Comprehensive Analysis of Electrical Distribution Network Operation An Approach of Electrical Load Modelling

Transcription

1 Jao Klter, Mat Meldorf Comprehensve Analyss of Electrcal Dstrbuton Networ Operaton An Approach of Electrcal Load Modellng JAKO KILTER, MATI MELDORF Department of Electrcal Power Engneerng Tallnn Unversty of Technology Ehtajate tee 5, 9086, Tallnn ESTONIA Abstract: The electrcal dstrbuton networ operaton depends consderably on networ busloads, whch are formed by actve and reactve power of the substatons. Therefore, the networ operaton varables such as power flows, currents, voltages, etc. change smlarly as do loads. It s possble to notce perodcty, temperature dependency, stochastcty etc. Ths paper descrbes the dstrbuton networ montorng methodology based on the mathematcal model of load,.e. n descrbed approach, the networ busloads are modeled usng the mathematcal model of load and afterwards, modeled load values n dfferent condtons are used for networ montorng. Montorng s understood as networ operaton forecastng, smulaton, and analyss. Success of montorng s guaranteed by an adequate mathematcal model, whch descrbes the changes of the load durng the entre observable perod, both n the past and n the future. The results, obtaned through networ montorng process could be used for long- and short-term plannng and dspatchng, consderng adequate changes n tme, temperature dependency, probable devatons of the state varables etc. Based on the results t s possble to assess networ operaton and possble future scenaros and ther effect on the networ and apply approprate solutons to enhance system relablty and securty. An applcaton of networ analyss, modellng and estmaton but also valdaton of results wth real measurements obtaned from real dstrbuton networ s presented. Key-Words: busloads, dstrbuton networ, mathematcal model of load, load montorng, networ operaton montorng, SCADA, state estmaton. Introducton The nature of a power system s operaton depends on ts load. Load changes regularly, depends on weather condtons, and has a stochastc nature [. The purpose of generaton, transmsson and dstrbuton system s to cover the load n all condtons. The balance between generaton and consumpton must exst at all tmes. The power system load s controllable to some extent, for example, through electrcal tarffs or usng the load dependency of operatonal parameters (voltage and frequency). Nevertheless, possbltes of load control reman secondary as adjustable features of the power system operaton. The behavour of the load and the regulartes of the load change are prmary features of the power system operaton. In power system analyss load values are bascally needed for three man purposes: system securty studes, short- and long-term plannng of system operatonal dynamcs and short- and long-term system plannng. Each of those applcatons need dfferent approach. For example, n long-term system plannng, country s development stuaton, forecasts and other soco-economc crtera are consdered, but n power system securty studes the load s modelled consderng the mmnent effect of system behavour to contngences. In [ a long-term pea forecast possblty based on general modfed exponental model s presented. In ths paper, the attenton s pad to the modellng and handlng of the load from the perspectve of modellng and analyss of the dstrbuton networ operatonal dynamcs. Over the decades, power system engneers have looed nto the world of forecastng of the electrcal system load. Dfferent methods based on regresson analyss, tme-seres models, neural networs [3, fuzzy logc [4, expert systems etc. have been developed and appled. Comprehensve overvew of dfferent load forecastng methods s presented n [5. The above mentoned methods could be gathered nto noton of conventonal approach of load forecast,.e. the needed load forecast s found usng formal approach based drectly on load data, whch s gven n tme seres. Load forecast models are ISSN: Issue, Volume 3, December 008

2 Jao Klter, Mat Meldorf chosen accordng to the nature of ntal data (amount of data) and on the requred result (e.g. forecast lead tme). In case of forecast models the man attenton s pad to the applcaton of formal mathematcal methods accordng to certan crcumstances, not to consder the nature of the load. In the dstrbuton networ, close connecton between the electrcal networ operaton and the change of networ busloads prevals. The dstrbuton networ operaton s consderably nfluenced by networ busloads, whch are formed by actve and reactve power of the substatons. The avalablty of nformaton s somewhat modest n dstrbuton networs and therefore comprehensve methods for networ montorng should be used. Over the years dfferent methods for dstrbuton networ power flow calculatons [6, [7 and state estmaton [8, [9 have been composed and mplemented for dfferent studes. The outlne of ths paper s as follows: n Secton an overvew and prncples of montorng of the dstrbuton networ operaton are presented, n Sectons 3 and 4 basc prncples and methods for modellng of load and state estmaton of the dstrbuton networ are presented, respectvely. In Secton 5 results of the conducted study and correspondence of appled methodology to real networ operaton s presented. Secton 6 present conclusons obtaned from the study. Mathematcal Model of Load Electrcal Dstrbuton Networ Networ representaton and gatherng of nformaton Networ operaton modellng and estmaton Modellng of load and estmaton of load model Verfcaton of results and models Networ Dspatchng, Short and Long-Term Operatonal Plannng Fg.. Prncple dagram of montorng of dstrbuton networ operaton U 0 V = [P,Q,U,I p = [P,Q Electrcal Networ Load Montorng of Dstrbuton Networ Operaton The prncples of montorng of the dstrbuton networ operaton are presented n Fg.. Montorng conssts of networ representaton, gatherng of nformaton, modellng of load, estmaton of load model, networ operaton modellng and estmaton, verfcaton of results and models, and adequate decson mang consderng the results obtaned n dfferent condtons. The results of the montorng process can be used for networ dspatchng and for short- and long-term plannng purposes. The medum voltage (MV) dstrbuton networ can be represented as a set of feeders gong out from a transmsson substaton (HV/MV), consstng of lne parts and dstrbuton substaton connected to the end of MV feeders. Swtchng dsconnectors at the dsconnecton ponts can change the confguraton of a feeder (Fg. ). Hence, dstrbuton networ has radal structure and ts functonng s drectly specfed by loads and ther regulartes. In addton, MV/MV substatons and voltage regulators may be ncorporated. Fg.. Prncpal scheme of electrcal dstrbuton networ The load of a MV feeder s formed by actve and reactve loads of dstrbuton substatons. The load of a dstrbuton substaton s formed as the sum of LV loads and losses of dstrbuton transformers. Dspatch system SCADA meters state parameters of a feeder perodcally. Measured data may nclude values of actve and reactve power, currents and voltages at varous ponts of the feeder. Manly these varables are measured only n HV/MVsubstatons. From the vewpont of montorng and avalablty of the measurement data, the dstrbuton net- ISSN: Issue, Volume 3, December 008

3 Jao Klter, Mat Meldorf wor should be dvded nto operatvely observable and unobservable part (Fg. 3). In the observable part of the dstrbuton networ, the data, whch can be used for handlng the networ operaton, s obtaned by the dspatchng system (System Control and Data Aqucton - SCADA). SCADA gathers actve and reactve power, currents and voltages of a feeder n HV/MV substatons and at varous ponts of the feeder. The samplng frequency n the SCADA s usually once or more tmes per mnute. Smlar data for the unobservable part of the dstrbuton networ, e.g. LV dstrbuton networ, s not avalable. Although, measurng hourly electrcty consumpton of consumers for commercal purposes of the electrcty maret (energy meter readng, EMR) has recently expanded sgnfcantly, but unfortunately, the operatve connecton between dfferent measurng systems s mssng. However, the commercal data may also be used for estmatng the load models. When even the commercally measured data s mssng, load models can be estmated accordng to the data from the clent nformaton system (CIS). A smple, two-way teraton process s used n the computaton of the dstrbuton networ operaton (Fg. 4). Frst, the power losses and power transmsson n lnes are found startng from the busloads at the end of the feeder. As an ntal value of the bus voltage, the nomnal voltage may be used. In the second phase, the bus voltages are calculated, startng from the HV/MV substaton bus, the voltage of whch s consdered as gven. In the second phase of the calculaton, the load dependency on the voltage and the effect of the voltage regulators are consdered. The descrbed algorthm usually converges n 5 teratons. Determne ntal condton for voltage Calculate power flows and power losses n lnes Calculate lne voltage drop and voltages No Is the process converges Yes End Fg. 3. Loads on the varous levels of electrcal networ Fg. 4. Scheme of steady-state calculaton of radal dstrbuton networ In dstrbuton networ followng smplfcatons are made: shunt conductances of lnes are neglected, transformer shunt conductances are neglected and transformer losses are only consdered when determnng networ actve power and energy losses, nductances of cables are also neglected. Due to the fact that the dfference of nput and output voltage angle δ of any element of dstrbuton networ s small, t s therefore consdered that when calculatng voltages only real component of voltage ' drop s consdered Δ U = Δ and the magnary " U U component Δ s neglected (Fg. 5). If for -th segment of lne (Fg. 6) voltage U and value of actve power P and reactve power Q s nown at the begnnng of lne, and also resstances R and X, then voltage drop s ΔU = I Z = ( I ji )( R + jx ) = () = ( I R + I X ) + j( I X I R ) whch real part s consdered as voltage drop. Δ U ( I R + I X ) () Multplyng and dvdng the result wth voltage U, we obtan the equaton wth actve and reactve power values P R + Q X Δ U = U U+ (3) U In the bac-loop, when voltages are gven and we search for power flows, then power losses n -th lne segment are found ISSN: Issue, Volume 3, December 008

4 Jao Klter, Mat Meldorf Ps + Qs + Δ P = + R, (4) U + Ps + Qs + Q = + U+ Δ X (5) and actve and reactve power values at the begnnng of lne may be expressed as P = Ps + + ΔP (6) Q = Q + + ΔQ (7) s Here, actve and reactve power P s + and Q s + are the sum of branches actve and reactve power values leavng from node + and load. Fg. 5. Voltage drop and voltage loss at dfferent networ elements Fg. 6. Lne segment calculaton The calculaton of the unobservable dstrbuton networ operaton does not dffer essentally from the calculatons n the observable part of the networ. The networ confguraton s radal, and the necessary nformaton concernng the load s receved from smlar load models, as n the hgher level of the dstrbuton networ. Among the measurements some errors and mstaes are presented. Therefore, data estmaton s needed, especally for clearng up bad data. As the redundancy of data requred for estmaton s usually not avalable, tradtonal estmaton methods are not drectly applcable n dstrbuton networs. To get addtonal data load models are used. The last stage of the dstrbuton networ montorng s the assessment of models and networ operaton. Modellng and analyss of dstrbuton networ operaton s needed for short- and long-term operatonal plannng of the electrcal networ. It s necessary to descrbe adequately changes n tme, temperature dependency, probable devatons of the state varables and cover dfferent cases and scenaros. Based on the results obtaned t s possble to mae more economcal and techncal decsons to obtan more effcent operaton of the dstrbuton networ and enhance networ relablty. 3 Mathematcal Model of Load Dfferent methods based on regresson analyss, tme-seres models, neural networs, fuzzy logc, expert systems etc. have been developed and appled to model the electrcal networ load [0. Those methods can be named as forecastng models n where the needed load forecast s found usng formal approach based drectly on load data, whch s gven n tme seres. Forecastng models are formal data models, consderng only the data. Nature of the load s not consdered. More comprehensve soluton s obtaned by composng the mathematcal model of load. The mathematcal model, descrbng changes of load (actve power, reactve power, or curren conssts of three basc components [, [: P ( = E( + Γ( + Θ( (8) where E( s mathematcal expectaton of the load Γ ( s temperature-senstve part of the load Θ ( s stochastc component of the load. Mathematcal expectaton E( descrbes regular changes of a load, such as general trend and seasonal, weely, and daly perodcty. Mathematcal expectaton s prncpally non-stochastc and corresponds to the normal temperature. The temperature-senstve part of a load Γ ( descrbes load devatons, caused by devatons of outdoor temperature from the normal temperature [. The normal temperature (mathematcal expectaton of the temperature) s the average outdoor temperature of the last 30 years on any gven hour of the year. If the real outdoor temperature corresponds to the normal temperature, the value of the temperature-senstve part of the load s zero. To compare the temperature dependences of dfferent loads, the component Γ ( s normalzed Γ( = R( γ ( (9) where R( s rate of the temperature dependency of the load and γ ( s normalzed temperature dependency component. Rate R( represents the load ncrease when the temperature rses by EC. Component γ ( descrbes other regulartes of the temperature dependency, e.g. delay etc. In Fg. 7 an example of load temperature dependency wth daly values s presented. For comparson, temperature and normal temperature s also presented (scaled on the rght axs). Here the load long-term forecast E( + R( γ ( s acheved ISSN: Issue, Volume 3, December 008

5 Jao Klter, Mat Meldorf by addng temperature dependency to mathematcal expectaton. The stochastc component Θ ( descrbes stochastc devatons of the load [3. Due to the autocorrelaton, the devatons are stochastcally dependent on each other. It s practcal to normalze the stochastc component. The proper rate s the standard devaton of the load S(. The result s Θ( = S( [ ζ ( + ξ ( + π ( (0) where ζ ( s expected devaton condtonal mathematcal expectaton of the stochastc component. The expected devaton of the load may be used for short-term forecastng of the load. In Fg. 8 an example of real value of the load and addtonally the values of long-term forecast E ( + Γ( and short-term expected value E( + Γ( + S( ζ ( are presented. ξ ( s normally dstrbuted noncorrelated resdual devaton (whte nose) of the load. π ( s pea component that consders the exstence of large postve or negatve devatons (pea devatons) that do not correspond to the normal dstrbuton. In practce those devatons may be observed n low- and medum voltage networs, where they cause dstorton of load dstrbuton. Load (MW) Tme (days of year) 4 5 Fg. 7. Load real value (), mathematcal expectaton (), long-term expected value (3), temperature value (4), and normal temperature (5), daly values The structure of the mathematcal model s the same for all loads. In order to use the load model to descrbe the specfc load the model parameters must be estmated. In the estmaton process all regular data and other avalable quanttatve and qualtatve nformaton about the load s used. If the exstng data s not enough to evaluate all parameters of the model, then type-models (.e., a typcal set of model parameters) may be used. In such cases, the sutable amount of load parameters are determned by load statstcal data, and the rest of the parameters wll comply wth the type-model. The result of estmaton wll be a complete model for all loads ndependently from the amount of used data Temperature (ºC) Load (MW) Tme (hours of day) Fg. 8. Real value of the load (), long-term expected value () and short-term expected value (3), hourly values Mathematcal model descrbes the load, but t does not drectly determne the values needed n practce (load characterstcs). But t s possble to fnd these load characterstcs on the base of the load model. Load characterstcs may be dvded nto ntal and derved characterstcs. Intal characterstcs wll be obtaned from the mathematcal model drectly (load real values, mathematcal expectaton, standard devaton, temperature dependency etc.). Derved characterstcs are acheved wth combnatons of prmary characterstcs by smple arthmetc relatons (short- and long-term expected values, smulated load etc.). Durng the research and plannng of electrcal power system securty and relablty the load changes n tme must be consdered. Those changes are prncpally expressed by the mathematcal expectaton of the load. The mathematcal expectaton can be found based on load model for any tme nterval n the future or n the past. It must be emphassed that the mathematcal expectaton s calculated based on the parameters of the load model wthout usng the currently avalable load data. The temperature dependency has an mportant role n evaluaton of possble load devatons. From the aspect of power system securty and relablty the load ncrease durng extreme temperatures s especally nterestng. For example, n Fnland, Lapland, where the electrcal heatng has a substantal role, the load ncrease caused by low temperature may reach up to 00 % and more compared to the load n normal temperature. In case of load analyss and short-term forecastng the temperature dependency s calculated on the base of real temperature data. For the purpose of long-term forecast and analyss when requred t s possble to ISSN: Issue, Volume 3, December 008

6 Jao Klter, Mat Meldorf smulate the temperature. For example, t s possble to add devaton to the normal temperature or use some earler year data that correspond to the exceptonal weather condtons (cold wnter etc.). The nfluence of load standard devaton and thus also load stochastc devaton to the electrcal transmsson networ busloads and regonal loads s relatvely small. The stochastcty s more of a problem of smaller loads, a problem of dstrbuton networs. However, the stochastc component of the model enables to fnd the expected devaton of load and accordngly the short-term forecast of the load. The parameters of the mathematcal model are estmated durng the load research usng the avalable load data and other nformaton. It s possble to estmate the model parameters for dfferent load cases, whch are caused, for example, by swtchngs n lower lever networ or by connectng or dsconnectng large consumers to or from electrcal networ n tme and space doman. Whle n realty, where dfferent loads may change smultaneously, t s possble to tal about load scenaros. Dfferent load scenaros and also the smulated load orgnated from dfferent temperatures could be one of the sources for conductng the electrcal system contngency analyss. An example of load dfferent load cases s presented n Fg. 9. It s possble to observe that the load values n the substaton may be on two dfferent level. That characterstc should be consdered when calculatng and analysng the networ operaton. Fg. 9. Electrcal networ busload real values and mathematcal expectaton on two dfferent levels (load cases) 4 Dstrbuton Networ State Estmaton The target of state estmaton s to refne measured data, but t s especally mportant to clarfy sgnfcant measurng errors or mstaes. As the redundancy of data requred for the estmaton s usually not avalable n dstrbuton networs, tradtonal estmaton methods used n the man grd are not drectly applcable n dstrbuton networs. For gettng requred addtonal data, load models are used. The estmaton procedure on the base of load models s observed at [4, [5. The calculatng of feeder state parameters s based on networ equatons through man operatng parameters supply voltage and node loads V j ( U 0, p, p, K, p n ) () Symbol p corresponds here to both actve and reactve power. So the general number of loads n s equal to double number of nodes and so there are n + man operatng parameters U 0, p, p...p n. Supposng that for consdered moment there are m measurements (P, Q, U or I), t s possble to obtan the refned operatng parameters (refned measurements) V ~ j from the crteron ~ [ V j V j = mn, j=...m () j Because of the needed data redundancy does not exst n dstrbuton networs an addtonal condton s appled. It s needed that the ncrements of state parameters to be as small as possble Δ p = mn, =...n (3) Let us see the networ equatons beng lnearzed over man operatng parameters, when marng p 0 = U 0 ΔV j = β 0 jδp0 + β j Δp + β jδp β njδpn (4) where V j β j =, = 0...n p (5) In the form of matrx Λ = BΔ (6) where Λ = [ ΔV0, ΔV... ΔV m (7) s the vector of ncrements of measurng data Δ = [ Δp0 Δp... Δp n (8) s the vector of ncrements of man state parameters β0 β... βn B = β 0 β... β n (9) β β... β m0 m s the senstvty matrx (Jacoban). Here the ncrements Δ p are found on the base mn ISSN: Issue, Volume 3, December 008

7 Jao Klter, Mat Meldorf of the values calculated by a load model. It s possble to compose the mathematcal model also for the supply voltage U 0. For smplcty t s the trval model, where mathematcal expectaton and standard devaton of voltage are constant and devaton s descrbed by means of Box-Jenns model. For fndng elements of the senstvty matrx B t s necessary, at frst, to assgn the ncrements of the model parameters Δ p0... Δpn. Then to fnd the correspondng load values and at last to calculate the ncrements Δ V j of consdered state parameters on the base of non-lnearzed networ equatons. As a result ΔV j β j =, = 0...n, j =...m (0) Δp Let us see the extended vector of ncrements of measurng data ~ ~ ~ ~ Λ 0 = [ ΔV, ΔV... ΔVm,0,0...0 () n whch the n last components are zeros. Next, matrx B 0 wth n + columns and where on the frst m rows there are elements of senstvty matrx B and on the next n there s a zero vector and a unt matrx, s composed. β0 β... βn β 0 β... β n β m0 β m... β mn B 0 = () As mentoned above, condtons are smultaneously satsfed, f ~ T ~ Λ B Δ Λ B Δ mn (3) ( 0 0 ) ( 0 0 ) = Δ From here a system of lnear equatons over the ncrement vector Δ follows T T ~ B 0 B 0Δ = B 0 Λ 0 (4) The ncrement vector Δ allows to refne all state parameters t s possble to calculate both the specfed measured parameters (estmates) and whatever other operatng parameters. The results of state estmaton are authentc, f there are no bad data and exclusve states are not observed. If bad data are obtaned, they have to be removed and the estmaton procedure must be repeated. In case of exstence of an exclusve state that do not correspond to the load model, estmaton s not possble. Measurements of ths moment are not used. But that does not obstruct the process of estmaton n the next moments. 5 Edtng of the load models For consderng the possble changes of the load character t s necessary to edt (specfy) the model parameters. In ths connecton the model components are fxed. Let us see the node loads p wth parameters of the model a, a...a r at the moment t p (t, a, a... a r ), =...n (5) where r s the number of parameters that have to be estmated. Next the networ equatons are presented V j = V j (U 0, p, p,... p n ) (6) descrbng the state parameters va the parameters of the load model V j = F j (a, a,... a l ), j =...m (7) where l = nr s the overall number of the parameters of all load models. The functon F j corresponds to the moment t on whch the load values and supply voltage depend. The parameters of the load model are calculated from crteron V [ j V j = j ~ mn (8) where V ~ j s the measurng data at the moment. Networ equatons, lnearzed over the model parameters, are ΔV j = α jδa + α jδa αljδal (9) where V j α sj =, s =...l as (30) In the form of matrx Λ = A Δ (3) where Λ = [ ΔV, ΔV... ΔVm (3) s the ncrement vector of measured parameters Δ = [ Δa, Δa... Δa l (33) s the ncrement vector of model parameters α... α l A = (34) αm... αml s the senstvty matrx (Jacobean) If the vector of meterng devatons s ~ ~ ~ ~ Λ = [ ΔV, ΔV... ΔVm (35) then the ncrements for model parameters are calculated from the crteron ISSN: Issue, Volume 3, December 008

8 Jao Klter, Mat Meldorf ~ T ~ ( Λ A Δ) ( Λ A Δ) = Δ mn (36) that gves the system of lnear equatons over the vector Δ T T ~ ( A A ) Δ = A Λ (37) The base for lnearzng the networ equatons s the load values, calculated by load models (shortterm forecasts). Relatve to the same values meterng devatons are found. Lnearzaton s acceptable, f the meterng devatons are not too large. Otherwse t s necessary to use the teratve process, accordng to whch the ncrements are added to the model parameters and new state parameters and meterng devatons are calculated. In ths connecton repeated lnearzaton (calculaton of the new senstvty matrx) s not needed and t s possble to contnue wth the old matrx. The elements of senstvty matrx are calculated as follows ΔV j α sj =, s =...l, j =...m. (38) Δas The number of measurng data must be larger than the number of parameters beng estmated. For example, f the number of the loads s 0 (5 dstrbuton substatons), parameters 0 and measurements 0, then the number of the requred values s l = 00 and so more than 0 meterng hours are needed. Therefore the daly meterng s enough to get the results. But the authentcty of results s a separate queston. It s clear that the model, estmated on the base of the data of one or some days, s not usable for a longer perod. For example, the data of wnter loads s not representatve for summer loads. Generally t s an adaptaton problem, whch can be resolved tang nto account the essental meanng of the model parameters. The degree of the equaton system, oblged to be resolved, s hgh (for the above-mentoned example t s 00). It means that the volume of calculatons s too large and t may mean that the equaton system s ll-condtoned. The way out s to use the results of state estmaton, by means of whch the node loads are always found ndependently from the structure of measured state parameters. Consequently, t s possble to receve all load values, state parameters and edt the parameters of all load models. If m = and l = r we can get A = α... α (39) r [ Δa Δa Δ a r Δ =,... (40) ~ = [ ΔV = ~ p T ( A ) Δ ~ Λ (4) T A = ~ pa (4) where p~ s the estmated value of the observed load at the moment. The degree of the equaton system s now r or for the above-mentoned example t s now 0, and problems about calculaton volumes are removed. 6 An Applcaton of Dstrbuton Networ Montorng Descrbed dstrbuton networ montorng methodology was appled and tested based on real 35 V radal dstrbuton networ. The purpose of the research was to assess the measurements and compose adequate load and networ models for further research. The networ conssted of three HV/MV supply substatons, sx MV/LV substatons connected by ten OHL (Fg. 0). The system was montored by SCADA. The measurements receved through SCADA were currents, actve and reactve power n transmsson lnes, voltages n substatons and transformer currents at low-voltage wndng. Before applyng the above mentoned estmaton methodology t s practcally ratonal to perform prelmnary estmaton to determne large errors and exclude very bad data. Prelmnary estmaton s performed based on Krchhoff s current law. Fg. 0. Dagram of observed dstrbuton networ The results of the prelmnary estmaton are presented n Fg.. The sold lne shows that the measurements receved were correct and they can be used for further research and calculatons of the networ, dashed lne shows that the measurements were slghtly out of predetermned correct threshold values and dotted lne shows that the measurements are completely wrong and they must not be used. Utlzng the composed substaton busload models, voltage values and other parameters t s poss- ISSN: Issue, Volume 3, December 008

9 Jao Klter, Mat Meldorf ble to calculate the dstrbuton networ operaton. Based on the above-mentoned montorng methodology t s possble to dentfy f the networ state s compatble wth the load and networ models. In Fg. the results of modellng the transmsson lne current compared to real measurements are presented. It s possble to observe that the obtaned results of modellng the networ state varables are suffcently acceptable and comparable to the measured values of the networ state varables and therefore, t may be concluded that based on the descrbed methodology t s possble to model the networ operaton and use dfferent ntal condtons to nvestgate the networ behavour on dfferent condtons. Fg.. Measurement values accordng to threshold values (sold lne relable values, dashed lne doubtful values, dotted lne unrelable values), daly values Fg.. Measured (dotted lne) and calculated (sold lne) values on transmsson lne current, hourly values In Fg. 3 an example of long-term and shortterm forecasts of load are presented. Here, the longterm forecast s acheved by addng temperature dependency to mathematcal expectaton. The shortterm forecast s acqured by addng the loads expected devaton to the long-term forecast. Fg. 3. Actual load (), long-term forecast (), and shortterm forecast (3), hourly values 7 Concluson The dstrbuton networ montorng methodology descrbed n ths paper s based on the physcally well-grounded mathematcal model that consders tme-dependences, stochastcty, temperature dependency and also voltage and frequency dependences of load. Based on the mathematcal model of the load t s possble to calculate, forecast and analyse the networ operaton for shorter and longer tme perods and use the obtaned results for networ plannng and dspatchng. The effectveness of modellng and estmaton of the dstrbuton networ operaton depends on the accuracy of the load model. In the observable part of the dstrbuton networ the descrbed methodology enables to determne f the networ operaton s compatble wth the load and networ models, regular operaton or not. Although, due to the defcency of avalable ntal data the adjustment of the measurements s not feasble, t s possble to clarfy the faulty measurements. There are no computatonal lmtatons to employ the methodology because laborous computatons are absent. Furthermore, t s mportant that durng the analyss both state estmaton and edtng of load model are performed. As a result, the load models should always correspond to the real stuaton. The modellng offers smlar possbltes of handlng the operaton varables, as n the case of the loads. The operaton forecastng, analyzng, and smulaton are possble for dfferent gven condtons. The results are obtaned for any gven tme nterval, not just sngle states le n tradtonal calculatons. References: [ Meldorf, M. Electrcal Networ Load Montorng. TUT Press, 008, 44 pp. ISSN: Issue, Volume 3, December 008

10 Jao Klter, Mat Meldorf [ Petros. C., Pandels, B. Mchal, P., Manthos, V. Long-Term Pea Forecast n the Gree Power System. In Proc. 006 IASME/WSEAS Internatonal Conference on Energy & Envronmental Systems. Chalda, Greece, May 8-0, 006. pp [3 Hayat, M., Karam, B. Applcaton of Neural Networs n Short-Term Load Forecastng. In Proc. 7 th WSEAS Int. Conf. On Mathematcal Methods and Computatonal Technques n Electrcal Engneerng. Sofa, 7-9. Oct pp [4 Mallesham, G. A Fne Short-Term Load Forecastng Usng Neural Networs and Fuzzy Neural Networs. In Proc. 4 th WSEAS Internatonal Conference on Power Engneerng Systems (ICOPES`05). Ro de Janero, Brazl, Aprl 5-7, 005, 8 pp. [5 Alfares, H. K., Nazeeruddn, M. Electrc load forecastng: lterature survey and classfcaton of methods. Internatonal Journal of Systems Scence, vol. 33, no., pp. 3-34, 00. [6 Thuaram, D., Wjeoon Banda, H. M., Jerome, J. A Robust Three Phase Power Flow Algorthm for Radal Dstrbuton System. Int J Electrc Power Systems Research, Vol. 50, 999, pp [7 Wu, W. C., Zhang, B. M. A Three-Phase Power Flow Algorthm for Dstrbuton System Power Flow Based on Loop-Analyss Method. Int J Electrcal Power and Energy System, Vol. 30, 008, pp [8 Thuaram, D., Jerome, J., Surapong, C. A Robust Three-Phase State Estmaton Algorthm for Dstrbuton Networs. Int J Electrc Power System Research, Vol. 55, 000, pp [9 Perera, J., Sarava, J. T., Mranda, V. An Integrated Load Allocaton/State Estmaton Approach for Dstrbuton Networs. Proc of 8 th Int Conf on Probablstc Methods Appled to Power Systems, Iowa State Unversty, 004, pp [0 Alfares, H. K., Nazeeruddn, M. Electrc load forecastng: lterature survey and classfcaton of methods. Internatonal Journal of Systems Scence, Vol. 33, no., pp. 3-34, 00. [ Meldorf, M., Klter, J. Pajo, R. Comprehensve Modellng of Load. Proc. of CIGRE NRCC Regonal Meetng, 007, Tallnn, 8-0 June, pp [ Meldorf, M., Treufeldt, Ü., Klter, J. Temperature Dependency of Electrcal Networ Load. Ol Shale, 007, Vol. 4, No. Specal, pp [3 Meldorf, M., Täht, T., Klter, J. Stochastcty of Electrcal Networ Load. Ol Shale, 007, Vol. 4, No. Specal, pp [4 Meldorf, M., Treufeldt, Ü., Klter, J. State Estmaton Technque for Dstrbuton Networs. IEEE Conference Proceedngs, PowerTech 05. St. Petersburg. June 005. [CD-ROM, paper no [5 Meldorf, M., Treufeldt, Ü., Klter, J. Estmaton of Dstrbuton Networ State on the bass of a Mathematcal Load Model. Ol Shale, 005, Vol., No. Specal, pp ISSN: Issue, Volume 3, December 008