P OWER FACTOR CORRECTION

NOKIAN CAPACITORS

1. INTRODUCTION

1.1 General

S 1 = apparent power before PFC

1.3 Reactive Power Demand

In addition to active power most electrical

Induction motors need reactive power to main- devices also demand reactive power.

S 2 = apparent power after PFC

tain the magnetic field essential for their op- If this reactive power is not provided by

P = active power

eration. The average reactive power demand capacitors in the immediate vicinity, it must be

of asynchronous motors is approx. 1 kvar per transmitted via the distribution system. In this

1 = reactive power before PFC

1 kW of active power. case the influence of the reactive power on the

Q 2 = reactive power after PFC

Q c =Q 1 –Q

2 = compensation power of the

Thyristor drives draw reactive current from

total current must be taken into account when

the network and also generate harmonics designing the system, and this can lead to a

which, among other things, tend to overload need for larger transformers and cables than

capacitor

capacitors. In addition to the equipment men- would otherwise be necessary.

ϕ 1 = phase angle before PFC

tioned above, transformers, loaded cables, Moreover, transmission of reactive power

ϕ 2 = phase angle after PFC

transmission lines and various electrical de- causes additional energy losses. By means of

vices all need reactive power to some extent. reactive power compensation the amount of reactive power has only little significance in

1.2 Power Factor

dimensioning the system and on transmission Table 1. Examples of power factors losses.

The total operating power, termed apparent power, can be expressed in terms of active

Load type

Approximate power factor

and reactive power:

(half ...full load)

S= P 2 +Q 2 (1)

Induction motor

<100 kW 0.6...0.8 250 kW 0.8...0.9

Power factor cos ϕ represents the following

Thyristor drives

relationship between active and apparent

Incandescent lamp (glow)

power:

Mercury arc lamp

0.5 Fluorescent lamp (hot cathode)

cos ϕ = P

= active power

Neon tube lamp

apparent power

Induction furnace 0.2...0.6

Arc furnace

Electric heater

Correspondingly

AC arc or resistance welder 0.5...0.6

tan ϕ = Q = reactive power

active power

Power factor correction (PFC) means that capacitors (or synchronous machines) are used to reduce the amount of reactive power

Fig. 1 The apparent power of a network can be

in electricity supplies to industrial and com-

reduced by means of power factor correction

mercial consumers, thus improving the power

(PFC).

factor to a higher value.

2. ECONOMIC EFFECT OF COMPENSATION

During recent years increasing attention has

(4) been paid to minimizing the energy costs and

the generators and synchronous machines

K=a.H

depends on the desired extra amount of reac-

K = annual cost

inefficiencies in electricity generation, trans-

a = cost factor of interest and mission, distribution and consumption.

tive power.

Generation of reactive power by synchro-

depreciation

H = procurement cost of capacitors one should attempt to achieve the most eco-

When designing a compensation scheme

nous machines incurs additional losses of

including installation nomical solution, in which the savings achieved

10...30 W/kvar, depending on the size and

construction of the machine and the amount

in equipment costs and transmission losses

An interest rate of 7...10 % is generally are significantly greater than the procurement

of reactive power generated. However, by

used for calculations of profitability. The de- cost of the reactive power.

raising the power factor, the additional losses

preciation period for power capacitors is When positioning capacitors note that

can be reduced.

Reactive power produced by rotating

15...20 years.

unfavourable ambient conditions can shorten

machines must be transmitted through the

the life of the units, effectively incurring extra

distribution system. This leads to extra capital

expense. The cost of installing capacitors, the

costs and additional transmission losses,

effect of power factor correction on the volt-

which are especially significant at high volt-

age level and the requirements of the electric-

age transmission.

ity supply authority in regard to overcompen-

It is now generally accepted that it is not

sation, should also all be taken into account.

advantageous to install such generators and synchronous motors specifically for the pro- duction of large amounts of reactive power

2.1 Procurement Cost of

and also that it is often uneconomical to pro-

Compensation

duce reactive power from synchronous ma- chines that are already in the system.

2.1.1 Generation of Reactive Power by

This is a consequence of the rapid rise in

Means of Rotating Machines

energy prices in the 1970’s and from develop-

Traditionally, reactive power has usually been

ment in system capital costs when compared with the purchase and maintenance cost of

generated by rotating machines and trans- mitted through the system to consumers in the

capacitors.

same way as active power. Large motors used in industry are often synchronous ma- chines which themselves generate the reac- tive power they need.

2.1.2 Procurement and Maintenance

It is often possible to arrange for these

Cost of Capacitors

machines to be overmagnetized and thus

The procurement cost of capacitors can, for

generate excess reactive power for compen-

Fig. 2 Cost factor (a) derived from interest and sation of other loads. The procurement cost of

economic comparisons, be expressed in an-

nual costs as follows:

depreciation.

If the power charge (or maximum demand maintenance and repair costs. Power losses

Annual operating costs comprise losses,

2.3 Reactive Power and

charge) is not included in the tariff, the annual have now been drastically reduced since film

cost of loss energy is simply proportional to has replaced paper as the dielectric material

Transmission Losses

the length of time the equipment is used. for capacitors.

Transmission of reactive power causes active

power loss in network resistance and loss of

Annual expenses for maintenance and

reactive power in reactances.

repair are usually 1...2 % of the purchase

Due to the former, such system compo-

price of the capacitor. Capacitor units have no

nents as cables and transformers experience

moving or wearing parts. Contactors, regulat-

a temperature rise, and the power loss (kW)

ing relays in automatic capacitors banks and

and corresponding energy (kWh) have to be

breakers in HV banks are the only compo-

paid for.

nents that require maintenance. An investment in capacitors will normally

be reimbursed in 0.5...2 years through lower

2.3.1 Active Power Losses

losses and reactive power/energy charges.

Active power losses in a 3-phase network can

The annual savings for the whole depreciation

be calculated from the following formula:

period are 30...100 % of the purchase price.

P =3xl 2 h xR=3xl 2 p xR+3xl 2 q xR

2.2 Transmission of Reactive Power

P h = active power losses

and Design of the Network

R = resistance of the transmission

The total current in the network is, as a rule,

network/phase

the basic criteria for designing the system. At low voltage in particular, the thermal current of

The above equation shows that power

the network is the critical factor, whereas at

losses generated by the reactive current com-

high voltage other considerations, such as

ponent (l q ) are independent of the active

short circuit power, are also vital.

power transmission and can be examined

When parallel compensation is included in

separately:

the system, less reactive power is transmitted. Fig. 4 Percentage decrease in total losses of a Hence the corresponding current component

network with improvement in power factor. lq decreases, and consequently reduces the

Ph q =3xl 2 q xR

Note especially that power losses are in-

total current I which is expressed as follows:

curred in proportion to the square of l q , i.e. when the current rises 2-fold, losses will in-

l = l 2 +l p 2 q

crease 4-fold. Correspondingly at a mean

l = current having effect on the

power factor of cos ϕ = 0.7 for asynchronous

design of the network

motor load, half of the total transmission losses

2.3.2 Reactive Power Losses

l p = current component caused by

Losses caused by reactive power transmis- active power transmission

are due to the reactive power.

sion can be examined separately in the same l q = current component caused by

way as active power losses. They are also reactive power transmission

Resistance of cables can be roughly cal-

culated from the formula:

independent of the active power transmis- sion.

Decreasing the current flowing in a new R =kx 1 3-phase reactive power losses can be networks means that lower rated transform-

calculated from the following formula: ers, conductors and cables can be used. In

A (9)

R = cable resistance

an existing system more active power can be

(13) transmitted (l p increases) when the reactive

Q =3xl k 2 = 0.020 Ω x mm2/m for Cu-cables hq q xX

power transmission is cut down (l q decreases)

= 0.033 Ω x mm2/m for Al-cable

and the total load (l) remains constant.

Q hq = reactive power losses due to By this means, replacement of the trans-

= cable length

reactive current component former or cables can possibly be postponed

A = cross section area of the cable

X = network reactance for some years or to the end of working life.

Resistance of transformers may be calcu-

The power that can be transmitted through the

lated as follows:

2 The reactance of an overhead line is

same network can be calculated from:

calculated from its inductance: cos ϕ

P 1 = transmission capability of active

X = line reactance power of the network at power factor

f = network frequency

L = specific inductance of the line P 2 = transmission capability of active

cos ϕ 1 S n

power of the network at power factor

= length of the line cos

R = transformer resistance

ϕ The reactance of overhead lines is generally

2 S n = rated power of transformer

of the order of 0.4 ohm/km which is consider-

U = supply voltage (by which the

ably more than that of cables. Reactive power

resistance is calculated)

losses generated in cables are normally insig-

r = relative short-circuit resistance

nificant.

The transformer reactance is calculated

P 1 = load losses at rated current (from

as follows:

tables or rating plate)

U X= x 2

When calculating losses, it is advisable to

examine the various parts of the network sepa- rately. By this method the corresponding losses

where

arising in cables, transformers etc. can be compared and the principal sources detected.

X k = z 2 k –r k 2 (16)

This then becomes one criterion for the eco- nomical location of capacitors.

X = transformer reactance S n = rated power of transformer

Annual costs of active power losses are:

U = supply voltage (at which reactance

C a = (P h x a) + (P h xt a x b)

is calculated) z k = relative short-circuit impedance

C a = annual cost of active power losses

X k = relative short-circuit reactance

r k = relative short-circuit resistance Fig. 3 Percentage degrease in design current of

t a = time that active power losses are

being used

a network when the power factor (cos ϕ 2 )

The relative short-circuit impedance (z k )

of power transformers is 2- or even 3-times is improved to near unity.

a = power charge

b = energy charge

that of distribution fransformers.

2.4 Reactive Power

This shows that the voltage drop in the

Transmission and Voltage Drop system reactances can be decreased by re-

ducing the reactive current component, typi-

2.4.1 Parallel Compensation

cally by using parallel or, as it is also called,

Transmission of active power produces volt-

shunt compensation (Fig. 5).

age drop across the resistances in a network and reactive power transmission causes volt-

With transformers, the voltage drop caused

age drop in the inductive reactances. The

by transmission of reactive power is relatively high. This drop can be calculated from the

total voltage drop can be calculated approxi- mately from the following formula:

following formula: u = l (r x cos ϕ +x x sin ϕ )

dU = l p xR+l q xX

dU = voltage drop (phase voltage) R = network resistance

u d = relative voltage drop in the

X = network reactance

transformer cos ϕ = power factor of load

Fig. 6

= rated current of transformer

Voltage may be raised to the desired level by

= load current

means of a series capacitors. When X c equals X l , the network reactance

2.4.2 Series Compensation

is zero (X l –X c = 0) and the voltage drop caused

As previously stated, shunt compensation

by reactive power transmission is therefore

reduces the reactive component of the net-

also zero. By inclusion of a suitable series

work current and, consequently, the voltage

capacitor, X c may be made greater than X l , in

drop. With series compensation, the line re-

which case the network reactance becomes

actance is decreased by connecting capaci-

negative. Thus, series compensation can also

tors in series with the line. The expression

reduce the voltage drop caused by active

(17) for line voltage drop is then modified as

power transmission (Fig. 6)

follows:

In addition, series capacitors provide the following advantages compared with uncom- pensated HV transmission systems: higher

dU = l p xR+l q x (X l –X c )

power transmission capability, better static and dynamic stability, fewer regulation requirements

and reduced losses through optimizing load Fig. 5

dU = voltage drop in the line

sharing in parallel lines. Series compensation Parallel compensation reduces the voltage

is also a cost-saving alternative compared with drop.

X l = line reactance

X c = capacitor reactance

building new, parallel lines.

3. METHODS OF COMPENSATION

Table 2 Factor K for calculating the necessary compensation power for a given active power

When selecting the method of compensation required one should consider the location of

Given values before

cos ϕ desired

the capacitors, the economic aspects re-

compensation

ferred to above such as tariffs, the param-

0.80 0.85 0.90 0.92 0.94 0.96 0.98 1.00 eters of the network, transmission losses and voltage drop, as well as the initial purchase

75.5 0.97 3.88 0.25 3.13 3.26 3.39 3.45 3.51 3.58 3.67 3.88 cost and maintenance expenses of the equip-

72.5 0.95 3.18 0.30 2.42 2.56 2.70 2.76 2.82 2.89 2.98 3.18 ment. In addition, there are factors such as

69.5 0.94 2.68 0.35 1.93 2.06 2.19 2.25 2.31 2.38 2.47 2.68 system harmonics and the ambient condi-

63.2 0.89 1.98 0.45 1.24 1.36 1.50 1.56 1.62 1.69 1.78 1.99 tions which may limit the effective utilization

of capacitors.

58.6 0.85 1.64 0.52 0.89 1.02 1.16 1.22 1.28 1.35 1.44 1.64 Tables and nomograms are available to

assist in calculating the capacitor rating re-

57.3 0.84 1.56 0.54 0.81 0.94 1.08 1.14 1.20 1.27 1.36 1.56 quired. In table 2 the cross-reading of given

54.7 0.82 1.41 0.58 0.66 0.79 0.92 0.98 1.04 1.11 1.20 1.41 and desired values of cos ϕ or tan ϕ gives the

53.1 0.80 1.33 0.60 0.58 0.71 0.85 0.91 0.97 1.04 1.13 1.33 factor K, by which the active power P shall be

51.8 0.79 1.27 0.62 0.52 0.65 0.78 0.84 0.90 0.97 1.06 1.27 multiplied. This yields the capacitor rating to

48.7 0.75 1.14 0.66 0.39 0.52 0.56 0.71 0.78 0.85 0.94 1.14 There is no single method of compensa-

be chosen.

47.3 0.73 1.08 0.68 0.33 0.46 0.60 0.65 0.72 0.79 0.88 1.08 tion to be recommended universally; various

45.6 0.71 1.02 0.70 0.27 0.40 0.54 0.60 0.66 0.73 0.82 1.02 methods can be applicable in each case.

43.8 0.69 0.96 0.72 0.22 0.34 0.48 0.54 0.60 0.67 0.76 0.97 In the following three methods or parallel

42.3 0.67 0.91 0.74 0.16 0.28 0.43 0.48 0.55 0.62 0.71 0.91 compensation will be discussed: individual,

40.7 0.65 0.86 0.76 0.11 0.24 0.37 0.43 0.50 0.56 0.65 0.86 group and central compensation.

33.0 0.55 0.65 0.84 0.03 0.16 0.22 0.28 0.35 0.44 0.65 By connecting the capacitors to the termi-

3.1 Individual Compensation

30.5 0.51 0.59 0.86 0.11 0.17 0.23 0.30 0.39 0.59 nals of the compensated equipment, one

28.4 0.48 0.54 0.88 0.06 0.11 0.17 0.25 0.33 0.54 can best consider the influence of the ca-

25.6 0.43 0.48 0.90 0.06 0.12 0.19 0.28 0.48 pacitors on the network dimensioning and on

23.0 0.40 0.43 0.92 0.06 0.13 0.22 0.43 power and voltage losses.

19.8 0.34 0.36 0.94 0.07 0.16 0.36 The reactive power demand of 3-phase

0.75 0.62 0.48 0.43 0.36 0.29 0.20 0.00 asynchronous motors varies between 0.5 and 1 kvar per kilowatt of active power de-

pending on the speed, size and load of the Example: What is the capacitor power rating needed to improve the power factor from 0.66 to motors. Most of the reactive power needed

0.98, if the active power requirement of the load is 750 kW?

can be produced by capacitors installed in parallel with the motor. The capacitor can be

From the above table the cross-reading gives K = 0.94.

connected either to the terminals of the motor The capacitor power rating should thus be 0.94 x 750 = 705 kvar. The nearest standard rating or of the starter (Fig. 7).

is 700 kvar, which can be selected.

Table 3. Reactive power requirement of various squirrel-cage motors at no-load... rated power and the nearest standard capacitor rating, when the compensation power limitations have been taken into account.

3000r/min

1500r/min 1000r/min 750r/min 600r/min 500r/min

rated

req. cap.

req.

cap.

req. cap.

req. cap.

req. cap. req. cap.

power kvar kvar

kvar

kvar kvar kvar

kvar kvar

kvar kvar kvar kvar

Fig. 7 Principle of individual motor compensa- tion.

The necessary capacitor rating may be cal-

P culated from the formula:

When dimensioning the capacitor cable

note that the fuses also protect the supply

Q= 1 e . tan ϕ 1 + 2 e . tan ϕ 2 + ... (22)

cable. Thus the capacitor cable shoud have

c e x (tan ϕ 1 – tan ϕ 2 )

the same cross-section as that of the main motor cable.

Q c = capacitor output

Also when setting any overcurrent relay,

P 1 ,P 2 ... = rated power of the motors

notice that the compensation reduces the

1 ,e 2 ... = efficiency of the motors

P = rated power of motor

e = efficiency of motor ϕ 1 , ϕ 2 ... = phase angles before PFC

current.

If the motor is equipped with an automatic

ϕ 1 = phase angle before PFC

Group compensation may often be advan- ϕ 2 = phase angle after PFC

star-delta starter where the motor is switched off directly from the delta configuration, a

tageously applied when a standby motor is

normally connected capacitor may be used for power factor correction.

installed, thus avoiding duplication of capaci-

A voltage rise caused by self-excitation

However, if a mechanical star-delta starter

tors.

can occur particularly when the motor is quickly

is used as in Fig. 8, capacitors that are specifi-

re-connected immediately after switching off.

cally designed for this purpose must be fitted.

3.3 Central Compensation at

It is therefore advisable to limit the compensa- tion power to:

Single-phase capacitors are connected in

Low Voltage

parallel with each winding of the motor.

Though individual or group compensation may Q c = 0.9 x l xUx 3

be used, additional capacitors are often in-

3.2 Group Compensation

stalled at the main supply point to achieve a

l = no-load current of the motor

0 sufficient degree of correction (cos ϕ = > 0.97). U = supply voltage

Sometimes it is possible to correct the power

A proportion of the required compensation

may be supplied as fixed units and the re- Because of self-excitation, it is not recom-

factor of several loads by means of a common

mainder in automatically controlled capacitor mended to use individual motor compensa-

capacitor. This kind of group compensation is

banks as shown in Fig. 10. tion if the machine driven by the motor can in

particularly advantageous for discharge lamps

controlled by 3-phase contactors. Group com-

turn rotate it at overspeed (cranes, carriers,

pensation of motors is also feasible where the

etc.) or if the brake magnet voltage is derived

motors are small or running simultaneously.

from the poles of the motor.

When a capacitor is connected into the network with a separate contactor, overvoltage due to self-excitation cannot occur. Thus the capacitor size can be chosen freely. The capacitor rating needed for cos ϕ = 1 may be calculated from the following formula:

Fig. 8

Fig. 10 Connection scheme comprising fixed Connection of a capacitor for a motor with a

Fig. 9 Compensation of a group of motors. The

capacitors and automatically controlled ca- mechanical Y/D starter.

motor M3 is always on whenever the mo-

tor group is running.

pacitor bank.

Capacitors that are permanently connected to the system are continuously producing re-

3.5 Technical Consequences of

of resonance at any of the common orders of harmonics (viz: 3rd, 5th, 7th, 11th and 13th).

active power, even at periods of low load.

The capacitor rating which could cause Thus, any excess reactive power is trans-

Compensation

resonance if connected to the network, can ferred into the main supply network.

be calculated for each harmonic as follows: Reactive power consumption of a distribu-

3.5.1 Voltage Rise

Fixed capacitors can cause the voltage to rise in an unloaded network. The rise in a trans-

tion transformer at no-load is 1...2 % and at full

load 4...7 % of its rated power (see table 4).

(26) To avoid the disadvantages of overcom-

former on no-load may be calculated from the

following formula:

d (%) = c u For example, if the short-circuit power of S .X k (%) transformer rating. A fuse switch or circuit

pensation, the total power of the fixed capaci-

the busbar is 15 MVA the equation (26) yields breaker is generally fitted, so that the capaci-

tors should be limited to 10...15 % of the

d = percentage voltage rise

for n=3: Q = 15

c 2 Mvar = 1.7 Mvar

tor may be switched off if required.

Q c = rated power of capacitor bank

S n = rated power of transformer x k = percentage short circuit reactance

for n=5: Q c = 15 2 Mvar = 0.6 Mvar Table 4. Approximate reactive power

of transformer

consumpiton of various 50 Hz distribution transformers (primary voltage 10...20 kV)

for n=7: Q c = experienced during no-load operation. 15 2 Mvar = 0.3 Mvar Power

In practice voltage rises of 1...2 % are

Reactive power consumption

If, for example, the proportion of fixed

rating kvar

capacitors is 20 % of the rated power of the

kVA no-load

full load

transformer and x k = 6 %, the voltage of the

Example

16 0.3 1.0 transformer rises 1.2 % during no-load opera-

1.5 5.5 3.5.2 Influence of Harmonics

3 13 Non-linear loads, such as thyristor drives,

6 31 converters and arc furnaces produce exces- sive harmonic currents causing both current

9 40 and voltage distortion. Capacitors offer a low

11 96 impedance to any higher frequencies flowing through them, but they also may amplify the

effect of harmonic currents flowing into other parts of the network.

The effect of harmonics on the phase

In an automatic capacitor bank, a power

voltage of a capacitor bank can be calculated

factor controller controls the switching of the

from the following formula:

capacitor steps according to the varying re- active power requirements. Inductive and ca-

∑ l cn

n.2.

.f .C pacitive operating limits for the power factor π 1 (24)

controller are set and the amount of reactive

= phase voltage of capacitor bank

power in the network is maintained within

these limits. Problems of overcompensation

n = order of harmonic (the harmonic

therefore do not arise.

frequency fn = n . basic frequency)

The effects of central compensation on the

dimensioning of a network and on the losses

cn

= ‘n’th harmonic current flowing

are mainly related to the distribution trans-

into capacitor bank

former and the connecting cable. The elec-

f 1 = basic frequency (e.g. 50 Hz)

tricity board system can therefore benefit from

C = capacitance of bank per phase

low voltage power factor correction, and this is usually taken into account when connection

In other words, the voltage component of

charges and annual tariffs are determined.

each harmonic is summed arithmetically at

Fig. 11 Schematic diagram of the example.

the basic frequency voltage. When designing

a compensation scheme, the harmonics flow- ing into the bank must be calculated on the basis of the harmonic current imposed by the

For higher harmonics the possibility of

load. The harmonics in an existing capacitor

resonance is generally slight but it must be

taken into account if the harmonic content is Compensation may also be carried out on the

3.4 High Voltage Compensation

bank can be measured by a harmonic ana-

lyser.

very high.

The rated current of the thyristor drive cost savings related to the dimensioning and

system shown in Fig. 11 is calculated by using losses of the distribution transformers. Be-

high voltage side, in which case there are no

The harmonics flowing into the capacitor

bank can in some circumstances be very

a power factor of 0.7, a diversity factor of 0.8 cause of the high reactance of transformers,

high. The worst situation arises when the ca-

and motor efficiency of 95 % as follows: considerable voltage drops and reactive power

pacitors and the network inductance form a

0.8 . 3 . 100000 losses are also incurred by reactive power

parallel or series resonant circuit under the

l=

3 . 380 . 0.95 . 0.7 transmission. Thus, compared with LV com-

following conditions:

3 . U . e . cos ϕ

pensation, more capacitors would be needed

on the HV side of a transformer.

individually in the same way as with low volt- The harmonics caused by thyristor drives

It is possible to compensate HV motors

age. For this purpose enclosed capacitor are usually generated by 6-pulse rectifiers in banks are manufactured, which can then, if

X c = capacitive reactance of bank at

the following percentages of rated current: required, be installed adjacent to the motor.

basic frequency

X l = inductive short circuit reactance

5th harmonic (30 %): compensate for the reactive power consumed

Generally HV capacitor banks are used to

of network at basic frequency

l 5 = 0.3 . 550 A = 165 A formers. Sometimes it is economical to com-

by long transmission lines and power trans-

Q c = reactive power of capacitor bank

7th harmonic (12 %): pensate for part of the reactive power of a

S k = short circuit power of network

l 7 = 0.12 . 550 A = 66 A large industrial plant by means of HV capaci-

11th harmonic (6 %): tor banks.

Connecting a harmonic source and ca-

l = 0.06 . 550 A = 33 A However, because of the relatively high

pacitors to the same busbar could create a

parallel resonant circuit. Similarly a capacitor

13th harmonic (5 %): circuitbreaker, protection, cables, busbar),

c ost of the c onnec ting eq uip ment (viz:

bank connected to the LV side of a tranformer

l 13 = 0.05 . 550 A = 28 A the total cost per kvar may seem unreason-

can form a series resonant circuit with the

transformer for harmonics originating on the

ably high if compared with straightforward HV

HV side. When carrying out reactive power

capacitor banks.

compensation, one should avoid the danger compensation, one should avoid the danger

The capacitance and reactance (at power

The harmonic voltages across the capaci-

would be nearly in resonance at the 13th har- Q c 200000

tor bank are

monic. The effective value of current in almost C=

2 2. -3 π .f.U 314 . 400 = 2 = 3.98 . 10 F Un = l cn .X cn (=l kn .X kn )

2.5 times the rated value. The capacitors could not withstand this degree of extra stress.

1 U 2 400 2 For n = 5: U5 = 82 A . 0.16 Ω = 13 V

X c = 2. .f.C Q = 200000 = 0.8 π Ω increases in proportion to the load, the danger

When the rating of capacitors in a system

of resonance is shifted toward the lower fre- If the network impedance is simplified,

c The total voltage stress is:

quencies which generally have higher har- consisting of only inductive reactance, it can

U = 400V + 3 . U 5 + 3.U 7 + 3.U 11 monic currents.

be expressed as + 3.U 13 It is also noteworthy that the currents flow-

ing into the network are considerably higher S

X k = U 2 = 400 2

Excess current caused by harmonics in a

compared with those generated by the thyristor

capacitor bank is calculated in terms of the

drives. However, in practice the above as-

At ’n’th harmonic frequency the reactances sumption that the impedance would be purely of the capacitor bank and network are

effective value of the current:

inductive is not valid. At higher frequencies harmonics are damped by the network resist-

ance and resonances are not as likely as in n

X cn X c (27)

c = = l c1 2 + ...l cn 2 (32)

l c = total current in capacitor bank

this example.

l c1 = current in capacitor bank at

The problems arising with harmonics are

X kn =n.X k

basic frequency (50 Hz)

solved by using a harmonic filter as described later.

X cn = capacitive reactance of the bank The temperature rise of capacitors caused

at ’n’th harmonic frequency

c1 A = 289 A

by any increase in losses is not generally a

3 . U 3 . 0.4

problem with modern low loss metallizedfilm

X c = capacitive reactive of the bank units. However, capacitors with paper dielec- at basic frequency

tric used to overheat rapidly with excessive

X kn = inductive reactance of the

harmonics in the network. network at ’n’th harmonic

Table 5. Current and voltage values due to the

example. The corresponding values are also given for other capacitor ratings.

X k = inductive reactance of the network at basic frequency

Cap. l

c1 l c5 l c7 l c11

l c13 l c

3.5.3 Ambient Conditions

kvar A A A A A A Unfavourable conditions will shorten the life of The harmonic currents flowing into the

a capacitor and thus incur extra repair and

bank (l ) and into the network (l ) are calcu- maintenance costs.

lated simply by using the current division rule kn

The temperature categories according when the currents of the harmonic source (l

to the new IEC standards for power capaci- are known:

Cap. l k5

tors cover the temperature range of -50 °

C to

C. For example, the highest permissible l cn =(

X kvar A A A A °

kn

).l mean ambient temperature according to cate- kn X –X cn

gory A is +40 °

C for a short period but only

C for 1 year. Higher

215 15 8 temperatures accelerate ageing of the die- l kn =(

Cap. U 1 U 5 U 7 U 11 U 13 U

lectric, thus shortening the life of the capaci- kvar V V V V V V tor. Power factor controllers for automatically controlled capacitor banks are usually made

C to monic currents are produced:

For the 5th harmonic the following har-

for an ambient temperature range of 0 °

In high humidity conditions outdoor type

X k5 = 5 . 0.01067 = 0.0533 capacitor units should be used since they are

X c5 = 0.8/5 = 0.16 suitably protected against corrosion. l 5 = 165 A

l c = 289 2 +82 2 +124 2 +87 2 +50 2 A=340 A

=( 0.0533 ) . 165 A = 82 A

Table 5 shows, at all the chosen ratings,

c5 0.0533 – 0.16

that the capacitors will operate at a consider-

4. COMPENSATION EQUIPMENT

4.1 Low Voltage Capacitors

Most low voltage capacitors are equip- ped with external discharge resistors so as to

4.1.1 Low Voltage Capacitor Units

decrease the residual voltage of the capaci-

A low voltage capacitor unit is built up of

tor from an initial value of √ 2 times the rated

several elements connected in parallel. An

voltage Un to below the level of ≤

50 V within

element consists in principle of two electro-

1 minute.

des and dielectric. The elements are made of

Low voltage capacitors are normally three-

metallized plastic film and inserted into a

phase with three bushings on the cover and

plastic cover.

star or delta connected internally.

Unlike capacitors made of aluminium foil

Among the unit sizes available for the

or metallized paper, metallized-film capaci-

most common voltage range 400...690 V are

tors are generally dry without impregnation

liguid.

75, 90 and 100 kvar, and the capacitance

The elements of metallized-film capaci-

tolerance is -5...+10 %.

tors are self-healing. After a disruptive discharge, a thin metallized layer will vapori- ze off from the surface around the breakdown point, and no permanent short-circuit will be left there. Elements are internally protected to ensure a reliable disconnecting at the end of the lifecycle.

Elements are set into a steel container and connected to the terminals of the capaci-

Fig. 12

tor by means of copper busbars and cables. Low voltage capacitor units Capacitor losses are very low, less than

0.5 watt per kvar.

4.1.2 Fixed Low Voltage Capacitor

Very large banks are usually divided into

The capacitor elements are inserted into a

Banks

steel container. The unit is then filled with a Fixed capacitor banks consist of parallel con-

smaller subgroups, each with an individual

connection cable and main fuses but with a

suitable, environmentally safe impregnation

oil, and the containers are hermetically closed. nected units installed in a rack. The bank is

common power factor controller.

HV units equipped with internal element fitted with a cable connection box. The ca-

The main fuses should be slow acting and

fuses are manufactured up to 9000 V of rated pacitance tolerance of a bank is –0...+10 %.

dimensioned for 1.38 times rated current.

voltage. Internal discharge resistors decrease Due to the large inrush current of a fixed

the residual voltage from bank, slow acting fuses dimensioned for 1.7

√ 2 x rated value to below 75 V within 10 minutes, according to

times the rated current must be used. Ac-

IEC standards.

cording to general standards, the connection The most common unit sizes are 50, 100, cable must be able to carry a continuous load

167, 200, 250, 300 and 333 kvar and the of 1.43 times rated current.

capacitance tolerance is –5...+10 %. The units are manufactured for the voltage range 1...22 kV, and the most common unit voltages are 3300, 4000, 4500, 6350, 6600, 7600 and 8000 V.

Fig. 15 Automatic capacitor bank with blocking reactors

4.2 High Voltage Capacitors

Fig. 13

4.2.1 High Voltage Capacitor Units

Cubicle type automatic capacitor bank

One-phase high voltage capacitor units are

4.1.3 Automatically Controlled Low

equipped with two bushings or one bushing with live case. Three-phase units are inter-

Voltage Capacitor Banks

nally either delta or star connected.

Automatically controlled capacitor banks

A capacitor unit consists of parallel and

are equipped with fuses and contactors con-

series connected elements. Series coupling

trolled by a power factor controller, on which

is needed to keep the element voltage at a

a desired target value of power factor (cos ϕ )

suitable level (about 2000 V).

and inductive and capacitive operating limits

The elements of modern HV capacitors

can be set.

are made of aluminium foil, separated by two

The level of reactive power is monitored by

or more layers of polypropylene film dielec-

means of current transformers and the power

tric. Units with paper or mixed dielectric,

Fig. 17

factor controller switches capacitors on and

One-phase high voltage capacitor units off according to demand.

commonly used before, have higher losses.

A single step may comprise either one or several capacitor units; in the latter case the second unit is controlled via an auxiliary con- tact on the contactor of the first unit and so on. In this way a time lag equal to the operating time of the contactor is introduced and the overall inrush current is thus reduced.

Fig. 14 Power factor controllers

Steps can be equal or of different sizes, but if they are unequal the first (i.e. the small- est) determines the increment. The ratio of steps with respect to the first can be any of the following:

1:1:1:1:..., 1:2:2:2:..., 1:2:3:3:..., 1:2:3:4:... or 1:2:4:4:...

It is generally advisable to use standard banks with steps of, say, 50 kvar. With smaller banks, units of 25...30 kvar may be used for the first steps and with the smallest, units of even smaller power rating. Such arrange-

Fig. 16

ments are obviously more expensive per kvar

Schematic diagram of an automatically controlled

than those comprising larger units.

capacitor bank with power factor controller

By using internal fuses, a reliab le High voltage capacitor banks are used at

4.2.2 High Voltage Capacitor Banks

internally fused units the need for spare units

unbalance protection can be performed, pro- substations and in industry, on long transmis-

is much lower than by using external fuses.

tecting the banks against any major damages sion lines, and at points in HV networks suit-

during a fault operation of the network or the able for maintaining reactive power balance.

4.3.2 Unbalance Protection

HV banks are usually wired in either single or

banks.

High voltage capacitor banks are usually

double star. If the impedance of one phase

built up of single-phase HV units, the required

changes with respect to the other two phases,

4.3.3 Overcurrent and overvoltage

number in series depending on the voltage

the star point of the bank shifts. This occurs

protection

and the number in parallel, on the power.

Overload and short-circuit protection of an HV In order to divide the voltage evenly, an

when element fuses in a capacitor are blown

bank is normally carried out by means of equal number of units are connected in paral-

as a result of a disruptive discharge.

current transformers and a two-step overcur- lel in each series group. Series groups are

At the same time the voltage division within

the bank is also changed. Hence, the bank

rent relay.

The capacitor bank is characteristically tors mounted between the racks. Capacitor

separated from each other by support insula-

must be switched off before the operation of

self-protective against switching and light- banks attached to a busbar are equipped with

the fuses would cause a voltage rise consid-

erably above the permitted 10 % overvoltage.

ning overvoltages because of its low imped-

a breaker. If necessary, current limiting reac- ance at high frequencies. tors can be supplied to reduce the inrush

Overvoltage protection is therefore usu- current to a value suitable for the breaker.

ally included in the protection of other equip- The main purpose of shunt capacitor banks

ment. If separate overvoltage protection is is to produce reactive power near enough to

required, the discharge capacity of the pro- point of consumption in order to reduce losses,

tective device is of great significance. Some- cut the price of reactive power, increase the

times a tripping overvoltage protection is voltage, and improve the power transmission

needed at power frequency during low-load capacity of the line section.

periods.

4.4 Harmonic Filters Banks

4.3 Protection of Capacitor

Harmonic filters provide another source of In electricity networks the purpose of all

compensation. In a filter, a reactor is con- protection is to protect the equipment against

nected in series with a capacitor bank. With a overcurrents and overvoltages and to mini-

suitable reactor inductance, the series circuit mize the effect of these, considering the eco-

of capacitor and reactor forms a low imped- nomical and technical restrictions and safety

ance at a desired harmonic frequency. Thus, regulations.

the major part of the harmonic current flows Internal protection of a bank comprises

into the filter and not into the network. either internal or external fuses and unbalance

At the same time the filter provides capaci- protection, whereas externally the bank is

tive reactive power at the base frequency. protected against overload, overvoltage and

Among the problems caused by harmon- short-circuit.

ics are interference to telecommunications,

Fig. 19

disturbances to the control and protection

4.3.1 Internal and External Fuses

system of the network, malfunctioning of re-

lays and dangerous overvoltages due to reso- There are two types of fuses used for capaci-

Schematic diagram of an HV capacitor bank

nance. The extra losses that occur in cables, tors, internal or external. When the reactive

connected in star with unbalance protection.

transformers, motors and generators are also power of a capacitor unit was only a few kvar,

of significance: they cause loss of energy and the most natural method to protect the capaci-

excess temperature rise in the equipment. tor was with an external fuse, since in the case

Double pole insulated voltage transform-

The most frequently encountered and poten- of a breakdown the lost reactive power was

ers are used for unbalance protection of sin-

tially harmful harmonics are the 5th and 7th, small. However, now that one capacitor ele-

gle star connected banks. The transformer

which are generated by 6-pulse rectifiers. ment has a capacity of about the same value

primaries are connected in parallel with the

Harmonic filters can be connected to ei- as a unit had previously it is reasonable to

phase banks and the secondaries form an

ther LV or HV circuits. Where there are several protect each separate element with an inter-

open delta. The unbalance voltage gener-

harmonic generating loads, each fed by a nal fuse.

ated in the open delta operates the breaker

through a voltage relay.

distribution transformer, it is often more eco-

Where there is a sufficient number of par-

nomical to eliminate the harmonics by install-

allel connected units, it is advisable to con-

ing filters centrally at the HV busbar, rather

nect the bank in double star. Unbalance pro-

than to have separate filter on the LV side of

tection is then carried out by a current trans-

each transformer.

former connected between the two star points,

A typical filter construction is shown in Fig.

and an overcurrent relay (Fig. 20). The time

21. The lower harmonics (5th and 7th) have

settings are 5 s for alarm and 0.1 s for tripping.

individual circuits and the higher harmonics (11th, 13th) a common high-pass filter.

Fig. 18 Internally

Typical filter construction. If the capacitor unit is protected with inter-

Externally

Fig. 21

fused unit

fused unit

nal fuses the lost reactive power in the case of

a blown fuse is very low (approximately 2 % of

a unit). Because of the low percentage power loss there is no need to replace the entire capacitor unit, hence preserving continuity of operation and saving replacement costs.

If the unit is protected with an external fuse

Fig. 20

the whole unit is lost and it is nearly always

Schematic diagram of an HV capacitor bank

necessary to replace the faulty unit immedi-

connected in double star with overload, short-

ately. It is, therefore, obvious that by using

circuit and unbalance protection.

4.5 Fast Static Compensators

Static compensators are also used to re- duce voltage variations caused by power

In some cases, for example arc furnaces and

changes in transmission lines.

welding machines, there are very rapid fluctu- ations in reactive power within a short period – i.e. a few cycles. Traditional methods of re-

4.6 Thyristor Controlled

active power control are not suitable since they are too slow for such variations.

Capacitors

The fast static compensator has been de-

Thyristor controlled capacitors, which are more

simple in construction than the fast static Fig. 22

veloped to deal with this problem.

compensators described above, are very Equivalent circuit of the harmonic filter and the

The Nokian Fast Static Compensator con-

suitable for fast reactive power compensa- network in accordance with Fig. 21.

sist of a fixed shunt capacitor bank, normally

tuned as a filter, and a thyristor-controlled

tion. The capacitor is equipped with a thyristor

shunt reactor. By controlling the reactor cur-

switch, which replaces the traditional contac-

The circuit in Fig. 22 can be simplified further- tor. Regulator operations are combined with

rent, the total reactive power supplied by the

more, consisting of parallel coupled network the automatic thyristor controls. This equip-

f.s.c. into the network is correspondingly ad-

impedance Z and filter impedance Z ment can rapidly compensate for fast reactive

justed.

impedance vary according to frequency as power fluctuations in welding machines and

nw

f . The

Thus the harmonics generated both by

shown in Fig. 23 (absolute values). The cur- the consequent voltage variations.

the load and the thyristors are eliminated.

Hence the disadvantages of fluctuations in

rents drawn consequently depend on them,

reactive power and the harmonics are both

and can be expressed as follows:

Fig. 23 Impedance curves of the harmonic filter and other network in accordance with figures 21

Fig. 24

and 22.

Fast static compensator for arc furnaces.

5. SUMMARY

The most economical way of producing reac- By series capacitor bank, voltage may be tive power required by most electrical devices

raised to a desired level. Parallel capacitor is by the use of capacitors.

banks can be used for individual, group or

Capacitors reduce network losses and

central compensation.

voltage drop, and the transmission of reactive The influence of possible harmonic com- power is avoided. This means considerable

ponents must be taken into account when annual savings.

designing the system.

NOKIAN CAPACITORS: PRODUCT GUIDE

Low Voltage Power Capacitors

Detuned Filters

High Voltage Capacitors

Air-Core Reactors

Harmonic Filters For High Voltage

High Voltage Capacitor Banks

Static Var Compensators (SVC)

Series Capacitors

In line with our policy of on-going product development we reserve the right to alter specifications

NOKIAN CAPACITORS

Kaapelikatu 3, P.O. Box 4, FIN-33331 Tampere, Finland Telephone +358 3 388 311, Telefax +358 3 3883 360 www.nokiancapacitors.com

EN-TH01-11/2002