A Two-Stage Optimization Framework for Validating Electric Vehicle Charging Infrastructure under Grid Constraints

This paper proposes a two-stage mixed-integer optimization framework linking infrastructure planning with grid-constrained operation to demonstrate that cost-minimal EV charging designs often fail to meet service needs due to spatial concentration, whereas uniformly distributed deployments significantly improve operational performance and reduce energy shortfalls.

The Gist

Imagine you are the mayor of a growing city, and suddenly, everyone is buying electric cars (EVs). Your job is to build charging stations so these cars can run.

The traditional way to solve this problem is like a budget-conscious accountant: "Let's build the cheapest possible network of chargers that theoretically works." You calculate the cost of the hardware, buy the cheapest units, and put them where they are mathematically cheapest to install.

This paper argues that the accountant is wrong.

If you just build the cheapest system, you might end up with a city where the chargers are all clustered in one neighborhood, leaving everyone else stranded, or where the local power lines get fried because too many cars try to charge at once.

Here is the paper's solution, explained simply:

The Two-Stage "Test Drive" Framework

The authors propose a new way to plan, which they call a Two-Stage Framework. Think of it like designing a new restaurant.

Stage 1: The Blueprint (The "Cheap" Plan)

First, you act as the architect. You look at the map and say, "Okay, to feed 500 people, I need the absolute minimum number of tables and chairs to keep costs low."

• The Goal: Spend the least amount of money (CAPEX).
• The Result: You might decide to put 50 tables in one big dining hall because it's cheaper than building five small rooms.
• The Flaw: You haven't actually served the customers yet. You just bought the furniture.

Stage 2: The Reality Check (The "Stress Test")

This is the paper's big innovation. Before you break ground, you run a simulation. You take your "cheap" blueprint and ask: "If 500 hungry people actually show up at 6:00 PM, can this system handle it?"

• You simulate the cars arriving, plugging in, and trying to charge.
• You check if the power lines (the "pipes" bringing electricity to the tables) can handle the flow without bursting.
• The Discovery: You realize that because all the tables are in one room, the kitchen (the power grid) can't keep up. People are waiting in line, their food (energy) never arrives, and the kitchen pipes are about to explode.

The Big Surprise: "Cheapest" $\neq$ "Best"

The paper ran this simulation with thousands of virtual cars and found a shocking truth:

The "Cheapest" Plan creates a "Bottleneck."
When you try to save money, the computer naturally wants to cluster all the chargers in one spot. It's like putting all the gas stations in one neighborhood.

• The Result: Cars in that neighborhood fight for a plug. Cars in other neighborhoods have nowhere to go. The power grid gets overwhelmed, and many cars leave with low batteries (low State of Charge).

The "Uniform" Plan is actually better.
The authors tested a different strategy: Spread the chargers out evenly, even if it costs slightly more or uses the same amount of hardware.

• The Analogy: Instead of one giant gas station, you build small gas stations on every corner.
• The Result: Even though you spent the same amount of money on hardware, the cars get charged much faster and more reliably.
• The Stat: In their tests, spreading the chargers out reduced the number of cars that failed to get enough energy by up to 74%.

The "Port" vs. "Power" Problem

The paper also discovered that the type of charger matters depending on how many cars you have:

1. Small Fleet (The "Seat" Problem): If you only have a few cars, the problem is just having enough plugs (ports). It doesn't matter if the charger is slow or fast; you just need enough seats at the table.
2. Large Fleet (The "Water Pressure" Problem): If you have hundreds of cars, having enough plugs isn't enough. You need high-pressure water (fast chargers). If you only have slow chargers, the cars will sit there for hours, and the grid will get clogged. The system needs to switch to "High Power" mode.

The Takeaway for Everyone

The main lesson of this paper is: Don't just build the cheapest thing.

If you design a charging network based only on saving money, you will create a system that looks good on paper but fails in real life. You end up with:

• Cars that can't charge.
• Neighborhoods with blackouts.
• Frustrated drivers.

The Solution: You must design the network by thinking about where the chargers go, not just how many you buy. Spreading them out evenly is like building a better road network; it prevents traffic jams and ensures everyone gets to their destination, even if the initial map looks a bit more complex.

In short: A cheap plan that doesn't work is more expensive than a slightly smarter plan that actually gets the job done.

Technical Summary

1. Problem Statement

The rapid deployment of Electric Vehicle (EV) charging infrastructure requires massive capital investment. Current planning approaches often focus on minimizing capital expenditure (CAPEX) or optimizing infrastructure sizing in isolation, without rigorously evaluating how these cost-optimal configurations perform under real-world distribution grid constraints (e.g., voltage limits, transformer capacities, and line loading).

The core problem addressed is the decoupling of infrastructure planning and operational feasibility. A configuration that is mathematically optimal for cost may lead to suboptimal or infeasible operational outcomes, such as:

• Inability to meet EV charging demand due to localized grid congestion.
• Low State-of-Charge (SOC) at departure times.
• Voltage violations or transformer overloading.

The paper argues that cost-optimal planning alone is insufficient and that a systematic mechanism is needed to evaluate whether a planned infrastructure can deliver the required service level under grid constraints.

2. Methodology

The authors propose a Two-Stage Optimization Framework that explicitly links infrastructure planning with grid-constrained operational evaluation. The framework is formulated as a Mixed-Integer Program (MIP) using a linearized Alternating Current Optimal Power Flow (AC-OPF) model.

Stage 1: Strategic Infrastructure Planning

• Objective: Minimize total CAPEX (installation costs) while incorporating a small regularization term to encourage charger utilization.
• Decision Variables: The number and type of chargers (Fast/Slow, Single-port/Multi-port) deployed at each network node.
• Constraints:
  • Grid Constraints: Linearized AC-OPF constraints ensuring nodal voltage limits (0.95–1.05 p.u.) and transformer thermal limits are respected.
  • Infrastructure Logic: Constraints linking the number of installed units to total available ports and aggregate power capacity.
  • EV Dynamics: Time-coupled SOC evolution and charging logic (binary connection states).
• Output: A cost-optimal spatial distribution and technology mix of charging infrastructure.

Stage 2: Operational Validation and Dispatch

• Objective: Evaluate the operational feasibility of the Stage 1 solution. The objective minimizes the deviation from target SOC (prioritizing end-of-horizon SOC satisfaction).
• Fixed Parameters: The infrastructure decisions ($N_{n,j}$) from Stage 1 are fixed.
• Process: The model simulates the charging schedule of the EV fleet over a 24-hour period, accounting for arrival/departure patterns, battery dynamics, and grid constraints.
• Outcome: Quantifies the "service gap," including unmet energy demand (shortfall) and achieved SOC levels.

System Modeling Details

• Heterogeneous Technologies: The model considers Fast (50–200 kW) and Slow (7.5–30 kW) chargers, both in single-port and multi-port (4-port) configurations.
• Grid Model: A 14-bus Medium Voltage (MV) distribution network (CIGRE test system) with radial feeders.
• EV Fleet: Deterministic commuting patterns (Home-Work) with randomized initial SOC and battery capacities (20 kWh and 40 kWh scenarios).

3. Key Contributions

1. Integrated Two-Stage Framework: Proposes a sequential planning-operation approach that explicitly tests cost-optimal infrastructure against strict grid constraints, revealing the gap between theoretical cost savings and operational reality.
2. Heterogeneous Technology Representation: Incorporates a flexible mix of fast/slow and single/multi-port chargers, allowing for a realistic assessment of how technology choices impact grid loading and utilization.
3. Scalable MIP Formulation: Develops a linearized OPF-based MIP model that balances computational tractability with physical accuracy (voltage and thermal limits), validated across fleet sizes from 250 to 600 EVs.
4. Identification of Fundamental Trade-offs: Demonstrates that minimizing CAPEX often leads to spatially concentrated resources, which creates bottlenecks, whereas uniform distribution significantly improves service performance.

4. Key Results

The framework was tested on a 14-bus MV grid with varying fleet sizes and battery capacities.

• Cost vs. Performance Trade-off:

  • Cost-Optimal (Stage 1) Strategy: Tends to concentrate multi-port chargers at specific nodes to minimize hardware costs. This leads to localized bottlenecks, resulting in lower average final SOC and higher unmet energy demand.
  • Uniform Distribution Strategy: When the same total capacity is distributed evenly across the network (ignoring cost minimization), operational performance improves drastically.
  • Quantitative Impact: Uniform distribution reduced energy shortfalls by up to 74.27% (in the 20 kWh, 550 EV scenario) and improved average final SOC by up to 31.90 percentage points compared to the cost-optimal plan.

• Non-Linear Scaling of Infrastructure:

  • Infrastructure requirements do not scale linearly with fleet size or battery capacity.
  • Regime Transition: At lower energy demands (20 kWh), the system is "port-limited" (bottleneck is the number of physical plugs). At higher demands (40 kWh, large fleets), the system shifts to being "power-constrained," necessitating high-power fast chargers despite their high cost.
  • CAPEX Sensitivity: Increasing battery capacity from 20 kWh to 40 kWh caused CAPEX to jump by nearly 80% in high-penetration scenarios (600 EVs), driven by the need for more expensive fast-charging technologies.

• Grid Impact:

  • Cost-optimal planning creates "hotspots" where nodal loading exceeds 0.25–0.30 p.u. during peak times.
  • Uniform distribution acts as a passive congestion management mechanism, flattening load peaks and keeping nodal intensities below 0.20 p.u., thereby utilizing latent grid capacity more effectively without hardware upgrades.

5. Significance and Conclusion

The paper concludes that cost-optimal planning alone is insufficient for designing robust EV charging infrastructure.

• Spatial Allocation Matters: The physical location of chargers is as critical as the total capacity. Concentrating resources to save money can render the system operationally infeasible under grid constraints.
• Need for Joint Optimization: Effective infrastructure design must jointly consider cost, spatial distribution, and grid constraints.
• Validation is Crucial: A two-stage validation process is essential to ensure that planned investments deliver reliable charging performance. Relying solely on CAPEX minimization risks creating systems that fail to meet user needs during peak operation.

The study provides a critical tool for Distribution System Operators (DSOs) and planners to avoid the pitfall of "cheap but ineffective" infrastructure, advocating for strategies that balance investment efficiency with service reliability and grid stability.