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Development of Economical Analysis and Technical Solutions for Efficient Distribution Transformers
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Development of Economical Analysis and Technical Solutions for Efficient
Distribution Transformers
Federal University of Itajubá and AES Sul Utility Company
Brazil
Federal University of Itajuba High Voltage Laboratory
Introduction
Operational Losses: No-load and load losses;
The losses are an important parameter in the evaluation of the total transformer costs: investment and operation costs;
Distribution systems: transformers are responsible for roughly one third of the total power losses;
Federal University of Itajuba High Voltage Laboratory
Introduction
The proposal is to design an efficient distribution transformer:
The model the supplied load for a specific region load, peak and factor, and the load increase rate;
The analysis a set of transformer designs presenting reduced losses;
The steps: recognition of the problem, construction of a set of problem solutions and search for the optimal design.
Federal University of Itajuba High Voltage Laboratory
Manufacturing and Total Costs Surfaces
The set of design possibilities considering manufacturing cost and total cost versus no-load and load losses.
coppercoppercorecorefixedingManufactur MCMCCC
WLWAnalysisTRTotal CCCC 0/
Federal University of Itajuba High Voltage Laboratory
Manufacturing and Total Costs Surfaces
WLWAnalysisTRTotal CCCC 0/
jj
jWNTC
n
n
WW
1
1100
TSMPjj
jWTC n
n
cuWLWL
1
11..
24
1
2
i N
i
kVA
kVATSMP
EW CT 76,80
0,365WL ET C
Federal University of Itajuba High Voltage Laboratory
Manufacturing Cost Surfaces
Variations in design parameters: magnetic induction density – no-load losses, LV winding current density and HV winding current density.
Each point on the surfaces represents a transformer design.
45 kVA mineral oilthree-phase Distributiontransformer
Federal University of Itajuba High Voltage Laboratory
Total Costs Surfaces
The total cost depends on the impact of the energy costs on the no-load and load losses.
Period of the day (in hours) that the transformer
operates in full load condition with the same area (energy)
below the load cycle profile.
72.824
1
2
i N
i
kVA
kVATSMP
Federal University of Itajuba High Voltage Laboratory
Total Costs Surfaces
Total cost surfaces considering variations in LV winding current density, HV winding current density and magnetic induction density.
Federal University of Itajuba High Voltage Laboratory
Design Surfaces: Establishing a set of solutions
The second step of this method : searching tool will try to find an optimal design;
Three-dimensional matrixes are built considering the variations in the design parameters;
• Thickness of the conductor of the LV winding;• Width of the conductor of the LV winding;
• Diameter of the conductor of the HV winding;• Magnetic induction;• Insulation thickness;• Clamp dimensions;
• Design of the end insulation;• Gap between LV and HV windings.
Federal University of Itajuba High Voltage Laboratory
Design Surfaces: Establishing a set of solutions
The design surfaces are based on solution sets considering variations and relation on several transformer parameters.
The design has a current density of the
HV winding, an insulation thickness and a
magnetic induction
Federal University of Itajuba High Voltage Laboratory
Optimal Design Based on the Surfaces
The optimal transformer design must present reduced loss costs: the points on the total cost surfaces represent an element of the three-dimensional design matrixes.
Federal University of Itajuba High Voltage Laboratory
Optimal Design Based on the Surfaces
a) The first minimum cost is a random value;
b) For the iteration k, in the column j, each element c(i,j,k) is compared with the minimum cost value;
c) The search must satisfy the level of the no-load losses, load losses and short circuit impedance according the national or utility standards in the set of solutions;
d) The payback is defined by the customer.
Federal University of Itajuba High Voltage Laboratory
Optimal Design Based on the Surfaces
The local minimum point results in a design in which the
purchase price is not attractive to the customer. Because
of this, global minimum points located between the local minimum
and the costs presented by a standard transformer
can be attractive economical solutions.
Federal University of Itajuba High Voltage Laboratory
Optimal Design Related to the Time Supplying the Maximum Rated Power
It is possible to express the concept that for each TSMP
there are several efficient transformers to supply the
load. Some of them have the “best” manufacturing
characteristic and therefore are a logical choice. In theory this is
the “optimal technical and economical solution”
6.1224
1
2
i N
i
kVA
kVATSMP
Federal University of Itajuba High Voltage Laboratory
Optimal Design Related to the Time Supplying the Maximum Rated Power
Energy cost of 59.87 US$/MWh,Interest rate of 8% per year
and 10 years analysis period.
6.1224
1
2
i N
i
kVA
kVATSMP
Federal University of Itajuba High Voltage Laboratory
Optimal Design Related to the Time Supplying the Maximum Rated Power
kReduction of Total
Cost [%]Reduction of No-Load
Losses [%]Reduction of Load
Losses [%]
0 5.66 4.44 33.60
1 5.60 3.15 30.36
2 5.40 2.70 30.11
3 5.35 3.03 29.84
4 4.91 1.46 29.88
5 4.84 2.01 33.42
6 4.78 0.64 28.10
7 4.67 1.93 24.87
8 4.66 0.90 25.50
9 4.34 2.17 32.52
10 4.04 1.66 23.68
Federal University of Itajuba High Voltage Laboratory
Optimal Design Related to the Time Supplying the Maximum Rated Power
kReduction of
the Total Cost [%]
Pay-back, [Years]
Operational Cost Reduction per unit,
[US$/Year]
Energy Saved [MWh/Year]
0 5.66 2.50 75.09 1.3248
1 5.60 2.06 67.02 1.1195
2 5.40 2.20 66.07 1.1036
3 5.35 2.22 65.82 1.0995
4 4.91 2.49 64.40 1.0757
5 4.84 3.00 72.39 1.2092
6 4.78 3.26 59.84 0.9996
7 4.67 1.98 54.29 0.9068
8 4.66 2.02 54.36 0.9125
9 4.34 3.31 70.64 1.1801
10 4.04 2.38 51.51 0.8604
Federal University of Itajuba High Voltage Laboratory
Optimal Design Related to the Time Supplying the Maximum Rated Power
This analysis considers point (k=0) as being the “best” solution: maximum total cost reduction;
A payback perspective, this is not the “best” solution: assuming that all design options are feasible for manufacturing, the final solution will be related to the utility policy. For instance, from a payback standpoint, the answer is design 7;
Federal University of Itajuba High Voltage Laboratory
Optimal Design Related to the Time Supplying the Maximum Rated Power
However, design 9, presents the second operational cost reduction, would also be a possible choice;
Set of solutions variations on the current density of the HV winding, on the gap between the coils and on the design of the end insulation.
Federal University of Itajuba High Voltage Laboratory
Optimal Design Related to the Time Supplying the Maximum Rated Power
170175
180185
190195
500
1000
1500
2000
25000.7
0.8
0.9
1
1.1
1.2
1.3
x 104
W0, WattsWcu, Watts
Tot
al C
ost
Federal University of Itajuba High Voltage Laboratory
Optimal Design Related to the Time Supplying the Maximum Rated Power
77.124
1
2
i N
i
kVA
kVATSMP
Energy cost of 59.87 US$/MWh,Interest rate of 8% per year
and 10 years analysis period.
Federal University of Itajuba High Voltage Laboratory
Optimal Design Related to the Time Supplying the Maximum Rated Power
k Pay-back, [years]Reduction of No-Load
Losses [%]Energy Saved
[MWh/Year]
0 1.18 8.84 0.041
1 1.94 8.84 0.035
2 2.68 8.28 0.030
3 4.45 7.73 0.016
Magnetic Induction of Silicon Steel(E004)
1.68 Watts/kg
Federal University of Itajuba High Voltage Laboratory
Optimal Design Related to the Time Supplying the Maximum Rated Power
160
170
180 5001000
15002000
6000
6100
6200
6300
6400
6500
Wcu, WattsW0, Watts
Tot
al C
ost
Federal University of Itajuba High Voltage Laboratory
Optimal Design Related to the Time Supplying the Maximum Rated Power
kReduction of No-Load
Losses [%]
0 17.12
1 16.57
2 16.57
3 15.46
Magnetic Induction of Silicon Steel1.52 Watts/kg
The strong Goss orientation of grain oriented Silicon Steel is developedby secondary recrystallization.
Federal University of Itajuba High Voltage Laboratory
Optimal Design Related to the Time Supplying the Maximum Rated Power
145
150
155
160500
10001500
2000
2500
5900
6000
6100
6200
6300
6400
Wcu, Watts
W0, Watts
Tot
al C
ost
Federal University of Itajuba High Voltage Laboratory
Study Case
83.2124
1
2
i N
i
kVA
kVATSMP
100 kVA Single-phase oil-immersed distribution
Transformer:Pay-back = 1.4 year
Saved money = 220.9 US$/year
Federal University of Itajuba High Voltage Laboratory
Study Case
Federal University of Itajuba High Voltage Laboratory
Conclusion
The time supplying maximum rated power (TSMP) is the first parameter to be considered in the design of an efficient distribution transformer;
This is related to the influence that this parameter bears on the cost of the transformer designs, mainly because it directly controls the load losses and plays an important indirect role in controlling the no-load losses;
Federal University of Itajuba High Voltage Laboratory
Conclusion
The final choice must consider financial
restrictions, manufacturing process restrictions
and recommendations, the price of the main
transformer commodities, the utility internal
policy and governmental energy saving
regulations, all of which are normally conflicting
issues and therefore must be properly balanced.
Federal University of Itajuba High Voltage Laboratory
Thank You for Your Attention
MSc. Alessandra Freitas Picanço
alessandra@lat-efei.org.br
Prof. PhD. Manuel L. B. Martinez
martinez@lat-efei.org.br
+55 35 3622 3546
Minas Gerais, Brazil
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