 1 represents an a.c. generator supplying a load through a line of series impedance (R+jX) ohms. Fig. 2(a) shows the phasor diagram when the line is delivering a complex power of (P+jQ) VA and Fig. 2 (b) shows the phasor diagram when the line is delivering a complex power of (P+jO) VA i.e. with the load fully compensated. A thorough examination of these phasor diagrams will reveal the following facts.

Current in the line, generator and intervening transformers ,if any, is higher by a factor of in the case of uncompensated load compared to compensated load. This results in a power loss, which is higher by a factor of () ²compared to the minimum power loss attainable in the system.
The loading on generator, transformers, line etc is decided by the current flow. The higher current flow in the case of uncompensated load necessitated by the reactive demand results in a tie up of capacity in this equipment by a factor of . i.e. compensating the load to UPF will release a capacity of (load VA rating X ) in all these equipment.
The sending-end voltage to be maintained for a specified receiving-end voltage is higher in the case of uncompensated load. The line has bad regulation with uncompensated load.
The sending-end power factor is less in the case of an uncompensated one. This due to the higher reactive absorption taking place in the line reactance.
The excitation requirements on the generator is severe in the case of uncompensated load. Under this condition, the generator is required to maintain a higher terminal voltage with a greater current flowing in the armature at a lower lagging power factor compared to the situation with the same load fully compensated. It is entirely possible that the required excitation is much beyond the maximum excitation current capacity of the machine and in that case further voltage drop at receiving-end will take place due to the inability of the generator to maintain the required sending-end voltage. It is also clear that the increased excitation requirement results in considerable increase in losses in the excitation system.

It is abundantly clear from the above that compensating a lagging load by using shunt capacitors will result in

Lesser power loss everywhere upto the location of capacitor and hence a more efficient system
Releasing of tied-up capacity in all the system equipments thereby enabling a postponement of the capital intensive capacity enhancement programmes to a later date.
Increased life of eqipments due to optimum loading on them
Lesser voltage drops in the system and better regulation
Less strain on the excitation system of generators and lesser excitation losses.
Increase in the ability of the generators to meet the system peak demand thanks to the released capacity and lesser power losses.

Shunt capacitive compensation delivers maximum benefit when employed right across the load. And employing compensation in HT & LT distribution network is the closest one can get to the load in a power network. However, various considerations like ease of operation and control, economy achievable by lumping shunt compensation at EHV stations etc will tend to shift a portion of shunt compensation to EHV & HV substations. Power utilities in most countries employ about 60% capacitors on feeders, 30% capacitors on the substation buses and the remaining 10% on the transmission system. Application of capacitors on the LT side is not usually resorted to by the utilities.

Just as a lagging system power factor is detrimental to the system on various counts, a leading system pf is also undesirable. It tends to result in over-voltages, higher losses, lesser capacity utilisation, and reduced stability margin in the generators. The reduced stability margin makes a leading power factor operation of the system much more undesirable than the lagging p.f operation. This fact has to be given due to consideration in designing shunt compensation in view of changing reactive load levels in a power network.

Shunt compensation is successful in reducing voltage drop and power loss problems in the network under steady load conditions. But the voltage dips produced by DOL starting of large motors, motors driving sharply fluctuating or periodically varying loads, arc furnaces, welding units etc can not be improved by shunt capacitors since it would require a rapidly varying compensation level. The voltage dips, especially in the case of a low short circuit capacity system can result in annoying lamp-flicker, dropping out of motor contactors due to U/V pick up, stalling of loaded motors etc and fixed or switched shunt capacitors are powerless against these voltage dips. But Thyristor controlled Static Var compensators with a fast response will be able to alleviate the voltage dip problem effectively.

2. Why Use Series Capacitor Compensation in Distribution Systems?

Shunt compensation essentially reduces the current flow everywhere upto the point where capacitors are located and all other advantages follow from this fact.But series compensation acts directly on the series reactance of the line. It reduces the transfer reactance between supply point and the load and thereby reduces the voltage drop. Series capacitor can be thought of as a voltage regulator, which adds a voltage proportional to the load current and there by improves the load voltage.

Series compensation is employed in EHV lines to 1) improve the power transfer capability 2) improve voltage regulation 3) improve the load sharing between parallel lines. Economic factors along with the possible occurrence of sub-synchronous resonance in the system will decide the extent of compensation employed.

Series capacitors, with their inherent ability to add a voltage proportional to load current, will be the ideal solution for handling the voltage dip problem brought about by motor starting, arc furnaces, welders etc. And, usually the application of series compensation in distribution system is limited to this due to the complex protection required for the capacitors and the consequent high cost. Also, some problems like self-excitation of motors during starting, ferroresonance, steady hunting of synchronous motors etc discourages wide spread use of series compensation in distribution systems.

3. Shunt Capacitor Installation types: -

The capacitor installation types and types of control for switched capacitor are best understood by considering a long feeder supplying a concentrated load at feeder end. This is usually a valid approximation for some of the city feeders, which emanate from substations, located 4 to 8 Kms away from the heart of the city. Ref Figs 3 & 4.

Absolute minimum power loss in this case will result when the concentrated load is compensated to upf by locating capacitors across the load or nearby on the feeder. But the optimum value of compensation can be arrived at only by considering a cost benefit analysis.

The reactive demand of the load varies over a day and a typical reactive demand curve for a day is given in Fig 5.

It is evident from Fig 5 that it will require a continuously variable capacitor to keep the compensation at economically optimum level throughout the day. However, this can only be approximated by switched capacitor banks. Usually one fixed capacitor and two or three switched units will be employed to match the compensation to the reactive demand of the load over a day. The value of fixed capacitor is decided by minimum reactive demand as shown in Fig 5.

Automatic control of switching is required for capacitors located at the load end or on the feeder. Automatic switching is done usually by a time switch or voltage controlled switch as shown in Fig 5. The time switch is used to switch on the capacitor bank required to meet the day time reactive load and another capacitor bank switched on by a low voltage signal during evening peak along with the other two banks will maintain the required compensation during night peak hours.

4. Economic Justification for Use of Capacitors-

The increase in benefits for 1 kVAR of additional compensation decrease rapidly as the system power factor reaches close to unity. This fact prompts an economic analysis to arrive at the optimum compensation level. Different economic criteria can be used for this purpose. The annual financial benefit obtained by using capacitors can be compared against the annual equivalent of the total cost involved in the capacitor installation. The decision also can be based on the number of years it will take to recover the cost involved in the Capacitor installation. A more sophisticated method would be able to calculate the present value of future benefits and compare it against the present cost of capacitor installation.

When reactive power is provided only by generators, each system component (generators, transformers, transmission and distribution lines, switch gear and protective equipment etc) has to be increased in size accordingly. Capacitors reduce losses and loading in all these equipments , thereby effecting savings through powerloss reduction and increase in generator, line and substation capacity for additional load. Depending on the initial power factor, capacitor installations can release at least 30% additional capacity in generators, lines and transformers. Also they can increase the distribution feeder load capability by about 30% in the case of feeders which were limited by voltage drop considerations earlier. Improvement in system voltage profile will usually result in increased power consumption thereby enhancing the revenue from energy sales.

Thus, the following benefits are to be considered in an economic analysis of compensation requirements.

Benefits due to released generation capacity.
Benefits due to released transmission capacity.
Benefits due to released distribution substation capacity.
Benefits due to reduced energy loss.
Benefits due to reduced voltage drop.
Benefits due to released feeder capacity.
Financial Benefits due to voltage improvement.

Which are the benefits to be considered in capacitor application in distribution system? Capacitors in distribution system will indeed release generation and transmission capacities. But when an individual distribution feeder compensation is in question, the value of released capacities in generation and transmission system are likely to be too small to warrant inclusion in economic analysis. Moreover, due to the tighty inter-connected nature of the system, the exact benefit due to capacity release in these areas is quite difficult to compute. Capacity release in generation and transmission system is probably more relevant in compensation studies at transmission and sub- transmission levels and hence are left out from the economic analysis of capacitor application in distribution systems.

4.1 Benefits due to released distribution substation capacity.

The released distribution substation capacity due to installation of capacitors which deliver Qc MVARs of compensation at peak load conditions may be shown to be equal to

in general and when
where
=Released station capacity beyond maximum station capacity at original power factor

=Station Capacity

=The P.F at the station before compensation

The annual benefit due to the released station capacity = where

C = Cost of station & associated apparatus per MVA

i = annual fixed charge rate applicable

4.2 Benefits due to reduced energy losses.

Annual energy losses are reduced as a result of decreasing copper loss due to installation of capacitors. Information on type of capacitor installation, location of installation nature of feeder loading etc. are needed to calculate this. The calculation can proceed as follows.

Let a current I₁+j I₂ flow through a resistance R. The power loss is (I₁²+ I₂²) R. The power loss due to reactive component is I₂² R. Compensating the feeder will result in a change only in I₂. Hence the new power loss will be (I₂²+(I₂-I_c)²) R where Ic is the compensating current. Hence the decrease in power loss due to compensating part of reactive current is (2 I₂Ic-Ic²) R.

Now, if I₂ is varying (it will be varying according to reactive demand curve) the average decrease in power loss over a period of T hours will be equal to (2 I₂Ic F_R-Ic²) R where I₂stands for peak reactive current during T hours through the feeder section of resistance R, Ic is compensation current flowing through the same section for the same period and F_R is reactive load factor for T hours in the same section. Thus total energy savings in this section of feeder for T hours will be 3(2I₂IcF_R-Ic²) RT.

One day can be divided in to many such periods depending on the number of fixed and switched capacitors and the sequence of operation of switched capacitors. Also, the feeder can be modelled by uniformly distributed load or discrete loading and total energy savings can be found out for each period over the entire period by mathematical integration or discrete summation. The daily and hence the annual energy savings for the entire feeder can be worked by an aggregation over the time periods.

Let be this value if total energy savings per year. Annual benefits due to conserved energy will be X cost of energy.

4.3 Benefits due to released feeder capacity.

In general feeder capacity is restricted by voltage regulation considerations rather than thermal limits. Shunt compensation improves voltage regulation and there by enhances feeder capacity. This additional feeder capacity can be calculated as where Qc is compensation (MVAR) employed, X and R are feeder reactance & resistance respectively and is the P.F before compensation. The annual benefits due to this will be Where C is the cost of the installed feeder per MVA and i is the annual fixed charge rate applicable.

4.4 Financial benefits due to voltage improvement.

Energy consumption increases with improved voltage. Exact value of the increased consumption can be worked out from a knowledge of elasticity of loads of the concerned feeders with respect to voltage. Let it be . Annual revenue increase due to this will be cost of energy.

4.5 Annual equivalent of total cost of the installed capacitor banks.

This will be equal to where Qc is total capacitive MVAR to be installed, C is cost of capacitors per MVAR and i is the annual fixed charge applicable.

The total annual benefits should be compared against the annual equivalent of total cost of capacitors to arrive at optimum compensation levels.

5. Optimum Capacitor Allocation On Distribution Feeders-

The benefits obtained from the release of feeder and substation capacities will depend only on total compensating MVAR available on the feeder during peak load hours. But benefits due to energy loss reduction will depend nearly on how this total MVAR is distributed on the feeder (i.e. the location, number and capacities of fixed and switched capacitor banks on the feeder), the daily reactive load curve at various sections of the feeder, the switching schedule of the switched capacitors etc. The energy savings calculations have been briefly touched upon in section 4.3. For a given total capacitive MVAR on the feeder during peak time there are many ways to divided it in to fixed and switched units and many possible locations where the banks can be placed. Hence a study on the optimum number of banks and optimum location of these banks in order to obtain maximum energy savings for a given amount of total compensation is in order. But how can the feeder be modelled for this purpose?

5.1 The feeder models for optimum capacitor allocation.

A practical 11 kV feeder is loaded in a non-uniform manner both with respect to the rating of distribution transformers and transformer to transformer distance. Hence, only a "discretely loaded feeder" model can give the exact solution to the above mentioned optimization problem. But, such a model can be solved only numerically with the help of a computer. Hence the need for a simpler model.

5.1.1 Analytical expression for the optimum solution can be attempted if closely located but non-uniformly distributed transformers can be aggregated into a small number of (say 2 or 3 or 4) discrete loads as shown in Fig 6(a) & 6(b). This is possible in the case of city feeders emanating from a substation, which is somewhat distant from town center.

5.1.2 The feeder can at times be modelled as a feeder with a concentrated load at the tail end. This is possible for a feeder emanating from a distant substation to supply power to distribution transformers located densly at the feeder end to supply the heart of the city.

5.1.3 The most frequently used feeder model is a feeder with a uniformly distributed load with a possible concentrated load at the tail end. This model is appropriate for city feeders, which emanate from substations quite close to the city. Transformers are likely to be distributed right from the beginning of the feeder onwards, more or less at equal distance and the transformers are likely to be of more or less same rating. Moreover these transformers will be supplying more or less similar type of loads. The concentrated load at the feeder and may be an actual concentrated load or equivalent lumped load of the rest of the feeder which for some reason or other need not be modelled in detail.

Another useful assumption is possible usually in the case of such feeders. The homogeneous nature of load on such a feeder makes it possible to assume that the load on a particular transformer at any time of the day is given by the following relation

This effectively means that the normalized daily active power and reactive power demand curves are of same shape in all feeder sections and same as the curves of the feeder load at substation. This assumption which is valid for most of the urban feeders simplifies the analysis considerably and makes a closed form solution for the capacitor allocation problem possible.

5.2 Optimum Allocation using uniformly distributed load model for the feeder-

Consider a feeder with a uniformly distributed load and a concentrated load at the end as shown in fig 7(a). The reactive current distribution in the feeder (for any time instant) is shown in fig 7(b).

The reactive current profile of the same feeder with a capacitor located at a distance x1 from station end is shown in fig 7(b) by dotted lines. The total power loss reduction after adding the capacitor will be

Where 'r' is resistance per unit length, and 'l' is the length of the feeder. The per unit loss reduction is obtained by dividing this by the loss without compensation. (Only loss contributed by reactive currents is considered here since loss contributed by active current will not change on compensation.) After simplifying the equation

P_LS in Pu =

Where

And

And = per unit distance of capacitor location from station end.

This method can be extended for n capacitor banks of equal rating (it can be proved that when multiple fixed capacitors are used they have to be of equal rating to be economical) located at various locations on the feeder. In that case

P_LS in Pu =

Where x_I=distance of i^th capacitor from station end.

The optimum locations are found by equating the partial derivatives of P_LS with respect to to zero and solving for . This yields

Substituting this in the expression for PLS, the maximum value of loss reduction with n capacitors of equal rating located at optimum locations can be obtained.

Maximising with respect to C yields the value of compensation, which yields the absolute maximum value of loss reduction with n optimum valued capacitors located at optimum points.

Hence total compensation required =x total reactive load at station end before compensation.

5.2.1 Special cases.

Distributed load, no lumped sum load (, single capacitor.

5.2.2 Conclusion from the analysis.

For a feeder with uniformly distributed load most of the power loss due to reactive loading can be eliminated by using a fixed shunt capacitor of (* total feeder reactive load) rating at (*length of feeder) away from source. There is not much advantage to be derived from increasing the number of capacitor banks from one or two.

(ii) a lumped load at tail end tends to shift the optimum location towards the tail end and does not have any influence on the optimum capacitor value.

5.3 Optimum allocation based On Maximum Energy Loss Reduction.

No mention about the particular value of total reactive loading on the feeder was made in the above analysis. With a changing reactive level over the day, optimality with respect to power loss reduction can be maintained only by employing capacitor MVARS which also change continuously. But using fixed capacitors this is not possible. So, which value of reactive loading must be used to calculate the optimum allocation?

It is obvious that more important than optimising the power loss reduction is the optimising of energy loss reduction.. It should equally be obvious that optimum compensation based on peak condition may result in a net increase in energy losses due to over compensation during off peak periods.

It was earlier pointed out that loss reduction in a feeder segment carrying a reactive load current of I amps and a compensation current of Ic amps will be 3R(2 I Ic - Ic² ) where R is the segment resistance. The average power loss reduction in T hours in this segment will hence be 3R(2 Iav Ic –Ic² ) where Iav is average reactive load current over T hrs and Iav= Ipeak * F where F is the reactive load factor over T hours.

The optimal allocation for maximum energy loss reduction may be carried out by taking reactive load factor into consideration. The results will be

The optimum location and optimum compensation level required for maximising energy loss reduction will be considerably different compared to the values obtained from maximising peak load power loss reduction for low values of reactive load factor, especially when the concentrated load at feeder end goes up in value.

5.4 Some rules for application of capacitor banks on distribution feeders.

The location of fixed shunt capacitors should be based on average reactive load.
There is only one location for each size of capacitor bank that produces maximum loss reduction.
One large capacitor bank can provide almost as much savings as two or more banks of equal size.
When multiple locations are used for fixed capacitors, the banks must have same rating to be economical.
The two- thirds rule for compensation level and location in the case of a uniformly loaded feeder is useful only when reactive load factor is high and a fixed capacitor is to be used.

5.5 Optimum location and size when switched capacitors are used along with fixed capacitors.

Absolute maximum energy loss reduction can be obtained only if the capacitors are maintained at optimum values with the changing reactive levels over the day. Fixed capacitors, hence, will give only a lesser energy loss reduction. Closer tracking of reactive load curve of feeder is possible by employing switched capacitor banks (switched either by time switch or voltage switch). Clearly, employing switched banks will result in greater reduction in energy loss especially when reactive load factor is low.

As explained before one fixed bank with two switched banks should be sufficient to track the reactive load curve. But how can the ratings and locations of these banks be fixed? It should be clear that the expressions based on uniform distribution will not be valid due to the discontinuity in reactive profile introduced by the fixed capacitor.

Extensive computations reported in the literature has revealed that maximum power loss reduction in a feeder with uniformly or nonuniformly distributed load or with discrete point loads is obtained when the capacitor bank is located at a point where its rating is equal to twice the reactive flow at that point before compensation. Hence, the method to arrive at ratings and locations of the three banks will be as follows.

Divide the daily reactive load curve in to three regions-light load period, medium load period, and heavy load period. Also find peak load for all the periods and reactive load factors for all the periods.
The rating of the fixed capacitor will be (peak reactive load in the light load period reactive load factor for this period.). This capacitor is to be located at a point where the reactive flow during light load condition is half the rating of capacitor.

Find the value of total capacitor required under medium load condition using the same rule as in (ii) i.e. assuming single bank compensation.

Find the rating of the first switched capacitor by subtracting the value of fixed capacitor from the value obtained in (iii)

Locate this switched capacitor at a point where the reactive load low after accounting for the fixed capacitor contribution is required to half the switched capacitor rating.

Repeat (iii) for heavy load period and find the rating of second switched capacitor by subtracting the values of fixed and first switched capacitors

Locate this switched capacitor at a point where the reactive load flow is after accounting for the contributions from fixed capacitor and first switched capacitor is equal to half the second switched capacitor rating.

Needless to mention that optimum ratings can be hand calculated only if feeder load before compensation can be considered as a uniformly distributed one.

Continued in Part II