WO2008020667A1

WO2008020667A1 - Method and apparatus for estimating electric load composition considering transformer and digital power meter adopting same

Info

Publication number: WO2008020667A1
Application number: PCT/KR2007/000632
Authority: WO
Inventors: Jung-Wook Park; Soon Lee
Original assignee: Industry-Academic Cooperation Foundation, Yonsei University
Priority date: 2006-08-16
Filing date: 2007-02-06
Publication date: 2008-02-21
Also published as: KR100797192B1

Abstract

A recent increase of facilities including power electronics and electric machinery devices has resulted in an increase in voltage or current waveform distortion. Thus, quick and correct evaluation of electric load composition having a power system signal distorted as a result of not only intermittent switching operations of nonlinear loads but also harmonics is required. The present invention suggests modeling for estimating electric load composition ratios for an electric power consumer having a distorted current signal considering an actual transformer. A Kalman filter algorithm or a conjugate gradient method, which is an optimization method, is applied to evaluate electric load composition. In particular, since the Kalman filter optimization method has robust blocking capability against process distortion and measurement distortion, a nonlinear electric load composition ratio in each waveform due to nonlinearity and complexity in an actual environment can be estimated.

Description

METHOD AND APPARATUS FOR ESTIMATING ELECTRIC LOAD COMPOSITION CONSIDERING TRANSFORMER AND DIGITAL POWER METER ADOPTING SAME

TECHNICAL FIELD

The present invention relates to a technique of estimating electric load compositi on for an electric-power consumer by employing a Kalman filter algorithm or a conjugat e gradient method as an optimization method for modeling and evaluating the electric Io ad composition, and more particularly, to a method and apparatus for estimating electri c load composition for an electric power consumer by considering differences between an ideal transformer and an actual transformer when the load composition is modeled.

BACKGROUND ART Electric power systems are getting bigger and more complicated, and thus, syste m stability analysis related to power supply and distribution of the electric power system s becomes important. In order to analyze the stability of an electric power system, sim ulation in which power flow or system stability is calculated has been used. Since an i nappropriate power system model in this simulation causes a simulation result to be unr eliable, it is very important to improve and develop an efficient and correct power syste m model.

When an electric power system is modeled, correct load estimation in a load bus is particularly needed. By carrying out various studies, it has been disclosed that the I imitation of system stability in power transmission lines can vary up to more than 50% a ccording to an estimation of a selected load model. The correct load estimation is con sidered to be the most vulnerable portion in stability analysis due to the uncertainty of v arious load components, and thus, it is necessary to develop an enhanced load estimati on system.

Various representative electrical loads, such as a lighting apparatus, a motor driv e, and a Personal Computer (PC), of an electric power consumer have a specific chara cteristic that when a voltage waveform having a sine curve is supplied to each system, i ts current may be distorted. Thus, it is necessary to estimate a ratio of each load sam pie to load samples of the entire system by measuring a current waveform and a voltag e waveform at a service input terminal of each system. In particular, a recent increase in facilities including complex nonlinear power ele ctronic devices has resulted in an increase in voltage or current waveform distortion in a system. Thus, requirements for quick and correct estimation of electric load composit ion having a power system signal distorted as a result of not only intermittent switching operations of nonlinear loads but also harmonics are increased.

DETAILED DESCRIPTION OF THE INVENTION

TECHNICAL PROBLEM

A recent increase in facilities including power electronics and electric machinery devices has resulted in an increase in voltage or current waveform distortion. Thus, qu ick and correct evaluation of electric load composition having a power system signal dis torted as a result of not only intermittent switching operations of nonlinear loads but als o harmonics is required. In addition, in order to supply good electrical energy to custo mers and maintain reliability, a load model of various typical load groups for power distri bution system analysis including the study of load flow and stability is required. In addi tion, correct load modeling for electric load composition evaluation of a digital power me ter is necessary for load flow analysis, voltage stability analysis, and effective analysis f or intelligent digital switchgears and power device diagnostic systems.

The estimation of electric load composition can be performed by suggesting mod eling for electric load composition ratio estimation for an electric power consumer by me asuring a current waveform from each load and employing a Kalman filter algorithm or a conjugate gradient method as an optimization method. However, as well as a curren t waveform from each load of an electric power consumer (home or factory) being meas ured, factors of a commercial transformer used by the electric power consumer must be considered.

Thus, the present invention provides a method and apparatus for estimating elec trie load composition for an electric power consumer, whereby modeling for electric load composition ratio estimation for an electric power consumer is performed by measurin g a current waveform from each load considering factors of a transformer in order to est imate electric load composition of an actual electric power consumer using the transfor mer, and power management and control of a power distribution system by using electri c load composition evaluation can be performed by applying an optimization method to the modeling. The present invention also provides a digital power meter using the method and apparatus for estimating electric load composition of an electric power consumer.

TECHNICAL SOLUTION

According to an aspect of the present invention, there is provided a method of es timating electric load composition for an electric power consumer, the method comprisin g: measuring current waveforms of a plurality of loads of the electric power consumer u sing sensors; deriving a final model function represented by the equation below by mod eling electric load composition based on the measured current waveforms

s electric Io ad composition ratios for the electric power consumer; and estimating the electric load c omposition ratios for the electric power consumer by calculating the load coefficient vec tor k from the final model function by using an optimization method.

The measuring of the current waveforms may comprise: dividing the loads of the electric power consumer into a first load group receiving a voltage without a transformer and a second load group receiving another voltage after the transformer; measuring a waveform of a total current flowing through the first and second load groups using a first sensor; measuring a waveform of a current flowing through each load belonging to the first load group using a second sensor; and measuring a waveform of a current flowing through each load belonging to the second load group using a third sensor.

According to another aspect of the present invention, there is provided an appar atus for estimating electric load composition for an electric power consumer, the appara tus comprising: a current waveform measurement member measuring current waveform s of a plurality of loads of the electric power consumer; a model function derivation me mber deriving a final model function represented by the equation below by modeling ele ctric load composition based on the measured current waveforms

where the load coefficient vector k denotes electric load composition ratios for t he electric power consumer; and an estimation member estimating the electric load co mposition ratios for the electric power consumer by calculating the load coefficient vect or k from the final model function by using an optimization method.

The current waveform measurement member may comprise: a first sensor meas uring a waveform of a total current flowing through a first load group receiving a voltage without a transformer and a second load group receiving another voltage after the trans former; a second sensor measuring a waveform of a current flowing through each load belonging to the first load group; and a third sensor measuring a waveform of a current flowing through each load belonging to the second load group.

The present invention suggests modeling for estimating electric load composition ratios for an electric power consumer having a distorted current signal. When the mo deling is performed, factors of a commercial transformer are considered. The Kalman fil ter algorithm or the conjugate gradient method, which is an optimization method, is appl ied to a modeled system in order to evaluate electric load composition. In particular, si nee the Kalman filter optimization method has robust blocking capability against proces s distortion and distortion in measurement, a nonlinear electric load composition ratio in each waveform due to nonlinearity and complexity in an actual environment can be est imated, and thus, the concept of the present invention is used to implement a new digit al metering system.

ADVANTAGEOUS EFFECTS

The present invention relates to a method of estimating electric load composition , in other words, a method of determining the amount of each load group by directly me asuring a total current waveform at a service input terminal of a power distribution syste m. Incandescent lighting, fluorescent lighting, PCs, and motor drives generally used b y a customer are selected as representatives of electric load samples, and in order to e stimate electric load composition, a conjugate gradient method and a Kalman filter algor ithm can be successfully applied. In particular, the Kalman filter algorithm can be first used to perform time-varying estimation. This has characteristics of states occurring d ue to process noise and observation results due to measurement noise. Electric loads to which voltages having different levels are supplied from a delta-wye (Δ- Y) transfor mer are considered. A simulation result shows that the delta-wye transformer changes phase correlations and sizes of harmonic frequency components of loads and causes a change of load composition. Studies of expanding the suggested estimation method to a big-scale multi-bus system and substituting a given harmonic load model into a st andard load flow program have been undertaken. A power system can be efficiently a nd stably controlled by applying correct load modeling for electric load composition eval uation to the analysis of load flow and voltage stability of a power distribution system for electric power consumers. By breaking from the conventional metering system conce pt for calculating the amount of electric power, a new demand creation effect can be pr edicted by the development of a real-time digital power meter for electric load compositi on evaluation and power quality monitoring/diagnosis, thus contributing to the electric p ower industry by means of the improvement of stability and reliability of operation of a p ower distribution system.

DESCRIPTION OF THE DRAWINGS

The above and other features and advantages of the present invention will beco me more apparent by describing in detail exemplary embodiments thereof with referenc e to the attached drawings in which:

FIG. 1 is a flowchart of a method of estimating electric load composition for an el ectric power consumer according to an embodiment of the present invention;

FIG. 2 is a diagram for describing a method of measuring a load current consider ing a transformer according to an embodiment of the present invention;

FIG. 3 shows a waveform of a total electric load current i(t) in a service input te rminal, which is measured during one period T of a fundamental frequency; FIG. 4 shows frequency components after Discrete Fast Fourier Transformation (

DFFT) is applied;

FIG. 5 shows typical current waveforms according to load types during one perio d T of the fundamental frequency; FIG. 6 shows distribution of estimated values of x(n)\

FIG. 7 shows the performance of an estimation result using a Kalman filter algori thm;

FIG. 8 is a flowchart of a method of estimating electric load composition for an el ectric power consumer when the conjugate gradient method is applied as an optimizatio n method according to an embodiment of the present invention;

FIG. 9 shows a delta-wye (Δ- Y) 3-phase transformer model;

FIG. 10 shows current waveforms of respective loads during one period when a delta-wye transformer is used in a service input terminal (it is assumed that Y = J);

FIG. 11 shows normalized distribution of estimated values of χ(«) after a delta- wye transformer is used; and

FIG. 12 shows the performance of an estimation result using the Kalman filter al gorithm after a delta-wye transformer is used.

BEST MODE

where the load coefficient vector k denotes electric load composition ratios for t he electric power consumer; and estimating the electric load composition ratios for the electric power consumer by calculating the load coefficient vector k from the final mod el function using an optimization method.

MODE OF THE INVENTION Hereinafter, the present invention will be described in detail by explaining preferr ed embodiments of the invention with reference to the attached drawings.

FIG. 1 is a flowchart of a method of estimating electric load composition for an el ectric power consumer according to an embodiment of the present invention. Referrin g to FIG. 1 , a waveform of a current flowing through each load of the electric power con sumer and a waveform of a current flowing through a power input terminal of the electri c power consumer (i.e., a total current flowing through the combined load of the electric power consumer) are measured using sensors in operation 100 and 100'. In this case, the current waveforms are measured during one period of a fundamental frequency.

A method of measuring the current waveforms is illustrated in FIG. 2. Referring to FIG. 2, a load group is divided into two groups. That is, the load group is divided int o a load group 27 directly receiving power from a power input terminal 21 of the electric power consumer (hereinafter, a first load group) and a load group 29 receiving a differe nt voltage via a transformer 28 (hereinafter, a second load group).

A first sensor 23 for measuring a total current (i_A + i_B) flowing through a main po wer line 22 toward the first load group 27 and the transformer 28 is installed. In the firs t load group 27, waveforms of currents i_{B l} , i_{B 2} through to i_{B m}__λ , and i_{B m} respectively flowing through electric branch lines 24a, 24b through to 24m-1 , and 24m connected t o respective loads 27a, 27b through to 27m-1 , and 27m are measured using second se nsors 25a, 25b through to 25m-1 , and 25m. Similarly, in the second load group 29, wa veforms of currents i_{A X} , i_{A 2} through to i_{A n}__x , and i_A>n respectively flowing through ele ctric branch lines 31a, 31 b through to 31 n-1 , and 31 n connected to respective loads 29 a, 29b through to 29n-1 , and 29n are measured using third sensors 33a, 33b through to 33n-1 , and 33n.

In most actual environments, load composition is not disclosed. In this situation , electric load composition can be deduced from a nominal current waveform of each in dividual load component. It is assumed that a total electric load current is measured at a service input terminal and a Fourier analysis result of the total electric load current is represented by Formula 1. i(t) = m.0∞s(ωt)+n5.5cos(3ωt -2°)+75.0cos(5ωt -4°)+ 65.0cos(7ωt -6°) (1) In Formula 1 , the fundamental frequency is 60 Hz. A voltage between lines at t he service input terminal is 480 V having a nominal sine wave (used as a peak value). Basically, the waveform of the total electric load current i(t) during one period T in F ormula 1 is illustrated in FIG. 3. In FIG. 3, the number of used samples is 16,668. A sampling frequency is high enough to satisfy the Nyquist theorem with respect to the fu ndamental frequency component and other frequency components (third, fifth, and sev enth harmonic waves). A response in the frequency domain after Discrete Fast Fourier Transformation (

DFFT) is applied to i(t) is illustrated in FIG. 4. In FIG. 4, i{t) sequentially shows the fundamental frequency component, the third harmonic component, the fifth harmonic co mponent, and the seventh harmonic component. The amplitudes of the frequency co mponents are equal to the values given in Formula 1. [Table 1]

When a sinusoidal voltage is supplied to the loads, typical load groups of the curr ent /(O are illustrated in Table 1 and FIG. 5. In Table 1 and FIG. 5, load types are typ es of incandescent lighting, fluorescent lighting, PCs, and motor drives and are represe nted using subscripts i, f, c, and m.

Referring back to FIG. 1 , in order to determine electric load composition ratios fo r the electric power consumer, the electric load composition is modeled based on the m easured current waveforms in operation 110.

In the current embodiment, since real-time estimation of the electric load compos ition is the objective, the basic concept for the electric load composition is required, and solving procedures for inducing system equations, which can be applied to and the rea l-time estimation, are required.

By referring to the typical load groups illustrated in Table 1 , the total electric load current /(O of Formula 1 is represented by Formula 2. /(O = tø(0+ k₂i_f(t)+ k₃i_c{t)+ V_M(0 (2)

Here, Ic₁ , k₂ , k₃ , and &₄ are unknown coefficients. This estimation problem c an be solved by minimizing the value of an objective function J represented by Formul a 3.

J = 0(0" tø(0+ k₂i_f(t)+ k₃i_c(t)+k₄i_m(t)}dt (3)

Formula 3 is the equation for transposing the items in the right side of Formula 2 related to load currents to the left side and integrating {(left side)-(right side)}² during on e period, i.e. t=O~T. In the minimum value calculated using Formula 3, a differential va lue of the objective function J related to the coefficients will become exactly 0. For th is calculation, four equations corresponding to the four unknowns, i.e. the four coefficie nts A₁ , k₂ , A₃ , and Ar₄ , are induced. Solutions of the four equations become a coeffic ient vector k = [k_v Jc₂, Jc₃, Jc₄]. Thus, an actual load amount of each electric load sample can be easily determined, and accordingly, a real power, an apparent power, and a pow er rate can be simply calculated.

The continuous-time objective function J of Formula 3 can be expressed as a d igital discrete-time function for computer simulation as represented by Formula 4. In F ormula 4, N denotes the number of samples obtained during one period T of the fun damental frequency.

J = Σ ['^"(«)- *.',(")+ V/M+ *3*c W + KL (4 (4)

In Formula 4, if the objective function J is differentiated with respect to the coef ficient vector k , Formula 5 is obtained.

The equations of Formula 5 are arranged in the form of a linear system equation of the pattern Ax = b as represented by Formula 6. As a result, the solution x of an equation is coefficient vector k and can be directly or iteratively obtained using various calculation algorithms. For example, a Kalman filter algorithm or a conjugate gradient method can be applied as the optimization method. These will be described below.

Referring back to FIG. 1 , after the electric loads of the electric power consumer a re modeled as represented by Formula 6, an optimization method, such as the Kalman filter algorithm or the conjugate gradient method, are used in operation 120 to calculate the load coefficient k . As described above, the load coefficient k indicates composi tion ratios of the electric loads of the electric power consumer. Application of the optimization method

The solution x of Formula 6 can be easily calculated by obtaining the inverse of A and multiplying a vector b by A i.e. x = k = A 'b = [k_{ι >}k₂,k_{3 )}k_i]= [0Λ935, 0.1220, 0.5443, 0.1412f (normalized).

As described above, considerable important factors are speed and stability of co nvergence for accomplishing a solution of a linear or nonlinear system equation. In a big-scale service input terminal having many electric load groups or a big-scale multi-bu s system, the system equation A in Formula 6 becomes a big matrix having the limitati on to directly obtain the inverse of A .

In addition, recently big-scale power systems employ a Supervisory Control And Data Acquisition (SCADA) system to transmit data from remote sites to the central com munication unit by disposing a plurality of Remote Terminal Units (RTUs) in the fields. An RTU in each electric branch line processes communication with the central commu nication unit and data acquisition via a channel of the SCADA system. In this situation , the size N_A of the matrix A that is handled when performing estimation in the centr al communication unit will become too large.

Thus, techniques for obtaining a solution as quick as possible within the number of calculable cycles must be used. Representative mathematical techniques for solvin g linear/nonlinear system equations are disclosed in "Todd K. Moon and Wynn C. Stirlin g, 'Mathematical Methods and Algorithms', Prentice Hall, New Jersey, 2000, ISBN 0-20

1-36186-8" and "G. J. Borse, 'Numerical Methods with MATLAB', PWS Publishing Com pany, 1997, ISBN 0-534-93822-1". In general, direct techniques, such as Gaussian eli mination, described in these papers are usefully employed when they are applied to a Ii near system having a matrix A of small JV₄. If N_A is increased, it is preferable to u se iterative techniques.

Estimation using the Kalman filter algorithm

The Kalman filter algorithm has a smoothing characteristic and a robust noise ca ncellation capability to process noise and measurement noise. In an actual environme nt (i.e., an environment in which each state occurs by the process noise and an observ ation result is generated due to the existence of the measurement noise), an estimation problem for electric load composition can be formularized using a linear time-varying st ate equation. In this case, the Kalman filter algorithm is first of all applied (reference: " Todd K. Moon and Wynn C. Stirling, 'Mathematical Methods and Algorithms', Prentice Hall, New Jersey, 2000, ISBN 0-201-36186-8"). In this study, a state model used for e stimation is given by Formula 7.

x(n + l) = Φx(n)+r<o(n), x(θ) = x_o

z(n) = y(n)+ \(n)

In Formula 7, φ(e R^nxn), τ(≡ R^nx"), and c(≡ R"^x") denote known decision variabl es, x(e i?"^xl) denotes a state vector where x = [k_vk₂,k₃,k₄], ω(e R"^xl) denotes a proces s noise vector, z denotes the measured total current i in Formula 1 , and v denotes normal measurement noise. Estimation of the state vector using the Kalman filter algo rithm is updated as follows.

D Kalman filter algorithm • Measurement update: obtain z(n) and calculate the following equations. k{n) = V^~(n)c^T[cV-(n)c^T + rY x(n) = x^" (n) + k(π)[z(n) -

P(») = P^"(«)-k(«>?p-(«) Here, k(e i?"^xl) denotes a Kalman gain, P denotes an absolute symmetric matr ix of positive numbers, and r denotes a positive number (in most cases, V(O) = XL (X >0) where I is the unit matrix).

• Time update: calculate previous values corresponding to the time n + \ . x^~(n + l) = Φx(n)

Here, Q(e R^mxm) denotes an absolute matrix of positive numbers.

• Time increment: increase n and perform iteration. D Meanwhile, an estimated result is obtained as follows. j(n) = cx(n) (8)

In the current embodiment, when the Kalman filter algorithm is applied, the last v alues of χ(n) are obtained as [0.1935, 0.1220, 0.5434, 0.1412J (normalized). These es timated values converge to values very close to a correct solution. Variation distributio n of estimated values of x(n) while iterating is illustrated in FIG. 6. In addition, FIG. 7 shows that a measured waveform almost matches a waveform estimated using the KaI man filter algorithm.

Application of the conjugate gradient method

In many multi-variable problems in engineering, mathematical optimization meth ods are important to obtain solutions of linear/nonlinear functions. A generally used "st eepest descent" method is easy to implement. However, the steepest descent method has a disadvantage in that a convergence speed is slow. The conjugate gradient met hod is obtained by improving the steepest descent method to achieve a surprising effec t. The greatest advantage of the conjugate gradient method is a quadratic converg ence characteristic (reference: J. Nocedal and SJ. Wright, Numerical Optimization, Spri nger-Verlag, New York, 1999), since a search direction is conjugated in relation to a He ssian matrix as a solution calculated using a second order differential equation in Newto n's method. In other words, since the conjugate gradient method does not require a s econd order differential equation, the conjugate gradient method is sometimes more effi cient. The conjugate gradient method applied to the estimation problem can be summa rized as follows. FIG. 8 shows that the conjugate gradient method is applied as the op timization method.

D Conjugate gradient method

Given the initial x₀ ,

Define initial residual vector g = A-χ_o-ib .

While (||g|L > l(T⁶)

Compute the step-size parameter a by

. x = x + a d .

.

Compute the search direction β by

/? = g^T - A -d/(d^r - A -d) . d = -,g + /? -d . k = k + l . End D Under the same initial value χ₀ and the same end condition |g|₂ > 1O^~6 , the perf ormance of the steepest descent method is compared to the performance of the conjug ate gradient method, and the comparison result is illustrated in Table 2. Table 2 show s the comparison of the performance of two mathematical methods for electric load esti mation. Referring to Table 2, it is obvious that the conjugate gradient method has a m uch stronger and more efficient convergence performance than the steepest descent m ethod. [Table 2]

As described above, by performing optimization using the optimization method, t he load coefficient k can be calculated from the modeling system of Formula 6, thereb y estimating electric load composition ratios for the electric power consumer (operation 130 of FIGS. 1 and 8). By applying the current embodiment to a digital metering syste m, load power of the electric power consumer can be measured in real-time in operatio n 140.

As described above, a transformer must be additionally considered in the modeli ng process. In an actual power system, various electric loads will receive different volt ages from a transformer. In an embodiment of the present invention, in order to consi der factors of a 3-phase transformer used by a typical electric power consumer, the mo deling process is performed as described below. A transformer used by a typical elect ric power consumer will now be described by assuming that a delta-wye (Δ-Y) transfo rmer supplies voltages having different levels to electric loads. However, the present i nvention is not limited to the delta-wye transformer. The description below can be appl ied to 3-phase transformers having different connections, such as delta-delta, wye-wye, and wye-delta.

For convenience of description, modeling considering an ideal 3-phase transform er, i.e. a lossless 3-phase transformer, will be first described, and then modeling consid ering an actual 3-phase transformer will be described.

It is assumed that the two kinds of lighting (incandescent lighting and fluorescent lighting) receive power from a 480V/280V delta-wye transformer (referring to FIG. 2). The delta-wye transformer changes phase correlations and harmonic components in a primary winding, i.e., a service input terminal. FIG. 9 shows a 3-phase transformer h aving a delta-wye (Δ- Y) connection for a 480V/280V voltage drop in primary and seco ndary windings. In FIG. 9, it is assumed that an ideal 3-phase transformer in which Y=∞ (i.e., sho rt-circuited) is used. Voltage correlations of the ideal 3-phase transformer are represe nted by Formula 9.

V_nB = a Ψ_m

V_BC = a-^lV_bn (9)

In Formula 9, a (280/480) denotes an effective wiring ratio of a transformer.

Phase voltages under a balanced operation state condition are represented by F ormula 10.

From Formula 10, voltages in the primary winding are represented by Formula 1 1 .

V ^V AB - ~ V ^V An - V ^V Bn ~ - V ^V An - V ^V AiF e^~jU0° = Λ ^.[W ^{D Y} AiF e^j30°

V ^VBC -~ V^VBn - V ^VCn -~ V^yAn p^e~β20° - V ^V AtF e^'j240° = * ^fi ^J>V' An e^^~j90° = -J * w ^{J y} BrF e^;30° ( V1' 1¹ )/

^VCA ~ ^yCn ^VAn - ^yAxF ^V An^e ^ ^ AtF ^ ^{D y} CiF

The correlations between the primary voltages and the secondary voltages are r epresented by Formula 12 by using Formulas 9 and 11.

When the electric loads receive different voltages, current waveforms of the inca ndescent lighting and the fluorescent lighting are , for example, re-calculated using For mula 12, and the four types of electric loads are illustrated in FIG. 10. As described ab ove, the phase correlations (phase transitions) and amplitudes (harmonic components) are changed through an operation of the transformer and the difference can be clearly s een when compared to those illustrated in FIG. 5.

When an actual 3-phase transformer in which Y=j is used as the 3-phase transfo rmer of FIG. 9, voltage correlations of the 3-phase transformer are as follows. An actu al 3-phase transformer model can be induced from appropriate interconnections of actu al single-phase transformers. Simply speaking, it is assumed that each single-phase tr ansformer is represented by its simplified model.

Thus, the relation between voltages and currents of the actual 3-phase transform er is represented by Formula 13.

In Formula 13, a (=280/480) denotes an effective wiring ratio of the transformer

Using Formula 13, the relation between inputs and outputs of voltages and curre nts can be represented by a matrix representation of Formula 14.

The relation between inputs and outputs, i.e. Formula 14, can be represented by a simple matrix of Formula 15.

In Formula 15, I denotes a 3x3 unit matrix, and the matrices E and F are re presented by Formula 16.

1 -1 0 2 -1 -1

E = 0 1 -1 -1 2 -1 (16)

-1 0 1 - 1 - 1 2

Originally, 3-phase transformers are composed of symmetric 3-phase elements. This means that a 3-phase transformer model can be transformed to three equivalent circuits using a symmetry transform method. These three equivalent circuits are comp osed of normal-phase, inverse-phase, and zero-phase equivalent circuits.

The phase voltages and the phase currents can be replaced with Formula 17 ac cording to the relevant symmetric elements.

In Formula 17, the matrix T is a transform matrix represented by Formula 18.

In Formula 18, a denotes e^jm° .

If phase values are replaced with the symmetric elements, Formula 15 can be co nverted to Formula 19.

If direct calculation is performed, values in the matrices of Formula 19 are repres ented by Formula 20.

The formula related to the single-phase transformers corresponding to the three equivalent circuits can be obtained using the above procedures. This formula is comp osed of 6 equations, two equations related to voltages and currents per equivalent circu it, as represented by Formula 21.

The symmetric element method is based on linear transformation of a system vol tage and current. This linear transformation replaces a solution for a problem of a full 3-phase system (Formula 14) with a solution for a problem of three divided single-phas e systems (Formula 21). This system analysis begins from the assumption that a 3-ph ase transformer is a symmetric 3-phase system. Since most actual parts of 3-phase p ower systems have the symmetric characteristic, the assumption may generate a very s mall error. In most actual applications, this error is within a predetermined tolerance. By considering the actual transformer, Formula 6 is represented by Formula 22. That is, Formula 22 represents electric loads finally modeled considering the actual tra nsformer. As described above, by obtaining k using the optimization method, the rea l-time estimation of the electric load, according to an embodiment of the present inventi on, can be accomplished.

The invention can also be embodied as computer readable codes on a computer readable recording medium. The computer readable recording medium is any data st orage device that can store data which can be thereafter read by a computer system. Examples of the computer readable recording medium include read-only memory (ROM ), random-access memory (RAM), CD-ROMs, magnetic tapes, floppy disks, optical data storage devices, and carrier waves (such as data transmission through the Internet). The computer readable recording medium can also be distributed over network coupled computer systems so that the computer readable code is stored and executed in a dist ributed fashion.

While the present invention has been particularly shown and described with refer ence to exemplary embodiments thereof, it will be understood by those of ordinary skill i n the art that various changes in form and details may be made therein without departin g from the spirit and scope of the present invention as defined by the following claims.

INDUSTRIAL APPLICABILITY

As described above, according to the present invention, a load composition esti mation method can be implemented as a single module device using software and hard ware. In addition, by employing the module device as a component in an existing or n ewly designed power meter, a digital metering system can be implemented. In order t o implement the load composition estimation method as the module device, software a nd hardware are necessary, and in this case, the software required to implement the Io ad composition estimation method can be recorded in a predetermined recording mediu m, and the recording medium is also included in the scope of the invention.

Claims

1. A method of estimating electric load composition for an electric power con sumer, the method comprising: measuring current waveforms of a plurality of loads of the electric power consum er using sensors; deriving a final model function represented by the equation below by modeling el ectric load composition based on the measured current waveforms

where the load coefficient vector k denotes electric load composition ratios for t he electric power consumer; and estimating the electric load composition ratios for the electric power consumer by calculating the load coefficient vector k from the final model function by using an opti mization method, wherein the measuring of the current waveforms comprises: dividing the loads of the electric power consumer into a first load group receiving a voltage without a transformer and a second load group receiving another voltage after the transformer; measuring a waveform of a total current flowing through the first and second loa d groups using a first sensor; measuring a waveform of a current flowing through each load belonging to the fir st load group using a second sensor; and measuring a waveform of a current flowing through each load belonging to the se cond load group using a third sensor.

2. The method of claim 1 , wherein the optimization method is a Kalman filter algorithm.

3. The method of claim 1 , wherein the optimization method is a conjugate gr adient method.

4. A computer readable recording medium storing a computer readable prog ram for executing the method of any one of claims 1 through 3.

5. An apparatus for estimating electric load composition for an electric power consumer, the apparatus comprising: a current waveform measurement member measuring current waveforms of a pi urality of loads of the electric power consumer; a model function derivation member deriving a final model function represented by the equation below by modeling electric load composition based on the measured cu rrent waveforms

where the load coefficient vector k denotes electric load composition ratios for t he electric power consumer; and an estimation member estimating the electric load composition ratios for the elec trie power consumer by calculating the load coefficient vector k from the final model fu notion by using an optimization method, wherein the current waveform measurement member comprises: a first sensor measuring a waveform of a total current flowing through a first load group receiving a voltage without a transformer and a second load group receiving ano ther voltage after the transformer; a second sensor measuring a waveform of a current flowing through each load b elonging to the first load group; and a third sensor measuring a waveform of a current flowing through each load belo nging to the second load group.

6. The apparatus of claim 5, wherein the optimization method is a Kalman filt er algorithm.

7. The apparatus of claim 5, wherein the optimization method is a conjugate gradient method.

8. A power meter measuring electric power of an electric power consumer, t he power meter comprising: a current waveform measurement member measuring current waveforms of a pi urality of loads of the electric power consumer and comprising a first sensor measuring a waveform of a total current flowing through a first load group receiving a voltage witho ut a transformer and a second load group receiving another voltage after the transforme r, a second sensor measuring a waveform of a current flowing through each load belon ging to the first load group, and a third sensor measuring a waveform of a current flowin g through each load belonging to the second load group; a model function derivation member deriving a final model function represented by the equation below by modeling electric load composition based on the measured cu rrent waveforms

where the load coefficient vector k denotes electric load composition ratios for t he electric power consumer; and an estimation member estimating the electric load composition ratios for the elec trie power consumer by calculating the load coefficient vector k from the final model fu nction by using an optimization method.