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Modeling Secondary in Mapping and Engineering. 2010 IEEE REPC Orlando, FL May 17, 2010 Greg Shirek, PE Milsoft Utility Solutions Abilene, TX. OUTLINE. Reasons For Modeling Modeling Requirements Center-Tapped transformers Secondary Triplex Conductor
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Modeling Secondary in Mapping and Engineering 2010 IEEE REPC Orlando, FL May 17, 2010 Greg Shirek, PE Milsoft Utility Solutions Abilene, TX
OUTLINE • Reasons For Modeling • Modeling Requirements • Center-Tapped transformers • Secondary Triplex Conductor • System Level Loss analyses with and without secondary • Calculating X/R for Transformers • Two Winding • Three Winding Center Tap • Sensitivity Analysis • Vary Transformer X/R and %Z • Load Balance • Summarize
WHY NOW? • Advances in computer processor speed and memory can now handle detailed models • Smart-Grid, Real-Time Analysis & State Estimation • Mapping-Engineering Analysis (GIS-EA) seamless integrations • Perform loss studies at all system component levels; aid in transformer and secondary conductor sizing practices • Arc Flash – Highest energy occurs at transformer low-side and service entrance
Transformer X/R Calculations • Transformer losses are a function of core (no-load) and copper (load) PLoss total = PCU + Pcore (1) • Need at least 2 of the 3 from (1) to get PCU • Cooper losses are a function of resistance PCU = I2R = I2Rp + I2Rs
Transformer X/R Calculations 3ph. 300 kVA, 208/120V, 4% Z, Load Losses = 4,000 W
Center-Tapped Transformer Impedance ZTWO Two-Winding non-Center-Tap Connection Three-Winding Connection (Center-Tapped)
Center-Tapped Transformer Impedance ZTWO Two-Winding non-Center-Tap Connection Three-Winding Connection (Center-Tapped) [ZTWO] = [RA + jXA]
Modeling Requirements • Center-Tapped Transformers • kVA • %Z • X/R • Nominal/Rated Input/Output Voltages • No-load losses • Diversity of 120V loads on each ½ winding • Diversity of 240V loads
Triplex Impedance Equations • Self Impedance i = 1, 2, n 1 2 j = 1, 2, n n • Mutual Impedance
Modeling Requirements • Triplex Secondary • Resistance at Operating Temperature • Secondary Service Conductor Length • Construction Spacing Between Phases and neutral • Geometric Mean Radius (GMR) • Conductor Diameter • Earth Resistivity
System Level Loss Analyses • How will models with varying levels of detail affect the allocation of system load • Primary Line Based • Primary Line & Distribution Transformers • Primary Line & Distribution Transformers and Secondary Conductor
Distribution System Losses • 10,000 kW - feeder peak • 22,000 kVA - installed transformer kVA
Sensitivity Analyses • Large variance on system transformer specs, how much detail do I need to maintain in the equipment database? • X/R • %Z • 1/0 AAC secondary conductor specs and conductor spacing were held constant
Sensitivity Analyses • 25 kVA 7200V - 120/240V center-tapped transformer • 100 feet of 1/0 AAC Triplex • Loads • 120V half-winding 1: 5 kW @ 95% P.F. • 120V half-winding 2: 5 kW @ 95% P.F. • 240V full-winding: 15 kW @ 90% P.F. • Total: 25 kW @ 92% P.F. • All loads constant kVA load mix type
Sensitivity Analyses • Transformer %Z varied from 1.0 to 4.0 percent • Transformer X/R varied from 1.0 to 3.0 • Delivered voltage held constant at 7,200V • 3 cases…..
Sensitivity Analyses Case 1 : Transformer only, no secondary
Sensitivity Analyses Case 2: Transformer with secondary
Sensitivity Analyses Case 3: Transformer and secondary with unbalanced 120V loads Transformer was set with Z=2% and X/R = 1.5 (mid-point values), while 120V load was varied
Sensitivity Analyses • Case 1: Transformer only Worst Case
Simplified Transformer Voltage Drop • Test Case 1 had 25 kW @ 92% P.F. => 113 Amps • Ir = 103.5 real amps • Ix = 44 reactive amps • For 25 kVA transformer with X/R of 1.0 and 4%Z • Ib = 25 kVA/240V = 104 Amps • Zb = Vb/Ib =240V/104A = 2.30 Ω • Z = 2.30 Ω * 4% = 0.092 ohms => R = X = 0.065 Ω Worst Case Test Point
Sensitivity Analyses • Case 2: Transformer and Secondary Same profiles as Case 1, with additional 2 Volt Drop on secondary conductor.
Sensitivity Analyses • Case 3: Transformer and Secondary with unbalanced 120V loads • Overall, a 40% unbalance with 7.5 and 17.5 kW on each ½ winding 0 kW 5 kW 5 kW 10 kW
Summary • No excuses for not modeling secondary since computing power and software capabilities now exist • Load allocation: Level of detail modeled will affect allocation of losses • Can calculate X/R for any transformer if given load losses and %Z • Sensitivity analysis proved X/R and %Z is extremely important when modeling distribution transformers • No right or wrong answer to how many transformers with unique X/R and %Z values to store in the equipment database. • Options: • Maintain low, high, or average %Z? • Maintain low, high, or average X/R? • Maintain separate databases for analysis type (Fault Current, Voltage Drop, Arc Flash, etc.)
_ Questions?