Dynamic Incentive Design for Demand Response in Energy System MicroGrids

Overview

This project focuses on optimizing demand response (DR) strategies for microgrids using a combination of Mixed-Integer Linear Programming (MILP) and Generalized Linear Model Upper Confidence Bound (GLM-UCB) Bandits. The objective is to maximize system operator revenue by incentivizing buildings to reduce energy demand during peak periods or when renewable generation is insufficient, thereby minimizing the use of costly diesel generation.

Key Components

1. MILP-Based Optimization

• Objective: Find the optimal set of incentives and diesel generation levels to balance demand and supply while minimizing costs.
• Features:
  • Enforces power balance constraints.
  • Uses step and sigmoid functions to model incentive acceptance probabilities.
  • Serves as an upper bound for revenue.

2. GLM-UCB Bandits

• Objective: Learn optimal incentive levels dynamically over time without prior knowledge of building behaviors.
• Features:
  • Incorporates contextual information (e.g., energy demand, price).
  • Adjusts incentives using a multi-bandit framework, treating each building as an individual bandit.
  • Updates Q-values and confidence bounds based on observed rewards.

3. Heuristic Baseline

• Provides a naive approach by greedily offering incentives to reduce demand during shortfalls.

Dataset

The dataset includes:

• Building Load: Simulated profiles from NREL ResStock Dataset.
• Renewable Generation: Simulated using NREL SAM Advisor tool.
• Pricing Data: NYISO Real-Time Market (RTM) prices for 2019.

Dependencies

• Python 3.8 or higher
• Required Python libraries:
  • numpy
  • pandas
  • cvxpy
  • matplotlib
  • statsmodels

Install the dependencies using:

pip install numpy pandas cvxpy matplotlib statsmodels

Files

File Name	Description
data_new.csv	Dataset with energy demand, renewable generation, and prices.
bandits_initial_half.ipynb	Implementation of GLM-UCB Bandits for the first half of the year.
bandits_later_half.ipynb	Continuation of Bandits implementation for the latter half of the year.
milp_experiments_initial_half.ipynb	MILP optimization for the first half of the year.
milp_experiments_later_half.ipynb	MILP optimization for the latter half of the year.
Output_initial_half_MILP.csv	MILP results for the first half of the year.
Output_later_half_MILP.csv	MILP results for the latter half of the year.
Demand_Response_Project_Report.pdf	Document detailing methodologies and approaches.

Methodologies

MILP Formulation

• Objective Function: $\text{Maximize} \quad \sum_{i=1}^n \left[P_t (D_{it} - E[\Delta D_{it}]) - I_{it}E[\Delta D_{it}]\right] - C B_t$

• Constraints:

  • Power balance equation: $\sum_{i=1}^n (D_{it} - E[\Delta D_{it}]) = G_t + B_t$

  • Incentive limits: $0 \leq I_{it} \leq I_{\text{max}}^t$

GLM-UCB Algorithm

• Reward Calculation: $R_k = P_t(D_{it} - \theta_k \Delta D_{it}) - \theta_k I_{it} \Delta D_{it}$

• UCB Calculation: $UCB_k = Q_k + U_k - \text{Penalty Term}$

Results

• No-Incentive Scenario:
  • Revenue: $0.42M$ (over 6 months).
  • High diesel generation costs due to lack of demand reduction.
• Heuristic Baseline:
  • 16.20% improvement over the no-incentive scenario.
• Bandits:
  • 2% improvement over the heuristic baseline.
  • Slightly disadvantaged due to discrete incentives but learns parameters dynamically.
• MILP:
  • Upper bound revenue: $0.52M$.
  • Assumes perfect knowledge of sigmoid parameters.

Visualizations

1. Power Balance Over Time: Stacked bar plot of renewable and diesel generation with line plots for total and reduced demand.
2. Revenue Comparisons: Line plots comparing revenues across different methods.
3. Decision Validation: Plots validating power balance constraints for MILP and Bandits.

How to Run

1. Clone the repository and navigate to the directory.
2. Open the respective Jupyter notebooks:
   • For Bandits: bandits_initial_half.ipynb, bandits_later_half.ipynb.
   • For MILP: milp_experiments_initial_half.ipynb, milp_experiments_later_half.ipynb.
3. Run the cells sequentially to observe results and visualizations.