⚡ electrical engineering

Probabilistic Flexibility Aggregation of DERs for Ancillary Services Provision

This paper proposes a grid-aware, probabilistic optimal power flow method that aggregates distributed energy resources' flexibility for multiple ancillary services by optimizing cost-effectiveness, handling uncertainties, and scaling to large networks through feeder decomposition.

Original authors: Matthieu Jacobs, Mario Paolone

Published 2026-02-19

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Matthieu Jacobs, Mario Paolone

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 the electrical grid as a massive, bustling city. In the past, this city was powered by a few giant, reliable power plants (like large factories) that could turn on and off whenever needed. But today, the city is changing. We are adding thousands of small, unpredictable power sources: solar panels on roofs (which only work when the sun shines) and electric cars (which charge when their owners want).

This creates a problem: Uncertainty. The city's power manager (the Transmission System Operator, or TSO) needs to know exactly how much "extra" power they can borrow or how much "extra" load they can handle to keep the lights on. But with all these small, scattered sources, it's hard to get a clear answer.

This paper presents a new, smart way for the local neighborhood manager (the Distribution System Operator, or DSO) to answer that question. Here is how it works, broken down into simple concepts:

1. The "Group Hug" of Energy (Flexibility Aggregation)

Think of thousands of small batteries, heat pumps, and solar panels in a neighborhood as individual dancers. Each dancer has their own rhythm and limits. The TSO doesn't want to talk to 10,000 dancers individually; they just want to know: "How much can this whole group move together?"

The paper proposes a method to aggregate (group) all these dancers into a single, powerful "super-dancer." This super-dancer represents the total flexibility the neighborhood can offer to the main grid.

2. The "Swiss Army Knife" of Services

Previously, these groups could only offer one type of help at a time. But the grid needs different things at different times:

FCR (Frequency Control): Like a tightrope walker needing immediate balance.
aFRR (Secondary Regulation): Like a runner adjusting their pace over a longer distance.

This paper's method is like giving the "super-dancer" a Swiss Army Knife. It allows the neighborhood to offer help for multiple services simultaneously. The algorithm figures out how to split the group's energy so they can balance the tightrope and adjust the pace at the same time, without running out of energy.

3. The "Weather Forecast" Problem (Handling Uncertainty)

The biggest headache is that solar panels depend on the sun, and heat pumps depend on the temperature. What if it's cloudy? What if everyone turns on their AC at once?

Old Way: Be super cautious. Assume the worst possible weather and only offer a tiny amount of help. This is safe, but it wastes money and potential energy.
The Paper's Way: Use Probability. Instead of assuming the worst, they use a "90% confidence rule." They say, "We are 90% sure we can deliver this much power."
The Analogy: Imagine you are packing for a trip.
- The Old Way: You pack for a blizzard, a heatwave, and a hurricane all at once. You carry a heavy tent, a snow shovel, and a fan. You are safe, but you are exhausted and over-prepared.
- The New Way: You look at the forecast. You know there's a 90% chance it will be sunny or partly cloudy. You pack a light jacket and an umbrella. You are still safe (90% of the time), but you are much more efficient and can carry more useful stuff.

4. The "Wallet" Check (Cost-Effectiveness)

Just because you can offer power doesn't mean you should if it costs too much.

The Analogy: Imagine you are a taxi driver. You could drive to the airport to pick up a passenger, but if the gas prices are sky-high and the fare is low, you lose money.
The paper's method includes a "Wallet Check." It calculates the cost of running the batteries or heat pumps. If the price the grid pays for the service is higher than the cost to run the equipment, the system says "Go!" If the cost is too high, it says "No." This ensures the neighborhood makes a profit, not a loss.

5. The "Traffic Jam" Check (Grid Constraints)

This is crucial. Just because a neighborhood has the energy doesn't mean they can send it. The local power lines might be too small (like a narrow country road). If everyone tries to send power at once, the lines will overheat and break (a traffic jam).

The Analogy: Imagine a group of people in a house trying to leave through a single front door. Even if there are 100 people ready to go, the door can only handle 10 at a time.
The paper's method looks at the "door" (the power lines and transformers). It calculates the maximum number of people (power) that can actually leave the house without breaking the door. It doesn't just count the people; it checks the door size.

6. The "Zoom Out" Strategy (Scalability)

Finally, the paper solves a big problem: What if you have 50 neighborhoods, not just one?

The Analogy: Instead of trying to solve a puzzle with 10,000 pieces all at once (which takes forever), the method solves 50 smaller puzzles (one for each neighborhood) and then snaps them together at the top level. This makes the math fast enough to run on a regular computer, even for huge cities.

Summary

In short, this paper gives the local power grid a smart, probabilistic, and cost-aware calculator. It allows neighborhoods to sell their extra energy to the main grid safely, efficiently, and profitably, even when the weather is unpredictable and the power lines are crowded. It turns a chaotic mess of small devices into a reliable, organized power plant for the future.

1. Problem Statement

The paper addresses the challenge of aggregating the flexibility of Distributed Energy Resources (DERs) within Active Distribution Networks (ADNs) to participate in Ancillary Services (AS) markets (e.g., Frequency Containment Reserve - FCR, and automatic Frequency Restoration Reserve - aFRR) at the transmission level.

Key challenges identified include:

Multi-Service Complexity: DERs must simultaneously provide multiple services with different time-coupling requirements and activation rules (symmetric vs. asymmetric).
Uncertainty: Stochastic fluctuations in prosumption (load and PV generation) create uncertainty in network constraints and DER capabilities. Traditional robust optimization often leads to overly conservative solutions, while ignoring uncertainty risks constraint violations.
Cost-Effectiveness: Existing methods often fail to ensure that the aggregated flexibility is economically viable, neglecting the operational costs of DERs (e.g., battery degradation, heat pump efficiency).
Scalability: Directly solving aggregation problems for large, realistic distribution networks with thousands of buses is computationally intractable.
Network Constraints: Aggregated flexibility must respect physical grid constraints (voltage limits, line thermal limits) to avoid adverse impacts on the distribution system.

2. Methodology

The authors propose a grid-aware, probabilistic, and cost-effective aggregation framework based on Optimal Power Flow (OPF) and robust optimization.

A. Mathematical Formulation

Objective: Maximize the value of the aggregated flexibility set, defined by service prices ( $\pi$ ) and the size of the flexibility set, rather than just the geometric volume.
Flexibility Representation: The aggregated flexibility at the Grid Connection Point (GCP) is modeled as ellipsoidal sets (or quadrant ellipsoids for asymmetric services).
- Symmetric services (FCR): Represented by ellipsoids symmetric around axes.
- Asymmetric services (aFRR): Represented by quadrant ellipsoids (positive or negative power only).
Uncertainty Handling: Instead of worst-case robust optimization, the paper uses Joint Chance Constraints (JCC) to ensure a predefined probability (e.g., P90) that flexibility is available. This is achieved by constructing empirical uncertainty sets (ellipsoidal or hyperbox) that cover 90% of historical scenarios.
Cost-Effectiveness: A convex constraint is introduced to ensure that the revenue from providing flexibility exceeds the operational costs of the DERs. This is modeled via an affine disaggregation policy that maps GCP flexibility to individual DER injections.
Time-Coupling: The model explicitly accounts for energy storage dynamics (State of Energy for BESS, temperature for Heat Pumps) across the entire time horizon, preventing decoupled time-step solutions.

B. Scalability: Feeder-Decomposition Approach

To handle large networks, the authors propose a two-step decomposition:

Feeder Level: Compute the aggregated flexibility ellipsoid for each feeder independently, considering local network constraints and a robust slack voltage constraint (allowing decoupling while maintaining feasibility).
System Level: Aggregate the feeder ellipsoids at the primary substation, considering the transformer rating constraints. This transforms the problem into a Second-Order Cone (SOC) program, which is computationally tractable.

3. Key Contributions

Multi-Service Aggregation: The first approach to simultaneously aggregate multiple AS types (symmetric and asymmetric) using a unified ellipsoidal framework, handling their distinct time-coupling and activation constraints.
Probabilistic Uncertainty Integration: Moving beyond conservative robust sets, the method uses empirical uncertainty sets to satisfy P90 availability requirements, balancing risk and flexibility volume.
Explicit Cost-Effectiveness: The formulation enforces that the selected flexibility is economically feasible by integrating DER operational costs directly into the aggregation constraints, ensuring the solution is not just technically feasible but profitable.
Scalable Framework: The feeder-decomposition strategy enables the application of the method to realistic distribution systems with a large number of buses, overcoming the computational bottlenecks of monolithic OPF approaches.
Grid-Awareness: The method explicitly incorporates linearized power flow constraints (voltage and current limits) to ensure the aggregated flexibility does not violate distribution network safety limits.

4. Results and Case Studies

The method was validated using the IEEE 33-bus benchmark system and synthetic multi-feeder networks.

Uncertainty Set Comparison:
- Hyperbox sets were found to be the least conservative, offering the highest flexibility but with higher constraint violation rates (6.25% in tests).
- Probabilistic Ellipsoidal sets (90% coverage) offered a balanced approach, resulting in 0% constraint violations in out-of-sample testing, proving the effectiveness of the P90 requirement.
Baseload vs. Self-Dispatching:
- In the Baseload case (where the DSO optimizes expected energy costs), significantly more flexibility could be offered to the TSO.
- In the Self-Dispatching case (where the DSO must balance local uncertainty internally), available flexibility was reduced because DER capacity was reserved to handle local stochastic deviations.
Multi-DER Integration: The framework successfully integrated BESSs, Heat Pumps (HPs), and PVs. Results showed that HPs and PVs participated in specific services (e.g., PVs provided downward aFRR via curtailment; HPs provided baseload control and aFRR), optimizing the overall portfolio.
Grid Constraints Impact: Comparing "grid-aware" vs. "grid-unaware" aggregation revealed that ignoring network constraints leads to overestimation of flexibility. In the grid-unaware case, proposed flexibility would have caused line overloads (violations), whereas the grid-aware method correctly reduced the offerable capacity to remain within thermal limits.
Computational Performance: The feeder-decomposition approach reduced computation times from "intractable" (for the full network) to manageable levels (approx. 24–45 minutes per feeder), enabling parallel processing.

5. Significance

This paper provides a critical step forward in the coordination between Distribution System Operators (DSOs) and Transmission System Operators (TSOs).

Market Participation: It enables DERs to participate in AS markets with higher confidence, as the aggregated bids are guaranteed to be feasible under uncertainty and network constraints.
Economic Efficiency: By enforcing cost-effectiveness, the method ensures that flexibility is provided by the most economical resources, maximizing the value for the system operator.
Regulatory Alignment: The probabilistic approach aligns with recent Nordic AS market regulations (P90 availability), offering a practical pathway for implementing these standards.
Scalability: The decomposition method makes the approach viable for real-world, large-scale distribution grids, moving beyond theoretical small-scale benchmarks.

In conclusion, the proposed framework offers a robust, scalable, and economically sound method for quantifying and aggregating DER flexibility, facilitating the integration of renewable energy into future power systems while maintaining grid stability.