7 th Symposium EKO TC 4 3 rd Symposium EKO TC 9 and 5 th WADC Workshop nstrumentation for the CT Era Sept. 8-2 Kosie Slovakia The universal model of error of ative power measuring hannel Boris Stogny Evgeny Tankevih nna akovlieva Gregory Varsky nstitute of Eletrodynamis National krainian Aademy of Sienes 56 Peremohy Avenue 368 Kyiv-57 kraine phone: +38(44)454-24-57 emailivya@ied.org.ua Abstrat-The types of the strutures of ative eletri power measuring hannel and features of funtions of measuring transformers in their onfigurations are onsidered. The universal mathematial model of measuring hannel error whih takes into aount influene of hannel s onfiguration individual metrologial performanes of separate measuring devies measuring operating onditions and the ontrolled eletri network mode on its value is developed. The example of appliation of the offered model is made. Keywords: model measuring hannel error.. ntrodution The problem of determination and redution eletri losses in networks is a very atual. n our opinion it is very important to provide high auray of eletri power measuring. The deision of this task must be based on an analysis and estimating errors of eletri power measuring. And it is important to take into aount as many as possible influening fators. Suh errors as ±(3 5)% or ( 2)% are onsidered as aeptable for the most measuring systems of eletri power in kraine whih depend on power of the eletrial power objet ()[]. n general over than 3 fators have an influene on the error of eletri power measuring. They are exeeding of normative terms of exploitation of separate measuring tools nononformity the seond loadings of measuring transformers to the set norms long-term eletri networks modes with parameters whih are onsiderably fewer than nominal bad quality of eletri power and et [2]. For example the error of measuring omplex whih onsists of measuring tools with auray lass 5 an exeed % at adverse onditions [3]. Therefore the wide appliation of eletroni watt-hour meters with high auray lasses does not provide neessary auray of eletri power measuring. At the same time the errors of eletri power measuring determine diffiulties in alulation of balanes of eletri power they an be reason of overrate of fuel and energy resoures or wrong estimation of produtive and eonomial ativity of separate enterprises and industry on the whole [4]. Therefore it s naturally that the problem of inreasing of auray of eletri power measuring remains in a fous of attention of subjets of krainian energy market. The plenty of publiations have appeared last years both in kraine and in Russia [5 6]. This is a result of interest to the problem. These publiations are devoted to the analysis of influene of errors of separate omponents of measuring hannel on auray of eletri power measuring and to possibility to orret the results of measuring. However most of these approahes didn t take into aount the influene of suh fators as struture of measuring iruit possible disagreements in the values of metrologial harateristis of phases measuring transformers unbalaned mode on measuring results. Some of these approahes onsider these fators roughly [6]. As set authors influene of the noted fators on the resultant error of measuring in a number of ases an be onsiderable. n this work authors propose the universal mathematial model of error of eletri power measuring hannel (C). This mathematial model takes into aount all above mentioned fators whih influene on the error value. The developed model is basis for the providing of high auray of eletri power measuring.. athematial model development The measurements of eletri power in high-voltage eletri networks are made by measuring omplexes. These omplexes onsist of groups of measuring urrent transformers (CT) and measuring voltage transformers (VT) ommuniation lines and measuring devies. Struture of omplex is determined by the types of applied metering devies by their number by voltage lass and by method of implementation of the eletri system neutral. Funtionally in suh omplex it is possible to selet C whih is providing ative power and energy measuring in one point of aount. Suh C onsists of three omponent parts: meter-three-phase voltage iruit meter-three-phase urrent iruit and three-phase eletri power meter (fig.). 34
7 th Symposium EKO TC 4 3 rd Symposium EKO TC 9 and 5 th WADC Workshop nstrumentation for the CT Era Sept. 8-2 Kosie Slovakia Current C CT group Link Voltage C VT group Link Ative energy meter Figure. Eletri power measuring hannel n three-phase eletri networks measuring of urrents are made by groups of transformers whih have two or three CT. easuring of voltages are made by groups of single-phase VTs or three-phase VT. sually there are three-phase energy meters with two or three measuring elements in suh C. Combinations of the three-phase urrent and voltage meter iruits and the number of measuring elements of meter determine six possible strutures of C. There are two most widespread C onfigurations in the eletri systems а) the Aron iruit whih is typial for the 6-35 kv eletri networks (neutral is isolated). t onsists of two-element meter of two phase CT and of two VT whih are onneted on the opened triangle; b) iruit onsisting of three phase CT of three phase VT and of three-element meter. This iruit is typial for kv and higher eletri networks (neutral is earthed). Studies of measuring transformers behavior in C have showed that the onditions of phase transformers operation in the hannel an differ from the onditions of single transformer operation. Their errors are different aordingly. Generally the behavior of every measuring transformer in a three-phase iruit is depend on intensity and harater of own input signal and seond loading and on intensity and harater of input signals and seond loadings all transformers of the group. nequality of number of transformers in a group and measuring elements in a meter the three-phase load unbalane in partiular due to onneting measuring devies for urrent and voltage monitoring only to the phase A define the differene of phase measuring transformers loadings. For example in the symmetrial mode seond loadings of two CT in phases A and C with onneted a three-element meter are equal on the module but their phases differ on 6. Thus at the analysis of ative power and energy measuring errors measuring transformers groups is neessary to onsider as the single measuring tool. Suh approah ompliates estimation of eletri power C errors but it provides high preision and top quality of solving energy-savings problems. Referene [7] offers the approah to develop the model of estimation of single measuring transformer errors. The authors apply this approah to develop the universal model of errors estimation of three-phase groups of suh transformers. The input and output signals of iruit of three-phase voltage measuring transformation an be desribed as follows omplex matries-vetors: A B C k where A B C phase voltages of ontrolled ; k input voltages of k-element meter. Generally proedure of signal measuring in C an be presented as a sequene of operations of transformation of information. There are four suh operations in three-phase voltage C. athematially multioperation proedure of three-phase voltage measuring an be presented in a next kind: 4 3 2 ( ) where [М ] the topologial matrix whih desribes sheme of phase VT primary winding onnetions; [М2 ] the matrix whih haraterizes the real sale transformation of voltages in separate VT; [М3 ] the matrix whih haraterizes potential drops in the onnetion lines between VT and their seondary loads; [М4 ] values of elements of this topologial matrix is determined the sheme of onnetion of VT seond windings and meter measuring elements; [ ] the matrix of general voltage transformation in C. Elements of matrixes [М ] [М4 ] are determined only the topology of iruit while values of elements of matrixes [М2 ] [М3 ] depend on the operation modes of network and the VT seond loading hanges. n partiular the elements of matrix [М2 ] whih haraterizes transformation of signals in the measuring transformers are determined the amplitude and phase errors of separate transformers of group. These errors depend on input signals and seondary loads of transformers. 35
7 th Symposium EKO TC 4 3 rd Symposium EKO TC 9 and 5 th WADC Workshop nstrumentation for the CT Era Sept. 8-2 Kosie Slovakia easuring transformation of three-phase urrent in the point of aount [ ] to the system of meter input urrents [ ] an be presented as the sequene of three operations. t is possible to ignore influene of onnetion line between CTs and meter: 3 2 (2) where matrixes [М ] [М2 ] [М3 ] are alulated like matrixes [М ] [М2 ] [М4 ] (). odel of transformation of information in the meter an be presented as a sequene of two operations: the first is T k whih simulates the algorithm of ative power alulation taking into aount the number k of meter measuring elements; and the seond is T whih haraterizes influene of meter metrologial performanes on the result of measuring. The alulation of ative power in a meter is exeuted on the following algorithm: P k Re j j (3) where urrent and voltage whih are given on the j-th measuring element of meter. j j j n a matrix kind (3) it is possible to write as follows: P Re (4) where the adjoint and transposed matrix. The meter error is a sum of a basi meter error b and additional errors i from l influening fators namely derivation of voltage of frequeny of ambient temperature of magneti-field and others: δ δ b Thus measuring power by a meter is given by the following equation: l Pmeas P δ P δb δi. (5) i On the basis of C strutural elements mathematial models ( 5) formalized mathematial desription of multiple-operation proedure of ative eletri power measuring has been exeuted and the diagram of determination of error of hannel has been built (fig.2). l i δ i. T id T id [ id ] [ id] T 3 P id P T [ ] T [ ] [ ] T [ ] T k P T P meas PC Figure 2. Flow diagram of determination of ative-power measuring error The modules T and T aordingly reflet measuring transformations of three-phase voltage () and of threephase urrent (2). Transformation of information in the meter is presented on flow diagram with two modules: T k and T whih are desribed on the top. The branh of the ideal power measuring is represented by a hannel whih onsists of three CT of three VT and of three-element energy meter. This hannel measures the power most exatly. There are three modules in it. The modules T id and T id simulate the ideal sale transformations of phase urrents and voltages of in aordane with the rated transformation ratio of CT and VT; T 3 simulate the algorithm of alulation of ative-power in a three-element meter as sums of phase powers. Thus total error of ative power measurement by C an be alulated using the following equation: 36
7 th Symposium EKO TC 4 3 rd Symposium EKO TC 9 and 5 th WADC Workshop nstrumentation for the CT Era Sept. 8-2 Kosie Slovakia P C = P meas P id = P ( + ) P id = P T + P. (6) The error omponent P T is equal to the differene between the meter input power P and power P id. t is determined by the metrology desriptions of CTs and VTs by their loadings by the number and harts of onnetion in groups by the number of measuring elements of meter and by parameters of onnetion lines. Thus P T takes into aount all of the soures of errors in C exept for basi and additional errors of meter. P T is alulated taking into aount () (2) and (4) as follows: Re М М М PT id Re (7) where matrix of measuring transformation of urrent and voltage in C: matrix of ideal sale transformations of urrent and voltage; id error P T : Converting (6) it is obtained: ; (8) matrix whih determines the id. (9) P meas = P id (+ T )( + ) = P id (+ T + + T ). Then total relative error of power measuring C at negleting omponents of the seond order infinitesimal equal: C = T +. (). Experimental test of the model The model was tested with the data of experiment from the parallel aount of eletri power by two eletroni meters ( Elvin kraine) of the same auray lass. One of them was onneting to the group of two CTs TPL- (auray lass 5) and the group of two VTs. Seond meter was onneting to the group of two CTs SL- (auray lass 2S) and the same group of two VTs. The errors of eah of these CTs had been experimentally determined at the real loading and at different values of primary urrents. The experiment was arrying out during a month on operating substation. The values of ative and reative energy were fixed by meters on 3-minute intervals. The errors of measuring of eletri power Cex were determined every day as differene of data of C with CT of auray lass 5 and data of C with CT of auray lass 2S. The developed model was used to alulate the error of C with CT of auray lass 5 on eah of the 3- minute intervals. From these data the error C was determined for every day. Aepted that the networks mode is symmetrial voltage is equal to its rated value and VT s errors an be negleted. The results of alulation of errors for two days with the middle and minimum urrents of are given in Table. Table. Comparison the experimental error Cex and the alulated error C Range of urrents / rat % Range Experimental error Cex% Calulated error C% 7 5 2 34-6 -64 4 3-4 -62-343 -76 V. The examples of appliation of mathematial model Let s onsider determination of error C of C on fig.3. The urrent errors and phase displaements of CTs in phases A and C are denoted by f CTA CTA ; f CTC CTC. The errors of VTs whih are onneted on voltages АВ and СВ are denoted by f VTAB VTAB ; f VTCB VTCB. Potential drops in the onnetion lines between group of VTs and their seondary loads do not take into aount. 37
7 th Symposium EKO TC 4 3 rd Symposium EKO TC 9 and 5 th WADC Workshop nstrumentation for the CT Era Sept. 8-2 Kosie Slovakia A B C CT A CT C eter VT AB VT CB Figure 3. C onsisting of two CT of two VT and of three-element meter The matrixes of measuring transformation of three-phase urrents and three-phase voltages in this iruit aording to () (2) are equal: 2 3 3 3 3 3 2 3 f Kn f VTAB jvtab f Kn VTCB jvtcb Kn CTA jcta f Kn here Kn Kn rated transformation ratios of VTs and CTs. The matrix for this iruit is alulated using the equations (8) (9): VTAB CTA ) f f f f CTA VTAB CTA Kn Kn CTC VTAB CTA ) jctc VTCB CTC ) f f f f CTC VTAB VTCB CTC VTCB VTCB CTC ).. Let s onsider that the VTs the CTs and the meter are the ideal measurement instruments i.e. their errors equal zero. Thus the error P T depends only on onfiguration of C. By performing transformation of (7) we obtain: P T Re Kn Kn n the ase of single phase-to-ground fault in three-phase isolated neutral system or in asymmetrial modes of grounded neutral systems there is zero-sequene urrent. Then we have the following value of error: B A B 3 PT B os B Kn Kn here В angle between vetors B and. Suh error an reah at a few perents of measuring power in networks with an isolated neutral under the longtime modes of earth-faults of one of phases on whih CT is set. C. 38
7 th Symposium EKO TC 4 3 rd Symposium EKO TC 9 and 5 th WADC Workshop nstrumentation for the CT Era Sept. 8-2 Kosie Slovakia 2. The developed model is used to alulate the errors C of C with CTs TPL- of auray lass 5 (see setion ) in balaned operating onditions at different primary urrents and power fators os. As an example fig. 4 shows the influene of the network mode (angle ) on an error of C. C % 25-3 -25 3 6-5 -75 - -25 Figure 4. Dependene of the error of C at the % nominal urrent from the angle For omparison the same dependene alulated by employing other model shows of the dotted line. This model desribed in the krainian normative doument [6] doesn t take into aount disagreements in the values of metrologial harateristis of phases measuring transformers and reommends alulating of C error by arithmeti average of CT errors. t explains the disagreement in a results. V. Conlusions The developed universal mathematial model of error of ative power measuring hannel on omparison with existent model allows additionally to take into aount omplex influene of different fators on the resultant error of measuring. These are the struture of hannel disagreements in the values of metrologial harateristis of phases measuring transformers the unbalaned mode et. t provides more exat analysis and evaluation of errors of eletri power measuring. The model is theoretial basis for the design the measuring hannels of optimum struture and high auray by implementation of effetive methods of errors orretion in the proess of power measuring. Referenes [] Coneption of design of the automated systems of aount of eletri power in the onditions of energeti market Department of Fuel and Energy of kraine 2. [2] Vasil'henko V.. Shpil'ka V.N. Panasyuk V.D. Cyapenko B.F. Features of the eletri measuring in main networks Eletriheskie seti i sistemi 3 p.63-7 27. [3] Zagorskiy Y.T. Komkova E.V. The limits of measuring error of at the ommerial and tehnial aount of eletri power Eletrihestvo 8 p.4-8 2. [4] Ginaylo V.A. Tankevih E.N. aevskiy N.D. Aount of eletri energy: problems and deisions Energetiheskaja politika kraini p.68-76 2 [5] N. E. ironyuk The proedure for measuring eletri power Мeasurement Tehnique vol.49 nº. 4 pp. 48-44 April 26. [6] Amount of eletri energy and eletri power. The typial proedure for measuring. V 3/8-27 K.: GRFRE 27.- 97 p. [7] Stogny B.S. Theory of high-voltage measuring transformers of alternating urrent and voltage Naukova dumka Kiyv 984 272p. 39