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POWER FACTOR CORRECTION NOKIAN CAPACITORS
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POWER FACTOR CORRECTION
NOKIAN CAPACITORS
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1.INTRODUCTION1.1 General ........................................................................ 3
1.2 Power Factor .............................................................. 3
1.3 Reactive Power Demand ........................................... 3
2.ECONOMIC EFFECT OF COMPENSATION2.1 Procurement Cost of Compensation ........................... 3
2.1.1 Generation of Reactive Power by Meansof Rotating Machines .......................................... 3
2.1.2 Procurement and Maintenance Costof Capacitors ....................................................... 3
2.2 Transmission of Reactive Power andDesign of the Network ................................................... 4
2.3 Reactive Power and Transmission Losses .................. 42.3.1 Active Power Losses .......................................... 42.3.2 Reactive Power Losses ...................................... 4
2.4 Reactive Power Transmission andVoltage Drop ................................................................... 52.4.1 Parallel Compensation ........................................ 52.4.2 Series Compensation .......................................... 5
3.METHODS OF COMPENSATION3.1 Individual Compensation ........................................... 5
3.2 Group Compensation ................................................ 6
3.3 Central Compensation at Low Voltage .................... 6
3.4 High Voltage Compensation ..................................... 7
3.5 Technical Consequences of Compensation............ 73.5.1 Voltage Rise ..................................................... 73.5.2 Influence of Harmonics ................................... 73.5.3 Ambient Conditions ......................................... 8
4.COMPENSATION EQUIPMENT4.1 Low Voltage Capacitors ............................................ 8
4.1.1 Low Voltage Capacitor Units .......................... 84.1.2 Fixed Low Voltage Capacitor Banks .............. 94.1.3 Automatically Controlled Low Voltage
Capacitor Banks .............................................. 9
4.2 High Voltage Capacitors ........................................... 94.2.1 High Voltage Capacitor Units ......................... 94.2.2 High Voltage Capacitor Banks ..................... 10
4.3 Protection of Capacitor Banks ............................... 104.3.1 Internal and External Fuses .......................... 104.3.2 Unbalance Protection .................................... 104.3.3 Overcurrent and overvoltage protection ..... 10
4.4 Harmonic Filters ....................................................... 10
4.5 Fast Static Compensators ...................................... 11
4.6 Thyristor Controlled Capacitors ............................. 11
5.SUMMARY
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2. ECONOMIC EFFECT OF COMPENSATION
1. INTRODUCTION
Fig. 1 The apparent power of a network can bereduced by means of power factor correction(PFC).
Fig. 2 Cost factor (a) derived from interest anddepreciation.
1.1 GeneralIn addition to active power most electricaldevices also demand reactive power.
If this reactive power is not provided bycapacitors in the immediate vicinity, it must betransmitted via the distribution system. In thiscase the influence of the reactive power on thetotal current must be taken into account whendesigning the system, and this can lead to aneed for larger transformers and cables thanwould otherwise be necessary.
Moreover, transmission of reactive powercauses additional energy losses. By means ofreactive power compensation the amount ofreactive power has only little significance indimensioning the system and on transmissionlosses.
S1 = apparent power before PFCS2 = apparent power after PFCP = active powerQ1 = reactive power before PFCQ2 = reactive power after PFCQc = Q1–Q2 = compensation power of the
capacitorϕ1 = phase angle before PFCϕ2 = phase angle after PFC
1.2 Power FactorThe total operating power, termed apparentpower, can be expressed in terms of activeand reactive power:
S = P2 + Q2 (1)
Power factor cos ϕ represents the followingrelationship between active and apparentpower:
cos ϕ = P = active powerS apparent power (2)
Correspondingly
tan ϕ = Q = reactive powerP active power (3)
Power factor correction (PFC) means thatcapacitors (or synchronous machines) areused to reduce the amount of reactive powerin electricity supplies to industrial and com-mercial consumers, thus improving the powerfactor to a higher value.
1.3 Reactive Power DemandInduction motors need reactive power to main-tain the magnetic field essential for their op-eration. The average reactive power demandof asynchronous motors is approx. 1 kvar per1 kW of active power.
Thyristor drives draw reactive current fromthe network and also generate harmonicswhich, among other things, tend to overloadcapacitors. In addition to the equipment men-tioned above, transformers, loaded cables,transmission lines and various electrical de-vices all need reactive power to some extent.
Table 1. Examples of power factorsLoad type Approximate
power factor(half ...full load)
Induction motor <100 kW 0.6...0.8250 kW 0.8...0.9
Thyristor drives 0.7Incandescent lamp (glow) 1.0Mercury arc lamp 0.5Fluorescent lamp (hot cathode) 0.5...0.6Neon tube lamp 0.4...0.5Induction furnace 0.2...0.6Arc furnace 0.6...0.8Electric heater 1.0AC arc or resistance welder 0.5...0.6
During recent years increasing attention hasbeen paid to minimizing the energy costs andinefficiencies in electricity generation, trans-mission, distribution and consumption.
When designing a compensation schemeone should attempt to achieve the most eco-nomical solution, in which the savings achievedin equipment costs and transmission lossesare significantly greater than the procurementcost of the reactive power.
When positioning capacitors note thatunfavourable ambient conditions can shortenthe life of the units, effectively incurring extraexpense. The cost of installing capacitors, theeffect of power factor correction on the volt-age level and the requirements of the electric-ity supply authority in regard to overcompen-sation, should also all be taken into account.
2.1 Procurement Cost ofCompensation2.1.1 Generation of Reactive Power byMeans of Rotating MachinesTraditionally, reactive power has usually beengenerated by rotating machines and trans-mitted through the system to consumers in thesame way as active power. Large motorsused in industry are often synchronous ma-chines which themselves generate the reac-tive power they need.
It is often possible to arrange for thesemachines to be overmagnetized and thusgenerate excess reactive power for compen-sation of other loads. The procurement cost of
the generators and synchronous machinesdepends on the desired extra amount of reac-tive power.
Generation of reactive power by synchro-nous machines incurs additional losses of10...30 W/kvar, depending on the size andconstruction of the machine and the amountof reactive power generated. However, byraising the power factor, the additional lossescan be reduced.
Reactive power produced by rotatingmachines must be transmitted through thedistribution system. This leads to extra capitalcosts and additional transmission losses,which are especially significant at high volt-age transmission.
It is now generally accepted that it is notadvantageous to install such generators andsynchronous motors specifically for the pro-duction of large amounts of reactive powerand also that it is often uneconomical to pro-duce reactive power from synchronous ma-chines that are already in the system.
This is a consequence of the rapid rise inenergy prices in the 1970’s and from develop-ment in system capital costs when comparedwith the purchase and maintenance cost ofcapacitors.
2.1.2 Procurement and MaintenanceCost of CapacitorsThe procurement cost of capacitors can, foreconomic comparisons, be expressed in an-nual costs as follows:
K = a . H (4)K = annual costa = cost factor of interest and
depreciationH = procurement cost of capacitors
including installation
An interest rate of 7...10 % is generallyused for calculations of profitability. The de-preciation period for power capacitors is15...20 years.
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Fig. 3 Percentage degrease in design current ofa network when the power factor (cosϕ2)is improved to near unity.
Fig. 4 Percentage decrease in total losses of anetwork with improvement in power factor.
Annual operating costs comprise losses,maintenance and repair costs. Power losseshave now been drastically reduced since filmhas replaced paper as the dielectric materialfor capacitors.
Annual expenses for maintenance andrepair are usually 1...2 % of the purchaseprice of the capacitor. Capacitor units have nomoving or wearing parts. Contactors, regulat-ing relays in automatic capacitors banks andbreakers in HV banks are the only compo-nents that require maintenance.
An investment in capacitors will normallybe reimbursed in 0.5...2 years through lowerlosses and reactive power/energy charges.The annual savings for the whole depreciationperiod are 30...100 % of the purchase price.
2.2 Transmission of Reactive Powerand Design of the Network
The total current in the network is, as a rule,the basic criteria for designing the system. Atlow voltage in particular, the thermal current ofthe network is the critical factor, whereas athigh voltage other considerations, such asshort circuit power, are also vital.
When parallel compensation is included inthe system, less reactive power is transmitted.Hence the corresponding current componentlq decreases, and consequently reduces thetotal current I which is expressed as follows:
l = l2p + l2q (5)l = current having effect on the
design of the networklp = current component caused by
active power transmissionlq = current component caused by
reactive power transmission
Decreasing the current flowing in a newnetworks means that lower rated transform-ers, conductors and cables can be used. Inan existing system more active power can betransmitted (lp increases) when the reactivepower transmission is cut down (lq decreases)and the total load (l) remains constant.
By this means, replacement of the trans-former or cables can possibly be postponedfor some years or to the end of working life.The power that can be transmitted through thesame network can be calculated from:
P2 = P1 .cos ϕ2
cos ϕ1 (6)
P1 = transmission capability of activepower of the network at power factorcos ϕ1
P2 = transmission capability of activepower of the network at power factorcos ϕ2
2.3 Reactive Power andTransmission LossesTransmission of reactive power causes activepower loss in network resistance and loss ofreactive power in reactances.
Due to the former, such system compo-nents as cables and transformers experiencea temperature rise, and the power loss (kW)and corresponding energy (kWh) have to bepaid for.
2.3.1 Active Power LossesActive power losses in a 3-phase network canbe calculated from the following formula:
Ph = 3 x l2 x R = 3 x l2p x R + 3 x l2q x R (7)Ph = active power lossesR = resistance of the transmission
network/phase
The above equation shows that powerlosses generated by the reactive current com-ponent (lq) are independent of the activepower transmission and can be examinedseparately:
Phq = 3 x l2q x R (8)
Note especially that power losses are in-curred in proportion to the square of lq, i.e.when the current rises 2-fold, losses will in-crease 4-fold. Correspondingly at a meanpower factor of cosϕ = 0.7 for asynchronousmotor load, half of the total transmission lossesare due to the reactive power.
Resistance of cables can be roughly cal-culated from the formula:
R = k x 1A (9)
R = cable resistancek = 0.020 Ω x mm2/m for Cu-cables
= 0.033 Ω x mm2/m for Al-cablel = cable lengthA = cross section area of the cable
Resistance of transformers may be calcu-lated as follows:
R = rk xU2
Sn (10)
where
rk = P1
Sn (11)
R = transformer resistanceSn = rated power of transformerU = supply voltage (by which the
resistance is calculated)rk = relative short-circuit resistanceP1 = load losses at rated current (from
tables or rating plate)
When calculating losses, it is advisable toexamine the various parts of the network sepa-rately. By this method the corresponding lossesarising in cables, transformers etc. can becompared and the principal sources detected.This then becomes one criterion for the eco-nomical location of capacitors.
Annual costs of active power losses are:
Ca = (Ph x a) + (Ph x ta x b) (12)
Ca = annual cost of active power lossesta = time that active power losses are
being useda = power chargeb = energy charge
If the power charge (or maximum demandcharge) is not included in the tariff, the annualcost of loss energy is simply proportional tothe length of time the equipment is used.
2.3.2 Reactive Power LossesLosses caused by reactive power transmis-sion can be examined separately in the sameway as active power losses. They are alsoindependent of the active power transmis-sion.
3-phase reactive power losses can becalculated from the following formula:
Qhq = 3 x l2q x X (13)
Qhq = reactive power losses due toreactive current component
X = network reactance
The reactance of an overhead line iscalculated from its inductance:
X = 2 x π x f x L x l (14)
X = line reactancef = network frequencyL = specific inductance of the linel = length of the lineThe reactance of overhead lines is generallyof the order of 0.4 ohm/km which is consider-ably more than that of cables. Reactive powerlosses generated in cables are normally insig-nificant.
The transformer reactance is calculatedas follows:
X = xk xU2
Sn (15)
where
Xk = z2k – r2
k (16)
X = transformer reactanceSn = rated power of transformerU = supply voltage (at which reactance
is calculated)zk = relative short-circuit impedanceXk = relative short-circuit reactancerk = relative short-circuit resistance
The relative short-circuit impedance (zk)of power transformers is 2- or even 3-timesthat of distribution fransformers.
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3. METHODS OF COMPENSATION
Fig. 5Parallel compensation reduces the voltagedrop.
Fig. 6Voltage may be raised to the desired level bymeans of a series capacitors.
2.4 Reactive PowerTransmission and Voltage Drop2.4.1 Parallel CompensationTransmission of active power produces volt-age drop across the resistances in a networkand reactive power transmission causes volt-age drop in the inductive reactances. Thetotal voltage drop can be calculated approxi-mately from the following formula:
dU = lp x R + lq x X (17)dU = voltage drop (phase voltage)R = network resistanceX = network reactance
This shows that the voltage drop in thesystem reactances can be decreased by re-ducing the reactive current component, typi-cally by using parallel or, as it is also called,shunt compensation (Fig. 5).
With transformers, the voltage drop causedby transmission of reactive power is relativelyhigh. This drop can be calculated from thefollowing formula:
ud = l (rk x cosϕ + xk x sinϕ) (18)ln
ud = relative voltage drop in thetransformer
cosϕ = power factor of loadln = rated current of transformerl = load current
2.4.2 Series CompensationAs previously stated, shunt compensationreduces the reactive component of the net-work current and, consequently, the voltagedrop. With series compensation, the line re-actance is decreased by connecting capaci-tors in series with the line. The expression(17) for line voltage drop is then modified asfollows:
dU = lp x R + lq x (Xl–Xc) (19)
dU = voltage drop in the lineXl = line reactanceXc = capacitor reactance
When Xc equals Xl, the network reactanceis zero (Xl–Xc = 0) and the voltage drop causedby reactive power transmission is thereforealso zero. By inclusion of a suitable seriescapacitor, Xc may be made greater than Xl, inwhich case the network reactance becomesnegative. Thus, series compensation can alsoreduce the voltage drop caused by activepower transmission (Fig. 6)
In addition, series capacitors provide thefollowing advantages compared with uncom-pensated HV transmission systems: higherpower transmission capability, better static anddynamic stability, fewer regulation requirementsand reduced losses through optimizing loadsharing in parallel lines. Series compensationis also a cost-saving alternative compared withbuilding new, parallel lines.
Table 2Factor K for calculating the necessary compensation power for a given active power
Given values before cosϕ desiredcompensationϕ sin tan cos 0.80 0.85 0.90 0.92 0.94 0.96 0.98 1.00
75.5 0.97 3.88 0.25 3.13 3.26 3.39 3.45 3.51 3.58 3.67 3.8872.5 0.95 3.18 0.30 2.42 2.56 2.70 2.76 2.82 2.89 2.98 3.1869.5 0.94 2.68 0.35 1.93 2.06 2.19 2.25 2.31 2.38 2.47 2.6866.4 0.92 2.29 0.40 1.54 1.67 1.81 1.87 1.93 2.00 2.09 2.2963.2 0.89 1.98 0.45 1.24 1.36 1.50 1.56 1.62 1.69 1.78 1.9960.0 0.87 1.73 0.50 0.98 1.11 1.25 1.31 1.37 1.44 1.53 1.7358.6 0.85 1.64 0.52 0.89 1.02 1.16 1.22 1.28 1.35 1.44 1.6457.3 0.84 1.56 0.54 0.81 0.94 1.08 1.14 1.20 1.27 1.36 1.5656.0 0.83 1.45 0.56 0.73 0.86 1.00 1.05 1.12 1.19 1.28 1.4854.7 0.82 1.41 0.58 0.66 0.79 0.92 0.98 1.04 1.11 1.20 1.4153.1 0.80 1.33 0.60 0.58 0.71 0.85 0.91 0.97 1.04 1.13 1.3351.8 0.79 1.27 0.62 0.52 0.65 0.78 0.84 0.90 0.97 1.06 1.2750.2 0.77 1.20 0.64 0.45 0.58 0.72 0.78 0.84 0.91 1.00 1.2048.7 0.75 1.14 0.66 0.39 0.52 0.56 0.71 0.78 0.85 0.94 1.1447.3 0.73 1.08 0.68 0.33 0.46 0.60 0.65 0.72 0.79 0.88 1.0845.6 0.71 1.02 0.70 0.27 0.40 0.54 0.60 0.66 0.73 0.82 1.0243.8 0.69 0.96 0.72 0.22 0.34 0.48 0.54 0.60 0.67 0.76 0.9742.3 0.67 0.91 0.74 0.16 0.28 0.43 0.48 0.55 0.62 0.71 0.9140.7 0.65 0.86 0.76 0.11 0.24 0.37 0.43 0.50 0.56 0.65 0.8638.7 0.63 0.80 0.78 0.05 0.18 0.32 0.38 0.44 0.51 0.60 0.8036.9 0.60 0.75 0.80 – 0.13 0.27 0.33 0.39 0.46 0.55 0.7535.0 0.57 0.70 0.82 0.08 0.22 0.27 0.33 0.40 0.49 0.7033.0 0.55 0.65 0.84 0.03 0.16 0.22 0.28 0.35 0.44 0.6530.5 0.51 0.59 0.86 0.11 0.17 0.23 0.30 0.39 0.5928.4 0.48 0.54 0.88 0.06 0.11 0.17 0.25 0.33 0.5425.6 0.43 0.48 0.90 0.06 0.12 0.19 0.28 0.4823.0 0.40 0.43 0.92 0.06 0.13 0.22 0.4319.8 0.34 0.36 0.94 0.07 0.16 0.36
Qc = K x P 0.75 0.62 0.48 0.43 0.36 0.29 0.20 0.00tanϕ desired
Example: What is the capacitor power rating needed to improve the power factor from 0.66 to0.98, if the active power requirement of the load is 750 kW?From the above table the cross-reading gives K = 0.94.The capacitor power rating should thus be 0.94 x 750 = 705 kvar. The nearest standard ratingis 700 kvar, which can be selected.
When selecting the method of compensationrequired one should consider the location ofthe capacitors, the economic aspects re-ferred to above such as tariffs, the param-eters of the network, transmission losses andvoltage drop, as well as the initial purchasecost and maintenance expenses of the equip-ment. In addition, there are factors such assystem harmonics and the ambient condi-tions which may limit the effective utilizationof capacitors.
Tables and nomograms are available toassist in calculating the capacitor rating re-quired. In table 2 the cross-reading of givenand desired values of cosϕ or tanϕ gives thefactor K, by which the active power P shall bemultiplied. This yields the capacitor rating tobe chosen.
There is no single method of compensa-tion to be recommended universally; variousmethods can be applicable in each case.
In the following three methods or parallelcompensation will be discussed: individual,group and central compensation.
3.1 Individual CompensationBy connecting the capacitors to the termi-nals of the compensated equipment, onecan best consider the influence of the ca-pacitors on the network dimensioning and onpower and voltage losses.
The reactive power demand of 3-phaseasynchronous motors varies between 0.5and 1 kvar per kilowatt of active power de-pending on the speed, size and load of themotors. Most of the reactive power neededcan be produced by capacitors installed inparallel with the motor. The capacitor can beconnected either to the terminals of the motoror of the starter (Fig. 7).
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Fig. 7 Principle of individual motor compensa-tion.
Fig. 8Connection of a capacitor for a motor with amechanical Y/D starter.
Fig. 9 Compensation of a group of motors. Themotor M3 is always on whenever the mo-tor group is running.
Fig. 10 Connection scheme comprising fixedcapacitors and automatically controlled ca-pacitor bank.
The necessary capacitor rating may be cal-culated from the formula:
Qc = P x (tanϕ1 – tanϕ2) (20)e
Qc = capacitor outputP = rated power of motore = efficiency of motorϕ1 = phase angle before PFCϕ2 = phase angle after PFC
A voltage rise caused by self-excitationcan occur particularly when the motor is quicklyre-connected immediately after switching off.It is therefore advisable to limit the compensa-tion power to:
Qc = 0.9 x l0 x U x 3 (21)l0 = no-load current of the motorU = supply voltage
Because of self-excitation, it is not recom-mended to use individual motor compensa-tion if the machine driven by the motor can inturn rotate it at overspeed (cranes, carriers,etc.) or if the brake magnet voltage is derivedfrom the poles of the motor.
Table 3. Reactive power requirement of various squirrel-cage motors at no-load... rated power andthe nearest standard capacitor rating, when the compensation power limitations have been takeninto account.
3000r/min 1500r/min 1000r/min 750r/min 600r/min 500r/minrated req. cap. req. cap. req. cap. req. cap. req. cap. req. cap.power kvar kvar kvar kvar kvar kvar kvar kvar kvar kvar kvar kvarkW7,5 3...5 2.5 4...5 2.5 6...7 5 6...7 5 7...8 5 7...8 511 5...7 2.5 6...8 5 7...10 5 9...10 8 9...12 8 10...12 815 7...9 5 7...10 5 9...11 8 9...13 8 13...16 10 15...17 12.522 8...13 5 13...14 10 12...16 10 12...17 10 20...28 15 22...26 1530 11...15 10 16...21 15 13...21 10 15...22 12.5 23...31 20 32...37 2037 13...19 10 17...25 15 16...25 12.5 20...28 15 25...34 20 43...47 3045 16...24 12.5 23...32 20 19...31 15 20...32 15 28...40 20 41...47 3055 17...29 15 26...38 20 23...37 20 26...39 20 35...48 30 50...52 4075 18...34 15 28...46 20 32...50 20 36...55 30 45...61 40 66...72 6090 21...42 15 32...55 20 43...61 30 42...64 30 60...80 50
110 24...50 20 38...67 30 48...75 40 63...83 50132 38...66 30 51...80 40 61...87 50160 41...79 30 54...92 40200 43...96 30 62...108 50
When dimensioning the capacitor cablenote that the fuses also protect the supplycable. Thus the capacitor cable shoud havethe same cross-section as that of the mainmotor cable.
Also when setting any overcurrent relay,notice that the compensation reduces thecurrent.
If the motor is equipped with an automaticstar-delta starter where the motor is switchedoff directly from the delta configuration, anormally connected capacitor may be usedfor power factor correction.
However, if a mechanical star-delta starteris used as in Fig. 8, capacitors that are specifi-cally designed for this purpose must be fitted.Single-phase capacitors are connected inparallel with each winding of the motor.
3.2 Group CompensationSometimes it is possible to correct the powerfactor of several loads by means of a commoncapacitor. This kind of group compensation isparticularly advantageous for discharge lampscontrolled by 3-phase contactors. Group com-pensation of motors is also feasible where themotors are small or running simultaneously.
When a capacitor is connected into thenetwork with a separate contactor, overvoltagedue to self-excitation cannot occur. Thus thecapacitor size can be chosen freely. Thecapacitor rating needed for cosϕ = 1 may becalculated from the following formula:
Q = P1 . tanϕ1
+ P2 . tanϕ2
+ ... (22)e1
e1
P1, P2... = rated power of the motorse1, e2... = efficiency of the motorsϕ1, ϕ2... = phase angles before PFC
Group compensation may often be advan-tageously applied when a standby motor isinstalled, thus avoiding duplication of capaci-tors.
3.3 Central Compensation atLow VoltageThough individual or group compensation maybe used, additional capacitors are often in-stalled at the main supply point to achieve asufficient degree of correction (cosϕ => 0.97).A proportion of the required compensationmay be supplied as fixed units and the re-mainder in automatically controlled capacitorbanks as shown in Fig. 10.
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Fig. 11 Schematic diagram of the example.
Capacitors that are permanently connectedto the system are continuously producing re-active power, even at periods of low load.Thus, any excess reactive power is trans-ferred into the main supply network.
Reactive power consumption of a distribu-tion transformer at no-load is 1...2 % and at fullload 4...7 % of its rated power (see table 4).
To avoid the disadvantages of overcom-pensation, the total power of the fixed capaci-tors should be limited to 10...15 % of thetransformer rating. A fuse switch or circuitbreaker is generally fitted, so that the capaci-tor may be switched off if required.
Table 4. Approximate reactive powerconsumpiton of various 50 Hz distributiontransformers (primary voltage 10...20 kV)
Power Reactive power consumptionrating kvarkVA no-load full load16 0.3 1.030 0.5 1.750 0.8 2.8100 1.5 5.5200 3 13315 4 20500 6 31800 9 401000 10 701250 11 961600 13 1092000 14 134
In an automatic capacitor bank, a powerfactor controller controls the switching of thecapacitor steps according to the varying re-active power requirements. Inductive and ca-pacitive operating limits for the power factorcontroller are set and the amount of reactivepower in the network is maintained withinthese limits. Problems of overcompensationtherefore do not arise.
The effects of central compensation on thedimensioning of a network and on the lossesare mainly related to the distribution trans-former and the connecting cable. The elec-tricity board system can therefore benefit fromlow voltage power factor correction, and this isusually taken into account when connectioncharges and annual tariffs are determined.
3.4 High Voltage CompensationCompensation may also be carried out on thehigh voltage side, in which case there are nocost savings related to the dimensioning andlosses of the distribution transformers. Be-cause of the high reactance of transformers,considerable voltage drops and reactive powerlosses are also incurred by reactive powertransmission. Thus, compared with LV com-pensation, more capacitors would be neededon the HV side of a transformer.
It is possible to compensate HV motorsindividually in the same way as with low volt-age. For this purpose enclosed capacitorbanks are manufactured, which can then, ifrequired, be installed adjacent to the motor.
Generally HV capacitor banks are used tocompensate for the reactive power consumedby long transmission lines and power trans-formers. Sometimes it is economical to com-pensate for part of the reactive power of alarge industrial plant by means of HV capaci-tor banks.
However, because of the relatively highcost of the connecting equipment (viz:circuitbreaker, protection, cables, busbar),the total cost per kvar may seem unreason-ably high if compared with straightforward HVcapacitor banks.
3.5 Technical Consequences ofCompensation3.5.1 Voltage RiseFixed capacitors can cause the voltage to risein an unloaded network. The rise in a trans-former on no-load may be calculated from thefollowing formula:
du (%) = Qc . Xk (%) Sn (23)
du = percentage voltage riseQc = rated power of capacitor bankSn = rated power of transformerxk = percentage short circuit reactance
of transformer
In practice voltage rises of 1...2 % areexperienced during no-load operation.
If, for example, the proportion of fixedcapacitors is 20 % of the rated power of thetransformer and xk = 6 %, the voltage of thetransformer rises 1.2 % during no-load opera-tion.
3.5.2 Influence of HarmonicsNon-linear loads, such as thyristor drives,converters and arc furnaces produce exces-sive harmonic currents causing both currentand voltage distortion. Capacitors offer a lowimpedance to any higher frequencies flowingthrough them, but they also may amplify theeffect of harmonic currents flowing into otherparts of the network.
The effect of harmonics on the phasevoltage of a capacitor bank can be calculatedfrom the following formula:
Up = ∑ lcn
n . 2 . π . f1 . C (24)
Up = phase voltage of capacitor bankn = order of harmonic (the harmonic
frequency fn = n . basic frequency)lcn = ‘n’th harmonic current flowing
into capacitor bankf1 = basic frequency (e.g. 50 Hz)C = capacitance of bank per phase
In other words, the voltage component ofeach harmonic is summed arithmetically atthe basic frequency voltage. When designinga compensation scheme, the harmonics flow-ing into the bank must be calculated on thebasis of the harmonic current imposed by theload. The harmonics in an existing capacitorbank can be measured by a harmonic ana-lyser.
The harmonics flowing into the capacitorbank can in some circumstances be veryhigh. The worst situation arises when the ca-pacitors and the network inductance form aparallel or series resonant circuit under thefollowing conditions:
n = Xc =
Sk
Xl Qc (25)
Xc = capacitive reactance of bank atbasic frequency
Xl = inductive short circuit reactanceof network at basic frequency
Qc = reactive power of capacitor bankSk = short circuit power of network
Connecting a harmonic source and ca-pacitors to the same busbar could create aparallel resonant circuit. Similarly a capacitorbank connected to the LV side of a tranformercan form a series resonant circuit with thetransformer for harmonics originating on theHV side. When carrying out reactive powercompensation, one should avoid the danger
of resonance at any of the common orders ofharmonics (viz: 3rd, 5th, 7th, 11th and 13th).
The capacitor rating which could causeresonance if connected to the network, canbe calculated for each harmonic as follows:
Qc = Sk
n2
(26)
For example, if the short-circuit power ofthe busbar is 15 MVA the equation (26) yields
for n=3: Qc = 15 Mvar = 1.7 Mvar 3
2
for n=5: Qc = 15 Mvar = 0.6 Mvar 5
2
for n=7: Qc = 15 Mvar = 0.3 Mvar 7
2
Example
For higher harmonics the possibility ofresonance is generally slight but it must betaken into account if the harmonic content isvery high.
The rated current of the thyristor drivesystem shown in Fig. 11 is calculated by usinga power factor of 0.7, a diversity factor of 0.8and motor efficiency of 95 % as follows:
l = P = 0.8 . 3 . 1000003 . U . e . cosϕ 3 . 380 . 0.95 . 0.7
= 550 A
The harmonics caused by thyristor drivesare usually generated by 6-pulse rectifiers inthe following percentages of rated current:
5th harmonic (30 %):l5 = 0.3 . 550 A = 165 A
7th harmonic (12 %):l7 = 0.12 . 550 A = 66 A
11th harmonic (6 %):l11 = 0.06 . 550 A = 33 A
13th harmonic (5 %):l13 = 0.05 . 550 A = 28 A
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Fig. 12Low voltage capacitor units
4.1 Low Voltage Capacitors4.1.1 Low Voltage Capacitor UnitsA low voltage capacitor unit is built up ofseveral elements connected in parallel. Anelement consists in principle of two electro-des and dielectric. The elements are made ofmetallized plastic film and inserted into aplastic cover.
Unlike capacitors made of aluminium foilor metallized paper, metallized-film capaci-tors are generally dry without impregnationliguid.
The elements of metallized-film capaci-tors are self-healing. After a disruptivedischarge, a thin metallized layer will vapori-ze off from the surface around the breakdownpoint, and no permanent short-circuit will beleft there. Elements are internally protected toensure a reliable disconnecting at the end ofthe lifecycle.
Elements are set into a steel containerand connected to the terminals of the capaci-tor by means of copper busbars and cables.
Capacitor losses are very low, less than0.5 watt per kvar.
Most low voltage capacitors are equip-ped with external discharge resistors so as todecrease the residual voltage of the capaci-tor from an initial value of √2 times the ratedvoltage Un to below the level of ≤ 50 V within1 minute.
Low voltage capacitors are normally three-phase with three bushings on the cover andstar or delta connected internally.
Among the unit sizes available for themost common voltage range 400...690 V are2.5, 5, 7.5, 10, 12.5, 15, 20, 25, 30, 40, 50, 60,75, 90 and 100 kvar, and the capacitancetolerance is -5...+10 %.
3.5.3 Ambient ConditionsUnfavourable conditions will shorten the life ofa capacitor and thus incur extra repair andmaintenance costs.
The temperature categories accordingto the new IEC standards for power capaci-tors cover the temperature range of -50 °C to+55 °C. For example, the highest permissiblemean ambient temperature according to cate-gory A is +40 °C for a short period but only+30 °C for 24 h and +20 °C for 1 year. Highertemperatures accelerate ageing of the die-lectric, thus shortening the life of the capaci-tor. Power factor controllers for automaticallycontrolled capacitor banks are usually madefor an ambient temperature range of 0 °C to+50 °C.
In high humidity conditions outdoor typecapacitor units should be used since they aresuitably protected against corrosion.
4. COMPENSATION EQUIPMENT
The capacitance and reactance (at powerfrequency) of a 200 kvar capacitor bank are
C = Qc = 200000 = 3.98 . 10-3 F
2 . π . f . U2 314 . 4002
Xc = 1 = U2 4002
= 0.8 Ω 2 . π . f . C Qc 200000
If the network impedance is simplified,consisting of only inductive reactance, it canbe expressed as
Xk =U2 = 4002
= 0.01067 Ω Sk 15 . 106
At ’n’th harmonic frequency the reactancesof the capacitor bank and network are
Xcn = Xc (27) n
Xkn = n . Xk (28)
Xcn = capacitive reactance of the bankat ’n’th harmonic frequency
Xc = capacitive reactive of the bankat basic frequency
Xkn = inductive reactance of thenetwork at ’n’th harmonic
Xk = inductive reactance of thenetwork at basic frequency
The harmonic currents flowing into thebank (lcn) and into the network (lkn) are calcu-lated simply by using the current division rulewhen the currents of the harmonic source (ln)are known:
lcn = ( Xkn ) . ln Xkn – Xcn (29)
lkn = ( Xcn ) . ln Xkn – Xcn (30)
For the 5th harmonic the following har-monic currents are produced:
Xk5 = 5 . 0.01067 = 0.0533Xc5 = 0.8/5 = 0.16l5 = 165 A
lk5 = ( 0.16 ) . 165 A = 248 A 0.0533 – 0.16
lc5 = ( 0.0533 ) . 165 A = 82 A 0.0533 – 0.16
The harmonic voltages across the capaci-tor bank are
Un = lcn . Xcn (=lkn . Xkn) (31)
For n = 5: U5 = 82 A . 0.16 Ω = 13 V
The total voltage stress is:
U = 400V + 3 . U5 + 3 . U7 + 3 . U11+ 3 . U13
Excess current caused by harmonics in acapacitor bank is calculated in terms of theeffective value of the current:
lc = lc12 + ...lcn
2 (32)lc = total current in capacitor banklc1 = current in capacitor bank at
basic frequency (50 Hz)
lc1 = Qc =
200 A = 289 A
3 . U 3 . 0.4
Table 5. Current and voltage values due to theexample. The corresponding values are alsogiven for other capacitor ratings.
Cap. lc1 lc5 lc7 lc11 lc13 lckvar A A A A A A100 144 33 32 137 250 323200 289 82 124 87 50 340400 577 330 281 48 36 724Cap. lk5 lk7 lk11 lk13
kvar A A A A100 198 98 171 221200 248 190 54 22400 495 215 15 8Cap. U1 U5 U7 U11 U13 Ukvar V V V V V V100 400 11 7 20 31 519200 400 13 14 6 3 462400 400 26 16 2 1 478
lc = 2892+822+1242+872+502 A=340 A
Table 5 shows, at all the chosen ratings,that the capacitors will operate at a consider-
able overvoltage. Note that a 100 kvar bankwould be nearly in resonance at the 13th har-monic. The effective value of current in almost2.5 times the rated value. The capacitorscould not withstand this degree of extra stress.
When the rating of capacitors in a systemincreases in proportion to the load, the dangerof resonance is shifted toward the lower fre-quencies which generally have higher har-monic currents.
It is also noteworthy that the currents flow-ing into the network are considerably highercompared with those generated by the thyristordrives. However, in practice the above as-sumption that the impedance would be purelyinductive is not valid. At higher frequenciesharmonics are damped by the network resist-ance and resonances are not as likely as inthis example.
The problems arising with harmonics aresolved by using a harmonic filter as describedlater.
The temperature rise of capacitors causedby any increase in losses is not generally aproblem with modern low loss metallizedfilmunits. However, capacitors with paper dielec-tric used to overheat rapidly with excessiveharmonics in the network.
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Fig. 13Cubicle type automatic capacitor bank
Fig. 14Power factor controllers
Fig. 15Automatic capacitor bank withblocking reactors
Fig. 16Schematic diagram of an automatically controlledcapacitor bank with power factor controller
Fig. 17One-phase high voltage capacitor units
4.2 High Voltage Capacitors4.2.1 High Voltage Capacitor UnitsOne-phase high voltage capacitor units areequipped with two bushings or one bushingwith live case. Three-phase units are inter-nally either delta or star connected.
A capacitor unit consists of parallel andseries connected elements. Series couplingis needed to keep the element voltage at asuitable level (about 2000 V).
The elements of modern HV capacitorsare made of aluminium foil, separated by twoor more layers of polypropylene film dielec-tric. Units with paper or mixed dielectric,commonly used before, have higher losses.
4.1.2 Fixed Low Voltage CapacitorBanksFixed capacitor banks consist of parallel con-nected units installed in a rack. The bank isfitted with a cable connection box. The ca-pacitance tolerance of a bank is –0...+10 %.
Due to the large inrush current of a fixedbank, slow acting fuses dimensioned for 1.7times the rated current must be used. Ac-cording to general standards, the connectioncable must be able to carry a continuous loadof 1.43 times rated current.
4.1.3 Automatically Controlled LowVoltage Capacitor Banks
Automatically controlled capacitor banksare equipped with fuses and contactors con-trolled by a power factor controller, on whicha desired target value of power factor (cosϕ)and inductive and capacitive operating limitscan be set.
The level of reactive power is monitored bymeans of current transformers and the powerfactor controller switches capacitors on andoff according to demand.
A single step may comprise either one orseveral capacitor units; in the latter case thesecond 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 operatingtime of the contactor is introduced and theoverall inrush current is thus reduced.
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 ofsteps with respect to the first can be any of thefollowing:
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 standardbanks with steps of, say, 50 kvar. With smallerbanks, units of 25...30 kvar may be used forthe first steps and with the smallest, units ofeven smaller power rating. Such arrange-ments are obviously more expensive per kvarthan those comprising larger units.
Very large banks are usually divided intosmaller subgroups, each with an individualconnection cable and main fuses but with acommon power factor controller.
The main fuses should be slow acting anddimensioned for 1.38 times rated current.
The capacitor elements are inserted into asteel container. The unit is then filled with asuitable, environmentally safe impregnationoil, and the containers are hermetically closed.
HV units equipped with internal elementfuses are manufactured up to 9000 V of ratedvoltage. Internal discharge resistors decreasethe residual voltage from √2 x rated value tobelow 75 V within 10 minutes, according toIEC standards.
The most common unit sizes are 50, 100,167, 200, 250, 300 and 333 kvar and thecapacitance tolerance is –5...+10 %. The unitsare manufactured for the voltage range 1...22kV, and the most common unit voltages are3300, 4000, 4500, 6350, 6600, 7600 and8000 V.
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Fig. 18 Internally Externallyfused unit fused unit
Fig. 19Schematic diagram of an HV capacitor bankconnected in star with unbalance protection.
Fig. 20Schematic diagram of an HV capacitor bankconnected in double star with overload, short-circuit and unbalance protection.
Fig. 21Typical filter construction.
4.2.2 High Voltage Capacitor BanksHigh voltage capacitor banks are used atsubstations and in industry, on long transmis-sion lines, and at points in HV networks suit-able for maintaining reactive power balance.
High voltage capacitor banks are usuallybuilt up of single-phase HV units, the requirednumber in series depending on the voltageand the number in parallel, on the power.
In order to divide the voltage evenly, anequal number of units are connected in paral-lel in each series group. Series groups areseparated from each other by support insula-tors mounted between the racks. Capacitorbanks attached to a busbar are equipped witha breaker. If necessary, current limiting reac-tors can be supplied to reduce the inrushcurrent to a value suitable for the breaker.
The main purpose of shunt capacitor banksis to produce reactive power near enough topoint of consumption in order to reduce losses,cut the price of reactive power, increase thevoltage, and improve the power transmissioncapacity of the line section.
4.3 Protection of CapacitorBanks
In electricity networks the purpose of allprotection is to protect the equipment againstovercurrents and overvoltages and to mini-mize the effect of these, considering the eco-nomical and technical restrictions and safetyregulations.
Internal protection of a bank compriseseither internal or external fuses and unbalanceprotection, whereas externally the bank isprotected against overload, overvoltage andshort-circuit.
4.3.1 Internal and External FusesThere are two types of fuses used for capaci-tors, internal or external. When the reactivepower of a capacitor unit was only a few kvar,the most natural method to protect the capaci-tor was with an external fuse, since in the caseof a breakdown the lost reactive power wassmall. However, now that one capacitor ele-ment has a capacity of about the same valueas a unit had previously it is reasonable toprotect each separate element with an inter-nal fuse.
If the capacitor unit is protected with inter-nal fuses the lost reactive power in the case ofa blown fuse is very low (approximately 2 % ofa unit). Because of the low percentage powerloss there is no need to replace the entirecapacitor unit, hence preserving continuity ofoperation and saving replacement costs.
If the unit is protected with an external fusethe whole unit is lost and it is nearly alwaysnecessary to replace the faulty unit immedi-ately. It is, therefore, obvious that by using
internally fused units the need for spare unitsis much lower than by using external fuses.
4.3.2 Unbalance ProtectionHV banks are usually wired in either single ordouble star. If the impedance of one phasechanges with respect to the other two phases,the star point of the bank shifts. This occurswhen element fuses in a capacitor are blownas a result of a disruptive discharge.
At the same time the voltage division withinthe bank is also changed. Hence, the bankmust be switched off before the operation ofthe fuses would cause a voltage rise consid-erably above the permitted 10 % overvoltage.
Double pole insulated voltage transform-ers are used for unbalance protection of sin-gle star connected banks. The transformerprimaries are connected in parallel with thephase banks and the secondaries form anopen delta. The unbalance voltage gener-ated in the open delta operates the breakerthrough a voltage relay.
Where there is a sufficient number of par-allel connected units, it is advisable to con-nect the bank in double star. Unbalance pro-tection is then carried out by a current trans-former connected between the two star points,and an overcurrent relay (Fig. 20). The timesettings are 5 s for alarm and 0.1 s for tripping.
By using internal fuses, a reliableunbalance protection can be performed, pro-tecting the banks against any major damagesduring a fault operation of the network or thebanks.
4.3.3 Overcurrent and overvoltageprotectionOverload and short-circuit protection of an HVbank is normally carried out by means ofcurrent transformers and a two-step overcur-rent relay.
The capacitor bank is characteristicallyself-protective against switching and light-ning overvoltages because of its low imped-ance at high frequencies.
Overvoltage protection is therefore usu-ally included in the protection of other equip-ment. If separate overvoltage protection isrequired, the discharge capacity of the pro-tective device is of great significance. Some-times a tripping overvoltage protection isneeded at power frequency during low-loadperiods.
4.4 Harmonic FiltersHarmonic filters provide another source ofcompensation. In a filter, a reactor is con-nected in series with a capacitor bank. With asuitable reactor inductance, the series circuitof capacitor and reactor forms a low imped-ance at a desired harmonic frequency. Thus,the major part of the harmonic current flowsinto the filter and not into the network.
At the same time the filter provides capaci-tive reactive power at the base frequency.
Among the problems caused by harmon-ics are interference to telecommunications,disturbances to the control and protectionsystem of the network, malfunctioning of re-lays and dangerous overvoltages due to reso-nance. The extra losses that occur in cables,transformers, motors and generators are alsoof significance: they cause loss of energy andexcess temperature rise in the equipment.The most frequently encountered and poten-tially harmful harmonics are the 5th and 7th,which are generated by 6-pulse rectifiers.
Harmonic filters can be connected to ei-ther LV or HV circuits. Where there are severalharmonic generating loads, each fed by adistribution transformer, it is often more eco-nomical to eliminate the harmonics by install-ing filters centrally at the HV busbar, ratherthan to have separate filter on the LV side ofeach transformer.
A typical filter construction is shown in Fig.21. The lower harmonics (5th and 7th) haveindividual circuits and the higher harmonics(11th, 13th) a common high-pass filter.
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4.5 Fast Static CompensatorsIn some cases, for example arc furnaces andwelding machines, there are very rapid fluctu-ations in reactive power within a short period– i.e. a few cycles. Traditional methods of re-active power control are not suitable sincethey are too slow for such variations.
The fast static compensator has been de-veloped to deal with this problem.
The Nokian Fast Static Compensator con-sist of a fixed shunt capacitor bank, normallytuned as a filter, and a thyristor-controlledshunt reactor. By controlling the reactor cur-rent, the total reactive power supplied by thef.s.c. into the network is correspondingly ad-justed.
Thus the harmonics generated both bythe load and the thyristors are eliminated.Hence the disadvantages of fluctuations inreactive power and the harmonics are bothminimized.
5. SUMMARY
Fig. 22Equivalent circuit of the harmonic filter and thenetwork in accordance with Fig. 21.
Fig. 23Impedance curves of the harmonic filter andother network in accordance with figures 21and 22.
Fig. 24Fast static compensator for arc furnaces.
The most economical way of producing reac-tive power required by most electrical devicesis by the use of capacitors.
Capacitors reduce network losses andvoltage drop, and the transmission of reactivepower is avoided. This means considerableannual savings.
The circuit in Fig. 22 can be simplified further-more, consisting of parallel coupled networkimpedance Znw and filter impedance Zf. Theimpedance vary according to frequency asshown in Fig. 23 (absolute values). The cur-rents drawn consequently depend on them,and can be expressed as follows:
ln = Zf . ln (33 a)
Znw + Zf
lf = Znw . ln (33 b)
Znw + Zf
Static compensators are also used to re-duce voltage variations caused by powerchanges in transmission lines.
4.6 Thyristor ControlledCapacitorsThyristor controlled capacitors, which are moresimple in construction than the fast staticcompensators described above, are verysuitable for fast reactive power compensa-tion. The capacitor is equipped with a thyristorswitch, which replaces the traditional contac-tor. Regulator operations are combined withthe automatic thyristor controls. This equip-ment can rapidly compensate for fast reactivepower fluctuations in welding machines andthe consequent voltage variations.
By series capacitor bank, voltage may beraised to a desired level. Parallel capacitorbanks can be used for individual, group orcentral compensation.
The influence of possible harmonic com-ponents must be taken into account whendesigning the system.
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Harmonic Filters For High Voltage
Detuned Filters
High Voltage Capacitor Banks
Prin
ted
in F
inla
nd b
y H
erm
es T
amp
ere
2002
EN-TH01-11/2002
In line with our policy of on-going product development we reserve the right toalter specifications
Kaapelikatu 3, P.O. Box 4, FIN-33331 Tampere, FinlandTelephone +358 3 388 311, Telefax +358 3 3883 360
www.nokiancapacitors.com
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