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A Julia/JuMP based Integrated Energy Resource Planning Model [alessandro@psr-inc.com] March - 2019 Quick Introduction Graduated in Electrical and Control Engineering at PUC-Rio Currently doing Masters in Optimization at PUC-Rio

SLIDE 1

A Julia/JuMP based Integrated Energy Resource Planning Model

[alessandro@psr-inc.com]

March - 2019

SLIDE 2

Quick Introduction

► Graduated in Electrical and Control Engineering at PUC-Rio ► Currently doing Masters in Optimization at PUC-Rio ► Optimization Engineer and Developer at PSR since 2017

SLIDE 3

Motivation

► Hourly resolution ► Unit commitment constraints ► Ramping constraints ► Exogenous calculation of system requirement reserve due to VRE intermittency and

unpredictability

SLIDE 4

Renewable generation - Investment Cost

SLIDE 5

Renewable generation - Capacity Factor (efficiency)

SLIDE 6

Global investments in renewable energy - Bloomberg

SLIDE 7

German system - Challenges

SLIDE 8

Consequences?

► High variability and uncertainty in the offer ► Large generation ramps ► Excess/Lack of generation ► Need for more system reserve ► Need for more thermal flexibility ► Thermal unit commitment influences expansion planning decision!!

SLIDE 9

Challenges

► An expansion planning model with an hourly time step ► Unit commitment in expansion planning ► Co-optimization of expansion planning and system reserve requirement (due to

renewable penetration) modeled as an exogenous variable

► Solving a MIP with all of that in a reasonable amount of time!

SLIDE 10

The Model - OptGen

SLIDE 11

Formulation – Objective Function

𝑛𝑗𝑜

𝑦,𝑕,𝑟,𝑤 ෍ 𝑢 𝜗 𝕌

෍

𝑗 𝜗 𝐽

𝐽𝑗𝑦𝑗,𝑢 + ෍

ℎ 𝜗 𝐼

෍

𝑘 ∈ 𝐻

𝑑

𝑘𝑕𝑘,ℎ

SLIDE 12

Formulation – Constraints

𝑤𝑗,𝒖

𝒕

≤ ҧ 𝑤𝑗 ෍

𝜐=1 𝑢

𝑦𝑗,𝜐 𝑟𝑗,ℎ

𝒕

≤ ത 𝑟𝑗 ෍

𝜐=1 𝑢

𝑦𝑗,𝜐 𝑤𝑗,𝑢+1

𝒕

= 𝑤𝑗,𝑢

𝒕 + 𝑏𝑗,𝑢 𝒕 − 𝑟𝑗,𝑢 𝒕 − 𝑥𝑗,𝑢 𝒕 +

෍

𝑘 𝜗 𝑁 𝑗

𝑟𝑘,𝑢

𝒕 + 𝑥 𝑘,𝑢 𝒕 Hydro maximum storage Hydro maximum turbining Water balance constraint

SLIDE 13

Formulation – Constraints

𝑕𝑘𝑧𝑘,ℎ

𝑡 ≤ 𝑕𝑘,ℎ 𝒕

≤ ҧ 𝑕𝑘𝑧𝑘,ℎ

𝑡

𝑧𝑘,ℎ

𝒕

≤ ෍

𝑘=1 𝑢

𝑦𝑘,𝜐 𝑕𝑚,ℎ

𝒕

≤ 𝐻𝑚

𝑡 ෍ 𝜐=1 𝑢

𝑦𝑚,𝜐

Thermal min/max generation Wind and Solar max generation Commitment constrained by investment decision

SLIDE 14

Formulation – Constraints

𝑔

𝑙,ℎ +𝑡 ≤ ത

𝐺

𝑙

𝑔

𝑙,ℎ −𝑡 ≤ ത

𝐺

𝑙

𝑔

𝑙,ℎ +𝑡 − 𝑔 𝑙,ℎ −𝑡 = 1

𝐵𝑙 ΔΘ𝑙,ℎ

Max capacity Second Kirchhoff Law

SLIDE 15

Formulation – Constraints

෍

𝑘 𝜗 𝐾

𝑕𝑘,ℎ + ෍

𝑗 𝜗 𝐼

𝜍𝑗𝑟𝑗,ℎ + ෍

𝑗 𝜗 𝑆

𝑕𝑚,ℎ + ෍

𝑐 𝜗 𝐶

𝐸𝑐,ℎ − 𝐷𝑐,ℎ ෍

𝑙 𝜗 𝐶𝑢𝑝

𝑔

𝑙,ℎ +𝑡 − 𝑔 𝑙,ℎ −𝑡

− ෍

𝑙 𝜗 𝐶𝑔𝑠𝑝𝑛

𝑔

𝑙,ℎ +𝑡 − 𝑔 𝑙,ℎ −𝑡 + 𝜗ℎ= 𝑒ℎ

Thermal Generation Hydro Generation Renewable Generation First Kirchhoff Law Deficit and Load Battery Net Generation

SLIDE 16

Formulation – Constraints

𝑕𝑘,ℎ

𝑡

− 𝑕𝑘,ℎ−1

𝑡

≤ 𝑆𝑉𝑄 𝑕𝑘,ℎ−1

𝑡

− 𝑕𝑘,ℎ

𝑡

≤ 𝑆𝐸𝑂 𝑡𝑢𝑘,ℎ

𝑡 ≥ 𝑧𝑘,ℎ 𝑡 − 𝑧𝑘,ℎ−1 𝑡

Ramp Start-up

SLIDE 17

Formulation – Constraints

෍

𝑢 𝜗 𝕌

𝑦𝑗,𝑢 ≤ 1 ෍

𝑢 𝜗 𝕌

𝑦𝑘,𝑢 ≤ 1 ෍

𝑢 𝜗 𝕌

𝑦𝑚,𝑢 ≤ 1

Investment Decision Constraint

SLIDE 18

Formulation – Constraints

෍

𝑘∈𝑏

𝑠

𝑘,ℎ 𝑡 + ෍ 𝑗∈𝑏

𝑠

𝑗,ℎ 𝑡 + ෍ 𝑐∈𝑏

𝑠

𝑐,ℎ 𝑡

≥ 𝑆𝑏,ℎ

𝑉𝑄

𝑕𝑘,ℎ

𝑡

+ 𝑠

𝑘,ℎ 𝑡 ≤ ഥ

𝐻

𝑘𝑧𝑘,ℎ 𝑡

𝑕𝑗,ℎ

𝑡 + 𝑠 𝑗,ℎ 𝑡 ≤ 𝐼𝑗𝑦𝑗,𝑢

Reserve Balance Thermal reserve Hydro reserve

𝑕𝑐,ℎ

𝑡

+ 𝑠

𝑐,ℎ 𝑡

≤ 𝐶𝑐𝑦𝑐,𝑢

Battery reserve

SLIDE 19

Formulation – Constraints

Ƹ 𝜉𝑚,ℎ = 𝐹[𝑕𝑚,𝑛,ℎ

𝑡

] 𝜀𝑏,ℎ

𝑡

= ෍

𝑚∈𝐵𝑚

𝑏

𝑕𝑚,ℎ

𝑡 − Ƹ

𝜉𝑚,ℎ 𝑦𝑚,𝑢 𝛦𝑏,ℎ

𝑡

≥ 𝜀𝑏,ℎ

𝑡

−𝜀𝑏,ℎ−1

𝑡

𝑆𝑏,ℎ

𝑉𝑄 ≥ (1 − 𝜇)𝐹[𝛦𝑏,ℎ 𝑡 ] + 𝜇𝐷𝑊𝑏𝑆𝛽 𝛦𝑏,ℎ 𝑡

Forecast Generation Forecast error Hourly Variation in Forecast error Dynamic Probabilistic Reserve Criteria

SLIDE 20

Assumptions and Approximations – Rolling Horizon

SLIDE 21

Assumptions and Approximations – Daily Aggregation

SLIDE 22

Basic Structure

SLIDE 23

International Studies – Chilean Energy System

http://generadoras.cl/prensa/mayor-aporte-solar-y-eolico-reducira-al-25-la-generacion-termica-al-2030-en-chile http://generadoras.cl/prensa/generadoras-participo-en-seminario-internacional-de-energia-renovable-variable-erv

SLIDE 24

International Studies – Brazilian Energy System

https://www.giz.de/en/worldwide/12565.html http://www.epe.gov.br/en/press-room/news/-cem-days-integration-of- renewables-in-the-electric-sector-paths-and-challenges-to-energy-planning

SLIDE 25

Chilean System Study Example

► 13 years horizon ► 54 scenarios ► 300 thermal plants (100 projects) ► 650 wind and solar plants (500 projects) ► 100 hydro plants ► 12 transmission lines / 6 buses (simplified network) ► ~5.6 MM constraints per year ► ~7.8 MM variables (3 MM integer) per year

SLIDE 26

Solving the Model

► FICO Xpress 8.5 solver ► c5.9xlarge amazon instance - 3.0 GHz Intel Xeon Platinum processors - 36 vCPU -

72 GB RAM

► Xpress control parameters were tuned by Xpress lead developer

(Michael Perregaard)

► Solve time: ~240 minutes per year

SLIDE 27

Results - Incremental Expansion

SLIDE 28

Results - Wind and Solar complementarity

SLIDE 29

Results - Marginal Costs

SLIDE 30

Brazilian System Study Example

► 1 year horizon ► 10 scenarios ► 600 thermal plants (400 projects) ► 100 wind and solar plants (30 projects) ► 200 hydro plants ► 10 battery projects ► 50 transmission lines / 30 buses (simplified network) ► ~5 MM constraints per year ► ~4 MM variables (1 MM integer) per year

SLIDE 31

Solving the Model

► FICO Xpress 8.5 solver ► c5.9xlarge amazon instance - 3.0 GHz Intel Xeon Platinum processors - 36 vCPU -

72 GB RAM

► Xpress control parameters were tuned by Xpress lead developer

(Michael Perregaard)

► Solve time: ~70 minutes

SLIDE 32

Incremental Expansion

SLIDE 33

Installed Capacity

2017 ~2036

SLIDE 34