[71 Baran M.E and WU, F. "Network rcconfiguration in distribution system for. References:

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1 References: (I) William H. Kersting, "Distribution system modeling and Analysis", CRC Press, Boca-Raton, langdon. September I 994. (2) M.H.J. Bollen, Understanding power quality problems- voltage sags and interruptions, New York, IEEE Press, (3] Liu, C.C., Lee, S.J. and Venkata, S.S. "An expert system operational aid for restoration and loss reduction of distribution system", IEEE Transaction on Power Systems, Vol. 3, No.2, May 1998, pp (4] loading and cconom}(.htm [5] Roger Bergeron, "Power Quality Measurement Protocol, CEA. Guide to Performing Power Quality Surveys, "CEA report 220 D 711, Canadian Electrical Association I, Westmount Square, Suite 1600 Montreal, Quebec, Canada H 3Z 2P9, 1996, 216 pp. [6] N. Carter, "Improvements in network performance in urban and rural llkv networks in improving power quality in transmission and Distribution", January 1998, Amsterdam. loss reduction and load balancing". IEEE Transaction on Power Delivery, Vol.4. No.2, April 1989, pp [8] A. Robert and J. Marqucst, "Assessing Voltage Quality with relation to Harmonics, Flicker and Unbalance", WG 36.05, Paper CJGRE 92. March/April, f9] Annettr von jouanne and Banerjee, "Assessment of voltage unbalance", IEEE Transaction on Power Delivery, Vol.l6, No.4, pp , Oct.2001 [ 1 0] Roger Bergeron,"A measurement protocol for power quality coordination", CIRED 1991 papcr.2. 17, A pri I 1991 configuration for an urban power distribution system". Proc. of the power systems Computation Conference, Cambridge [ 12] Shirmohammadi D. and Hong. H. W. "Reconfiguration of electric distribution works for resistive line losses reduction.", IEEE Transaction on Power Delivery, Vol.4. No.2, April 1989, pp.l (II) Merlin A. and Back, H. "Search for a minimal loss operating spanning~ee [71 Baran M.E and WU, F. "Network rcconfiguration in distribution system for

2 , [13] Civanlar, S, Grainger. J.J, Yin, H. and Lee S.S.H. "Distribution Feeder Reconfiguration for loss reduction", IEEE Transaction on Power Delivery. Vol 3. No.3, Jully 1988, pp.l [ 14] Aoki, K., Kuwahara, H., Satoh, T. and Kanezashi, M. "An efficient algorithm for load balancing of transformers and feeders by switch operation in large scale distribution systems", IEEE Transaction on power delivery, Vol.3, No.4, October 1988, pp [ 15] Rudnick, H. and Munoz, M. "Innucnce of modeling in load flow analysis of three phase distribution systems", Proceedings of de 1990 IE~ Colloqium in South America, IEEE No. 90 Tll , August - September 1990 pp

3 , Appendix A Effect of Voltage Unbalance Electrical equipment especially motors and their controllers will not operate reliably on unbalanced voltages in 3-phase system. Generally, the difference between the highest and the lowest voltages should not exceed 4% of th/ lowest voltage. Imbalanced motor voltages may cause a current imbalance that increases the operating temperature and energy losses of the motor. Greater imbalance may cause overheating of components especially motors and intermittent shut down of motor controllers. Motors operated on unbalanced voltages will overheat and many overload relays can't sense the overheating. When the voltage imbalance is more than 1%, derating the motor wi ll help to mitigate its effects. If the imbalance exceeds 5%, it is not advisable to operate the motor at all even it is derated. Voltage imbalance that exceeds 2% is detrimental to reliable long-term 3-phase motor operation. Three phase induction motors are one of the most common loads in industrial environments. When a three-phase induction motor is supplied by an unbalanced system, the resulting line current show a degree of unbalance, which is several times the voltage unbalance. This can be explained with reference to the two contra- rotating fields established when the motor is subjected to voltage unbalance. In relation to the positive sequence set of voltages, the slip corresponding to the positive sequence set of voltage would be: Ns-Nr s:;::: Ns Ns :;::: synchronous speed Nr:;::: the rotor speed The slip corresponding to the negative sequence set of voltage would be: Effects of voltage unbalance on induction motors

4 s2 -Ns-Nr -Ns Slip S2 can be expressed in terms of slip S 1 and hence: As the positive sequence slip s 1 is normally very small (close to zero) the negative sequence slip s2 would be very large (close to 2). From the basic theory of induction motors the impedance of an induction motor is very dependent on te slip where at high slip (e.g. at start or under locked rotor conditions) it is small and conversely at low slip it is very large. Hence it can be approximately stated that the ratio of the positive sequence impedance to negative sequence impedance is given by: --=--- AS the positive sequence current is given by: and the negative sequence current is given by It can be shown that: frmmlrt~ ' = ~ z, h= Vz As an example, a motor with a locked rotor current that is 6 times the running current would give rise to a very significant 30% unbalance in the motor line current if the voltage unbalance is 5%. Furthermore, voltage imbalance generates unwanted heat in motors. This excessive heating is due mainly to negative- sequence currents attempting to cause the motor to tum in a direction opposite to its normal rotation. These higher temperatures result in power loss, insulation breakdown, and improper/inefficient motor operation. [8] As 61 Zz )oo...,, v2 /,tart - X II V1 Z 1 f start z2 l runnmg -Ns-Nr ={2-s, ) S2 = _ Ns

5 we can see from the opposing motor overheating graph, a 5% voltage imbalance would result in a 50% increase in temperature. Per NEMA limits, a motor should not be operated with a voltage imbalance at or above 5%. ~ I) ~ MOTOR OVERHEATING IMBALANCED PHASE VOLT AGES Voltage Imbalance (%) Figure 1.1 Effect of voltage imbalance to the AC motors In addition to a motor getting a supply voltage within 10% of the rated voltage, the three voltages of the 3 phases must be close to the same voltage on each line. When there are unequal incoming voltages between the three supply lines the motor will over heat and is subject to a shorter life span. 1.1 Quick assessment of voltage unbalance The maximum allowable voltage imbalance is 2% as measured at the motor terminals or as close to the motor as can be done safely. The following formula is used to determine the percent or voltage imbalance quickly. Maximum Imbalance xi 00 % Voltage imbalance = A veragc Imbalance 62 ::loooo. ~ ~ 200 ~ ~ I'""P'' I s 0 I I I G I ~ 300

6 Example 3-Phase Motor Measured voltage between phases Ll to L2 230 L2 to L3 236 Ll to L3 237 Then average vollage=234.33volts Maximum deviation = =7 Volts 7 % Voltage Imbalance= x %voltage Imbalance= 2.987% The imbalance factor is very important to the life of the motor. Results of the calculation will show how much hotter the motor windings become compared to the normal. This can be calculated very easily and should cause to think every time that the voltage imbalance causes problems. 1.2 Motor Winding heat due to voltage and current imbalance As the voltage is out of balance the motor winding current also become out of balance. A small voltage imbalance causes a larger current imbalance, which in tum causes the motor windings to get heated. The winding with the largest current is the hottest one and will be the winding, which will bum out first, a second winding may burn out soon after the first and then the motor will stop. The percent of winding heat increase due to a voltage imbalance is expone?rttal. The percent increase in temperature of the highest current winding is approximately two times the square of the voltage unbalance. For example a 3 percent voltage unbalance will cause a temperature rice of about 18 percent calculated as follows. % Temperature rise in motor winding = 2 x (%Voltage Imbalance) 2 % Temperature rise in motor winding = 2 x (3) 2 =18% 63 / L, L2 L_1

7 The result of the calculation shows that the temperature of the motor is 18% hotter than normal due to 3% voltage imbalance. The following chart gives the percent of temperature increase over normal for several voltage imbalances in one percent increases. 1.3 Imbalance Current % Voltage imbalance % Temperature Rise ;1 Table 5.1 Temperature rise of motor with voltage imbalance Imbalance currents often arise when single-phase loads are employed unevenly on system. Therefore it is requested that all single phase loads, especially those with non linear characteristics, in an electrical distribution system with a three phase supply should be evenly and reasonably distributed among the phases. The maximum unbalanced single-phase load distribution in term of percentage of current unbalance shall not exceed I 0%. When the imbalance approaches I 0%, the following problems may surface in an electrical distribution system. Increased current in neutral conductor. Over heating of motors. Wasted investment and operating capital. 64 Negative voltage sequence. Circulating currents Increased Neutral to Ground voltage. --- Reduced motor efficiency. Motor bearing fai lure. Increased maintenance of equipment and machinery. Wasted energy, higher electric bills 5 50

8 The percentage current unbalance can be determined by the following expression. 1. ~c: 1x 100 Where I.,= percentag~ current unbalance ld =Maximum Current Deviation from the average current la = Average current among three phases 65 I -.. '