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Supplementary Information: Data-driven planning of dis-tributed energy resources (DER) amidst socio-technicalcomplexities

Rishee K. Jain1, Junjie Qin2, Ram Rajagopal1

1Department of Civil & Environmental Engineering, Stanford University

2Institute for Computational and Mathematical Engineering, Stanford University

Supplementary Note 1: Benchmark analysis of proposed greedy algorithm

We conducted a benchmark analysis of our proposed greedy algorithm (see Algorithm 1)

against the true optimal solution for a small numerical example of 25 consumers (U = 25).

The 25 consumers are derived from the same data utilized in the study and therefore fol-

low the same types, ratios, probabilities and demand profiles specified. We also utilize the

same input prices and parameters for supply infrastructure as specified in Supplementary

Table 2. The true optimal solution for the small numerical example is found by conducting

an exhaustive search across the entire solution space. Results of the benchmark analysis

are provided in Supplementary Table 7.

Results of the benchmark analysis indicate that our proposed greedy algorithm per-

forms well and finds a solution that is only 8% more expensive than the true optimum

found by the exhaustive search. The key difference in the solutions lie in the discrepancy

1

Data-driven planning of distributed energyresources amidst socio-technical complexities

© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

SUPPLEMENTARY INFORMATIONVOLUME: 2 | ARTICLE NUMBER: 17112

NATURE ENERGY | DOI: 10.1038/nenergy.2017.112 | www.nature.com/natureenergy 1

http://dx.doi.org/10.1038/nenergy.2017.112


http://www.nature.com/natureenergy

between construction of natural gas infrastructure and battery infrastructure. We postu-

late that by installing DER modules one at a time our algorithm is limited in its ability to

take into account the cost benefits that several battery modules have over a single battery

module in a small scale example with only 25 consumers.

2



SUPPLEMENTARY INFORMATION



Supplementary Note 2: Planning Algorithm

Algorithm 1 Forward Step-wise planning

1 Initialization xR = 0, xM = 0, cR = c(xR, xM), c̃R = 0, R̄ = {1, . . . , R̄}2 for n = 1, . . . , N do � N is the maximum number for planning iterations3 for r ∈ R̄ do4 x̃R ← xR + er � er ∈ RR̄ is the rth elementary vector5 cM ← c(x̃R, xM)

6 x̃M ← xM

7 for m = 1, . . . ,Mr do8 x̃M

r ← x̃Mr + em � em ∈ RMr is the mth elementary vector

9 c̃M ← c(x̃R, x̃M)

10 if c̃M > cM then11 x̃M

r ← x̃Mr − em

12 break13 end if14 cM ← c̃M

15 end for16 c̃Rr ← cM

17 end for18 c̃R ← minr∈R̄ c̃Rr19 r� ← argminr∈R̄ c̃Rr20 if cR > c̃R then21 xR ← xR + er�

22 xMr� ← x̃M

r�

23 cR ← c̃R

24 R̄ ← R̄\{r�}25 else26 break27 end if28 end for

3






Supplementary Figure 1 Example of a three stage scenario tree representing two sce-

narios for natural gas prices (NG1, NG2) and two scenarios for consumer demand (D1,

D2). The final stage has four nodes representing the four deterministic scenarios of the

system.

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4






Supplementary Figure 2 Schematic of supply infrastructure hierarchical modeling on

the resource, module and node levels

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5






Supplementary Figure 3 Pictorial representation of simplified min-flow problem setting

for DER planning

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(23232)

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6






Supplementary Figure 4 Plots of the solar (k = 2 profile profiles Gm(ω̃) representing a

”sunny” day and a ”cloudy” day

7






Supplementary Figure 5 Plots demand profiles for each consumer type used in the

case study. No demand-side management policy are displayed as solid lines, demand-

side management policy impacted demand capacity profiles are displayed as hashed

lines

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8






Supplementary Table 1: Cost ce(fe), lower bound fe

and upper bound f e of feasible

edge types

Edge Cost Lower Upper Physical

type ce(fe) bound fe

bound f e interpretation

E1 cOPr,m(gm,t, ω̃) 0 Gm(ω̃) Cost of generation; limited by capacity; fe = gm,t

E2 0 0 ∞ Cost of power losses (assumed to be zero)

E3 cOPr,m(bm, ω̃) 0 Bm(ω̃) Cost of battery charging loss; fe = −bm,t

E4 cOPr,m(bm,t, ω̃) 0 Bm(ω̃) Cost of battery dis-charging loss; fe = bm,t

E5 0 0 Bm(ω̃) Cost of battery self-discharge (assumed to be zero)

E6 0 du,t(ω̃) ∞Cost of servicing demand (assumed to be zero);

all consumer demand must be met

9






Supplementary Table 2: Input prices and parameters for supply infrastructure 1–3, and

market prices for a 400W solar PV panel and 10kW natural gas turbine. Battery input cost

parameters estimated from published installation costs of Tesla Powerwall (7 kWh) 4

Solar, k = 1 NG turbine, k = 2 Grid, k = 3 Battery, k = b

cRr (ω̃) $3,000 $65,000 $0 $13,000

cMr,m(ω̃) $300 $25,000 $0 $3,000

cOPr,m(gm,t, ω̃) / cOP

r,m(bm,t, ω̃) $0 $0.18, $0.06 $0.233 $0.019

Mr 25 3 1 5

10






Supplementary Table 3: Number of each consumer type in the 10,000 consumer nu-

merical example

Consumer type Number

A 746

B 3,318

C 888

D 1,159

E 3,889

11






Supplementary Table 4: Probabilities of demand capacity profiles for each consumer

type

Consumer type / Demand 1 2 3 4 5

A 0.017 0.289 0.272 0.069 0.352

B 0.163 0.212 0.197 0.163 0.264

C 0.057 0.178 0.112 0.090 0.562

D 0.158 0.214 0.205 0.194 0.229

E 0.139 0.202 0.181 0.164 0.314

12






Supplementary Table 5: Demand-side management policy 1 (h = 1) response by

consumer type

Consumer DM response for DM response for peak load

type base load (all hours) (single hour with highest usage)

A Reduce by 5% Reduce by 10%

B Reduce by 10% Reduce by 10%

C Reduce by 5% No response

D Reduce by 5% Reduce by 20%

E Reduce by 10% Reduce by 15%

13






Supplementary Table 6: Capacity and per capita capital results for the numerical ex-

ample

Case I (no DM) Case II (DM)

Solar (kW) 1,320 1,232

Natural gas (kW) 6,000 5,600

Battery (kWh) 2,100 1,960

Capital per kW generation $6,200 $6,202

Capital per consumer $5,805 $5,419

DM cost per consumer $860

14






Supplementary Table 7: Results of benchmark analysis for proposed algorithm

Exhaustive searchProposed

greedy algorithm

SolarModules 11 11

Resources 1 1

Natural gasModules 0 2

Resources 0 1

BatteryModules 10 0

Resources 2 0

Total cost $284.5k $309.6k

15






Supplementary References

1. National Renewable Energy Laboratory. Distributed Generation Renewable Energy Es-

timate of Costs Database (2013). URL http://www.nrel.gov/analysis/tech_

lcoe_re_cost_est.html.

2. United States Environmental Protection Agency. Catalog of CHP Technologies. Tech.

Rep. (2015).

3. United States Department of Labor. Average Energy Prices, San Francisco-Oakland-

San Jose, July 2015. Tech. Rep. (2015).

4. Loveday, E. Solarcity reveals installed pricing for tesla powerwall (2015). URL

http://insideevs.com/solarcity-reveals-installed-pricing-for-

tesla-powerwall/.

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