⚡ electrical engineering

BOOST: Microgrid Sizing using Ordinal Optimization

This paper introduces BOOST, a hybrid sizing technique that combines ordinal optimization with mixed-integer linear programming to efficiently identify optimal residential microgrid configurations by screening candidates with a simple model before re-evaluating the most promising ones with a detailed dispatch model, thereby significantly reducing computational runtime while maintaining accuracy across diverse synthetic benchmarks.

Original authors: Mohamad Chehade, Sami Karaki

Published 2026-04-09

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Mohamad Chehade, Sami Karaki

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to build the perfect off-grid home energy system. You need to decide two big things:

How big should your solar panel array be?
How big should your battery storage be?

You also have a backup diesel generator and access to the main power grid, but you want to use them as little as possible to save money.

The problem is that there are thousands of possible combinations of solar and battery sizes. If you try to test every single combination to see which one saves the most money over a year, it would take a supercomputer years to crunch the numbers. It's like trying to find the best route through a maze by walking every single path, one by one.

This paper introduces a clever shortcut called BOOST (Battery-solar Ordinal Optimization Sizing Technique). Here is how it works, using a simple analogy:

The Analogy: The "Taste-Test" vs. The "Full Banquet"

Imagine you are a chef trying to find the single best soup recipe out of 1,000 possibilities.

The "Expensive" Way (The Old Method): You cook every single soup recipe to perfection, serve it to a panel of judges, and wait for their detailed reviews. This takes forever and uses up all your ingredients.
The "BOOST" Way: You realize you don't need to cook the full, perfect soup for every recipe to know which ones are promising.

Step 1: The "Taste-Test" (The Simple Model)
You take a spoonful of every soup and taste it quickly. You don't worry about the perfect seasoning or the exact cooking time yet; you just want to know: "Is this soup gross, okay, or amazing?"

You rank them from "Worst" to "Best" based on this quick taste.
You throw away the 900 soups that tasted bad or just "okay."

Step 2: The "Full Banquet" (The Accurate Model)
Now, you only have 100 soups left. You take the top 18 from your quick taste-test and cook them to perfection. You serve them to the judges with full details.

Because your quick taste-test was good at spotting the order (ranking), the "Best" soup from the quick test is almost certainly the "Best" soup from the full banquet.

Why is this smart?

It saves time: Instead of cooking 1,000 perfect meals, you cook 1,000 quick samples and only 18 perfect meals. The paper shows this cuts the time in half (saving about 52% of the computing power).
It's accurate: The math proves that even though the "quick taste" isn't perfect, it gets the ranking right. If Soup A is better than Soup B in the quick test, it's almost guaranteed to be better in the full test, too.
It handles the "Diesel" problem: The tricky part of these energy systems is the diesel generator. It's like a car that is expensive to start but cheap to run once it's going. You can't just turn it on for a tiny bit; it needs to run at a certain minimum speed. The paper uses a very complex math model (MILP) to handle this "start-up" logic, but only for the top candidates, not for the thousands of bad ones.

What did they find?

The researchers tested this method using a "fake" but realistic year of weather and electricity prices (a synthetic dataset).

The Winner: They found that the best setup was a 500 kWh battery (enough to power a house for a day or two) and 1,833 kW of solar panels.
The Cost: This setup costs about 13.2 cents per kilowatt-hour, which is a great deal.
The Proof: When they compared their "BOOST" method to other methods (like guessing or using simpler math), BOOST found the best solution faster and cheaper.

The Bottom Line

This paper doesn't just say "here is a battery size." It gives us a new way to think about solving hard problems. Instead of trying to be perfect at every single step, it says: "Let's be fast and good at sorting things out first, and then be perfect only on the winners."

It's like hiring a scout to find the best athletes in a huge stadium. The scout doesn't need to time every runner with a stopwatch; they just need to watch who looks the fastest, pick the top 20, and then time those 20 with a stopwatch. You get the same result, but in a fraction of the time.

1. Problem Statement

The paper addresses the sizing problem for residential microgrids that integrate photovoltaic (PV) generation, battery storage, diesel backup, and grid interconnection.

Core Challenge: Sizing (determining capacity) and operation (dispatching energy) are tightly coupled. A specific battery/PV configuration is only economically viable if it can be dispatched efficiently over time.
Computational Bottleneck: Finding the optimal sizes requires solving an operational optimization problem for every candidate design in a large search space.
- Exact Approach: Using Mixed-Integer Linear Programming (MILP) for every candidate is highly accurate (capturing diesel generator minimum load constraints) but computationally expensive (NP-hard), making exhaustive search infeasible.
- Approximate Approaches: Heuristics or Dynamic Programming (DP) scale better but often rely on discretized state spaces or greedy logic, which can degrade dispatch quality and fail to capture complex operational constraints (like diesel commitment logic).

2. Methodology: BOOST

The authors propose BOOST (Battery-solar Ordinal Optimization Sizing Technique), a two-phase framework that combines Ordinal Optimization (OO) with Mixed-Integer Linear Programming (MILP). The core philosophy is that preserving the order of designs is sufficient to find a "good-enough" solution, even if the exact cost values are approximated.

Phase 1: Screening (Simple Model)

Model: A Linear Program (LP) is used to evaluate a large set of $N$ candidate designs.
Logic: This model ignores the binary constraints of diesel generator minimum loads (treating it as a continuous variable) to ensure fast computation.
Objective: Minimize the sum of operational costs (grid + diesel) and annualized investment costs.
Process: The $N$ designs are ranked based on their total cost. The top $s$ designs are selected for re-evaluation.
Parameter Selection:
- $N$ is calculated to ensure a high probability ( $P$ ) that at least one "top-performing" design exists within the sample.
- $s$ is determined using alignment probability theory to ensure the top $s$ designs contain the global optimum with high confidence.

Phase 2: Re-evaluation (Accurate Model)

Model: The top $s$ candidates from Phase 1 are re-evaluated using the MILP.
Logic: This model includes binary variables ( $u_D$ ) to enforce the diesel generator's minimum power threshold ( $P^{min}_D$ ), ensuring operational realism.
Outcome: The design with the lowest total cost among these $s$ candidates is selected as the final optimal sizing solution.

3. Key Contributions

Hybrid Algorithm: Proposes a novel integration of Ordinal Optimization with MILP for microgrid sizing, bridging the gap between computational speed and operational accuracy.
Methodological Refresh: Updates the quantitative analysis using a new synthetic benchmark dataset suite generated from a clean reimplementation. This suite includes five scenarios:
- Base case
- Cheap battery
- Cheap PV
- Expensive diesel
- High peak tariff
Validation of Ranking Robustness: Demonstrates that the simple LP model preserves the ranking order of designs almost perfectly compared to the accurate MILP, validating the use of OO for pruning the search space.
Operational Superiority: Shows that the MILP-based inner solver outperforms Dynamic Programming (DP) and Greedy strategies in terms of Levelized Cost of Energy (LCOE).

4. Key Results

The results are based on a $10 \times 10$ design grid (100 candidates) and the specific "paper-style" parameters of $N=90$ and $s=18$ .

Optimal Design (Base Case):
- Configuration: 500 kWh Battery + 1833.3 kW PV.
- Performance: Achieves an LCOE of 13.169 ¢/kWh.
Ranking Fidelity:
- The Spearman rank correlation ( $\rho$ ) between the LP screening and the accurate MILP rankings is 1.000, indicating the simple model perfectly orders the designs.
- The top 18 designs ( $s=18$ ) recovered 100% of the true top-10 designs and the global optimum.
Computational Efficiency:
- Exhaustive MILP: 169.9 seconds.
- BOOST (90 LP + 18 MILP): 82.0 seconds.
- Savings: A 51.8% reduction in runtime compared to exhaustive evaluation.
Comparison with Baselines:
- BOOST vs. DP: BOOST is slightly better (13.169 vs. 13.178 ¢/kWh).
- BOOST vs. Greedy: BOOST is significantly better (13.169 vs. 13.251 ¢/kWh).
Sensitivity Analysis: The synthetic datasets confirmed that the methodology adapts correctly to economic shifts (e.g., cheaper batteries lead to larger storage capacities; expensive diesel reduces reliance on it).

5. Significance

Scalability: BOOST offers a scalable solution for microgrid planning where exact MILP evaluation is too slow for large search spaces, yet heuristic methods lack the necessary precision for critical infrastructure.
Operational Realism: By using MILP for the final selection, the method ensures that the chosen design respects physical constraints (like diesel minimum loads) that simpler models miss.
Methodological Rigor: The paper moves beyond theoretical claims by providing a rigorous, reproducible synthetic benchmark suite. It proves that "order information" is robust to estimation noise, allowing engineers to screen thousands of designs quickly without sacrificing the quality of the final solution.
Practical Application: The workflow provides a clear, computationally efficient path for utilities and planners to determine optimal PV and battery capacities under varying economic conditions.