electric distribution load characteristics & diversity factor

8/13/2019 Electric Distribution Load Characteristics & Diversity Factor

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CHAPTER 24CHARACTERISTICS OF DISTRIBUTION LOADS

Author:H. L. Willis

A T&D system exists to deliver power to electricconsumers in response to their demand for electric energy.This demand for electricity, in the form of appliances, lightingdevices, and equipment that use electric power, creates electricload, the electrical burden that the T&D system must satisfy.In a de-regulated power industry, quality of service - basicallyquality in meeting the customers needs - is paramount.Quality begins with a detailed understanding of the customersdemand requirements, and includes the design of a system tomeet those needs. This chapter discusses electric load andpresents several important elements of its behavior that bear onT&D system engineering aimed at satisfying thoserequirements as economically as possible.

I. ELECTRICAL LOADS1. Consumers Purchase Electricity for End Use Application

Electricity is always purchased by the consumer as anintermediate step towards some final, non-electrical product.No one wants electric energy itself, they want the products itcan provide: a cool home in summer, a warm one in winter, hotwater on demand, cold beverages in the refrigerator, and 48inches of dazzling color with stereo commentary duringMonday-night football. Different types of consumers purchaseelectricity for different reasons, and have differentrequirements for the amount and quality of the power they buy,but all purchase electricity as a way to provide the end-products they want. These various products are called end-uses, and they span a wide range, as shown in Table 1.

TABLE ICUSTOMER CLASSES AND END-USE CATEGORIES

Some end-uses are satisfied only by electric power(televisions, computers). In others, electricity dominates inusage over other alternatives (there are gasoline-poweredrefrigerators, and natural gas can be used for lighting). But formany end-uses, such as water heating, home heating, cooking,and clothes drying in the residential sector, and pulp heatingand tank pressurization in the industrial sector, electricity is butone of several possible, competing energy sources.

2. Power Systems Exist to Satisfy Customers, Not LoadsThe traditional manner of representing customer

requirements for power system engineering has been aggregate electric loads assigned to nodes for electrical designFor example, customer needs in an area of a city may bestimated as having a maximum of 45 MW. That value then assigned to a particular bus in engineering studies aimedat assuring that the required level of power delivery can bprovided by the system.

Traditionally, the engineering methods used in those desigstudies have been system-based: performance and criteria aevaluated against the power system itself, not against thcustomers needs. Equipment loading limits, singlecontingency backup criteria, and voltage drop/power factoguidelines defined on the distribution system and even at thcustomer meter point, all view electrical performance from thsystem perspective, and do not directly address customeneeds.

Such engineering methods, while necessary to tailor manaspects of T&D design, are not sufficient to completelyaddress the maximization of customer value. Power systemexist to satisfy customers, not loads. Understanding tspecific needs of the customers how much quality therequire in power delivery as well as the quantity of power theneed can improve the value provided by the power systemThe two Qs quantity and quality both need to considered in designing and operating a power system provide maximum customer value.

A: System Peak - 3,492 MW B: Residential - 4.2 kW/customer

Fig. lLeft: peak electric demand for a power system in tsouthern United States, broken out by customer class. Righwithin the residential class, which accounts for 58 of the systepeak, per capita usage at peak conditions falls into the end-uscategories as shown.

End-use analysis of electric load the study of the bascauses and behavior of electric demand by customer type aend-use category is generally regarded as the most effectivway to study consumer requirements from the standpoints quantity, quality, and schedule. In any one household


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Chapter 24 Characteristics of Distribution Loads 785

business, or factory, the various individual end-use loadsoperate simultaneously, forming the composite load, asdepicted in Fig. IB. The T&D system sees this composite loadthrough the meter as a single load. In aggregate, the loads ofall customers produce the system load (Fig. 1A), with eachtype or class of customer contributing a portion to the overallsystem demand.

understanding of how customer loads interact with the powersystem. Most critical, however, is simply the act of keeping inmind that the electric loads used in T&D engineering studiesrepresent the energy needs of people using electricity. Thebest power system is one that satisfies their needs aseconomically as possible.

The amount of electric load created on a power systemwithin any end-use category, for example residential lighting,depends on a number of factors, beginning with the basic needfor lighting. People or businesses who need more lighting willtend to buy more electricity for that purpose. Also importantare the types of appliances used to convert electricity to theend-use. Consumers using incandescent lighting rather thanfluorescent lighting will use appreciably more electric powerfor otherwise similar end-uses.

II. CUSTOMER ELECTRIC LOAD BEHAVIOR3. Connected Load

The schedule of demand for most end-uses varies as afunction of time. In most households, demand for lighting islowest during mid-day and highest in mid-evening, after duskbut before most of the residents have gone to bed. The dailyschedule of lighting demand usually varies slightly throughoutthe year, too, due to seasonal changes in the daily cycle ofsunrise and sunset. Some end-uses are only seasonal. Demandfor space heating occurs only during cold weather. Peakdemand for heating occurs during particularly cold periods,usually in early morning, or early evening, when householdactivity is at its peak.

The connected load is the sum of the full load (nameplate)continuous ratings of all electrical devices in the compositeload system. A typical household in a developed countrymight have a 4,000-watt water heater, a l,OOO-watt water-wellmotor, a 5,000-watt central air conditioner, a 6,500-watt spaceheater, thirty lighting fixtures or lamps with an average load of100 watts each, a 4,000 watt cooking range, a 3,500 wattclothes washer/dryer, a 500 watt refrigerator, and 2,500 wattsof miscellaneous home entertainment, personal grooming, andother small appliances, for a total of 30,000 connected watts ofload. Whether all or any of these are operating at any one timedepends on a number of factors, including the demand for theirvarious end-use products. It is rare that all the connected loadin a system or at any one customers location would beoperational at one time (for example, air conditioning andheating would not be running simultaneously).

The quality of the electric power supplied is more critical tosome end-uses than to others. A power system that canprovide the quantity of power required may still not satisfy theconsumers, either because it does not provide sufficientavailability of power (reliability), or because it does notprovide sufficient voltage regulation or transient voltageperformance (surges, sags). Reliability and voltage regulationneeds vary from one end-use to another, as will be discussedlater in this chapter, and depends mostly on the value of theend-use to the customer.

4. Electric Load Curves

The value that consumers place on any particular end-use isa function of its importance to their quality of life, or to theproductivity of their factory or commercial business. Animportant (but for many power engineers, counter-intuitive)concept is that end-use value is not of a function of the cost ofthe electric power. For example, most personal computers andworkstations use only 2-3 worth of power per hour, yet userstypically report that an hours interruption due to lack of powerhas a cost of a dollar or more.

Use of the products created by electric power - light, heat,hot water, images on the TV, and so forth, varies as a functionof time of day, day of week, and season of year. As a result,the electric load varies. A load curve plots electricconsumption as a function of time. Fig. 2 shows seasonal peakday load curves for residential loads from two electric systemsin the United States. In one system, demand is highest insummer, during early evening, when a combination of airconditioning demand and residential activity is at a peak. Inthe other, peak demand occurs on winter mornings, when aelectric heating demand is highest.

Cost is a major factor in T&D design. In fact, cost is often aconsumers primary concern, for which they are willing toaccept major compromises in quality, and quantity, or service.The challenge facing T&D engineers is to meet consumerneeds for both Qs - quantity and quality - at the lowestpossible cost. Building a system that delivers higher reliabilitylevels than customers need is exactly the same as building onethat can deliver much more power than they need.

Fig. 2Typical summer (solid line) and winter (shaded line) peakday load curves for a metropolitan power system in the southernUS (left) and a rural system in New England (right).

Knowledge of the customer needs for quantity and scheduleof power delivery, and of the value they place on reliability,voltage regulation, surge and sag protection, and other factors,are important factors in modern power factor design, as is an

Load curve shape - when peak load occurs and how loadvaries as a function of time - depends both on the connectedload (appliances) and the activitv and lifestvles of the


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786 Characteristics of Distribution Loads Chapter

consumers in an area. Differences between the electricdemand patterns of otherwise similar types of customer (as inFig. 2) occur because of differences in climate, demographics,appliance preferences, and local economy.5. Demand

Demand is the average value of load over a period of timeknown as the demand interval. Often, demand is measured onan hourly or quarter-hour basis, but it can be measured on anyinterval - seven seconds, one minute, 30 minutes, daily,monthly, annually. The average value of power, p(t) duringthe demand interval is found by dividing the kilowatt-hoursaccumulated during the interval by the number of hours in theinterval.

Demand is the average of the load during the interval. Thepeak and minimum usage rates during the interval may havebeen quite different from this average (Fig. 3). Demandintervals vary among applications, but commonly used intervallengths are 5, 15, 30, and 60 minutes.

Peak demand, the value often called peak load, in designstudies, is the maximum demand measured over a billing ormeasurement period. For example, a period of 365 dayscontains 35,040 fifteen-minute demand intervals. Themaximum among these 35,040 readings is the peak fifteen-minute demand. This value is often used as the basis for anannual demand charge if the readings measure a singlecustomers usage, and as a capacity target in engineeringstudies: the maximum amount the system must deliver.6. Demand Factor

The demandfactor of a system is expressed as the ratio ofmaximum demand to the connected load. Normally thedemand factor is considerably less than 1 O.7. Load Factor

Load factor is the ratio of the average demand to the peakdemand during a particular period. Load factor is usuallydetermined by dividing the total energy (kilowatt hours)accumulated during the period by the peak demand and thenumber of demand intervals in the period, as

LF = Total usage during period (1)(Peak Demand) x m

where m = number of demand intervals in periodLF = Average Demand

Peak Demand(2)

Load factor gives an indication of the degree to which peakdemand levels were maintained during the period under study.Load factor is typically calculated on a daily, monthly,seasonal, or an annual basis.8. Power FactorAll loads require real power - kilowatts - to perform usefulwork such as mechanical rotation or illumination. Reactiveloads also require reactive volt-amperes (VAR) to do a type of

non-productive work required for their function, such produce the magnetic field inside a transformer or motowithout which they can not function.

VAR flow on a power system consumes capacity conductors, transformers, and other equipment, but provides useful real work. It is mitigated by the use of capacitors aother devices, or by changes in the end-use device so thatconsumes fewer VARS (see Chapter 8).

Fig. 3Demand on an hourly basis (blocks) over a 24 hour periContinuous line indicates demand measured on a one-minuinterval basis. Maximum one-minute demand (at 552 PMabout 4 higher than maximum one-hour demand (S-6 PM).

9. Voltage Sensitivity of LoadsThe various electrical appliances connected to the pow

system exhibit a range of different load vs. voltasensitivities. Important characteristics include their responto transient voltage changes and their steady state load voltage behavior.

Transient voltage response is difficult to characterize animportant, should be modeled with detailed, and specific, stuof the transient response of the particular loads involveClassification of transient load response into categories useful in some cases, but no simple generalization works incases.

For steady state representation, individual electric loare generally designated as falling into one of three categordepending on how they vary as a function of voltage

Constant impedance loads, for example an incandescentlight or the heating element in an electric water heater,are a constant impedance, whose resulting load variesas the square of the voltage.

Constant current loads, including some types of powersupplies, many electroplating systems, and otherindustrial processes, are basically constant currentloads. Energy drawn from the system is proportional tovoltage.

Constant power loads, such as some types of electronicpower supplies, and to an approximate degree,induction motors, vary their load only slightly iresponse to changes in voltage.

In each category, reference to a load as 1 kW refers tovalue at 1 O PU voltage. Table 2 shows the value of a 1load in each category, as a function of voltage.


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Chapter 24 Characteristics of

TABLE2 ACTUALLOAD OFA 1 KWLOAD OFVARIOUSCATECKRIESAS A FUNCTION FTHEPERUNIT SUPPLYVOLTAGE- WATTS

Correct representation of voltage sensitivity can be animportant factor in analysis of power system performance,particularly on systems that are near permissible limits.Usually, engineering studies of transmission system are carriedout using representations of the load as constant power. Thisworks well, because the customer loads are usuallydownstream of load-tap changing transformers and voltageregulators and so are insensitive (in the steady state case) tochanges in the voltages being modeled.

On the distribution system, however, correct representationof voltage sensitivity is critical for accurate analysis of voltagedrop and equipment loads. As can be determined from study ofTable 2, the difference between constant power and constantimpedance 1 kW loads, at 8% voltage drop (typical of themaximum primary feeder voltage drop permitted on manysystems), is 15%. Thus, the incorrect categorization of loadvoltage sensitivity could lead to a significant over or underestimation of voltage drop and loading on a feeder.

Tests to determine voltage sensitivity on a feeder circuit orlow-side bus basis, by varying LTC or voltage regulator tapposition at the substation, are recommended to determine exactbehavior. In the absence of specific information,representation as a constant current (load is proportional tovoltage) is recommended. Within the United States, thefollowing rule-of-thumb works somewhat better

Summer peaking residential and commercial feeders as asplit of 67% constant power and 33% constantimpedance.Winter peaking residential and commercial feeders as asplit of 40% constant power and 60% constantimpedance.Industrial feeders as constant power feedersIn developing countries, rural loads are best represented as

25% constant power and 75% constant impedance and those inurban areas as an even split of constant power and impedance.

Load flow and similar iterative engineering computationsare faster and more stable in convergence if loads arerepresented as constant power than as constant impedance orcurrent (fewer factors change value from iteration to iteration).In some cases, when a load flow commutation will not

Distribution Loads 787

converge, changing input data to represent all loads as constantpower will promote convergence to an approximate solution.

Analytical studies and digital programs can be simplifiedby deleting the constant current category and using onlyconstant power and constant impedance type loads. Constantcurrent load behavior (the rarest of the three types) can berepresented over the range .88 to 1.12 PU voltage, with lessthan .75% error, if modeled as a mixture of 49.64% constantpower, and 50.35% constant impedance load. The columnlabeled Ratio in Table 2 shows this mix of load types, withthe right-most column giving the percentage error inrepresentation of an actual constant current load.10. Characterizing Customers by Class

Usually, electric consumers are grouped into classes ofbroadly similar demand behavior. A class is any subset ofcustomers whose distinction as a separate group helps identifyor track load behavior in a way that improves the effectivenessof the analysis being performed. Electric utilities most oftendistinguish customers by rate class (pricing category).Customer studies (load research) often make additionaldistinctions based on demographics, income, or SIC (standardindustrial classification) code.

Regardless, usually all customers in a class have similardaily load curve shapes and per-customer peak demands,because they employ similar types of appliances, have similarneeds and schedules, and respond in a similar fashion toweather and changes in season. Table 3 and Fig. 4 illustratehow customer class values vary in one power system.TABLE 3PEAK HOURLY DEMAND VALUES FOR CUSTOMERS N A

UTILITYSYSTEM NNEW ENGLAND.1992

11. Customer Class Peaks Occur at Different TimesOften, the various classes do not demand their peak energy

at the same time, as shown in Fig. 4. As a result, the systempeak load may be substantially less than the sum of theindividual customer class loads (Fig.5). This is called inter-class diversity, or inter-class coincidence, of load. A classsor customers load at time of system peak is its contribution tosystem peak, and the ratio of its peak contribution to its ownpeak load is its peak responsibility factor. Table 4 shows thepeak load and responsibility factors of various classes in autility system in the central United States.


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788 Characteristics of Distribution Loads Chapter

III. CONVERSION OF ELECTRICITY TO END USE12. Appliances Convert Electricity to End Uses

Each end-use, such as lighting, is satisfied through application of appliances or devices that convert electricity the desired end product. For lighting, a wide range illumination devices can be used, from incandescent bulbsfluorescent tubes, to sodium vapor and high-pressure mochromatic gas-discharge tubes and lasers. Each uses elecpower to produce visible light. Each has advantages wrespect to the other illuminating devices that gives it an appin some situations. But regardless of type or advantages, althese devices require electric power to function, and createelectric load when activated.

Fig. 4Customer classes typically display different daily loadcurves. Shown here are the class summer peak-day loads from ametropolitan utility system in the southern United States.

Fig. 5Peak system load in this metropolitan system in Europeoccurs when a combination of both residential and commercial-industrial load is at a maximum.

TABLE4SYSTEM EAKRESPONSIFHLITVY CUSTOMER LASS FORAUTILITYSYSTEM N THECENTRALUNITEDSTATES, 1992

The term load, in this context, refers to the electric porequirement of a device that is connected to and draws enefrom the T&D system to accomplish some purpose (openinggarage door) or to convert that power to some other formenergy (light, heat). Loads are usually rated by the levelpower they require, measured in units of volt-amperes, watts. Large loads are measured in kilowatts (thousands watts) or megawatts (millions of watts). Power ratings of loand T&D equipment refer to the device at a specific nomivoltage. For example, an incandescent light bulb might rated 100 watts at 115 volts. If provided more or less voltaits load would be different from 100 watts. Loads cansingle-phase or multi-phase, and they can have real (resistonly) or complex impedance (reactance), too.

The electric load in any one end-use category depends only on the number of customers and their aggregate demfor the end-use, but also on the types of devices they are uto convert electricity to that end-use. For example, lighload will be higher if most customers are using incandescelighting to meet their needs, than if they are using fluorescent lighting. Similarly, if a large percentage customers use only resistive space heating instead of mefficient heat pumps, electric demand will be greater, evethe end-use demand is the same. Power quality needs alsofunction of appliance type. For example, variable-spechillers are more sensitive to voltage sags than traditioconstant-speed building cooling systems.

Therefore, detailed analysis of electric load in a utsystem generally proceeds into subcategories within customer classs end-use categories, with the subcategorcharacterized by appliance type, as shown in Fig. 6. The bindicate load curve models, the ellipses are multiplcorresponding to the number of customers or the percentagecustomers in a class that have a certain appliance (e.g., therstorage heating). Only part of the model is shown. Dolines indicate links to portions not illustrated.

In detailed load studies, behavior of load in each categoranalyzed by use of temporal curves, plotting demand forend-use (e.g., gallons of hot water, BTU of heating requiredthe electrical load, or cost of service interruption, as a funcof time. Information on the percentage of customemploying each type of appliance, their end-use demschedules, and the electrical and efficiency characteristicsthe appliances, comprises the end use model.


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Chapter 24 Characteristics of Distribution Loads

Fig. 6Structure of an end-use analysis based on customer, end-use, and appliance subcategory load curves.

13. Appliance Output Is Controlled by Varying Duty CycleOnly a minority of electrical devices vary their load as a

function of the end-use demand placed upon them. Forexample, the motor drive in a variable speed heat pump willcontrol its RPM (and hence electric load) to correspond to thepumping requirements of the system, on a moment to momentbasis. However, such appliances are a rarity. The majority ofloads connected to a power system vary their output as afunction of time by changing their duty cycle. Duty cycle isthe portion of time the device spends operating during anyperiod.

Fig 7Electric load (bottom) and internal water temperature (top)of a 4,000 watt, 50-gallon storage electric water heater as afunction of time.

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For example, most storage water heaters function in asimple manner to keep the water they provide at a constanttemperature, regardless of demand, as illustrated in Fig. 7. Athermostat is set at the desired temperature, for example172.5F. The thermostat has a deadband, a narrow range oftemperatures on each side of the setting, within which thethermostat does nothing. A typical deadband might be 5F -for example from 170F to 175F when the thermostat is set to172.5F. Whenever the temperature drops below thedeadbands lower limit, the thermostat activates a relay (orelectric circuit) that turns on the heating element. The elementis left in operation until it raises the water temperature abovethe upper limit of the thermostats deadband (175F), at whichpoint the thermostat activates the relay to shut off the heater.The water temperature rises and falls slightly as the unit cycleson and off, as shown, but the electric load cycles completelyfrom all on to all off, as the device tries to maintain aconstant temperature.

The 4,000-watt water heater, as illustrated in Fig. 7, createsa load of 4,000 watts whenever it is energized by itsthermostat. Otherwise it creates no load at all. Over a periodof 24 hours, it will vary its duty cycle in response to demandfor hot water. When water heating demand is lightest, thewater heater may operate only a few minutes in each hour. Butwhen demand is highest, for example in the evening whendishwashing, clothes washing, bathing, and other activities areat a peak, it may operate continuously for an hour or more, asshown in Fig. 8.

Fig. 8The water heaters load profile over a typical day.

A large portion of the electric appliances in most electricsystems, often a majority of the electric demand, operates inthis manner. The consumer does not directly control theappliances on-off operation. Instead, the consumers sets adesired end-use measure (temperature, air pressure) on acontrolling device (a thermostat, a pressure switch), and thisdevice varies the appliances duty cycle in response to end-usedemand. In the residential class, air conditioners, spaceheaters, refrigerators, freezers, water heaters, irons, and ovensfall into this category. In the industrial class, process heaters,air and water pressurization systems, and many fluid handlingsystems use this method of control. Fig. 8 shows the resultingdaily load curve for a water heater. It cycles on and off,operating for longer times during periods of high demand, andonly briefly when there is no demand and it must only makeup for thermal losses. In all cases, however, when the waterheater is operating its load is the same - 4 kW.


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790 Characteristics of Distribution Loads Chapte

Fig. 9Daily cycle of THI (temperature-humidity-illuminationindex) and air conditioner operation. The air conditionersconnected load varies slightly as a function of THI.

Fig. 9 shows a slightly more complicated appliancebehavior, in which duty cycle and device characteristics bothvary. Here, an air conditioner cycles between on and off underthermostatic control. As temperature rises throughout the day,demand for cooling increases, and the air conditioner spends agreater portion of its time in the on state, until in lateafternoon it is operating all but a few minutes in every hour.The diagram illustrates a common secondary effect due to ACunit compressor design. When ambient temperature(temperature of the air around the AC radiator) rises, backpressure in the compressor increases, forcing the unitsinductive motor to work harder and creating a slightly higherelectrical load. Thus, its connected load varies withtemperature, as shown.14. Appliance Duty Cycles and Coincidence of Load

Fig. 10 shows the type of load curve widely usedthroughout the power industry as representative of a residentialwater heaters daily load curve. This particular load curve wastaken from a comprehensive water heater load survey done inthe 1980s by a utility in the northern United States, prior todesign and implementation of a water-heater load controlprogram. This curve shown has a maximum value of 1,100watts during a brief early morning household activity peak, anda lower, but broader early evening peak.

Fig. 10A average residential water heaters coincident demandcurve - l/100,000 of the load resulting from 100,000 waterheaters. Any single water heater has a load curve similar to thatshown in Fig. 8, but its contribution to system load is depicted asshown here. This curve is also the expectation of any one waterheaters load by time of day.

The daily water heater load curve in Fig. 10 looks nothlike the daily water heater load curve in Fig. 8. In Fig. 10, varies smoothly from moment to moment, between a minimof .53 kW and a maximum of 1.1 kW, displaying none ofblocky, on-off cycling shown in Fig. 8. Neither Fig. 10Fig. 8 is incorrect. Each is accurate, but only within its context. Their difference is attributable to intra-ccoincidence of load.

Fig. 11 illustrates the relationship between the two wheater load curves. On the top row, load curves A, and B sthe load curves for two electric water heaters in neighborhomes on the same day. Curve C shows the curve forwater heater in B, on another day. All three represent the sappliance under nearly identical conditions. Timing of the blocks varies, but in all cases the load is all or nothing.

Load curve D shows the combined loads of neighboring water heaters (the sum of curves A and BFebruary 6, 1994. Even during the peak hour, the avewater heater operates only a fraction of the time (in the sywhose average water heater is shown in Fig. 10, exa1,100/4,000 of the time, assuming all water heaters are 4watts connected load). For this reason, instances when thewater heaters operate simultaneously are rare, but this happen several times each day, for brief periods.

Curve E shows the curve for five water heaters (the unifive neighboring homes, including A and B). With five uthe likelihood of two or more units operating at any one timincreased considerably. However, the likelihood of all fiveoperating at the same time is quite remote (roughly 1100/4raised to the fifth power, or less than .l percent). Curvshows the combined load curve of 50 water heaters (all tserved by one primary-voltage lateral).

Fig. 11Daily load curves for different sized groups of residewater heaters.


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.Chapter 241 Characteristics ofP Distribution Loads 791

As an increasingly large number of water heaters isconsidered as a group, the erratic, back-and-forth behavior ofthe individual water heater load curve gradually disappears.The load curve representing a groups load becomes smootheras the size of the group is increased, the peak load per waterheater drops, and the duration at lengthens. By the time 1,000water heaters are reached (Fig. 1 IG) the curve shape is quitesmooth, and peak load is at its coincident value of 1,100watts/unit.

While no single customer within the group depicted in Fig. 12would have an individual load curve that looked anything likeFig. 12B (every customers load curve looks something likeFig. 12A), the smooth coincident load curve for the group hastwo legitimate interpretations.

Thus, Fig. 10 (same as Fig. 1 lG), while unlike anyindividual water heaters actual load curve, is an accuraterepresentation of water heater behavior from either of twoperspectives. First, it is a diagram of average contribution tosystem load, or coincident load, on a per water heater basis l/l 00,000 of the load of the 100,000 water heaters in thesystem. Second, it is the expectation of a water heaters loadas a function of time. To a certain extent, the exact timing ofthe on load blocks in Fig. 7- 9, and Fig. 11 is random fromday to day. Fig. 10 is a representation of the expected load ofone water heater, as a function of time; the best estimate, a dayahead, of load as a function of time.

I. The curve is an individual customers contribution tosystem load. On the average, each customer of thisclass adds this load to the system. Add ten thousandnew customers of this type, and the system load curvewill increase by ten thousand times this curve.

Note that energy per water heater (area under the loadcurve) is not a function of group size. The energy used perwater heater is constant in any of the load curves in Fig. 11.

2. The curve is the expectation of an individualcustomer's load. Every customer has a load that lookssomething like the on-off behavior shown in Fig. 12A,but each has slightly different on-off times that vary inan unpredictable manner from day to day. Fig. 12Bgives the expectation, the probability-weighed value ofdaily load that one could expect from a customer ofthis class, selected at random. The fact that theexpectation is smooth, while actual behavior is erratic,is a result of the unpredictability of timing in whenappliances switch on and off.

15. Coincident Load Behavior in GeneralMost of the major loads in any home or business behave in

a manner similar to the on-off, coincident behavior shown inFig. 7 - 9 and Fig. 11. Refrigerators and freezers, airconditioners, space heaters, water heaters, and electric ovens inhomes; and pressurizers, water heaters, process and otherfinish heaters, and other equipment in industry; all turn on andoff in a performance-regulated duty cycle manner. As a result,individual household load curves, and many commercial andindustrial site load curves, display the blocky, on-off loadbehavior shown in Fig. 12A. As with the water heaters, whena group of similar loads (homes in this case) is considered as asingle load, the load curve becomes smoother, the peak loaddrops, and the minimum load rises. Note that the vertical scaleof all six load profiles shown in Fig. 12 is in load percustomer for each group.

Commercial and industrial customers exhibit intra-classcoincident behavior qualitatively similar to that discussed here,but the shape of their coincidence curves may be (usually is)different than for residential. By contrast, inter-classcoincidence is the difference in timing of peak periods amongclasses (Fig. 4).

The 22 kW non-coincident needle peak demand shown inFig. 12A for a single household is high, but not extraordinaryfor homes in the southern United States. Load curve Arepresents a 2100 square foot residence with 36 kW connectedload (sum of all possible heat pump, water heater, garage dooropener, washer-dryer, other appliance and lighting loads).While customer characteristics vary from one system toanother, the qualitative curve shape behavior shown in Fig. 12,as well as the tendancy of load curves to become smoother,and peak loads lower, as group size is increased, apply to allpower systems.16. Coincident Curve: Expectation of Non-Coincident Load

The interpretation of coincident load behavior as theexpectation of non-coincident load behavior, as explained insub-section 14 (water heater example) is generally applicable.

Fig. 12Non-coincident (A) and coincident (B) winter peak dayload curves for home in a suburban area of Florida. Curves Bthrough F show the gradual transformation from non-coincidentto coincident behavior as group size increases. Feeders see loadcurves similar to B. Every service drop sees a load curve like A.


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792 Characteristics of Distribution Loads Chapter 2

17. Importance of Coincidence Assessment in T&D DesignCoincidence behavior of load, as depicted in Fig. 12, is

important to T&D planning and engineering. Equipment suchas service drops, service lines (LV), and service transformers,which serve small numbers of customers, must be designed tohandle load behavior, including customer needle peaks, of thetype depicted in Fig. 12A. Normal service does not requirethis equipment to handle these load levels for more than a fewminutes at a time, a factor that can be considered indetermining the load rating of this equipment. By contrast,equipment serving large groups of customers sees fullycoincident load curve behavior (Fig. 12B). Peak load percustomer is lower, but peak duration is much longer.

Usually, in spite of the high needle peak values, the thermalcapacity of service drops, service (LV) circuits, and servicetransformers can be determined based on coincident peak loadvalues. The thermal time constants for most conductor, cable,and transformers are much longer than the duration of anyneedle peak. As a result, thermal loading calculated on thebasis of coincident curve shape is usually representative of thethermal loads that will result from the actual non-coincidentload curves.Voltage drop and losses are another matter, however. Fig.13 compares the losses that result in a set of triplex servicedrops, for the two load curves Fig. 12A and Fig. 12B. Theresult shown is typical. Use of coincident rather than non-coincident load curve typically results in errors of up to 50% inestimating low voltage system losses, and up to 16% inestimating the total voltage drop to the customers meter.

18. Coincidence Factors and Curves

Fig. 13Electric losses through a typical set of residential servicedrops, for the load curves in Fig. 12A (left) and 12B (right).Voltage drop would similarly show a significant difference.

Usually, coincident load behavior is summarized foapplication to power distribution system engineering by thcoincidence factor, and the coincidence curve. Coincidencefactor is a measure of how peak load varies as a function ogroup size for customers

C = observed peak for the groupI( individual peaks)

(3Fig. 12 illustrates well that as the number of customers in thgroup increases, the peak load/customer usually drops by considerable amount. Coincidence factor, C, can brepresented of as a function of the number of customers, n, in group

C(n) = peak load of a group of n customersn x (average individual peak load) (4

where n is the number of customers in the group,and 1 < n < N = number of customers in theutility system

Diversity factor, D(n), is the inverse of coincidence factorIt measures how much higher the customers individual peak than its contribution to group peak.

D = Diversity factor = l/ Coincidence factor (5The coincidence factor, C(n), has a value between 0 and

and varies with the number of customers in a fashion identicato the way the peak load varies. Fig. 14 shows a coincidencecurve, a plot of how C(n) varies with n. Typically, foresidential and small commercial load classes, C(n) tendtoward an asymptotic value of between .33 and SO for largvalues of n. The value for larger commercial and industrialcustomers is usually higher, - .75 to .85 is typical, Table gives representative asymptotic coincidence values for typicacustomer classes. Coincidence behavior varies greatly fromone utility to another, and among customer classes. The curveand tables shown here are representative of the typebehavior seen in all power systems, but can not bquantitatively generalized to all power systems.

Usually, coincident load curve data is readily available, butaccurate non-coincident load curve data is not. In addition,many types of recording systems and analysis methods distortnon-coincident load curve data when it is recorded, producinga smoother curve and lower peak loads than actually existed inthe load. Gathering and verifying accurate load curve shape,load factor, and losses factor data for non-coincident andpartially coincident (groups of 5-20 customers) equipmentanalysis requires care and attention to detail. However, it is Frecommended, due to the potential error that inexact data lg. 14Peak load per customer as a function of the number customers in a group (left scale) and coincidence factor (righcreates in losses and voltage drop and flicker computations. scale) for residential class, from a power system in the central US


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794 Characteristics of Distribution Loads Chapter 24

Fig. 18Examples of coincidence curve modification due to various types of demand-side management (DSM) programs. Thin solidline indicates base coincidence behavior. Heavier lines indicate the coincidence behavior of the load after DSM modification.

21. Coincidence Curve and DSM InteractionMany integrated resource methods, such as appliance

interlocking and load control, and other demand-sidemanagement (DSM) measures, change the coincidencebehavior of customer loads, not the loads themselves. Forexample, adding insulation and weather-sealing to a buildingdoes nothing to change the load of its air conditioning andheating system. These energy conservation measures slowheat transfer into and out of the building, lengthening the theoff portions of every on-off cycle. The same needle peaksoccur, but spaced farther apart in time. Basically, this DSMmeasure cuts the percent of time the AC/heater is on, andhence the coincidence of these appliances.

Fig. 18A illustrates the change in coincident load behaviormade by universal use of appliance interlocking among allresidential customers in a large group. Interlocking involvesjointly wiring the thermostats for the electric water heater, andthe air-conditioner/heater, so that the water heater cannotoperate if the air-conditioner/heater is operating. It is a simpleform of the appliance schedule optimization that can beaffected with home automation systems.

The broad line in Fig. 18A shows the resulting coincidencecurve. The 22 kW peak values, which occasionally resultedfrom the random overlapping of appliances activatingsimultaneously, are now completely avoided. As a result, the22 kW peak values, and the value of the coincidence curve atthe Y-axis, are both reduced by the magnitude of the waterheaters connected load (4 kW in this example).

However, the water heater is not denied energy. Its use ismerely deferred until periods when the air conditioner or heateris switched off. As soon as the master (AC-heater) appliance

switches off, the water heater will activate. Over any lengthyperiod of time (an hour or more) both appliances usuallyreceive all the energy they need. Thus, over any large group ofcustomers, coincidence of energy usage within any demandperiod will not be affected. The asymptote is unchanged.

An opposite type of effect is shown by the broad line in Fig.18B. Appliance load control is basically a method to limitduty cycle, and thus coincidence of load. Typically, loadcontrollers are set to limit the operation of any appliance to nomore than a certain number of minutes per demand period. Forexample, a controller might be set to limit its air conditioner tono more than 12 minutes operation out of any 15 minuteperiod, a duty cycle of 80%. During peak conditions, theaverage thermostat may want to operate its air conditioner 90%of the time. Thus, this load control effects an 11% reduction inair conditioner energy usage. As a result, the asymptotic valueof the coincidence curve, for large groups of customers withload control, is reduced.

Such a load control measure makes no impact on themaximum height of the needle peaks produced by anyhousehold. The AC unit is still the same connected load, andstill likely to overlap with other appliances to create highneedle peaks. As a result, load control has no impact on thevalue of the coincidence curve for individual customers. Incases where control is poorly coordinated, or the load control isaggressively used to maximize the reduction of coincidentpeak load, it can produce a rebound effect, increasing peakloads on some levels of the system, as shown by the dotted linein Fig. 18B. Fig. 18C through Fig. 18F represent the actions ofother often-used DSM approaches.

Fig. 18 illustrates two very important points about DSMprograms. First, DSM programs do not necessarily produce


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Chapter 24

similar amounts of load reduction on all levels of the powersystem. Second, by use of coincidence curve analysis of thetype shown in Fig. 18, it is possible to target a DSM programsload reductions at particular levels of the power system. DSMmeasures that affect the peak loads of large groups ofcustomers, or small groups, can be selected as needed to targetfeeder or service (LV) levels.

to zero. Demand recorders as used in revenue metering andmost (but not all) electronic meters use this type of loadrecording.

IV. MEASURING LOAD CURVE DATARegardless of the actual behavior of the electric load, it is

measured and sampled through the eyes of equipment andprocedures which may introduce errors by not capturingcompletely all of the loads characteristics. Many types of loadrecording perform a type of filtering that makes load behaviorlook more coincident (smoother, lower peak) than it actuallywas. Other types mis-recording of load cycles in a way thatrenders the load curve data virtually useless. In both cases, thedata looks like load curves, but is inaccurate. Regardless,power engineers must be aware of the source of all load data,the method used in its recording, and any limitations it createson the accuracy or use of the resulting data.

Essentially, instantaneous sampling records the actual loadvalue at specific instants spaced an interval apart. Periodintegration averages its load measurement over the entiresample interval between two of those instances. There can be,and usually is, a considerable difference in the recorded data,depending on which of these two different sampling techniquesis used.

22. Load Sampling Rate and TypeMost load measurement, recording, and analysis equipment

and procedures work with load curve data as sampled data.Load values are measured and recorded at uniform intervals oftime. For example, often load curves are represented inengineering studies as 24 hourly loads. Many load recordersmeasure and store load behavior on a 15-minute basis. Thereare two very important aspects of sampling. The first is thetype of sampling used, the second is the rate of its application.

Discrete sampling measures and records the loads value atspecific periodic instances. For example, load recorder maymeasure electrical load every 15 minutes. Every quarter hour,this device opens its eyes to sample the load, and records thevalue, and begins a waiting period until the next samplinginstant. What the load does in between those 15-minutesample periods is immaterial to the recorder.

This kind of sampling, which is often called instantaneoussampling, is the type normally dealt with in textbooks on signalprocessing as discrete sampling. Much of the load data usedin power systems studies comes from this type of sampling.Many types of distribution load recorders (load loggers) doonly instantaneous sampling. SCADA systems that trap loadreadings on a periodic basis do instantaneous sampling.Manual reading of load strip charts is basically discretesampling: typically, load data is prepared for computerprocessing from strip charts by an engineer or analyst whoreads the value every so often from the strip chart and codes itinto the computer data base.

Fig. 19Two different load sampling methods (middle, bottom)applied on an hourly basis to the residential load curve from Fig.12A (top), produce quite different data.

Fig. 19 shows the single all-electric household daily loadcurve from Fig. 12A, along with versions of it obtained bysampling on an hourly basis with period integration (middle)and discrete sampling (bottom).nor instantaneous discrete sampling on an hourly basiscaptures all the details of the load behavior. However, in thiscase, discrete sampling produces a very spurious-looking loadcurve. for reasons that will be discussed later.23. Observed Load Behavior and Sampling Rate

Demand sampling, also called period integration,measures and records the total energy used during each period.If applied on a 15-minute basis, period integration records theenergy (demand) during each 15-minute period. At thebeginning of each measurement interval, a watt-hour meter isre-set to zero and begins counting the energy used. At the endof the period, the reading is recorded, and the counter is re-set

The second important aspect of load curve sampling is thesampling rate. Fig. 20 shows Fig. 12A load curve sampledwith period integration on a 5, 15, 60 and 120-minute basis.Note that the resulting data displays significantly differentThe load curve in Fig. 12A was obtained using period(demand sampling) on a five-minute interval basis.

795

Neither demand sampling

integration


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796 Characteristics of Distribution Loads

behavior, depending on sampling rate. As the sampling isdone faster, the curve shape displays more of its blocky, on-offnature: the recorded data comes closer to representing the trueload curve shape peak value.

But as shown, if a load is sampled by period integrationapplied at a slow rate, the resulting load data may look smooth,when, in fact, actual behavior is erratic, with high needlepeaks. Fig. 21 shows peak demand for the data in Fig. 12,plotted as a function of period integration sampling rate. Themeasured peak load decreases as the sampling period increasesfrom five-minutes to one hour. The reason is that the samplingrate, or demand interval, defines the meaning of peak.Sampled at one-minute intervals, the peak is the maximum 60-second demand. Sampling on an hourly basis smoothes out alot of the needle peaks, and yields a curve whose peak is themaximum one hour demand. A non-coincident curve (top ofFig. 20) can look like it was smoother and very coincidentsimply because it was demand-sampled at too low a samplingrate.

Fig. 20Single household load (Fig. 12A) sampled by periodintegration (demand recorder) on a 5,30,60,120-minute basis.

Fig. 21Measured peak demand of a single residential customervaries greatly depending on the intervals used to sample its load.

As shown in Fig. 20 and Fig. 21, changing the samplingrate changes the perceived or measured peak value and thechoppiness (variance) seen in the load curve. However, notall types of load curves are equally sensitive to thisphenomenon, This effect is most pronounced when samplingnon-coincident load curves - those representing small sets ofappliances or just a few customer. It is minor or undetectablewhen sampling load of large groups of customers, such as anentire system.

Thus, the apparent coincidence of load changes as afunction of sampling rate. Fig. 22 shows coincidence curvesfor the residential customers used earlier in Fig. 12- 16, re-computed based on period integration sampling intervals of 5,15, and 60 minutes. Because the peak load of a singlecustomer, upon which coincidence factor computation is based,changes a great deal as a function of sampling rate (Fig. 21),the coincidence curve, itself, will change. Characteristics andsensitivity discussed here involve only period integrationsampling (i.e., demand recorders), which is the most commonapproach to gathering load research and load curve data.

Fig. 22Coincidence curves based on data measured at 60, 15, and5 minute demand intervals for residential all-electric homes.

Aliasing. Instantaneous sampling has a far differentinteraction with sampling rate and recording accuracy than theperiod integration method discussed above. Fig. 23 shows theload for a single household (Fig. 12A) measured byinstantaneous sampling on an hourly basis. One profile is theresult of sampling instantaneously every hour, on the hour.The other is sampled hourly a quarter past the hour. Theapparent load curve shape, and peak load of these two curvesare different. Neither is an accurate representation of theactual load curve behavior.


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Chapter 24 Characteristics of Distribution Loads 797

The problem with instantaneous sampling applied in this 24. Signal Engineering Perspective on Load Samplingcase is that its rate is much to slow to see the load behavior.But unlike period integration, which smooths the load curvewhen applied at a slow rate, instantaneous discrete samplingdistorts it, badly, as shown. The load being recorded in thiscase (Fig. 12A), has very erratic on-off load behavior commonto non-coincident loads. It is simply random chance whether aparticularly hourly recording instant, falls upon a needle peak,or a needle valley. For a load that has needle peaks, as doesany individual household load, instantaneous sampling at a lowsampling rate gives very poor, even completely unusableresults.

Load as a function of time is a signal, a value measured as afunction of a continuously varying indexing parameter. Afundamental concept of signal engineering is that any signalcan be represented as the sum of a set of sine waves ofdifferent frequencies and magnitudes. Low frequencies areslowly undulating sine waves, high frequencies represent rapidshifts in value. Any behavior that is characterized by rapidshifts in value is high frequency behavior. A load curve with agreat deal of on-off choppiness, as for example Fig. 12A, hasa large amount of relatively high frequency behavior. On theother hand, a smooth coincident load curve (Fig. 12B) has nohigh frequencies.

Fig. 23Single household load curve (top of Fig. 20) sampled withhourly discrete sampling. Left: load curve sampled discretelyevery hour at the beginning of the hour. Right; sampled everyhour 15 minutes after the hour.

A fundamental theorem of sampled signal theory is that for

cycling on an individual household basis. Better yet, one-minute samples can be used when trying to identify applianceor individual household load behavior in detail.

instantaneously discrete sampled data to be valid, the samplingmust be done at twice the rate o the highest frequency in thesignal. Thus, to capture completely behavior of a load curvethat has rapid shifts in load (and thus avoid errors as depictedin Fig. 23), it is necessary to sample it twice as often as itsappliance loads cycle on and off. Since many appliances turnon and off within a fifteen or even ten-minute period, aminimum rate of five-minute sampling is necessary to see peakload, coincidence, and load curve behavior of such rapid

As mentioned in sub-section 23, instantaneous discretesampling and period integration sampling differ dramatically inwhat they do if sampling rate falls short of these requirements.Essentially, period integration samples a load curve but filtersit simultaneously. The averaging over each demand interval,as discussed above, smoothes out choppiness (removes highfrequencies). To a very good approximation, this type ofsampling can be thought of as responding only to frequenciesin the signal that are in the band of frequencies below one-halfits sampling rate. The period integration responds tofrequencies in the band it can see (those below its samplingrate limit) and ignores those above that limit.

While the two load curves in Fig. 23 look quite different,and bear no resemblance to the actual load curve shape, theyshare one characteristic: Both seem to oscillate back and forthevery three to five hours. This is called aliasing, or frequencyfolding in signal theory, and is essentially a beat frequencygenerated by interference between the sampling rate, and theduty cycle rate of the appliances in Fig. 12A. Somethingsimilar to this occurs any time the measured quantity beingsampled cycles back and forth at a faster rate than thesampling. In this example, appliances are cycling on and offat a rate much too fast for the hourly sampling rate to track.The beat frequency, or aliasing profile shown here, is acharacteristic of under-sampled curves, something to watch forin load data. This type of distortion is common. It is fairlyeasy to detect by manual inspection (at least if given sometraining and understanding of what causes it), and its presencemeans that the load curve data is probably completely invalid.

In the presence of a great deal of erratic on-off load shifts,as occurs in most non-coincident loads, neither periodintegration (demand sampling) or instantaneous discretesampling gives a completely accurate measurement of the loadcurve behavior. The integration method averages behaviorover each period. The instantaneous method may chance uponany value. If the load being measured is fairly smooth, forexample the load of an entire power system, then the level of

Thus, sampling a load at half-hour intervals with periodintegration will obtain valid information on all frequencies inthe load up to one cycle/hour, but will smooth out, or filter,fluctuations that are due to more rapid load behavior. (Thisperspective is slightly simplistic - i.e., only approximate onseveral minor technical points - but sufficient for thisdiscussion). Instantaneous sampling, on the other hand, doesnot filtering, and tries to respond to everything it sees.However, it can only validly see frequencies below twice itssampling rate. It responds to frequencies above that limit byaliasing them, interpreting high frequency changes as lowfrequency. The result is a recorded load curve that may beinvalid for most engineering and analysis purposes, as arethose in Fig. 23.

error in either case is minute and the issue unimportance. Onthe other hand, if there is a good deal of non-coincident load 25. Determination of the Sampling Method and Typebehavior, as usually with loads measured on the distribution Both period integration and instantaneous sampling recordsystem, then the sampling rate phenomena discussed here are only approximate data when applied at too low a samplingof concern in the load analysis and subsequent engineering. rate to track non-coincident behavior in the load. Instantaneous


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798 Characteristics o Distribution Loads Chapter 24

sampling aliases high-frequency load behavior, producing loadcurve data that is useless for engineering and load analysispurposes. On the other hand, period integration filters out thehigh-frequency behavior in the load, producing curves thatappear more coincident than the actual load. While thisintroduces an inaccuracy in subsequent load analysis andengineering, the curves are at least correct within the context ofcoincident load analysis.

dividing by 1,000 may seem to be a proper way to produce arepresentative single-household non-coincident load curve, itgives a smooth coincident curve instead.

In all cases, the preferred approach is to use periodintegration applied at a high enough rate to sample all thebehavior pertinent to the engineering. However, choice ofsampling rate and method is often a compromise between costand accuracy. There will always be some load behavioroccurring at a rate faster than can be sampled. Most loadscontain motor starting transients and switching fluctuationsthat can only be captured by very high (10 Mhz) sampling

Addition is a signal filtering process. The average curveobtained by addition/division of a number of customer sampleload curves is filtered, in a way that removed high frequencyload fluctuations. This is the major reason why many T&Dengineering studies and load analysis procedures consistentlyunderestimate non-coincident load behavior and oftenunderestimate the amount of coincidence (value of C(n) for nvery large). Most of the load curve data available to engineershas been obtained and processed by averaging a group ofsampled customer load curves. This averaging produces onlycoincident load curve data. Most load curve data in use atelectric utilities has been produced by averaging, over largeenough customer samples, that it is effectively representation

rates. of completely coincident behavior.The engineers and load analysts performing load research It makes no difference, in the example cited above, whether

must either select a load recording method that suits their the load curves added together were samples for 1,000needs, or make only valid use of the data that has been given to households on the same day, as described above, or perhapsthem. Recommended practice is to research fully where the 1000 days worth of one minute readings for one house. Inload curve data came from and how it was recorded, and if it either case, the result of adding together the sampled curveshas gone through any type of aggregation, filtering, or other and averaging them to create an average with create a smooth,process that might have altered coincident demand behavior. coincident load curve.Although a majority of recorded load research data comes from The usual reason that a set of load curves is averaged is todemand interval recorders (period integration), a surprising produce a single curve that is most representative of the setsnumber of sources produce discrete sampling. This includes behavior. Simply put, algebraic methods (averaging) cannotdata taken from SCADA systems, certain types of signal be used to produce average non-coincident curves: there is norecorders, as well as most portable devices made for logging work-around within normal algebraic approaches. Instead,

some form of pattern recognition or clustering analysis must beapplied to find the load curve most like all the others. For

loads on feeder and service level circuits. In addition, manypeople forget that data read by hand from strip and circularcharts is essentially discretely sampled data

The fact that instantaneous sampling can, and often does,example, the k- means method of cluster analysis can be used toidentify one or more curves which have, individually, the most

severely alias non-coincident load behavior does not mean it is average peak load, variation rates, energy usage, and dailynecessarily a bad recording method, but it must be used with curve shape.caution. Similarly, while period integration (demandrecorders, etc.) always records accurately within its samplingrate limitations, it can be applied at too slow a rate to seeneedle peaks and non-coincident load behavior that are present.

High sample rate does not guarantee high frequencies.Sampling a signal at a fast rate does not guarantee that therewill be high frequencies in the data. It could very well be thatthe load being sampled is smooth and has no high frequencies.Often, the sensors in recording machinery have a poor

27. Sampling Rate Influences Load Duration Curve ShapeLoad duration curves will appear different depending on the

sampling rate of the load data, too, as shown in Fig. 24. Sincedata sampled at faster rates sees non-coincident needlepeaks, it yields load duration curves that reflect that loadbehavior. Fig. 24 shows annual load duration curves for Fig.12A, based on 5- and 60-minute demand period sampled data.

response to high-rate fluctuations. For example, strip chartrecorders with a very tight dampers cannot respond to fast loadshifts. Essentially, such mechanical stabilizers remove highfrequencies from the load curve signal.26. Addition and Averaging Filter Load Curve Data

Suppose every one of 1,000 households served by aparticular feeder is sampled on a one-minute demand basis, fora full day (creating 1,440 samples per customer). An averageload curve can then be formed by adding all 1000 load curvesand dividing by 1000. The result will be a smooth, coincidentcurve, in fact the same curve shape (except for losses) thatwould have been recorded by measuring the feeder load at the Fig. 24Load duration curves of single residential customer (e.g.substation. While adding together 1,000 load curves and Fig. 12A) based on two sampling rates.


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Chapter 24 Characteristics o Distribution Loads 799

IV. DISTRIBUTION LOSSES ARE NOTPROPORTIONAL TO DEMAND SQUARED

One result of the coincidence behavior and sampling issuesillustrated in this chapter is that the load-related losses on apower distribution system generally do not correspond to thesquare o the metered demand. The difference is due tointeraction of demand sampling with the coincidence effects ofthe loads being served. Fig. 25 illustrates an extreme case, inwhich losses are a purely linear function of measured demand.The water heater operates for 15 minutes during the hour from6 to 7 AM, and 30 minutes in the hour from 7 to 8 AM.Demand measured on an hourly basis doubles. Electricallosses in the wiring serving this water heater also double.They do not quadruple (as they would if losses varied as thesquare of demand) because the peak load in every demandinterval is the same: as the demand changes from hour to hour,only the load factor changes.

In the extreme case shown in Fig. 25, losses in the lineserving only the water heater, are a purely linear function ofdemand. This will be true regardless of the demand periodintervals. Whether measured and compared on a minute, hour,day, or annual basis, losses are a linear function of demand.

Fig. 25Load of a water heater over a four-hour period (left) andthe losses that result in the line serving it (right).

Load behavior at the service (LV) level is seldom theperfect all or nothing on-off load situation depicted in Fig.25, but neither is the relationship between losses and load anIR relationship. Observed losses vs. demand behaviorgenerally falls somewhere between two extremes characterizedby fundamentally different behavior of the load:

Losses are a linear function o demand. In such cases, thepeak load is identical in every demand period and loadfactor changes from one demand period to another.Losses are a squared (quadratic) function o demand. Thelosses factor remains constant in each demand period butpeak load varies in proportion to demand. Fig. 2&A: Hourly losses vs. hourly demand over a one-weekThe exact nature of the losses vs. demand relationship period for the secondary circuit/drops serving one of the 282

observed in any situation will depend on the load curve itself, homes in a neighborhood served exclusively by a singlethe demand period with which load and losses are measured, distribution primary feeder* Lower (curved) line indicates aand possible errors in the monitoring and recording of the data. squared losses vs. demand relationship, upper (straight) lineFig. 26 shows three examples of losses vs. demand indicates a linear relationship. B: Hourly load-related losses vs.measurements on the distribution system. In all three, the hourly demand for the 12.47 kV distribution feeder serving theseobserved 1OSSeS VS. demand relationship lies within an envelope 282 homes. C: Monthly load-related losses vs. monthly energy(this can be converted to monthly demand be dividing energy bydefined by the two extremes - linear and squared behavior. 731 hours/month) for the same feeder over the same period.


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800 Characteristics o Distribution Loads Chapter 24

28. Relationship Between Losses and DemandUsually, electrical losses are modeled as a function of

demand with an equation fitted to measurements taken duringselected periods (e.g., the data in Fig. 26). Most often, thefunction used estimates hourly losses as a function of hourlydemand, using the maximum recorded hourly demand, andmaximum recorded hourly losses as factors in the computation.Either of two functional representations are often used. Asapplied to hourly data, they would be:

Losses(h) = L,,, x (a x D (h)/D,,, + b x (D(h)/Dma.J2) (6)Losses(h) = L,,, x (D(h)/ D,,,)

Where h indicates the hour,D(h) is the demand observed in hour h,Dmax = maximum recorded hourly demandLmax = losses during maximum demand houra+b=le is a value between 1 O and 2.0

The values a and b in equation 6 are essentially the same asthe a and b factors used in traditional computations of lossesfactor from load factor.2 They represent the extent to whichlosses behave in a linear, or squared, manner, respectively.Where losses are a linear function of load, a = 1 and b = 0, andthe value e in equation 7 would be 1 O. Where losses have asquared relationship to demand, a = 0, b = 1, and e = 2.0.

Significant non-squared losses behavior on distributionsystems usually occurs in the equipment that serves individualcustomers with small loads. The most extreme non-squaredlosses vs. demand behavior that is routinely encountered is asingle household load, as shown in Fig. 26A (data is takenfrom the same load as in Fig. 12A. This is the losses vs. loadsituation for the service drops leading to this single house.

As the measured hourly demand in Fig. 12A varies, both itspeak load and load factor vary roughly in proportion to oneanother. As a result, hourly losses vs. demand behavior is amixture of the two extremes discussed above. Modeling ofhourly losses as a squared function of hourly demand (a = 0and b = 1 in equation 6, or e= 2.0 in equation 7) gives 35%average absolute error. Error is 13.5% when using 15 minuteintervals. Modeling of the losses as a linear function ofdemand gives roughly twice these levels of error (almost alldistribution losses behavior is closer to squared than to linear).

Usually, proper selection of a, b, and e coefficients can cuterror by about 3/4. Use of a = .33 and b = .66 in equation 6minimizes average absolute error, reducing it from 35% to8.9%. Use of e = 1.51 in equation 7 similarly minimizes error,at 9.1%. The two equations provide different estimates on anhourly basis (with an average absolute difference of 4%) butare roughly equal in overall modeling accuracy. When usingquarter-hour demand periods in this example, a = .24, b = .76,and e = 1.6 minimizes average absolute error, at less than 5%.

The load curve shown in Fig. 12A is one of 282 residentialloads in a neighborhood served by a 12.47 kV feeder. Fig. 26B

For example, see Electric Utility Distribution Systems Engineering ReferenceBook, Westinghouse Electric Company, 1959, page 28.

shows the losses vs. demand data for this feeder, on an hourlydemand period basis. The relationship appears much closer tosquared than when the individual customer data was examinedon the same hourly basis (Fig. 26A). Error in estimating lossesas a function of demand occurs with a = .07, b = .93, and e =1.91. (A larger value of b, and a value of e closer to 2,indicates a more squared relationship). Generally, losses vs.demand behavior or equipment serving large groups ocustomers appears less linear and more quadratic (squared)than or smaller groups.

In Fig. 26C, the feeders losses and energy (essentially thesame as demand, demand = energy/173.33 hr./mth.) arecompared on a monthly basis, instead of the hourly basis usedin Fig. 26B. The observed relationship between losses anddemand is much more linear than when hourly intervals wereused to analyze the same load: error is minimized with a = .4 1,b = .59, and e = 1.52. The monthly demand period is muchlonger than the major cycle periods of the feeders load (dailyand weekly variations). Generally, losses vs. demand behaviorappears more linear if longer demand intervals are used in theanalysis.29. Mean Error in Estimating Loads

Representation of losses as a squared function of demand inequations like 6 and 7 usually results in underestimation of theaverage level of losses. Note the plotted lines, representinglinear and squared losses behavior in Fig. 26. The curverepresenting losses as a function of demand squared is lower inall cases than the measured losses. The line representinglosses as a linear function of demand is uniformly higher thanany of the losses measurements. This is always the case whenusing losses estimation equations such as 6 or 7, calibratedagainst peak period demand and the values D,,, and L,,,.

Generally, if the long-term performance of a load analysisand prediction equation is to overestimate losses, then it is toolinear in the calibration of its a and b, or e terms, regardless ofthe level of its average absolute hourly error. Similarly, if itconsistently shows a bias toward underestimating the amountof losses over many demand periods, then it has beencalibrated as too quadratic, even if it is giving satisfactoryaverage error on a demand-period basis.

T BLE 6COEFFICIENTSOR LOSSES vs. DEMAND ON AN HOURLYDEMANDPERIOD ASISAS A FUNCTION F SYSTEMLEVEL


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Chapter 24

30. Modeling Losses on the Distribution SystemThe relation observed between losses and demand on a

T&D system will depend on the customer load behavior, themeasuring and recording equipment being used, and thedemand period length of the recording and analysis.Generally, coincidence and demand period affect results:

I. Coincidence. Equipment that serves small groups ofcustomers, exhibits more linear losses vs. demandbehavior (higher ratio of a/b; lower e) than equipmentwith many customers downstream. For example, thesingle customer hourly data shown in Fig. 26A is muchmore linear than that for the group of 282 customers inFig. 26B. The two plots show essentially the same loadtype, observed on the same (hourly) demand periodbasis. Losses vs. demand for coincident load situationsis closer to quadratic. For non-coincident situations itis usually closer to linear.

Thus, the best values of a and b, or e, to estimatelosses as a function of demand on an hourly basis, willdepend on the level of the system being modeled.Table 6 gives typical values for b and e on powersystems in North America.

2. Demand period length. The losses vs. demandrelationship shown in Fig. 26A, for the service dropsleading to a household like that shown in Fig. 12A, is amixture of linear and squared behavior when sampledon an hourly demand basis. The hourly sampling rate ismuch longer than the natural on-off cycles of many ofthe major appliances (see sub-section 13 of thischapter). The losses vs. demand relation would appearto be nearly a perfect squared relationship if evaluatedon a minute by minute basis (not shown).

Similarly, losses vs. demand data for the feeder has aconsiderable non-quadratic behavior when viewed on amonthly basis (Fig. 26C), because the demand periodsare much longer than the daily and weekly load swingsnormally seen in the load, as well as the three- to six-day weather-front cycles which often affect theweather-sensitive portion of these loads. Hourlydemand periods (Fig. 26B) are much shorter than thesecycles, and observed losses vs. demand behavior at thisdemand period length is very nearly a perfectly squaredrelation. Short demandperiods produce more quadraticlosses vs. demand behavior; while long demand periodsresult in a relationship that appears more linear.Short and long as used here are relative to thedynamic cycles or periodicities of the load behavior.

Therefore, the overall losses vs. demand relationshipdepends on both the equipment level of the system beingstudied (amount of load or customers downstream) and thedemand period being used for data and analysis. Fig. 27 showsvalues of b (for equation 6) that work well as a function oflevel of the system and demand period in a typical residential

801

Fig. 27Values of b for equation 4 that give minimum error inestimating losses from demand for residential load in a utilitysystem in the southwestern United States. Losses vs. demandbehavior on other systems will differ quantitatively from thevalues shown here, but is generally qualitatively similar.Number of Customers less than 1 refers to individualappliances loads and household circuits.

31. Losses vs. Demand on the Entire Distribution SystemFrom 25% to 66% of distribution losses occur on portions

of the distribution system near the customer, portions thatdeviate significantly from a squared losses vs. demandrelationship. As a result, the overall losses vs. demandrelationship for an entire distribution system will usuallydeviate noticeably from a squared relationship. Thequantitative relationship varies from one system to anotherdepending on customer loads, system equipment types, andlayout and design used in the primary and service levels.Generally, b is in the range of .75 to .88, behavior is morequadratic than linear, but sufficiently non-quadratic thatsignificant error(on the order of 25%) results in predictinghourly losses from demand if a purely squared relationship isassumed.

Fig. 28Monthly energy vs. load-related losses for the system thatarea in the southwestern United States. The qualitative includes the feeder aid loads shown in Fig. 26. This includesbehavior shown occurs on all power systems. losses on feeders, laterals, and secondary/service drops. b 578


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802 Characteristics o Distribution Loads

VI. T&D SYSTEMS ARE BUILT TO SATISFYCUSTOMERS, NOT LOADS

32. Quantity, Quality, and ValueThe diverse types of consumers purchasing electric power

from the distribution system have different uses for the powerthey buy, different needs for quantity (amount of powerpurchased), and needs for quality (continuous availability, tightvoltage regulation), and different dispositions to pay apremium price to get exactly what they need. The value aparticularly consumer places on electric power is a function ofhis or her needs for electricity, primarily as defined by theeconomic or personal value of the end-use (i.e., watchingtelevision and keeping food cool, stamping sheet metal intoequipment cases, operating a cash register/inventory system),and as fashioned by the demands of the appliances used toconvert electricity into the end-use.

A personal computer exhibits demand characteristicsexactly the opposite of the water heaters. A typical PC has aconnected load of about 180 watts, and a contribution tocoincident peak of the same magnitude. But while itsconnected load is one twentieth, and its peak demand only onesixth of the water heaters, its demand for quality is muchhigher. Measured as the time it can go without power whilecontinuing to perform its end-use function, a PC is about15,000 times more sensitive to power continuity problems thana water heater. It is also vastly more sensitive to voltage sagsand surges, and long-term changes in voltage.

The major element of customer quality is availability ofsufficient quantities of power. Quality can be as or even moreimportant than quantity in determining the customer value, butthe important point is that both quantity and quality are majorfactors to be considered in determining how to maximizecustomer value. Two common residential appliances thatillustrate the opposite extremes in these two Q dimensionsthat can exist among customers. These are an electric waterheater and a personal computer.

Largely because of the different needs of their appliancesand equipment, and the difference values of the net end-useproducts, electric customers vary greatly in their demand forelectric power quality. Fig. 29 gives five examples of cost ofinterruption value of electric customers. The cost vs. timefunctions shown are not typical, because there is no typicalneed for power quality, just as there is no typical quantity ofpower requirement that suits all customers. In general,commercial and industrial consumers have a higher demandfor both quantity and quality of power than residentialconsumers.

A typical 50-gallon storage water heater has a connectedload of 4,000 watts, and a coincident contribution to systempeak of about 1,100 watts. This is a relatively high demand forquantity of power as compared to most household appliances(typically only central air conditioners or heaters use morepower). Power to a water heater can be interrupted routinelyfor several hours at a time (and often is under peak-shavingload control programs). Such interruptions make little impacton its value to the customer, because it can supply reasonablequantities of hot water from its storage tank during powerinterruptions. In addition, its end-use performance is virtuallyimmune to voltage sags, surges, and even significant long termvariations in supply voltage. Thus, while a water heater has ahigh demand for quantity, it has a low demand for powerquality.

In a competitive electric power industry, and a world whereattention to quality is taken for granted in many otherindustries, power system engineers should anticipate increasinglevels of attention on quality of power delivered. This does notnecessarily mean that quality must be or will be improved.Cost is an important element of value, and a large portion ofconsumers in most power systems would prefer to pay a lowerprice for power, even if that means they must sacrifice someamount of power quality in return. The important point is thatlike quantity of power, quality is an important attribute. As itis with quantity, it is possible to overbuild or underbuild apower system with respect to the amount of quality that needsto be delivered. The challenge facing power engineers is todesign the lowest cost system that can deliver the requiredlevels of both, and no more.

VI. GROWTH OF ELECTRIC LOAD AND T&DCAPACITY REQUIREMENTS

Fig. 29-Cast vs. interruption duration when an interruptionunexpected (top), and when one days notice is given (bottom).is

Chapter 24

33. Spatial Distribution of Load Defines T&D NeedsElectric load is not evenly spread throughout a power

systems service area, but instead, non-homogeneouslydistributed, with high load density in some areas and no load inothers, as shown in Fig. 30. This is due to the heterogeneousdistribution of land use and activity within any city, town, orrural region - some areas are more densely settled and activethan others. Not shown in Fig. 30, but an important fact indetermining electric load, is that customer class varies bylocation, too. Some areas of a system are nearly entirelyresidential, others commercial, or industrial, and others mixed.

The load map in Fig. 30 shows some very commoncharacteristics of spatial load distribution, shared by most largemetropolitan areas: high load density in the urban core,gradually decreasing toward the periphery, with tendrils ofhigher load density following major transportation corridors.


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Chapter 24 Characteristics o Distribution Loads 803

Fig. 30Spatial distribution of electric load for a city of about 1 million population in the eastern United States. Shading indicatesload density. Lines indicate major roads. At the left, 1998 winter peak load. At the right, a forecast of peak load for year 2010,based on projected trends in load density, customer count, area development, peripheral expansion, and end-use loads. The city isprojected to grow both up and out during the 12-year period. Some interior areas are projected to increase in load density, but othersare not, and load density decreases in a few areas. Load develops in previously vacant areas, particularly along the south periphery.

The load maps in Fig. 30 outline the mission of the T&Dsystem for the region shown. In the year 1998 it must deliver2,3 10 MVA of electric power in the geographic pattern shown.Its ability to do so reliably and economically is the majormeasure of its performance as a power delivery system.34. Load Density Varies With Location

Fig. 30 illustrates how load density varies as a function oflocation within a power system. Analysis of load in terms ofkW/acre or MW/square mile is a convenient way of relating itto local T&D capacity needs and is often used in powerdelivery planning. Load density is an important aspect ofT&D planning, since the capacity and location requirements ofT&D equipment depend on local load characteristics, notsystem averages. Typical ranges of values for urban, suburban,and developed rural areas are given in Table 7. The valuesshown are typical, but values specific to each particular systemshould be obtained by measurement.

TABLE7TYPICAL OAD DENSITIES ORVARIOUS TYPESFAREAS

35. Growth Drives System ExpansionFig. 30B shows the projected load 12 years later than Fig.

30A, based on a detailed evaluation of economic growth of theregion, land availability, demographic and zoning factors, andexpected changes in per capita and end-use loads. After this12-year period of growth, the T&D system will be expected todeliver 3,144 MW in the pattern shown. During the intervening12 years, additions and changes to the system must be made sothat it can grow along with the load. This load growth is themotivation for the equipment additions, and the expansionbudget will be well spent only if the equipment is located, andlocally sized properly, to match the evolving load pattern inFig. 30B.

Comparison of Fig. 30A and Fig. 30B reveals severalcharacteristics of load growth as it affects T&D systems:

Previously vacant areas develop load, e.g., the swath ofload growth across the entire southern frontier of this citybetween 1998 and 2010. Entirely new parts of the systemmust be built into these areas.Some vacant areas do not grow. For whatever reason,some areas remain vacant, often because of localcovenants or because they are for public use (parks, etc).Load in some developed areas increases in load density,perhaps substantially. Examples in Fig. 30 include theurban core and some areas in outlying areas.Load in some developed areas remains constant, or fallsslightly due to increasing appliance efficiency in areasthat otherwise remain unchanged (no new buildingconstruction or population increase).


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804 -_Chapter 24

The difference between Fig. 30A and Fig. 30B representsthe challenge facing this systems T&D planners. They mustmake additions whose equipment types, capacities, locations,and interconnections to the existing system result in a 12-years hence system that can reliably and economically servethe pattern shown.

36. Two Causes of Load GrowthTwo simultaneous processes create electric load growth or

change, both at the system and at the distribution level.Increases in the number of customers in the utility servicearea, and increases in the usage per customer cause electricload to grow. No other process causes load growth: If theelectric demand on a power system increases from one year tothe next, it can be due only to one or a combination of both ofthese processes:

I) New customers are added to a system due to migrationinto an area (population growth) or electrification ofpreviously non-electric households. Customer growthcauses the spread of electric load into areas that werevacant from the power systems standpoint.

2) Changes in per capita usage occur simultaneously andlargely independently of any change in the number ofcustomers. In developing economies this is driven bythe acquisition of new appliances and equipment inhomes and businesses. In developing nations, percapita load growth often decreases, due to improvingappliance efficiency.

In cases where per capita consumption is increasing, it isusually due to major shifts in appliance market penetration. Forexample, the percentage of homes and businesses using electricpower to heat the interior of buildings may increase from 20%to 26% over a decade. In such a case, even if applianceefficiency is increased slightly, electric load will grow.37. Spatial Load Growth and the S Curve Characteristic

When viewed from a total system basis, a growing powersystem generally exhibits a smooth, continuous trend of annualpeak load growth. Given a healthy economy, and corrected forvariations due to weather, the load in the region will simplycontinue to grow at a continuous rate.

Planners of the power supply to an entire region have noneed of specific geographic information on the locations ofloads

electric distribution load characteristics & diversity factor

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