Bilevel Optimization for Energy Storage Bidding

This project implements a bilevel optimization model for strategic storage bidding in electricity markets. The upper level optimizes storage bidding decisions, while the lower level solves the economic dispatch problem that clears the market. The repository also contains the Python scripts that reproduce every table and figure in the paper from the model outputs.

Contents

• Key Features
• Installation
  • Julia model
  • Python analysis
• Project Structure
• Model Usage
  • Quick Test Run
  • Scenario Runs
  • Model Outputs
  • Batch Processing
  • Overview of All Scenarios
• Analysis and Figure Reproduction
  • Overview of Reproduction Steps
  • Generate Summary Statistics
  • Generate Tables and Figures
• Data Sources
• License
• Maintainer

Key Features

• Bilevel Optimization: Implements convex bilevel formulation for storage bidding
• Economic Dispatch: Solves lower-level market clearing with variable renewable energy (VRE) integration
• Storage Modeling: Supports configurable storage capacity, duration, and efficiency parameters
• Scenario Setting: Supports different VRE penetration levels, storage capacities, renewable production incentives, and other sensitivity factors
• Reproducible Analysis: One Python script per table/figure, reading either the processed results included in this repo or your own model runs

Installation

Julia model

Prerequisites

• Julia 1.9.3
• Gurobi Optimizer 10.0.1 with a valid license (academic licenses available)

Setup

1. Clone the repository:

   git clone https://github.com/Power-Lab/EnergyEcon_Storage_2026.git
   cd EnergyEcon_Storage_2026

2. Install the Julia packages used by the scripts in code/:

   using Pkg
   Pkg.add([
       PackageSpec(name="JuMP",        version="1.15.1"),
       PackageSpec(name="BilevelJuMP", version="0.6.2"),
       PackageSpec(name="Gurobi",      version="1.0.4"),
       PackageSpec(name="HiGHS",       version="1.7.2"),
       PackageSpec(name="DataFrames",  version="1.6.1"),
       PackageSpec(name="CSV",         version="0.10.11"),
       PackageSpec(name="PrettyTables",version="2.2.8"),
       PackageSpec(name="FileIO",      version="1.16.1"),
       PackageSpec(name="Plots",       version="1.39.0"),
       PackageSpec(name="VegaLite",    version="3.2.3"),
   ])

3. Set up the Gurobi license (follow the Gurobi installation instructions).

Python analysis

The scripts in analysis/ require Python 3.9 and the following package versions:

pip install numpy==1.26.4 pandas==1.5.3 plotly==5.14.0 kaleido==0.2.1

Project Structure

├── code/                          # Julia source code
│   ├── bilevel_cvx.jl             # Strategic Storage: convex bilevel formulation
│   ├── ed.jl                      # Central Control: economic dispatch model
│   ├── run.jl                     # Quick single-period test run (parameters set inside the script)
│   └── run_all_periods.jl         # Full multi-period run (parameters set by the run name)
├── data/                          # Input datasets
│   ├── data_WECC_small_mod/       # WECC system used for all model runs in the paper
│   ├── data_WECC_large/           # Full WECC system
├── batch/                         # SLURM batch scripts
├── result/                        # Raw model output, one folder per scenario (created by the model)
├── analysis/                      # Reproduces the tables and figures in the paper
│   ├── common.py                  # Shared helpers and plot styling
│   ├── result_summary.py          # Builds result_summary.csv from the scenario folders
│   ├── result_summary.csv         # Scenario-level summary metrics
│   ├── plot_table1.py             # Table 1
│   ├── plot_table2.py             # Table 2
│   ├── plot_table4.py             # Table 4
│   ├── plot_table5.py             # Table 5
│   ├── plot_figure3.py            # Figure 3
│   ├── plot_figure4.py            # Figure 4
│   ├── plot_figure5.py            # Figure 5
│   ├── plot_figure6.py            # Figure 6
│   ├── output/                    # Tables (.csv) and figures (.pdf) written by the plot scripts
│   └── result_simplified/         # Processed model outputs used by the plot scripts
└── LICENSE                        # MIT License

Model Usage

Quick Test Run

To check that your Julia and Gurobi setup works, run the single-period test script:

julia code/run.jl

run.jl simulates one 4-day window (week 2) on the small data_WECC_very_small dataset with 80 GW of 4-hour storage, 95% one-way efficiency, and wind and solar capacity scaled by 8x and 4x.

Scenario Runs

All scenarios in the paper are run with code/run_all_periods.jl. Every scenario parameter is encoded in the run name passed on the command line, so no script editing is required to reproduce any configuration used in the paper:

julia code/run_all_periods.jl <run_name>

The run name format is:

b{storage_gw}_hrs{duration}_w{wind_scale}_s{solar_scale}_days{simulation_days}_ptc{production_incentive}[_eff{efficiency}][_rc{ramping_charge}]

Field	Meaning	Values used in the paper
b{storage_gw}	Storage capacity, GW	0, 20, 40
hrs{duration}	Storage duration, hours	4
w{wind_scale} / s{solar_scale}	Wind / solar capacity multiplier	w1_s1 = 15% VRE, w3_s3 = 40%, w5_s5 = 65%, w7_s7 = 80%
days{simulation_days}	Length of each simulation window, days	4
ptc{incentive}	Renewable production incentive, $/MW	0, 5, 10
eff{efficiency} (optional)	Storage one-way efficiency, %	85, 98 (default: 95 if omitted)
rc{charge} (optional)	Ramping charge on strategic storage, $/MW	rc01 = 0.1, rc05 = 0.5, rc1 = 1.0, rc2 = 2.0 (default: off if omitted)

Example:

julia code/run_all_periods.jl b20_hrs4_w3_s3_days4_ptc10_eff85

runs 20 GW storage, 4-hour duration, 40% VRE, a $10/MWh incentive, and 85% efficiency, with no ramping charge.

Model Outputs

Each run writes to result/<result_name>/, where the folder name is derived from the run name, e.g. b20_hrs4_w3_s3_days4_ptc10 becomes tscc_all_weeks_3w_3s_20b_4hrs_-10ptc_4days. Optional eff/rc tokens are appended at the end.

File	Content
hourly_dispatch_central.csv	Hourly dispatch, net demand, and prices under Central Control, all windows concatenated
hourly_dispatch_strategic.csv	Same for Strategic Storage, plus the storage's charge and discharge price offers
summary_system.csv	System cost, storage profit, average price, true generation cost without the incentive, and negative-price statistics for both regimes (and ramping charge totals if applicable)
summary_weekly.csv	Status, MIP gap, system cost, storage profit, and average price for each window
params.csv	Key simulation parameters
params_cap_mix.csv	Installed capacity by resource type
generation/	Per-generator output of each window (iso_gen_<n>.csv, bi_gen_<n>.csv)
figure/	Generation mix, storage dispatch, price, and state-of-energy plots of each window (*.pdf)

Batch Processing

For running the full multi-period simulation, run directly on a local machine or submit as a batch job on an HPC cluster:

# Run directly on a local machine
julia code/run_all_periods.jl <run_name>

# Submit a batch job on an HPC cluster
cd batch
sbatch <run_name>.sh

Overview of All Scenarios

The table below lists every model configuration used to produce the paper's results. Each row gives the run command and the resulting output folder under result/. The last column shows which tables and figures each scenario feeds: to reproduce a table or figure, run every scenario that lists it. Scenarios not used by any table or figure are marked "Supplementary" — these were run as part of the broader sensitivity analysis but are not individually referenced in the published text.

Baseline scenarios — VRE share × renewable incentive (20 GW, 95% efficiency, no ramping charge)

VRE share	PTC ($/MW)	Run command	Output folder	Paper reference
15%	0	julia code/run_all_periods.jl b20_hrs4_w1_s1_days4_ptc0	tscc_all_weeks_1w_1s_20b_4hrs_0ptc_4days	Table 4
15%	5	julia code/run_all_periods.jl b20_hrs4_w1_s1_days4_ptc5	tscc_all_weeks_1w_1s_20b_4hrs_-5ptc_4days	Table 4
15%	10	julia code/run_all_periods.jl b20_hrs4_w1_s1_days4_ptc10	tscc_all_weeks_1w_1s_20b_4hrs_-10ptc_4days	Table 4
40%	0	julia code/run_all_periods.jl b20_hrs4_w3_s3_days4_ptc0	tscc_all_weeks_3w_3s_20b_4hrs_0ptc_4days	Table 2, Figure 5, Figure 6
40%	5	julia code/run_all_periods.jl b20_hrs4_w3_s3_days4_ptc5	tscc_all_weeks_3w_3s_20b_4hrs_-5ptc_4days	Table 4
40%	10	julia code/run_all_periods.jl b20_hrs4_w3_s3_days4_ptc10	tscc_all_weeks_3w_3s_20b_4hrs_-10ptc_4days	Table 2, Table 4, Figure 3, Figure 4, Figure 5, Figure 6
65%	0	julia code/run_all_periods.jl b20_hrs4_w5_s5_days4_ptc0	tscc_all_weeks_5w_5s_20b_4hrs_0ptc_4days	Supplementary
65%	5	julia code/run_all_periods.jl b20_hrs4_w5_s5_days4_ptc5	tscc_all_weeks_5w_5s_20b_4hrs_-5ptc_4days	Table 4
65%	10	julia code/run_all_periods.jl b20_hrs4_w5_s5_days4_ptc10	tscc_all_weeks_5w_5s_20b_4hrs_-10ptc_4days	Table 4
80%	0	julia code/run_all_periods.jl b20_hrs4_w7_s7_days4_ptc0	tscc_all_weeks_7w_7s_20b_4hrs_0ptc_4days	Table 2, Table 4, Figure 5, Figure 6
80%	5	julia code/run_all_periods.jl b20_hrs4_w7_s7_days4_ptc5	tscc_all_weeks_7w_7s_20b_4hrs_-5ptc_4days	Table 4
80%	10	julia code/run_all_periods.jl b20_hrs4_w7_s7_days4_ptc10	tscc_all_weeks_7w_7s_20b_4hrs_-10ptc_4days	Table 2, Table 4, Figure 3, Figure 5, Figure 6

No Storage benchmark (0 GW)

VRE share	PTC ($/MW)	Run command	Output folder	Paper reference
40%	10	julia code/run_all_periods.jl b0_hrs4_w3_s3_days4_ptc10	tscc_all_weeks_3w_3s_0b_4hrs_-10ptc_4days	Table 2, Figure 3
80%	10	julia code/run_all_periods.jl b0_hrs4_w7_s7_days4_ptc10	tscc_all_weeks_7w_7s_0b_4hrs_-10ptc_4days	Table 2, Figure 3

Table 5 — Storage capacity sensitivity (40 GW, 95% efficiency, no ramping charge)

VRE share	PTC ($/MW)	Run command	Output folder	Paper reference
15%	10	julia code/run_all_periods.jl b40_hrs4_w1_s1_days4_ptc10	tscc_all_weeks_1w_1s_40b_4hrs_-10ptc_4days	Supplementary
40%	0	julia code/run_all_periods.jl b40_hrs4_w3_s3_days4_ptc0	tscc_all_weeks_3w_3s_40b_4hrs_0ptc_4days	Table 5
40%	10	julia code/run_all_periods.jl b40_hrs4_w3_s3_days4_ptc10	tscc_all_weeks_3w_3s_40b_4hrs_-10ptc_4days	Table 5
65%	0	julia code/run_all_periods.jl b40_hrs4_w5_s5_days4_ptc0	tscc_all_weeks_5w_5s_40b_4hrs_0ptc_4days	Supplementary
65%	10	julia code/run_all_periods.jl b40_hrs4_w5_s5_days4_ptc10	tscc_all_weeks_5w_5s_40b_4hrs_-10ptc_4days	Supplementary
80%	0	julia code/run_all_periods.jl b40_hrs4_w7_s7_days4_ptc0	tscc_all_weeks_7w_7s_40b_4hrs_0ptc_4days	Table 5
80%	10	julia code/run_all_periods.jl b40_hrs4_w7_s7_days4_ptc10	tscc_all_weeks_7w_7s_40b_4hrs_-10ptc_4days	Table 5

Table 5 — Storage efficiency sensitivity (20 GW, no ramping charge)

VRE share	PTC ($/MW)	Efficiency	Run command	Output folder	Paper reference
40%	0	85%	julia code/run_all_periods.jl b20_hrs4_w3_s3_days4_ptc0_eff85	tscc_all_weeks_3w_3s_20b_4hrs_0ptc_4days_eff85	Supplementary
40%	0	98%	julia code/run_all_periods.jl b20_hrs4_w3_s3_days4_ptc0_eff98	tscc_all_weeks_3w_3s_20b_4hrs_0ptc_4days_eff98	Supplementary
40%	10	85%	julia code/run_all_periods.jl b20_hrs4_w3_s3_days4_ptc10_eff85	tscc_all_weeks_3w_3s_20b_4hrs_-10ptc_4days_eff85	Table 5
40%	10	98%	julia code/run_all_periods.jl b20_hrs4_w3_s3_days4_ptc10_eff98	tscc_all_weeks_3w_3s_20b_4hrs_-10ptc_4days_eff98	Table 5
80%	0	85%	julia code/run_all_periods.jl b20_hrs4_w7_s7_days4_ptc0_eff85	tscc_all_weeks_7w_7s_20b_4hrs_0ptc_4days_eff85	Supplementary
80%	0	98%	julia code/run_all_periods.jl b20_hrs4_w7_s7_days4_ptc0_eff98	tscc_all_weeks_7w_7s_20b_4hrs_0ptc_4days_eff98	Supplementary
80%	10	85%	julia code/run_all_periods.jl b20_hrs4_w7_s7_days4_ptc10_eff85	tscc_all_weeks_7w_7s_20b_4hrs_-10ptc_4days_eff85	Table 5
80%	10	98%	julia code/run_all_periods.jl b20_hrs4_w7_s7_days4_ptc10_eff98	tscc_all_weeks_7w_7s_20b_4hrs_-10ptc_4days_eff98	Table 5

Figure 6 — Ramping charge sensitivity (20 GW, 95% efficiency)

VRE share	PTC ($/MW)	Ramping charge ($/MW)	Run command	Output folder	Paper reference
40%	0	0.1	julia code/run_all_periods.jl b20_hrs4_w3_s3_days4_ptc0_rc01	tscc_all_weeks_3w_3s_20b_4hrs_0ptc_4days_rc01	Figure 6
40%	0	0.5	julia code/run_all_periods.jl b20_hrs4_w3_s3_days4_ptc0_rc05	tscc_all_weeks_3w_3s_20b_4hrs_0ptc_4days_rc05	Figure 6
40%	0	1.0	julia code/run_all_periods.jl b20_hrs4_w3_s3_days4_ptc0_rc1	tscc_all_weeks_3w_3s_20b_4hrs_0ptc_4days_rc1	Figure 6
40%	0	2.0	julia code/run_all_periods.jl b20_hrs4_w3_s3_days4_ptc0_rc2	tscc_all_weeks_3w_3s_20b_4hrs_0ptc_4days_rc2	Figure 6
40%	10	0.1	julia code/run_all_periods.jl b20_hrs4_w3_s3_days4_ptc10_rc01	tscc_all_weeks_3w_3s_20b_4hrs_-10ptc_4days_rc01	Figure 6
40%	10	0.5	julia code/run_all_periods.jl b20_hrs4_w3_s3_days4_ptc10_rc05	tscc_all_weeks_3w_3s_20b_4hrs_-10ptc_4days_rc05	Figure 6
40%	10	1.0	julia code/run_all_periods.jl b20_hrs4_w3_s3_days4_ptc10_rc1	tscc_all_weeks_3w_3s_20b_4hrs_-10ptc_4days_rc1	Figure 6
40%	10	2.0	julia code/run_all_periods.jl b20_hrs4_w3_s3_days4_ptc10_rc2	tscc_all_weeks_3w_3s_20b_4hrs_-10ptc_4days_rc2	Figure 6
80%	0	0.1	julia code/run_all_periods.jl b20_hrs4_w7_s7_days4_ptc0_rc01	tscc_all_weeks_7w_7s_20b_4hrs_0ptc_4days_rc01	Figure 6
80%	0	0.5	julia code/run_all_periods.jl b20_hrs4_w7_s7_days4_ptc0_rc05	tscc_all_weeks_7w_7s_20b_4hrs_0ptc_4days_rc05	Figure 6
80%	0	1.0	julia code/run_all_periods.jl b20_hrs4_w7_s7_days4_ptc0_rc1	tscc_all_weeks_7w_7s_20b_4hrs_0ptc_4days_rc1	Figure 6
80%	0	2.0	julia code/run_all_periods.jl b20_hrs4_w7_s7_days4_ptc0_rc2	tscc_all_weeks_7w_7s_20b_4hrs_0ptc_4days_rc2	Figure 6
80%	10	0.1	julia code/run_all_periods.jl b20_hrs4_w7_s7_days4_ptc10_rc01	tscc_all_weeks_7w_7s_20b_4hrs_-10ptc_4days_rc01	Figure 6
80%	10	0.5	julia code/run_all_periods.jl b20_hrs4_w7_s7_days4_ptc10_rc05	tscc_all_weeks_7w_7s_20b_4hrs_-10ptc_4days_rc05	Figure 6
80%	10	1.0	julia code/run_all_periods.jl b20_hrs4_w7_s7_days4_ptc10_rc1	tscc_all_weeks_7w_7s_20b_4hrs_-10ptc_4days_rc1	Figure 6
80%	10	2.0	julia code/run_all_periods.jl b20_hrs4_w7_s7_days4_ptc10_rc2	tscc_all_weeks_7w_7s_20b_4hrs_-10ptc_4days_rc2	Figure 6

Analysis and Figure Reproduction

Overview of Reproduction Steps

In scope:

• Table 1, Table 2, Table 4, and Table 5 (saved as .csv)
• Figure 3, Figure 4, Figure 5, and Figure 6 (saved as .pdf)

Out of scope:

• Table 3 — lists the parameter values used in the sensitivity analysis; not derived from model outputs.
• Figures 1 and 2 — conceptual/framework diagrams, not derived from model outputs.

The scripts in analysis/ reproduce the tables and figures of the paper in two steps:

1. Generate summary statistics — result_summary.py condenses the model outputs of all scenarios into one file, result_summary.csv.
2. Generate tables and figures — one plot_table*.py / plot_figure*.py script per table or figure reads the summary file and/or the detailed per-scenario outputs.

By default the scripts read the processed model outputs included in this repository (analysis/result_summary.csv and analysis/result_simplified/), so no model run is needed to reproduce the paper's results. A processed copy of result_summary.csv is already included, so Step 1 is only needed if you want to regenerate it (for example after running new scenarios).

Make sure the Python dependencies are installed. Every script writes the result to analysis/output/. All commands below are run from the analysis/ directory:

cd analysis

Generate Summary Statistics

Tables 2, 4, 5 and Figures 5, 6 read result_summary.csv, which holds one row per scenario and regime (system cost, storage profit, average price, negative-price statistics, etc.).

To regenerate result_summary.csv from the processed outputs included in this repository:

python result_summary.py --root result_simplified --out result_summary.csv

If you have run new scenarios (raw output is under result/ at the repository root), summarize them into a separate file:

python result_summary.py --root ../result --out result_summary_new.csv

Generate Tables and Figures

Run each script below. Together, they reproduce every table and figure in scope.

Step	Command	Reproduces	Output
1	python plot_table1.py	Table 1: capacity mix in the WECC region	output/table1.csv
2	python plot_table2.py	Table 2: system costs and storage profits	output/table2.csv
3	python plot_table4.py	Table 4: market outcomes by VRE share and incentive	output/table4.csv
4	python plot_table5.py	Table 5: storage capacity and efficiency sensitivity	output/table5.csv
5	python plot_figure3.py	Figure 3: price duration curves	output/figure3.pdf
6	python plot_figure4.py	Figure 4: storage dispatch and prices in a representative period	output/figure4.pdf
7	python plot_figure5.py	Figure 5: supplier surplus by resource type	output/figure5.pdf
8	python plot_figure6.py	Figure 6: impacts of ramping charges	output/figure6.pdf

Data Sources

The project uses WECC (Western Electricity Coordinating Council) system data from PowerGenome, an open-source tool for building input files for power system models. Data includes:

• Generator parameters and costs
• Load profiles
• Variable renewable energy capacity factors
• Fuel prices

License

This project is licensed under the MIT License - see the LICENSE file for details.

Maintainer

Zhenhua Zhang
Email: zhenhua@ucsd.edu
Affiliation: University of California, San Diego