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

smhambri@ncsu.edu

Dr. Stan Atcitty Sandia National Laboratories

satcitt@sandia.gov

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