Uncertanty n measurements of power and energy on power networks E. Manov, N. Kolev Department of Measurement and Instrumentaton, Techncal Unversty Sofa, bul. Klment Ohrdsk No8, bl., 000 Sofa, Bulgara Tel./fax: (+ 359 965 4 47, 965 3 8, e-mal: manov@ vme.acad.bg n_kolev@vme.acad.bg Abstract. The problem on measurement of power and energy n sngle-phase and three-phase networks s always very mportant. The accuracy and precson of measurement s of equal mportance for both manufacturers and consumers. The general problem s to determne the uncertanty of the energy produced n a specfed power staton and delvered to dfferent consumers. Measurng nstruments used for energy measurement are voltage and current nstrument transformers and electrcty meters. The approach proposed combnes the nformaton that can be derved from the nomnal accuracy specfcatons of the nstrument transformers wth the nformaton resultng from the calbraton of the electrcty meters. The combnaton allows achevng the evaluaton of uncertanty n power and energy measurement. Both nstrument transformers are subject to rato error and phase error. In the paper an expresson for maxmum (postve and negatve errors as a functon of the relatve load current s derved. A method for calbraton of electrcty meters, measurement nstruments used n the procedure, processng and presentaton of the fnal results are presented as well. Havng the nformaton about the accuracy of both voltage and current nstrument transformers and fndng the uncertanty of electrcty meter (accordng to the method outlned, t s possble to determne the total uncertanty of energy (power measurement n condtons of load current varatons and dfferent modes of operaton. The fnal accuracy of energy measurement may be presented by gvng the specfcaton lmts n terms of measured value. Key words measurement, power, network, uncertanty, procedure.. Introducton The problem on measurement of power and energy n mono-phase and three-phase networks s always very mportant. The accuracy and precson of measurement s of equal mportance for both manufacturers and consumers, takng nto account world globalzaton and ncreasng market demand and exchange of electrcal energy. It should be mentoned that consderng the great number of publcatons n the feld of power measurement t s dffcult to realze sgnfcant contrbuton to the above problem. On the other hand every scentfc research leadng to the mprovement of metrology characterstcs and features of power and energy measurement systems s valuable and. wth practcal applcaton. Currently the large number of the power and energy measurng devces are sophstcated computer-based systems usng dgtal converson of nput current and voltage and havng varous features for measurement, calculaton and vsualzaton of dfferent parameters.. Statement of the problem In the paper the general problem s to determne the uncertanty of the energy produced n a specfed power staton and delvered to dfferent consumers. Ths problem s very mportant now for Bulgara because the energy home trade wthn country has been recently ntroduced. The electrcal energy area ncludes the generaton of energy, the dstrbuton of energy and fnally the utlzaton of energy. It s clear that the generated energy should be measured before dstrbuton for each one of the power staton outputs. Measurng nstruments used for energy measurement usually are: Voltage and current nstrument transformers; Electrcty meters The above mentoned nstruments should be wth compatble characterstcs. 3. Uncertanty Analyss A. Voltage and current nstrument transformers It s well known that both nstrument transformers are subject to rato error and phase error. These errors are set by Natonal and Internatonal Standards and are outlned nto the transformer documentaton. Both rato errors and phase errors are very mportant when voltage and current nstrument transformers are used to extend the range of watt meters and electrcty meters (watt-hour meters. The voltage rato error (f u of the voltage nstrument transformer s a result of the dfference between nomnal and real transformaton coeffcent. Phase error (δ u s defned by the phase angle dfference between the vectors of the prmary and secondary voltage. The dfference s zero when transformer s deal. Both rato and phase errors depend on: Burden values; Power factor; Range of the nput voltage devaton; The current rato error (f of the current nstrument transformer s a result of the dfference between nomnal
and real transformaton coeffcent. Phase error (δ s defned by the phase angle dfference between the vectors of the prmary and secondary current. The dfference s zero when transformer s deal. Both rato and phase errors depend on: Burden values; Power factor; Range of the prmary current varaton; Maxmum postve error f p+ for power measurement usng both voltage and current nstrument transformers s defned by the formula: ( + f ( + f cos( φ δ δ u u f p+ = ( cos φ Maxmum negatve error fp- for the above mentoned case s: ( f ( f cos( φ + δ + δ u u f p- = ( cos φ Where: f u & f are rato errors of the voltage and current nstrument transformers; δ u & δ are phase errors of the voltage and current nstrument transformers; cos φ - power factor of the burden; All errors are taken wth a postve sgn. Both expressons defne an area where the real error due to nstrument transformers n power measurement s stuated. The graphcal presentaton of ths area as a functon of the relatve load current s shown n Fg.. For practcal applcatons when the nformaton about transformers s avalable (graphcs for both rato and phase error these errors can be determned and consdered as systematc. Fg.. Error presentaton B. Calbraton of sngle-phase and three-phase electrcty meters The followng method defnes the prncple of calbraton, measurement nstruments used n the procedure, processng and presentaton of the fnal results. The prncple of calbraton The calbraton s based on drect comparson between measured energy values for both standard and electrcty meter. The relatve error s gven by the formula: N N r = 00, [%] (3 N c r where: N c =T.C pz T- base tme (tme of measurement, n sec. C pz - frequency of the standard for 00 % Р (Q, n p/s (Р actve power; Q reactve power; N r real value of the pulses proportonal to the energy; Measurng nstrument (standard The standard used n calbraton s a 3-Phase Precson Measurng Instrument TPZ 303. The followng parameters are measured, calculated and dsplayed to provde a comprehensve analyss of a three phase system showng nstantaneous and ntegrated values: True RMS values for each voltage and current nput; Analyss of DC component and harmonc content; Phase angles between all voltages and currents; Actve, reactve and apparent power; Power factor for each phase; Total actve, reactve and apparent power; Phase rotaton sequence and frequency. It s possble to nput external current and voltage transformers ratos, measured parameters wll then be shown as prmary values. 3 Processng of the results n calbraton The matematcal model descrbng the relaton between output value (percentage error and nput values s: = + (4
The estmate of the measured value, denoted by δ results from equaton (4 after substtutng the estmates of all nput values: δ = δ δ + δ, (5 where: δ estmate of the electrcty meter error; δ - estmate of the measured electrcty meter error; δ - estmate of the standard error, presented n the calbraton certfcate; δ correcton for the resoluton of the standard dsplay; All values are n percents. The estmate of measured electrcty meter error δ s obtaned by calculatng the arthmetc mean of a set of n measurement results: n λ = δ = λ, (6 n where : λ value of the error for λ result n the calbraton pont, n number of the measurement results n the calbraton pont. Standard uncertanty u(δ s determned by the standard devaton of the estmated error value accordng to the expresson: n λ = ( δ = ( λ -δ. u (7 n(n - Standard uncertanty of the standard s gven n ts calbraton certfcate. If the expanded uncertanty s U for a coverage probablty P = 95 % t can be wrtten: δ U u( δ =. (8 The correcton due to the fnte resoluton of the standard dsplay s wth rectangular probablty ' dstrbuton. The estmate s zero and margns δ, beng a half of the least sgnfcant dgt dsplayd by the standard.. Based on the above nformaton the standard uncertanty s: Uncertanty contrbutons ( δ ' u( δ =. (9 3 u δ related to the output estmate δ, are calculated by the followng expresson: u ( c u( δ, δ = (0. where c are senstvty coeffcents related to nput estmate δ,.е. fractonal dervatves of the model functon wth a respect to and estmates δ of the nput values: c = = = ; c = = = ; c3 = = = and u( δ are standard uncertanty of the nput values. The standard uncertanty assocated wth output estmate s: u 3 u = pc ( = ( δ, δ ( where: u( δ = u( δ ; u ( - u( δ ( δ = u( δ. u 3 pc δ = ; The expanded measurement uncertanty U s found as a product of standard uncertanty u ( δ of the output estmate and coverage factor k : U = k. u( δ. ( For a normal dstrbuton of measured quantty and a coverage probablty 95 %, k may be assumed = and formula ( s modfed: U =. u( δ. (3 4 Presentaton of calbratons results The frst part of the presented results ncluds nformaton about the calbrated electrcty meter and condtons of calbraton-table. The second part s Uncertanty budget presented n the TABLE.
TABLE I. Measurement results for dfferent load currents (calbraton ponts. Current value Power factor Error value, % 0 % I н 0 % I н 50 % I н 00 % I н Quantty I Error of the measured Energy Error of the Standard Correcton due to the dsplay resoluton Estmate δ,% 0,5 laggng 0,5 laggng 0,5 laggng 0,5 laggng Artmetc mean of the error, %... λ... λ... λ... λ... λ... λ... λ... λ TABLE II. Uncertanty budget Probablty Dstrbuton Standard uncertanty u(δ, % Uncertanty, % δ u ( δ δ u ( δ δ u ( δ δ u ( δ δ u ( δ δ u ( δ δ u ( δ δ u ( Senstvty Coeffcent c I δ Uncertanty Contrbuton u (δ=c.u(δ % δ Normal u( δ u ( δ δ Normal u ( δ - - ( δ 0 Rectangular u ( δ 3 u 3( δ Normal U(δ u 4. Electrcal crcuts Fg. Four-Wre Energy Measurement
Fg.3. Three-Wre Energy Measurement Fg. 4. Two-Wre Energy Measurement 5. Concluson Havng the nformaton about the accuracy of both voltage and current nstrument transformers and fndng the uncertanty of electrcty meter (accordng to the method just outlned, t s possble to determne the total uncertanty of energy (power measurement n condtons of load current varatons and dfferent modes of operaton. The fnal accuracy of energy measurement may be presented by gvng the specfcaton lmts n terms of measured value. References [] BSS 737-95 "Statc Electrcty Meters (electronc. Techncal requrements and testng methods. [] BSS 7397-98 Metrology. Dctonary of the basc and comon terms n metrology [3] BSS ISO IEC 705 General requrements for competence of testng and calbraton laboratores [4] BSS ISO 000 Unts SI and recommendatons for applcaton of dvsble and other unts [5] BSS ISO 3-5 Quanttes and Unts. Part 5: Electrcty and magnetsm [6] ЕА, publcaton ЕА-4/0 Expresson of the Uncertanty of Measurement and Calbraton