CALCULATION OF LOSSES FROM CONVENTIONAL CURRENT VALUES IN UNBALANCED ELECTRICAL NETWORKS

Transcription

1 Scientific Bulletin of the Electrical Engineering Faculty Year 4 No. (7) SSN AUAON OF OSSES FROM ONVENONA URREN VAUES N UNBAANED EERA NEWORKS EENA OA VÎRJOGHE, DANA ENESU, V. FORESU VAAHA University of argoviste, Electronics, elecommunications and Electrical Engineering Faculty, Automatics, nformatics and Electrical Engineering Department, 8-4 Unirii Boulevard, 008 argoviste, Dambovita, Romania, Office Phone: ; Office Fax: VAAHA University of argoviste Electronics, elecommunications and Electrical Engineering Faculty, Electronic, elecommunications and Energy Department, 8-4 Unirii Boulevard, 008 argoviste, Dambovita, Romania, Office Phone: ; Office Fax: S FSE Electrica Serv SA - SSE Electrica Muntenia Nord, 58 Andrei Muresan, 0079, Ploiesti, Dambovita, Romania, Office Phone: ; Office Fax: otiliavirjoghe@yahoo.com, enescudiana@yahoo.com, florescu.victor@yahoo.com Abstract. Unbalanced voltages affect the normal operation of the system loads due to the different level of phase voltages (some phases are overstressed, while other phases may take values the under minimum admissible voltage). Unbalanced currents affect the electrical network operation due to the additional losses of electrical power and energy. his paper presents a method for the calculation of power and energy losses that uses directly the RMS values of the load currents that can be measured on the three phases of the system. Keywords: electrical networks, three-phase system, waveform distortion, unbalance, power losses, energy losses, load currents.. NRODUON he operating regimes of electrical distribution networks affect the distribution, supply and consumption processes from the technical and economical points of view. he appearance of unbalance of the three-phase voltages affects the voltage quality at the terminals of the electrical customers. n this case, additional electrical energy losses occur in some electrical loads and induction motors []. n terms of technical and economical performance in the electric distribution networks, the additional active energy losses impact on the efficiency of distribution and electricity supply service []-[4]. he power and energy losses can be calculated by using the classical methods, by using the input data at each network component and determining the partitioning of the currents in the phase and neutral conductors in each network feeder or terminal line [5]. his procedure needs to determine a large number of input data and requires several calculations, due to the fact that the analysis has to cover all the phase and neutral conductors in all the lines of the network. For large networks with many unbalanced loads, such as in low-voltage networks, when the results are effectively needed only in some sections of the distribution system, the calculations can be simplified by resorting to an analytic method such as in [6] or the one proposed in this paper, in which the calculation of the power and energy losses can be carried out in a conventional way by using network topology concepts and the measured root mean square (RMS) values of the currents measured at the load terminals. he proposed procedure can reduce the number of calculations and can be easily embedded in a computation code that can be used for different networks. n order to show the characteristics of the proposed approach, let us consider the electrical lines at rated voltage 0.4 kv, in particular those representing an overhead electric circuit of low-voltage public distribution, in the conventional design often used in the electricity supply of the rural areas. he analyzed circuits are part of the 0.4 kv networks which supplies three rural locations (villages). he transmission line is three-phase and has a branched configuration being connected in the distribution substation without looping possibilities with other electric circuits. he electric scheme analyzed is shown in Figure. he circuit is formed by five sections, the circuit is formed by 7 feeders, the circuit is formed by three feeders, and the circuit 4 supplies a three-phase circuit. he input data acquisition is carried out to provide the electrical variables of the permanent operating regime, for the substations and electrical networks at 0.4 kv rated voltage. 4

2 SSN Scientific Bulletin of the Electrical Engineering Faculty Year 4 No. (7) able. he results of the measurements. OMPUAON OF POWER AND ENERGY OSSES N EQUVAEN BAANED REGME Figure. Electric scheme analyzed. he input data acquisition is periodically performed through voltages and currents measurement at maximum load. herefore, the measurements of currents and voltages were performed in all 0 kv/0.4 kv substations connected by overhead line at 0 kv, as well as in the electrical lines of 0.4 kv connected in these substations as follows: - load current measurement on the general circuit and electrical lines of 0.4 kv from the substations of 0 kv/0.4 kv; - phase and line voltages measurement at the 0.4 kv busbars of the substations; - measurement of phase voltages in the load nodes and at the farthest point of the network for 0.4 kv overhead lines from the rural areas. he results of measurements for all circuits at 0.4 kv rated voltage and for the 00 kva substation at 0 kv/0.4 kv, connected to the 0 kv overhead line, are shown in able. he analysis of measurements performed in the electric distribution networks at 0 kv and 0.4 kv, taking into account the structure of the consumers supplied by electricity allows highlighting the following aspects concerning the real regime of electrical networks: - the maximum load expressed by P max and Q max and the maximum load simultaneously absorbed P max and Q max corresponding to the maximum apparent power S max ; - the power factor: cosφ max corresponding to the maximum power recorded (P max, Q max ); the power factor cosφ min corresponding to the maximum reactive power recorded Q max ; and the medium value cosφ med on the different time intervals (day, month, year); - the annual medium load expressed by P med, Q med and S med ; the time of utilization max of the maximum apparent power during a year; - the maximum losses time on the time interval under analysis; - the coefficients of utilization of active maximum power, reactive maximum power and apparent maximum power, respectively indicated as k UP, k UQ and k U. he input data for overhead line of 0.4 kv (the network with 4 multiple aluminum conductors and uniformly distributed load) are the following: - the length of the i feeder l i, in km or m; - the specific resistance corresponding to the phase conductors R 0fi and neutral conductor R 0Ni on the i th section, in Ω/km; - the specific reactance of the phase conductor X 0, in Ω/km; - the total number of household customers n and the number of household customers n i on each feeder i of the electric network; - the RMS values of the maximum load currents on the three phases A, B, and the RMS value of the neutral current N in A. able shows the network data. able. onfiguration and power line structure here is a three-phase branch placed in the circuit, on the feeder r, respectively in the circuit on the feeder r. he active and neutral conductors are from aluminium with the sections of 5 mm and 5 mm, namely Al (x5+5) mm. he specific parameters of the line for circuits, and are: the specific resistance corresponding to the section of phase conductors is 0.88 Ω/km and the specific resistance corresponding to the neutral conductor section is.8 Ω/km. he specific reactance of all conductors is Ω/km. he circuit 4 supplies a three-phase customer and is composed of an aluminium conductor with the phase conductor section of 55 mm and neutral conductor section of 5 mm, Al (x55+5) mm. 5

3 Scientific Bulletin of the Electrical Engineering Faculty Year 4 No. (7) SSN he specific resistance corresponding to the phase conductor section is Ω/km, and the specific resistance corresponding to the neutral is 0.88 Ω/km. he specific reactance for all conductors is 0.48 Ω/km. With the input data for each element of the network and after the distribution of the phase and neutral currents on the network feeders is achieved, the power and energy losses can be determined by conventional methods. his procedure presents the drawback due to the big number of input data and the large volume of computation, because the procedure is performed on each phase, on neutral conductor and each feeder of the electrical network. A simplified formulation based on the RMS currents and on the network topology is presented below... Determination of the load currents he average value of the load currents considering an equivalent balanced consumption is computed as follows: - conventional average RMS value of the maximum load current (since the maximum RMS load currents are considered at each phase, the calculation is conventional as it does not takes into account the phase angles of the currents): - the current value at the beginning of each feeder i is computed, which consists of the load current absorbed by the consumers connected to the feeder i and the current flowing for supplying the consumers connected to the feeders located downstream with respect to the feeder i: (4) DMi Mtzi n k i Mtrk he values of the load current absorbed on the feeder i of electrical network, the current flowing on the feeder i considered Mtzi and the current on each feeder Mi are presented in able. able. onfiguration and power line structure M A, B, f f A B () For the circuit M = (+50+49) / = 0 / =4. A 4 A For the circuit M = (7+9+44) / = 0 / = 6.66 A 7 A For the circuit M = (5+6+4) / = 9 / = 4 A - value of the absorbed load current on the feeder i of the electrical network, calculated by using the numbers of customers: ni M () n When a feeder serves a number of loads, a typical assumption made to obtain simplified but meaningful results is that loads are uniformly distributed along the feeder. n the overall distribution system, the lines considered can be a three-phase, two-phase, or singlephase feeder or lateral. he case with uniformly distributed loads is naturally the one in which singlephase laterals with the same rating are uniformly spaced over the length of the lateral. When the loads are uniformly distributed, it is not necessary to model each load in order to determine the total voltage drop from the source to the last loads. Figure shows a generalized line with n uniformly distributed loads. - the current flowing at the end of the feeder i is computed by taking into account the configuration of the electrical line, identifying the sum of the load currents on each feeder k located downstream with respect to the feeder i (excluding the feeder i): () DMtzi Mtrk k i where D i indicates the set of the feeders located downstream with respect to feeder i; Figure. Uniformly distributed loads. Figure shows n uniformly spaced loads dx kilometers apart. he loads are all equal and will be treated as constant current loads with a value of di each. he total current into the feeder is. t is desired to determine the 6

4 SSN Scientific Bulletin of the Electrical Engineering Faculty Year 4 No. (7) total voltage drop from the source node (S) to the last node n. et us consider the following notation: l length of the feeder z = r + jx specific impedance of the line in Ω/km dx length of each line section di load currents at each node n number of nodes and number of line sections total current into the feeder For n loads, with dx=l/n, the load currents are given by di= /n and impedance Z=zl. An important issue is the placement of the equivalent load. he question is at what distance it is possible to put the equivalent load. n this sense there are two criteria to consider [7]: ) criterion of maintaining the same voltage drop V Re Z (5) for the first segment, ΔV =Re{z. dx. (n. di)} for the second segment, ΔV =Re{z. dx. [(n-). di]}. he total voltage drop from the source node to the last node is then given by: n n V Re z dx di n... (6) Equation (6) can be reduced by recognizing the series expansion: n n... n Using Equation (7), Equation (6) becomes: nn V Rez dx di V Re Z n Equation (9) gives the general equation for computing the total voltage drop from the source to the last node n for a line of length l. n the limit case where n goes to infinity, the final equation becomes: V Re Z (7) (8) (9) (0) n equation (0), Z represents the total impedance from the source to the end of the line. he voltage drop is the total from the source to the end of the line. he equation can be interpreted in two ways. he first interpretation is to recognize that the total line distributed load can be lumped at the midpoint of the lateral. A second interpretation of equation (0) is to lump one-half of the total line load at the end of the line (node n). Figure. Models of the distributed loads. Figure gives two different models that can be used to calculate the total voltage drop from the source to the end of line with uniformly distributed loads. However, the voltage drop is the only criterion considered in this case. ) criterion of maintaining the same total branch losses Another criterion used in the analysis of a distribution feeder is the power loss. o derive the correct model for power losses, reference is made to Figure and the definitions for the parameters in that figure. he total three-phase power losses are the sum of the power losses in the various segments. for the first segment, ΔP =r. dx. n. di for the second segment, ΔP =r. dx. (n-). di he total power loss over the length of the line is then given by: r dx di n n P total... () he series inside the brackets of Equation () is the sum of the squares of numbers and is equal to:... n n n n () l n Ptotal r n n 6 aking the limit for n : 6 n n () P total R (4) A circuit model for equation (4) is given in Figure 4. Figure 4. A circuit model for calculation of the power losses. he first models of Figure can be used only for the computation of the voltage drop in the line. However, the model of Figure 4, used to represent the power losses of the feeder, is different. Hence, the same models cannot be used for the representation of both the voltage drop and the total power loss in the feeder. he conclusion is that it is not possible to use a lumped representation of the uniformly distributed loads with a 7

5 Scientific Bulletin of the Electrical Engineering Faculty Year 4 No. (7) SSN single load. he exact model for all cases has two lumped loads, as shown in Figure 5. Figure 5. Model for two lumped loads. Figure 5 shows the general configuration of the exact model that will give correct results for voltage drop and power losses. A portion x = (-c) of the total line current will be modeled kl kilometers from the source, and the remaining current c will be modeled at the end of the line. he values of k and c need to be calculated. n Figure 5 the total voltage drop down the line is given by: V Re k Z k Z c (5) where Z total line impedance in ohms k factor of the total line length where the first part of the load current is modeled; c factor of total current to place at the end of the line such that = x +c. he coefficients c and k are obtained by considering: Vtotal Re Z RekZ kzc (6) from which: c k kc k c (7) Ptotal R k R kr c (8) resulting in the following condition: kc k c c k (9) After substituting the expression of k into the last equation, the first result is c = /. hen, by replacing back the value of c in Equation (7), the other value is k = /4. he final solution for the circuit with two lumped loads is represented in Figure 6. Figure 6. Exact lumped load model... alculation of the power and energy losses he active power losses ΔP and the energy losses ΔW are computed like in the case of the balanced load regime for the three circuits. he active power losses are computed by applying of the following specific relations for the different network elements for overhead line of 0.4 kv with uniformly distributed load, according to Equation (0). he energy losses are computed with Equation (), taking into account the time at which the maximum losses are detected, τ = 545 hours. he active power and energy losses computed are shown in able 4. P Pi ri li Mtqi ri li (0) Mi 4 4 i where the total lumped load at the ending terminal of the line is composed of the portion of the load representing the uniformly distributed load of the line (i.e., the one located at the end of the feeder in Figure 6) together with the total load located downstream of the line: Mtqi Mtzi () W P () able 4. he active power and energy losses ircuit ircuit ircuit ΔP [kw] ΔW [kwh] OMPUAON OF POWER AND ENERGY OSSES N HE UNBAANED REGME o determine the active power and energy losses in the unbalanced regime, the following procedure is adopted: - the unbalance coefficient for the elements of the electric networks is computed by means of Equation (): A B k () D M M M - a correction factor is then applied to the active power and energy losses in the balanced load regime and in the currents. onsidering that the network elements work under an unbalanced system, the correction factor for the overhead line of 0.4 kv with 4 conductors and uniformly distributed loads can be written as follows: R on N k kd (4) Rof M able 5 shows the values of unbalance coefficients and correction factors for the three circuits. he correction 8

6 SSN Scientific Bulletin of the Electrical Engineering Faculty Year 4 No. (7) coefficient k c for distribution electrical networks can represent a performance indicator in the electricity supply process, because: it characterizes the unbalanced regime of load currents and can be computed knowing their RMS values; it allows determining the percentage value of additional power and energy losses for both medium voltage electrical networks and low voltage electrical networks according to Equation (4). able 5. he unbalance coefficients and correction factors for the three circuits. ircuit ircuit ircuit k D k..06. he correction factor value according to Equation (4) highlights its dependence referring to the material characteristics of electrical network, respectively the sections or the phase conductors resistances and neutral conductor resistance. - he active losses in unbalanced load regime are computed as: P k P (5) D he active energy losses in unbalanced regime are considered by taking into account the time period τ with maximum losses, applying the usual relations for electric distribution networks: W P k P (6) D D - the percentage additional losses are determined as the difference between the active power and energy losses in unbalanced regime and respectively, in balanced regime according to Equations (7) and (8): PD P p% 00 % (7) P WD W w% 00 % (8) W his percentage difference represents an indicator which characterizes the influence of unbalanced load regime concerning the energy and power losses in operation of electric distribution networks. able 6. he power and energy losses in unbalanced regime ircuit ircuit ircuit ΔP D [kw] ΔW D [kwh] Δp [%] 6 4. ONUSONS he unbalanced currents corresponding to the unbalanced load regime are caused by inequality of the load impedances and sometimes of electric line impedances. n the distribution networks (especially at 0.4 kv), this inequality is produced by the single-phase loads of household and tertiary (e.g., commercial) consumers connected to the electric network in threephase or single-phase systems. he unbalanced load regime in these networks represents the main cause of voltage unbalances. Supplying the loads under a non-symmetrical system of three-phase voltages produces a non-negligible voltage on the neutral point, leading to different voltage drops in the three phases of the electrical networks. Some numerical calculations can be performed for computing the active power and energy losses in the real operating regimes being characterized by the unbalanced systems of the load currents. hese calculations depend on the type and configuration of the distribution network, with four conductors for overhead lines of 0.4 kv or with three conductors for electric lines with voltage in the range 6-0 kv. 5. REFERENES [] Albert, H. Power and energy losses in electric networks (in Romanian) Pierderi de putere şi energie electrică în reţelele electrice, ehnic Publishing House, Bucharest, 998. [] Popescu, S. Electric plant for consumer supply (in Romanian) nstalaţii electrice pentru alimentarea consumatorilor, Macarie Publishing House, argovite, 988. [] Golovanov, N., Darie, E., Dogaru-Ulieru, V., Goia, M.., onescu,., Mira, N., Mucichescu,., Popescu, S., Postolache, P., Răşcanu, V., Şmilovici, M., oader,., Vîrjoghe, E.O. Electrical Energy onsumers. Materials. Measurements. Equipments. Plants (in Romanian) onsumatori de energie electrică. Materiale. Măsurări. Aparate. nstalatii, Agir Publishing House, Bucharest, 009. [4] P.E. / 99 Standard for design of public distribution electrical networks (in Romanian) Normativ pentru proiectarea reţelelor electrice de distribuţie publică. [5] hiang, H.-D., Wang, J.-., Miu, K.N. Explicit loss formula, voltage formula and current flow formula for large-scale unbalanced distribution systems, EEE ransactions on Power Systems, Vol. (), 997, pp [6] Brice,. W. Voltage-drop calculations and powerflow studies for rural electric distribution lines, EEE ransactions on ndustry Applications, Vol. 8 (4), 99, pp [7] Kersting, W.H. Distribution System Modeling and Analysis, R Press, 00. 9