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Multi-Objective Optimization for Power Electronics … placed in horizontal position with even...
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Photos placed in horizontal position with even amount of white space between photos and header Multi-Objective Optimization for Power Electronics used in Grid-Tied Energy Storage Systems Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. SAND No. 2011-XXXXP Grid Battery DC/DC DC/AC Sarah Hambridge North Carolina State University [email protected] Dr. Stan Atcitty Sandia National Laboratories [email protected] 1: = 2 2exp ( 1 − 1 ) 20 40 60 80 100 120 140 160 0 0.5 1 1.5 2 2.5 x 10 -6 Junction Temperature in degrees Celsius Failure Rate (# failures per equivalent device hours) Failure Rate vs Junction Temperature Where T j = Junction Temperature in deg C f sw = Switching Frequency controlled by PWM R sink = Heat sink to ambient thermal resistance in deg C/W y = 5E+10x 2 + 5E+06x + 69.139 R² = 0.9951 0 100 200 300 400 500 600 700 0.00E+00 2.00E-05 4.00E-05 6.00E-05 8.00E-05 Cost ($) uHenry Cost versus uHenry 0.5 1 1.5 2 x 10 4 1 2 3 4 5 6 7 8 x 10 -5 Switching Frequency in Hz Inductor Size in Henries Inductor Size vs Switching Frequency y = 20.167x -0.404 R² = 0.8829 0 50 100 150 200 250 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Cold Plate Cost ($) R_sink (deg C/W) Lytron Cold Plate Cost vs R_sink Value 0.5 1 1.5 2 x 10 4 0 0.005 0.01 0.015 0.02 0.025 0.03 Decision Variable 1: Switching Frequency (Hz) Decision Variable 2: R sink (deg C/W) R sink vs Switching Frequency 20000, 0.0045 20000, 0.0288 5000, 0.0288 5000, 0.0045 0 0.2 0.4 0.6 0.8 1 1.2 x 10 -6 4400 4500 4600 4700 4800 4900 5000 5100 Obj 1: IGBT Failure Rate (# failures per equivalent device hours) Obj 2: Cost: Inductor plus Cooling System (Dollars) Cost vs Failure Rate 20000, 0.0045 20000, 0.0288 Fsw, R sink 5000, 0.0045 5000, 0.0288 MOTIVATION Increased penetration of renewables and greater loads will present an opportunity for wide spread use of energy storage systems (ESS) in the future. ESS needs to be cost effective, reliable, and safe, among other objectives. Demonstration of multi-objective optimization applied to ESS is needed. OBJECTIVE Demonstrate multi-objective optimization using a genetic algorithm for ESS, specifically applied to a DC/AC power electronics inverter for a grid-tied Battery Energy Storage System (BESS). Develop an optimization model which consists of objective functions, decision variables, and a Pareto front of optimal non-dominating solutions. Figure 1. Battery Energy Storage System (BESS) BACKGROUND A highly important component of the DC/AC inverter is the semiconductor switch. For this application, the IGBT switch was studied. The genetic algorithm used for multi-objective optimization minimizes two or more objective functions (dependent variables) by coming up with a Pareto set of solutions consisting of the decision variable(s) determined for the problem (independent variable(s)). Two objective functions and two decision variables were determined for this optimization. The two objective functions were failure rate and cost. ANALYSIS AND RESULTS IGBT failure rate is a function of Junction Temperature, T j, which is subsequently impacted by the switching frequency, f sw , and the thermal resistance, R sink. Figure 3. IGBT Module with Thermal Resistances Figure 2. Three-phase DC/AC Inverter, consisting of six switches and an LCL output filter Where FR = in number of failures per equivalent device hours, T use = T j , Use temperature at the junction (deg C + 273) in K 2: = + + 1 3 y = 5E+10x 2 + 5E+06x + 69.139 R² = 0.9951 0 100 200 300 400 500 600 700 0.00E+00 2.00E-05 4.00E-05 6.00E-05 8.00E-05 Cost ($) uHenry Cost versus uHenry Failure Rate Equation: Figure 4. Failure Rate vs. T j Figure 5. Cooling System T j as a function of f sw and R sink : Cost Function: The inductor size for the cost function is a function of the switching frequency, f sw . The inductor size affects the ability of the LCL filter to filter harmonics. The R sink value is a characteristic of the cold plate used to cool the IGBT. Conclusion: Higher switching frequencies are sensitive to cooling (changes in R sink ) FUTURE WORK Incorporate more parts of the inverter in the optimization process. Include BESS battery, DC/DC . Add safety, load management as a objective functions. Figure 6. Cost vs. Inductor Size Figure 7. Cost vs. R sink value Figure 8. Pareto Set in Decision Variable space Figure 9. Pareto Set in Objective Function space =( + + ) ∗ ( + 1 1000 + )+ ACKNOWEDGMENTS Dr. Imre Gyuk and the Energy Storage Program in the Office of Electricity Delivery and Energy Reliability
Transcript of Multi-Objective Optimization for Power Electronics … placed in horizontal position with even...
Photos placed in horizontal position
with even amount of white space between photos and header
Multi-Objective Optimization for Power Electronics used in Grid-Tied
Energy Storage Systems
Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.
SAND No. 2011-XXXXP
GridBattery
DC/DC DC/AC
Sarah Hambridge North Carolina State University
Dr. Stan Atcitty Sandia National Laboratories
𝑂𝑂𝑂 1: 𝐹𝐹 =𝑋2
2𝑁𝑁exp 𝐸𝑎𝑘 ( 1
𝑇𝑢𝑢𝑢− 1𝑇𝑢𝑠𝑠𝑢𝑢𝑢
)
20 40 60 80 100 120 140 1600
0.5
1
1.5
2
2.5x 10
-6
Junction Temperature in degrees Celsius
Failu
re R
ate
(# fa
ilure
s pe
r equ
ival
ent d
evic
e ho
urs)
Failure Rate vs Junction Temperature
Where Tj = Junction Temperature in deg C fsw = Switching Frequency controlled by PWM Rsink = Heat sink to ambient thermal resistance in deg C/W
y = 5E+10x2 + 5E+06x + 69.139 R² = 0.9951
0
100
200
300
400
500
600
700
0.00E+00 2.00E-05 4.00E-05 6.00E-05 8.00E-05
Cost
($)
uHenry
Cost versus uHenry
0.5 1 1.5 2
x 104
1
2
3
4
5
6
7
8x 10
-5
Switching Frequency in Hz
Indu
ctor
Siz
e in
Hen
ries
Inductor Size vs Switching Frequency
y = 20.167x-0.404 R² = 0.8829
0
50
100
150
200
250
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
Cold
Pla
te C
ost (
$)
R_sink (deg C/W)
Lytron Cold Plate Cost vs R_sink Value
0.5 1 1.5 2
x 104
0
0.005
0.01
0.015
0.02
0.025
0.03
Decision Variable 1: Switching Frequency (Hz)
Dec
isio
n V
aria
ble
2: R
sin
k (d
eg C
/W)
R sink vs Switching Frequency
20000, 0.0045
20000, 0.02885000, 0.0288
5000, 0.0045
0 0.2 0.4 0.6 0.8 1 1.2
x 10-6
4400
4500
4600
4700
4800
4900
5000
5100
Obj 1: IGBT Failure Rate (# failures per equivalent device hours)
Obj
2: C
ost:
Indu
ctor
plu
s C
oolin
g S
yste
m (D
olla
rs)
Cost vs Failure Rate
20000, 0.0045
20000, 0.0288
Fsw, R sink
5000, 0.0045
5000, 0.0288
MOTIVATION Increased penetration of renewables and greater loads will present an opportunity for wide spread use of energy storage systems (ESS) in the future. ESS needs to be cost effective, reliable, and safe, among other objectives. Demonstration of multi-objective optimization applied to ESS is needed.
OBJECTIVE
Demonstrate multi-objective optimization using a genetic algorithm for ESS, specifically applied to a DC/AC power electronics inverter for a grid-tied Battery Energy Storage System (BESS). Develop an optimization model which consists of objective functions, decision variables, and a Pareto front of optimal non-dominating solutions.
Figure 1. Battery Energy Storage System (BESS)
BACKGROUND
A highly important component of the DC/AC inverter is the semiconductor switch. For this application, the IGBT switch was studied.
The genetic algorithm used for multi-objective optimization minimizes two or more objective functions (dependent variables) by coming up with a Pareto set of solutions consisting of the decision variable(s) determined for the problem (independent variable(s)). Two objective functions and two decision variables were determined for this optimization. The two objective functions were failure rate and cost.
ANALYSIS AND RESULTS
IGBT failure rate is a function of Junction Temperature, Tj, which is subsequently impacted by the switching frequency, fsw, and the thermal resistance, Rsink.
Figure 3. IGBT Module with Thermal Resistances
Figure 2. Three-phase DC/AC Inverter, consisting of six switches and an LCL output filter
Where FR = in number of failures per equivalent device hours, Tuse = Tj, Use temperature at the junction (deg C + 273) in K
𝑂𝑂𝑂 2: 𝐶𝐶𝐶𝐶= 𝐶𝐶𝐶𝐶 𝐶𝑜 𝑂𝑂𝑂 𝐼𝑂𝐼𝐼𝐼𝐶𝐶𝐼 + 𝐶𝐶𝐶𝐶 𝐶𝑜 𝑂𝑂𝑂 𝐶𝐶𝐶𝐼 𝑃𝐶𝑃𝐶𝑂
+ 𝐶𝐶𝐶𝐶 𝐶𝑜13𝐶𝑜 𝐶𝑡𝑂 𝐶𝑡𝐶𝐶𝐶𝑂𝐼
y = 5E+10x2 + 5E+06x + 69.139 R² = 0.9951
0
100
200
300
400
500
600
700
0.00E+00 2.00E-05 4.00E-05 6.00E-05 8.00E-05
Cost
($)
uHenry
Cost versus uHenry
Failure Rate Equation:
Figure 4. Failure Rate vs. Tj Figure 5. Cooling System Tj as a function of fsw and Rsink: Cost Function: The inductor size for the cost function is a function of the switching frequency, fsw. The inductor size affects the ability of the LCL filter to filter harmonics. The Rsink value is a characteristic of the cold plate used to cool the IGBT. Conclusion: Higher switching frequencies are sensitive to cooling (changes in Rsink)
FUTURE WORK Incorporate more parts of the inverter in the optimization process. Include BESS battery, DC/DC . Add safety, load management as a objective functions.
Figure 6. Cost vs. Inductor Size
Figure 7. Cost vs. Rsink value
Figure 8. Pareto Set in Decision Variable space
Figure 9. Pareto Set in Objective Function space
𝑇𝑗 = (𝐹𝑗𝑗+𝐹𝑔𝑠𝑢𝑎𝑢𝑢 + 𝐹𝑢𝑠𝑠𝑠) ∗ (𝑂𝑢𝑠𝑠𝑠𝑗𝑠𝑜𝑢𝑠 𝐸𝑜𝑠 + 𝐸𝑜𝑜𝑜1
1000+ 𝐼𝑜𝑢𝑠𝑜𝑢𝑠𝑉𝐶𝐶) + 𝑇𝑎
ACKNOWEDGMENTS
Dr. Imre Gyuk and the Energy Storage Program in the Office of Electricity Delivery and Energy
Reliability
