Voltage unbalance in delta secondaries serving single-phase and 3-phase loads [includes discussion]

There seems to be no limit to the applica- tion of cathode-ray oscillography nor any limit to the imagination that one may apply to conditions of traveling waves on transmission systems. The graphics and the analogue have saved the cost of endless full-scale experimentation. It should not be inferred, however, that this particu- lar approach is a complete substitute for all experimentation since it can be readily understood that either is an adjunct to the other. Unfortunately some of the references in the paper do not seem to be generally available to the readers. They do, how- ever, make valuable source material, and show the wide interest and application of traveling wave phenomena. Voltage Unbalance in Delta Secondaries Serving Single-Phase and 3-Phase Loads A. S. ANDERSON R. C. RUETE FELLOW AIEE ASSOCIATE MEMBER AIEE made in innumerable such instances where the cost of other corrective measures would have resulted in lower costs and more satisfactory installations. Accept- ance of some degree of voltage unbalance as a fair allocated apportionment of the service factor, resulting in a reasonable approach to a minimum over-all cost for all concerned, should be the aim of a representative national group. IT IS a fairly widespread practice in the utility industry to serve both single- phase and 3-phase loads simultaneously from 120/240-volt 4-wire delta secondary circuits. The unprecedented growth of 3-phase residential and small commercial air-conditioning load in our southern states is extending this practice very rapidly. The practice creates unbalanced loads on the 3-phase portions of the power system, hence customer service voltages on these systems are generally unbalanced to some degree. A reasonable amount of voltage unbalance should be tolerated to achieve optimum economy, taking into consideration all interests of the user, the manufacturer, and the supply utility. The purposes of this paper are three- fold: 1. To present equations for determining the unbalances in voltage in 4-wire single- and 3-phase delta secondaries. 2. To stimulate interest which may lead to acceptance by manufacturers and utilities of some degree of voltage unbalance in the supply. 3. To promote a definition of voltage unbalance in a 3-phase system which should eventually receive industry acceptance. Voltage and Current Unbalance Unequal voltage drops in conductors and transformers caused by simultaneous single-phase and 3-phase load currents produce unbalanced load voltages. Since in general, the negative-sequence imped- ance of rotating 3-phase equipment is small compared with the positive-se- quence impedance, very little voltage un- balance is required at the load to produce rather large current unbalance. For example, if the negative-sequence im- pedance is 15 per cent of positive- sequence impedance, and negative-sequence volt- age is 2.5 per cent of positive-sequence voltage, the negative-sequence current is 16.7 per cent of positive-sequence current. Negative-sequence current reduces torque of a motor slightly and increases losses in a more significant degree. When it is present the three line currents are un- equal. The largest of these may trip out thermal overload protection while the over-all heating of the motor may be only slightly in excess of normal. Unbalance Factor Voltage unbalance has been defined in various ways, none of which seem to be fully accepted as a standard in this country. In this paper, voltage un- balance is defined as the ratio of negative- sequence voltage to positive-sequence voltage and is called the voltage un- balance factor. This should be a suitable definition since it is based on the theory of symmetrical components, which con- cept has greatly simplified calculations involving unbalance. It is suggested that this definition be considered for adoption as an industry standard. (In the case of current unbalance, it is suggested that the term "current unbalance factor" be used and that it be defined as the ratio of negative-sequence current to positive- sequence current.) In applying motors engineers are aware, and frequently make use, of the service factor which is a part of the rating of a motor and which allows for devia- tions in operation from rated values of temperature, voltage magnitude, fre- quency, and mechanical load. It is cus- tomary, however, for manufacturers and many utility engineers to assume that the supply voltage is balanced in magnitude and phase angle. In many cases of un- satisfactory motor operation, the utility has been blamed for unbalanced voltage where other deviations from rated condi- tions, frequently not under control of the utility, also existed. Large utility invest- ments in transformer capacity have been Equations to Determine Voltage Unbalance Factor Equations for voltage unbalance factor (as defined in the foregoing) in terms of the secondary supply system and load impedances have been developed for the three most usual transformer connec- tions applicable to a 4-wire delta second- ary. These transformer connections are: un- grounded wye-delta, herein called wye- delta; open-wye to open-delta, herein called open-wye; and open-delta to open-delta, herein called open-delta. With the open-wye and open-delta con- nections, both the leading and lagging phase relations of the two transformers are considered. The connection is con- sidered leading when the transformer carrying the single-phase load (lighting transformer) is connected to a voltage which leads by 120 degrees the voltage to which the other transformer (power trans- former) is connected. The connection is considered lagging when the lighting transformer is connected to a voltage which lags by 120 degrees the voltage to which the power transformer is connected. Assumptions used in the derivation of the equations are: 1. Primary voltages are balanced (or source impedance is zero). Paper 54-195, recommended by the AIEE Trans- mission and Distribution Committee and approved by the AIEE Committee on Technical Operations for presentation at the AIEE North Eastern District Meeting, Schenectady, N. Y., May 5-7, 1954. Manuscript submitted October 29, 1953; made available for printing February 18, 1954. A. S. ANDERSON is with Ebasco Services, Inc., New York, N. Y., and R. C. R UETE iS with the General Electric Company, Pittsfield, Mass. The authors wish to acknowledge the assistance of Chase Hutchinson, Henry Rudolph, C. R. Joy, and others of Ebasco Services, Inc., in the prepara- tion of this paper. Special credit is due to Prof. J. G. Tarboux of the University of Michigan for his assistance in the initial stages of the study. Anderson, Ruete- Voltage Unbalance in Delta Secondaries AUGUST 1954928 2. The transformers have identical turn- ratios. 3. Three-phase motors are represented by equivalent positive- and negative-sequence impedances, the zero-sequence impedance being infinite since the neutral is not con- nected. 4. The single-phase and 3-phase loads are connected at the end of the secondary lines. 5. The 120-volt single-phase loads are balanced and no current flows in the single- phase neutral. The equations for three transformer connections are given as equations 1, 2 and 3, in which the loads are represented by ZL = single-phase load impedance Zp = 3-phase load positive-sequence im- pedance Zn =3-phase load negative-sequence im- pedance The impedances of the lines and trans- formers for the open-wye connections are represented by Za = impedance of secondary line and lighting transformer Zb=impedance of secondary line common to both transformers Zc=impedance of secondary line and power transformer The impedances of the lines and trans- formers for the wye-delta connections are represented by Z= lighting transformer impedance Z2, Z3=power transformer impedance Za, Zb, Z,=secondary line impedances Voltage Unbalance Factor for Open- Wye or Open-Delta Leading Connection Eabn Eabp 1 (aZa+a2Zb+Zc)±+ (aZa-Zb) a(Za+Zb+Zc+3Zn)- (aZa-Zb)Zn ZL (1) The equivalent circuit is shown in Fig. 1. Equation 1 applies to the open- wye leading connection and to the open- delta leading connection since the only circuit change would be in the connec- tion of the high-voltage windings of the transformers Voltage Unbalance Factor for Open- Wye or Open-Delta Lagging Connection Eabn Eabp 1 V/gfj30 1(a2Za+aZb+Zc)++ (aZ -Za) ZP ZL (Za+Zb+Zc+3Zn>)- (aZb-Za) Zn ZL (2) For the equivalent circuit refer to Fig. 1. For lagging connection the phase sequence is the reverse of that shown, i.e., the sequence of voltage vectors is changed from Eab, Ebc, and Eca as shown to Eab, Eca and Ebc, This may be done by changing the primary connection from line C to line A. Voltage Unbalance Factor for Ungrounded Wye-Delta Connection Eabn Eabp 1/ Z1 aZ2 a2Z3\ (aZa +a2Zb +z,-_Z _ +23 ZKa +bZ 3 -3 3/ ,-.r3d3o(aa -Z 1(I 2Z1+c2Z2+aZ3\ ZL (aZa-Zb)+Z -3 Z1 z2 z3 Za+Zb+Zc+3Zn+ ± ±+--)zn ~ 3 3 3/ 'r&j0(a,,, 1Z ( 2Z,+a2Z2+aZ3\ZL (aZa-Zb)-z (- 3 + +-ZL ~~ZL 3 31 (3) For the equivalent circuit refer to Fig. 2. The transformer impedances cannot be converted to an equivalent wye be- cause the division of current in the delta is independent of transformer imped- ances. The primary wye connection is isolated from ground; therefore balanced 3-phase currents divide evenly and the single-phase current divides two-thirds in the lighting transformer and one-third in each of the other two transformers. Equation 3 applies only for phase rota- tion Eab, Ebc, and Eca. Effect of Transformer Connection on Unbalance Factor The voltage unbalance factor for open- wye or open-delta leading connection, the open-wye or open-delta lagging con- nection, or the wye-delta connecti on may be determined from equations 1, 2, and 3 respectively. These equations are long and cumbersome so that general solutions have not been attempted. However, calculations were made for certain as- sumed conditions, and the data obtained are summarized now. The assumed conditions were as follows: 1. Single-phase and 3-phase load each ranged from 0 to 100 kva. 2. Maximum length of secondary of 300 feet. Length of 300 feet assumed or length reduced to keep unbalance factor below 0.025 for leading connection. 3. Maximum size of copper conductor of 1,000,000 circular mils. 4. Maximum transformer loading of 150 per cent. 5. Maximum voltage drop across lighting phase of 16 volts. 6. Maximum conductor loading 2/3 ampere per thousand circular mils. 7. The following combinations of power factor: a. Single-phase load power factor of 0.95 and 3-phase load power factor of 0.80. b. Single-phase and 3-phase power fac- tors of 0.80. c. Single-phase power factor of 0.70 and 3-phase power factor of 0.90. A summary of the conclusions drawn from partial calculations for voltage un- balance factors for installations covered by the limitations and range of assump- tions given in the foregoing are as follows: 1. The 2-transformer (open-wye or open- delta) connection causes lower unbalance factors than the 3-transformer (wye-delta) connection for power factor conditions a, except where the ratio of 3-phase load to single-phase load is three or more; however, the unbalance factor is within reasonably small limits even where single-phase load is zero. 2. The unbalance factor is lower for the leading connection than for the lagging connection with load power factors between 0.70 and 0.95 with one exception. This exception is where the ratio of 3-phase to single-phase load is greater than approxi- mately one and the power factor of 3-phase load is greater than that of single-phase load. Where the unbalance factor is larger for the leading connection the difference is usually not great enough to be signifi- cant. C NEUTRAL A I Zol a Z3 AAz Zp 1 2 Za Z I- Z3 P. b :1 Zn 3 vy Fig. 1. Equivalent circuit for open-wye connection Fig. 2. Equivalent circuit for wye-delta connection Anderson, Ruete- Voltage Unbalance in Delta Secondaries A AUGUST 1954 929 Conclusions 1. There is need for a definition of un- balanced voltage which will receive industry acceptance. 2. The ratio of negative-sequence to positive-sequence voltage appears to be the most logical definition of unbalanced voltage. 3. The use of equations for unbalanced voltage as given in this paper should aid in determining unbalanced voltage in 4-wire delta secondaries supplying single-phase and 3-phase loads, including induction motors. 4. The open-wye leading connection generally has a lower unbalanced voltage than the open-wye lagging connection. from the voltage drops in the line and transformer impedances. The line currents can be found by adding negative- and positive-sequence currents of the 3-phase load and the current of the single-phase load Ila =IaOp+IaOn+IL I2b IbOp+IbOn-IL I3C = IcOp+IcOn where IL = single-phase current from a to b. From symmetrical components Eaop = Eabp _j30 Eaon = ~Eab 3 (12) (13) (14) flowing unbalance for the different transformer connections will be found. Referring to equivalent circuits and equations ZL= 1.38 /18.2 ohms. /18.2 denotes positive angle of 18.2 degrees. Zp = 5.76 /36.8 ohms Zn = 0.749 /90 ohms Open-Wye or Open-Delta Connection Using transformers rated 37.5 kva and 5 kva (15) Za= 0.0718 /62.5 ohms Zb=0.0293 /65.4 ohms (16) Zc = 0.397 /32.7 ohms Appendix 1. Derivation of Equation for Open-Wye Leading Connection The derivation of the equation for un- balance factor in the open-wye leading connection is as follows: Refer to Fig. 1 for the equivalent circuit and symbols. Double subscript notation is used throughout. Additional subscripts n and p refer to negative- and positive- sequence quantities respectively. ZL = single-phase load impedance Zp =3-phase load positive-sequence im- pedance Zn =3-phase load negative-sequence im- pedance ejO=vector rotation of 0 degrees a= j120 From the definition of negative-sequence voltage 3Eabn = Eab+a2Ebc+aIEca (4) From the equivalent circuit Eab =Eai +E12+E2b (5) Ebc =Eb2+E23+E3C (6) Eca= Ec3+E31+Eia (7) Substituting equations 5, 6, and 7 in equation 4 3Eabn =Eal+El2+E2b+a2(Eb2+E23+ E3c)+a(EC3+E31+Eia) (8) Since primary voltages are balanced and turns-ratios are equal E12+a2E23+aE31 = 0 (9) Substituting equation 9 in equation 8 and rearranging 3Eabn = (a-1 )Eln+( 1-a2)E2b+(a2-a)E3c (10) Substituting the identities involving the operator a 3Eabn = /3Einae j50+ UE2 bE30 ±X'+vE3E3CC270 (11) Equations 9 and 11 indicate that if the primary voltages are balanced the negative- sequence voltage at the load can be found IaOp =Eaop= Eabp >-j30 (17) Zp Zp 'non-Eann Eabn j30la 4= (18)ZP -\-Zn I Eabp+Eabn ( 19) The zero-sequence voltage is zero since the sum of three line voltages is zero (20) (21) ITbop = a2laop IcOp = aTaop 'bCn = aIaon IcOn = a2Iaon The voltage drops in line and transformer are Eia IiaZa (24) E2b =I2bZb (25) E3c 13cZc (26) Substituting equations 24, 25, and 26 in equation 11 3Eahn = -\/-3liaZaZEj+ 3I2bZb Ej3° + -/3cZcei270 (27) Substituting equations 12 to 23 in equa- tion 27 and rearranging, the equation for Eabn/Eabp is obtained as given here and shown as equation 1. Equations 2 and 3 may be obtained in a similar manner. Appendix II. Example The following example is worked out to illustrate the use of the equations and the comparisons between the different trans- former connections. Consider a secondary circuit 300 feet long made up of two 300,000-circular-mil copper conductors carrying single- and 3-phase load and one American Wire Gauge no. 4 conductor carrying 3-phase load only. This secondary circuit serves 40 kva of single-phase load and 10 kva of 3-phase motor load. Power factors are assumed as 0.95 and 0.80 for single- and 3-phase load respectively. The voltage LEADING CONNECTION Eabn Eabp (aZa+a2Zb+Zc)+ (aZa-Zb)4t ZL 1 -\/32E330(Za+Zb+Zc+3Zn)- (aZa-Zb) zn ZL Eabn 0.0585 /-3.0+0.1118 /211.3 Eabp 3.45 /-8.5+0.1118 /31.3 0.0718 .=50.0203 (22) LAGGING CONNECTION (23) Eabn Thabp (a2Za+aZb +Zc)+ 3 (aZb-Za) ZP ZL -(Za+Zb+Zc+3Zn)-> (aZb-Za) Zn ZL Eabn 0.0654 /-13.1+0. 1140 /238.6 Eabp 3.45 /-8.5+0.1140 /58.6 0.1122- =0.0321 3.50 Wye-Delta Ungrounded Connection Using 25-kva, 15-kva, and 10-kva trans- formers for the lighting phase, the phase lagging the lighting phase, and the phase leading the lighting phase respectively Za= 0.0293 /65.4 Z1 =0.0618 /55.5 Zb=0.0293 /65.4 Z2=0.1041 /51.3 Zc = 0.0920 /22. 1 Eabn _ Eabp Z3=0.1632 /42.5 1 /Z, aZ2 a2Z3\ + aZ,+a2Zb+Zc-3--> -3+ W/e(Z3 Z)±1 _-2Z3 a2Z+ aZ3 ZL ZL\ 3 3 3 It Zl z2 zAZa+Zb+Zc+3Z+n+ 3+-3-Zn\ 3 3 3/ N/30 1 (2Z1 a2Z2 aZa) ZL ZL 3 3 3 Anderson, Ruete-Voltage Unbalance in Delta Secondaries habp AUGUST 19549.30 0.0160 /-12.0+0.0638 /227.2+ Eabn 0.0581 /200.3 Eabp 3.23 /-4.3+0.0638 /47.2+0.0581 /20.3 0.1082 = = 0.0326 3.33 The unbalance factor for the open-wye leading connection was 0.0203; for the open-wye lagging connection, 0.0321; and for the wye-delta connection, 0.0326. Discussion J. E. Gerngross and H. M. Bankus (General Electric Company, Schenectady, N. Y.): We would like to congratulate the authors on their contribution to the literature on the subject of voltage unbalance which occurs with unbalanced transformer con- nections serving combined single-phase and 3-phase loads. We agree with conclusions 1 and 2 that there is need for a definition of unbalanced voltage which will receive industry ac- ceptance, and that the ratio of negative- sequence to positive-sequence voltage ap- pears to be the most logical definition. This is the definition which we used in calculating voltage unbalance in our recent AIEE paper.' Equations 1, 2, and 3 should be very useful to the distribution engineer for checking the performance of an occasional transformer bank. However, we agree with the authors that these equations are long and cumbersome and therefore are not suitable for calculating a large number of points such as in a general solution. It is interesting to note that equations 1, 2, and 3 agree except for sign equation 53 of reference 1, when the proper changes in notation are made. Reference 1 derives equations for voltage unbalance which are suitable for use when a large number of calculations are to be made. The equations derived can easily be solved by means of modern automatic digital computers which are available at various locations. Power systems engineers are becoming more and more conscious of the advantages of using this type of equipment, both from the standpoints of saving time and money.2,3 The economics of time and money depend very much upon the individual problem, but in general the more complicated the problem, and the more personnel time which would be involved in computing to solve the problem longhand, the more economic advantages can be gained by going to some type of digital computer. An approximate picture of the savings involved in using digital computers is provided in reference 3. Judging from the data given in Appendix II, and also from the result of the study presented in reference 1, the general order of magnitude of voltage unbalance which may be attributed to the transformer and secondary conductors is of the order of 1, 2, or 3 per cent for many common combina- tions of transformers and loads. While any unbalance is definitely undesirable, it would be rather difficult to economically justify any substantial expenditure to further reduce very small unbalances. However, it must be remembered that the voltage unbalance given by equations 1, 2, and 3 does not include that already existing in the primary. The primary voltage unbalance must be added to the secondary unbalances according to the phase relationships of primary and second- ary negative-sequence voltages. Under the worst conditions these would add directly. With increasing voltage unbalance in a circuit, currents become unbalanced at an even more rapid rate. Therefore a rela- tively small primary unbalance added to the voltage unbalance occurring in the secondary circuit will cause reduced motor torque and excessive motor heating to such an extent that it may become economically feasible to consider remedial measures other than derating the induction motors. An indication of the derating which must be applied to motors operating with un- balanced voltages was provided in a recent AIEE paper by J. E. Williams.4 To reduce the problem of voltage un- balance to a minimum, the primary system should be designed in so far as possible so that good voltage balance is obtained at points where 3-phase load is tapped off. In actual practice it will be impossible to achieve perfect balance at all times. How- ever, if the unbalance is consistently in a given phase (i.e., one phase voltage is consistently low) there are a number of different possibilities which may be con- sidered to improve the situation. Two of the most direct approaches are as follows: 1. Rotate the phase connections on the primary side of the 3-phase transformer bank until a minimum total voltage un- balance on the secondary at the load appears. 2. Connect secondary shunt capacitors to the low-voltage phase at the load. Both of these solutions can be used con- currently if the situation warrants it. The capacitance which would be required will depend upon the individual conditions. It can be calculated from symmetrical components theory or can be determined by trial and error. REFERENCES 1. UNBALANCED LOADING AND VOLTAGE UN- BALANCE ON 3-PHASE DISTRIBUTION TRANS- FORMER BANKS, H. M. Bankus, J. E. Gerngross. AIEE Transactions, vol. 73, pt. III, April 1954, pp. 367-76. 2. DIGITAL COMPUTERS AID ENGINEERS, T. L. Lee, A. P. Fugill. Electrical World, New York, N. Y., March 8, 1954, pp. 89-91. 3. PROGRESS IN THE APPLICATION OF DIGITAL COMPUTERS TO POWER SYSTEM PROBLEMS, F. J. Maginniss. Proceedings, American Power Con- ference, Chicago, Ill., 1954. 4. OPERATION OF 3-PHASE INDUCTION MOTORS ON UNBALANCED VOLTAGES, J. E. Williams. AIEE Transactions, vol. 73, pt. III, April 1954, pp. 125-33. Bela B. Mohr (Oklahoma Gas and Electric Company, Oklahoma City, Okla. ): The authors have presented valuable equations for calculating the voltage unbalance caused by different transformer secondary designs. The practice of serving 3-phase and single-phase loads simultaneously from a 120/240-volt 4-wire delta secondary is usually adopted for economic reasons. The advantage of this system as compared to a separate light and power system and a 4- wire wye system is the savings in distribu- tion transformers, secondary services, and meters. These savings come at a sacrifice of voltage unbalance. The savings can be sizable where the open-wye open-delta or the open-delta open-delta transformer con- nections are used. This problem of voltage unbalance is similar to flicker voltage drop and steady voltage drop and will affect motor manufacturers, motor application companies, dealers of electric equipment, electrical utilities, and the users of electric equipment or the customer. In commercial areas our company uses the 4-wire delta and the 4-wire wye systems. The 4-wire delta system is used on over- head distribution where the load is largely 3-phase motors and a relatively small lighting load. The 4-wire wye is used on the overhead system where the load is pre- dominantly lighting or single-phase where the 3-phase load is small. The 4-wire delta provides a higher voltage to the customer but the transformer bank is also a source of some voltage unbalance. The 4-wire wye transformer bank does not create any additional voltage unbalance, but the voltage is usually 120/208. Small dry-type autotransformers have been used in specific cases to improve motor opera- tion. Neither the delta nor the 120/208 wye system seems to be the solution for all cases. In residential areas we use 120/240-volt 3-wire secondary. An economical method of providing 3-phase service for light satura- tions of 3-phase motors has recently been adopted. This method provides service by the addition of one transformer on the pole where the 3-phase service is required. This transformer, with the existing single-phase secondary, provides a 120/240-volt 4- wire delta supply. This design has the usual voltage unbalance that is found in any 4-wire delta supply. The amount of voltage unbalance will depend on the size of the lighting transformer, the distance from the 3-phase service to the lighting transformer, the leading or lagging con- nection of the lighting transformer, and the relative per cent of 3-phase load to the single-phase load. In most cases voltage unbalance will be no worse and in many cases better with this split type of installa- tion. The best voltage balance will be obtained if the power transformer is as small as the 3-phase load will permit. Some voltage unbalance troubles have been experienced in the last few years. One source of trouble has been the packaged air-conditioning equipment designed so that any deviation from optimum service conditions resulted in unsatisfactory opera- tion. Another source of trouble is the 2- phase thermal protection of a 3-phase motor. If the largest phase current hap- pens to be in the unprotected phase, the motor will burn up before there is any indication of trouble. This is not a serious problem where the motor is not overloaded. We have had two specific cases in which this condition occured. The motor was overloaded in both cases. Our company has been using the "maxi- mum deviation from average" method of defining voltage unbalance since May 1952. We find it satisfactory because the per cent of voltage unbalance can be Anderson, Ruete-Voltage Unbalance in Delta SecondariesAUGUST 1954 931 determined from any set of measurements by simple mathematics. The simplicity of application and understanding makes this method more desirable for nonprofessional operating and service personnel. The "symmetrical components" method, as recommended by Mr. Anderson and Mr. Ruete, requires the reference to a chart to determine the per cent of voltage un- balance. If a chart is required, it will have to be made available to all service and operating personnel when and where it is needed. The chart would also add the possibility of an error in its use. If due consideration is given to the large number of nonprofessional people who are going to be operating and servicing polyphase motors, the simple method would certainly be adopted. It seems that the most practical solution would be the adoption of the "maximum deviation from average" as the standard with the "symmetrical components" method adopted for use in design problems. The average difference between the two methods is 4.7 per cent. The solution to the voltage unbalance problem requires an economic study in- cluding initial cost and operating cost covering distribution system, services, me- ters, customers wiring, and polyphase motors. The system that would provide the necessary horsepower for the customer at the lowest annual cost should be adopted by all. To properly consider all of the factors involved would require a great deal of time and work. However, a look at the other sources of voltage unbalance at this time would seem desirable. The other sources of voltage unbalance, in addition to the transformer bank and secondary system pointed out by the authors, are the unbalanced loading on the distribution primary and unbalanced load- ing of the customer's wiring. The authors assume balanced primary voltages but our company experience is that distribution primary system almost always contains some voltage unbalance. The primary unbalance can be traced to several things. The basic cause is the type of load. The load is mostly single-phase on a large majority of feeders and it is impossible to maintain a perfect balance between the primary phases. If the loads are balanced in the afternoon the night load will be different, so the result is a compromise to give the best continuous operating balance. Modern feeder regulators are designed to operate in a range of + 1 volt. It has only recently been reduced from i 1.5 volts. Voltage balance is not improved by the regulator. At any point on the 3- phase distribution primary where an unbalance in load occurs, there will be an unbalance in voltage due to this unbalanced demand. Since the regulators operate in a 2- or 3-volt band, it is possible to have over 1.5-per-cent voltage unbalance at the most perfectly balanced point on the primary feeder with single-phase regulators and no overcompensation. It is possible to have a considerable amount of voltage unbalance as the load changes throughout the day. To assume that the primary distribution system is balanced is to assume that all of the electric equipment has a balanced 3- phase demand. Since it appears that single- phase equipment will be in use indefinitely, Table 1. Motor Characteristics Fixed Kilovolt-Ampere Motor General-Purpose 4O-Degree-Centi! Volt Motors Applied voltage.90 ... Service factor' ...............1.04. Maximum heat dissipated (service factor) squared ... 1 .09 . Approximate voltage un- balance equal to service factor, per cent .......... .2 ... we should expect to find some N balance in the distribution prim Another source of voltage unb< the customers' wiring and is pr the customers' changing requirel the design of the customers' syste out engineer balances the simulta as well as he can estimate the mand. New equipment and me result in altogether different us dividual circuits by the custc voltage unbalance from this sour in excess of 1 per cent. The design of the transformer produce from 2- to 3-per-cent N balance as shown in the paper. from all these sources could be it were all added together and th pen in some cases, but one unbalai can be used to reduce the otl the total voltage unbalance can b To maintain the voltage bala tolerable limits requires a methi tinuous checking and supervisio loading by the utility. With th mind, it seems desirable that a di zones (acceptable and undesiral be adopted. Corrective measur made when the voltage unbalanci undesirable zone. The characteristics of the motor as it relates to the voltage problem are shown in Table I. analysis of this subject is given i 2. An examination of Table I motors manufactured to mee Electrical Manufacturers Associa ards do not require perfectlv bal ages for successful operation. frequency in the present-day po is relatively stable, a large por service factor could be allocal balanced voltages. If 50 per service factor is allocated to balanced voltages. If 50 per service factor is allocated to balance at rated conditions an tional service factor provided b at 10-per-cent overvoltage is alh to voltage unbalance, a motor se volts could have 4 per cent for vol ance and still leave 2 per cent ft from rated conditions. A gene motor served at 240 volts shoi satisfactorily with 6-per-cent a balance for a period of time, if plate ratings are not exceeded. The amount of the service f, allocated to voltage unbalance further considered by all conce hope the preceding comments wi more data to the discussion ani further consideration of the "ma viation from average" method Based on Demand. grade 220- nition with the "symmetrical components" method recommended for design purposes. REFERENCES 1. STANDARDS FOR MOTORS AND GENERATORS. Pub. No. MGI-1949, National Electrical Manu- 100 ... 110 facturers Association, New York, N. Y., section 1.15. . 1.26 4.15, 1949. 1.30 ... 1.60 2. See reference 4 of Mr. Gerngross and Mr. Bankus' discussion. 4 ...6 A. S. Anderson and R. C. Ruete: In com- paring the paper by Bankus and Gerngross vroltage un- with ours it can be seen that an entirely Lary. different method of approach was used in alance is in each case. Their derivation is based on the -oduced by interconnection of positive- and negative- ments. In sequence networks. In our derivation the m, thelay- positive- and negative-sequence currents ineous load were applied to the actual circuit directly. circuit de- We have not tried to compare the equations thods may developed by the two methods; Mr. sage of in- Bankus and Mr. Gerngross have found them mer. The to be in agreement. ce could be We agree with the discussers that the use of digital computers would be economical bank could in fully exploring equations with as many voltage un- parameters as must be considered in this The total problem. However, we have developed excessive if working tables showing transformer and Lis will hap- conductor sizes which appear to be good nce at times practical guides. Such tables can be de- her so that veloped in a reasonable time using system- ie tolerated. atic methods of calculations and assuming a .nee within minimum set of conditions to represent od for con- practical cases. )n of phase We agree with all the discussers that the Lese facts in problem of determining allowable unbalance efinition by of voltage in circuit design and operation is ble) should not simple. Utility engineers need to deter- es would be mine practical limits of primary voltage e was in the unbalance as caused by unbalanced loading, flat spacing of primary conductors and polyphase operation of single-phase regulators. It unbalance is also necessary that manufacturers estab- A detailed lish allowable limits of voltage unbalance in reference based on design of motors and protective devices. With a knowledge of practical shows that limits of voltage unbalance that should be t National allowed on motors and that can be main- ition stand- tained in primary voltage, the utility en- lanced volt- gineer will then be able to design the second- Since the ary system using equations that have been ower system presented in our paper. tion of the Mr. Mohr makes a plea for the acceptance ted to un- of the standard definition of voltage un- cent of the balance to be the "maximum deviation from voltage un- average." He does this on the basis that cent of the such a definition is needed because "simplic- voltage un- ity of application and understanding makes d the addi- this method more desirable for nonpro- y operation fessional operating and service personnel." so allocated He further states that the definition advo- rved at 240 cated in the paper could be used for design Itage unbal- purposes. We believe that just the reverse or deviation of what Mr. Mohr advocates should be zral-purpose adopted. A definition of unbalance should uld operate be adopted by the AIEE based on the best voltage un- mathematical procedure available to study the name- unbalanced problems. The theory of sym- metrical components fulfills this require- actor to be ment. Any short-cut method of determin- should be ing unbalance could then be adopted for erned. We field use. There are several methods avail- ill add some able including the arithmetical definition of .d stimulate 'maximum deviation from average." lximum de- XVe are very grateful for the interesting as the defi- and informative discussions. Anderson, Ruete-Voltage Unbalance in Delta Secondaries932 AUGUST 1954