Electrical Power System Calculations Chap 11 a4

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APTE R

CHAPTER 11

METERING AND LOAD  MANAGEMENT  11.1 Introduction to metering The SUPPLY AUTHORITY is the source of electrical energy, which is the main commodity which is being sold to a customer i.e. kWh. However, a related but unintended unintended component of electricity supply is DEMAND usually usually measured in kVA. This component is related to WHEN and at what what RATE energy is supplied. For measuring the energy, the calculation is as given in chapter 6, i.e. -3

Energy = kWh = V x I x cos φ x time x 10

The traditional method of measurement measurement is an electromechanical electromechanical meter with a rotating disc, which drives a cyclometer to give the reading of kWh. See fig 1.

Figure 11.1: Single phase electromechanical meter

This type of meter uses the interaction of magnetic flux from the voltage to interact with the magnetic flux from the current, to drive a disc. The disc’s rotation is directly proportional to the power being drawn, drawn, and by using a cyclometer attached to the shaft, the total number of revolutions are summed together to finally give a reading of  energy used. This is proportional to the calculated energy energy and with correct gearing to the cyclometer, the reading will be the actual value invoiced to a customer. As electrical supply to customers is predominantly three phase, the above meter is made into a three phase meter by using three sets of electromagnets one each coupled to the three phases (voltage and current). For larger consumers, supplied at higher voltages and currents, it is not possible to measure the voltage and current directly, so interposing Current Transformers (CTs) and Voltage Transformers (VTs) are used to supply suitable currents and voltages voltages for measurement. The reading must then be modified modified with a CT and VT factor to get the correct amount of energy used,e.g. Actual energy = meter reading x CT ratio x VT ratio. Specially ordered meters can have the constant built in for specific CT and VT ratios! The cyclo reading then becomes actual with no multiplying constant.

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Figure 11.2: Cyclometer register of kWh

Figure 11.3: Direct reading meter

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Energy metering is well defined with no major problems of interpretation and no problems in building suitable metering equipment. Modern high accuracy metering is now electronic with commercial metering accuracies to 0.2% for the meter. The demand measurement is defined as being a tariff cost element to cover the usage of part of the electrical system to supply power at the highest rate required by a consumer. As the power system must be able to supply all the consumers’ summated demand at any time, the installed generation, transformers and lines / cables have to be suitably rated so as not to sustain thermal damage. Thus a demand charge is linked to the thermal response of  the system. The time necessary to heat the equipment in the supply chain has been taken as 30 minutes. Thus kVA demand charges are for the highest average VOLTS x AMPS for a half hour period. There are some tariffs which use 60 minutes, but these are being phased out! The early metering systems used a thermal measuring device with a 15 minute response time for a 90% value of  the average kVA and 100% measurement after 30 minutes. These type of meters did the measurement in a similar way to effect of heating on the primary electrical distribution system! A disadvantage is that the measured value was not highly accurate (+/- 5%) and would record a maximum when it actually occurred and not necessarily when the electrical system was at it’s maximum load. This is relatively unfair to some consumers!

Figure 11.4: Thermal element

Another method of electro mechanical measurement was the use of a standard watthour meter, with the voltage deliberately shifted by a pre-settable angle, close to the angle associated with the load’s power factor (PF) at maximum load. A pointer was driven by the disc to display the demand, but every half hour the driving pointer is reset, leaving a second “friction” pointer at the highest point reached.

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Figure 11.5: Thermal element basic response

Figure 11.6: Thermal element varying load response

Various other electro mechanical methods were used, such as pulsing systems of kWh and kVARh which registered maximum kVA for a half hour period. (Landis and Gyr tri-vector systems). The half hour reset pulses are known as BLOCK INTERVAL MET ERING.

Figure 11.7: Block interval meter

These older methods of measurement have been superceded with electronic meters which have better accuracy.

Figure 11.8: Block interval response to varying loads

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However, whereas kWh is well defined, there are many controversial problems with kVA demand measurement, e.g. a) If the maximum demand recorded is not at system maximum demand, should billing be done on the value measured. Time of use tariffs try to remedy this problem. b) If a pulse load of 100% only occurs for half an hour, when it starts as the block interval starts, 100% is measured, while if the load starts fifteen minutes later, half of the pulse load occurring in one block interval and the other half in the next block interval, only 50% is recorded. (A one minute “moving interval” measurement of  30 minutes would overcome this problem). c) For single phase traction where a train moves through sections using different phase for one half hour each, each phase is effective loaded to three times the “average” three phase kVA demand!

10.2

Metering Accuracy

As stated above metering of kWh for tariff purposes can be as accurate as 0.2%, while kVA metering is less accurate at closer to 1% or possible 0.5% with electronic meters. However, this will be quoted as an accuracy class, and there are defined variations with the percentage load ( up to 125%) , such as 0.5% shown below. There additional limits related to PF of the load. Domestic consumers are metered with 2% meters to reduce cost of metering installation!

Figure 11.9: Metering error limits for 0.5%

With larger consumers, the use of CTs and VTs al so affect accuracy, as each has it’ s own limits of accuracy. With Class 0.2 metering, CTS and VTs of the same class error are used, i.e. 0.2%. As the voltage is normally near 1 00%, VTs only work over a small range, but CTs can have load vari ations from 0% to 125%. Allowable VT and CT metering errors are given below.

Figure 11.10: VT and CT error limits

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The effective total must allow for the individual errors, but these are not directly summated, but are the square root of the sum of the squares, i.e. Total error = ©  (meter error + CT error + VT error ) 2 2 2 = ©  (0.2 + 0.2 + 0.2 ) = 0.346% at 100% load 2

2

2

Note that a CT class 0.2 actually has an allowed error of 0.35% in the range where the load normally occurs, thus Total error = ©  (meter error2 + CT error2 + VT error2) = ©  (0.22 + 0.352 + 0.22) = 0.45% for 20 – 80% load For the consumer, an advantage is that a CT with burden tends towards a negative error, thus th e errors would be to the benefit of the consumer

10.3 Metering Tariffs Metering tariffs are designed to enable the electricity supply authority to recover the costs of energy supplied and the capital cost of equipment installed to make the supply available. A typical Eskom tariff table for Mega Flex is attached. Again, the costs for energy and the billing of such is relatively easy and well defined. The costs related to the demand side are less well defined and have technical variations on how the measurement should be done. Thus the supply authority has to apply an equitable and r easonable cost method of measurement to obtain a montly value used for billing purposes. From previously simple methods of billing, t ariffs have been varied such as to “manipulate” an end result of  electricity usage. This is defined as Demand Side Management, where Eskom on their Mega Flex tariff, charge up to 4x for energy used in winter compared to energy used in summer. .

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This “manipulation” of tariffs has already persuaded Furnace operators to do maintenance of plant in winter and produce extra product in summer! The demand of most consumers varies on a daily basis and also on a weekly basis. The usual pattern is similar for industrial consumers, with a different pattern for domestic consumers, who create the typical peak demand at 6 to 9 pm because of cooking, bathing and home heating after work hours. Industry creates peaks on start up of equipment at the start of the work day.

Figure 11.12: Tariffs - Megaflex

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Top – electrical geyser, Middle – commercial area, Bottom – industrial area Figure 11.13: Load patterns

The charges based on demand, attempt to change these load patterns by penalizing high demand values, and thus attempting to encourage consumers to flatten these demand patterns on an individual basis, such that the total load pattern is also flattened. This is particularly true for consumers on the Time of Use Tariff. (see Eskoms tariff tables). To cover the commitment of making power available to a comsumer, the supply authority has certain fixed or minimum charges. For Eskom’s Mega flex these are:1) 2)

Service charge in R/Account/day Administration charge in R /POD/day

And there are government imposed levies based on energy usage, i.e. 3) Electrification and rural subsidy of 3.09c / kWh 4) Environmental levy of 2.00c / kWh And finally the demand costs of  5) Transmission network charge of R3.67 / kVA / month 6) Network access charge of R7.32 /kVA / month (but max of past 12 months) 7) Network demand charge of R13.88 / kVA / month The actual R--.-- values for energy and demand vary with the defined options / geographical area..

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10.4 Load Factor The load profiles shown above, show that the consumer does not have a constant load. A measurement of this non constant load is the load factor, calculated from: Load Factor (LF) = actual energy used (kWh) in a a particular period (week or month) Max demand in kVA x No of hours in the period x average PF Thus kWh / kWh gives a per unit value (P.U.) as a measure of how effectively a system is being used to it’s maximum. For South Africa, with mining and furnace loads, the overall is high at 0.72. Industries such as Alusaf have LF of  probably 0.95, while that for a domestic consumer could be as low as 0.2! Thus consumers are encouraged through the Demand Charge to improve their load factor, i.e. reduce their peak  demand compared to their average demand without actually increasing energy (kWh) used. With a typical load factor of 60% (0.6 PU), the spread of the total cost can be assessed, e.g. take a load (max demand) near 30 MVA , Fig 11.14 gives 2009 costs:

Figure 11.14: Typical costs

10.5 Load Management For most consumers, it is not possible to reduce energy in kWh used. However, there is wastage of energy, which can be looked at, such as unnecessary heat loss (geysers), low efficiency lighting, lighting on with no personnel in the area,

Chapter 11 Page 11 of 14 low efficiency motors, low efficiency transformers, etc. Unnecessary wastage needs to be eliminated both from a cost and environment point of view. The load factor given above can be improved by moving some loads to times when the consumed load is lower than average, thus reducing maximum demand (kVA). The ability to move loads is often very limited, but must be assessed by operational personnel to allow a power management system to be set up. In terms of the total invoice of costs, the above example shows that energy is 80% of the total, while demand related costs are only 20%. In winter the ratio is worse a the increase in kWh costs push Energy to 86% of the total cost! A management system can predict that the present load will cause the maximum demand to be exceeded if the load remains the same. From the definition of block interval metering (still used by Eskom), the beginning and end of each block interval must be signaled from the supply authority, so that the load management system is in time synchronism with the supply authorities metering system! If not in synchronism, the management system will not apply the correct control! Once a new maximum demand is registered, it will be applicable for the rest of the month, unless a further increase occurs. For example, if power factor (explained in next section) correction is lost for even one half hour period, an unnecessary maximum demand could be incurred with it’s additional costs. Control / management of maximum demand is important to minimize monthly bills. If LF can be increased from 60% t0 70%, approximately 15% of the DEMAND related costs can be saved, e.g. for January, 15% of approximately R 600 000-00 would be R 90 000-00. This represents 2.9% of the total invoice.

10.6 Reactive Power In the circuit shown in Fig 11.15, let the instantaneous values of voltage and current be e = ©  2 x E sin(ωt + φ) i = ©  2 x I sin(ωt) The instantaneous power P = ei = (©  2 x E sin(ωt + φ) x (©  2 x I sin(ωt)) = EI cos - EI cos (2ωt + φ)

As Also

- EI cos (2ωt + φ) = -EI (cos 2ωt x cos φ - sin 2ωt x sin φ )

Thus

p = ei = (EI cos φ- EI cos 2ωt cos φ) + (EI sin 2ωt x sin φ) = (instantaneous real power) + (instantaneous reactive power)

Figure 11.15 Voltage source and load

The mean power = EI cos φ, where E and I are RMS values

Chapter 11 Page 12 of 14 The mean value of EI sin 2ωt x sin φ = 0, but the maximum value = EI sin φ. The voltage source is supplying energy to the load in one direction only. At the same time an interchange of energy is taking place between the source and the load of average value zero, but of peak value EI sin φ.. This later value is known as REACTIVE POWER Q and the measurement unit is the Var  (volt amps reactive).The interchange of energy between the source and inductive and capacitive elements (i.e. magnetic and electric fields) takes place at twice the system frequency. Therefore it is possible to think of a power component P (watts) of magnitude EI cos φ and a reactive power component Q Vars equal to EI sin φ, where φ is the power factor angle, i.e. the angle between E and I. It must be emphasized the P and Q are physically quite different. The quantity S (volt amps, known as the complex power, is found by multiplying E by the conjugate I. For the case where I lags E and assuming S = EI*. Referring to Fig 11.16;  j 1 -j 2 –( 1 - 2) S = E e φ x I e φ = EI e φ φ = EI e –φ = P - jQ Next assume *

S = EI  j( 1 = EI e φ = P + jQ

φ2)

Obviously both methods give the correct magnitudes of P and Q but the sign of Q is different. The method is arbitrarily decided and the convention recommended is:The volt-amps reactive absorbed by an inductive load shall be considered positive, and by a capacitive load negative; hence S = EI*. This convention is recommended by the IEC.

Figure 11.16 Voltage source and load

Using complex numbers, let E = a + jB, and I = c + jd, thus I* = c - jd So

*

S = EI = (a + jb) x (c + jd) = (ac – bd) + j(bc + ad) = P + jQ

This vector notation is used more easily in the following section. The main result from above is that inductive loads have POSITIVE kVArs.

10.7 Power factor Correction For most loads, the power factor is not unity and because of motors being a high percentage of load, the load has a lagging PF , i.e. inductive typically 0.9. As shown in chapter 6, using shunt capacitors (capacitors in parallel with the load), the load can be corrected to unity. However, if capacitance is added in equivalent step changes, it will be noted that each new step has less effect on improving the PF. This creates the effect of diminishing returns, so that it is usual only to correct to about 0.98 PF.

Chapter 11 Page 13 of 14 The actual amount of correction can be calculated to find the value at which the payback period becomes too long. The accepted IEC standard is that for the lagging current of an inductive load, the associated inductive Vars are positive, i.e.positive inductive Vars are shown in the FIRST quadrant of a Cartesian diagram. To obtain a positive value of Vars, it is necessary mathematically to use the complex conjugate of the inductive current, multiplied by the voltage vector. Where voltage of say 230v is used as the reference with no angle, then V = 230 + j 0.0 For say 10 amps of current at PF = 0.9, then The associated VA = Vx I*

I = 9.0 + j 4.36 (see below)

= (230 +j0.0) x (9.0 – j 4.36) = 2070 – j 1002.8 = 2300 «  25.84 deg

The Var inductive component = 1002.8 and the watts = 2070

Figure 11.17 Positive inductive VArs

For the example above for costs, Fig 11.14, the power factor is not given. Thus assume that it is 0.9 at peak kVA of  30,000 kVA. Now PF = 0.9 would be a lagging angle of 25.84 deg. And kVAr = kVA x sin 25.84 = 30000 x 0.436 = 13070 for correction to unity, full compensation. However for correction to PF = 0.98, the kW must be the same at 0.9 x 30 000 = 27 000 kW and S = kW / PF = 27000 / 0.98 = 27551 VA Since PF now = 0.98, the angle has reduced to 11.45 deg. So Q = S sin 11.45 = 27551 x 0.985 = 5469 kVAr Thus required kVArs to get to 0.98 PF = 13070 – 5469 = 7601 kVArs Note that this is almost half that necessary for full correction to PF = 1, i.e. 13070 kVArs. The capital outlay for the smaller bank will be about half that for the larger bank! An assumed cost for a R 1.5 M for an 11kV 13 MVAr bank and R 0.75M for a 7.6 MVAr bank, the simple pay back  periods are related to a reduction of demand costs. For the 13 MVAr bank, PF changes from 0.9 to 1.0 and demand costs reduce by 10% or R 600000 x 0.1 = R 60000-00 per month. The payback period (without interest) is Payback in months = R 1500000/ R 60000 = 25 months. For the 7.6 MVAr bank, PF changes from 0.9 to 0.98 and demand costs reduce by 8% or R 600000 x 0.08 = R 48000-00 per month.

Chapter 11 Page 14 of 14 The payback period (without interest) is Payback in months = R 750000/ R 48000 = 15.6 months. These are reasonable assumptions, but actual payback periods must be calculated with present day cost and interest repayments on capital loaned, plus the possibility that the contractual agreement may limit the reduction in demand costs by clauses such as Notified Maximum demand.

Figure 11.18 Effect of correction to PF = 0.98 from PF = 0.9