⚡ electrical engineering

Quantification and Regulation of Energy Reserves for Distributed Frequency and Voltage Control of Grid-Forming Inverters

This paper proposes a novel framework for quantifying and regulating battery energy reserves in grid-forming inverters using a modified Distributed-Averaging Proportional-Integral (DAPI) controller to bridge the gap between distributed secondary control and tertiary-level service reserves, thereby enhancing frequency, voltage, and power sharing in microgrids as validated by Controller Hardware-In-the-Loop simulations.

Original authors: Ahmed Saad Al-Karsani, Maryam Khanbaghi

Published 2026-04-17

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Ahmed Saad Al-Karsani, Maryam Khanbaghi

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 a power grid not as a giant, one-way highway where electricity flows from massive power plants to your house, but as a bustling neighborhood where everyone has their own little generator (like solar panels) and a battery in the garage. This is the world of Microgrids.

In this neighborhood, when the sun shines or the wind blows, these local generators feed power to the grid. But here's the problem: the weather is unpredictable. Sometimes the sun hides, and the neighborhood needs to pull power from the batteries. Sometimes everyone turns on their AC at once, and the batteries have to work overtime.

The Problem: The "Unfair" Battery

The paper tackles a specific annoyance in this neighborhood: Unfair wear and tear.

Imagine three neighbors (let's call them Inverter 1, 2, and 3) who all have identical batteries. They agree to share the work of keeping the neighborhood lights stable (frequency) and the voltage steady.

The Old Way: They use a simple rule: "If the lights flicker, we all push a little harder."
The Flaw: Because of how the wires are laid out in the neighborhood, Inverter 1 might end up doing 80% of the heavy lifting while Inverter 2 and 3 barely break a sweat.
The Result: Inverter 1's battery drains way faster than the others. It's like asking one person to carry all the groceries while the others walk empty-handed. Eventually, Inverter 1's battery dies, leaving the whole neighborhood vulnerable.

In the old days, when we had giant power plants, this didn't matter much because they had endless fuel (coal, gas). But with batteries, energy is limited. If one battery runs out, the system fails.

The Solution: The "Fairness Team"

The authors of this paper propose a new system to ensure everyone shares the burden equally. They call it an Energy Reserve Framework.

Think of it like a group chat where the neighbors don't just talk about "how much power we are making right now," but also "how much energy we have spent since we started."

Counting the Steps: Instead of just looking at the speed (frequency) or the pressure (voltage), the system tracks the "distance traveled" by each battery. It calculates exactly how much energy each inverter has used to fix problems.
The Fairness Algorithm: They introduce a new rule (a modified DAPI controller) that acts like a smart referee.
- If Inverter 1 has done too much work, the referee says, "Okay, you take a break; Inverter 2 and 3, you step up."
- If Inverter 2 has been lazy, the referee says, "You need to help out more."
The Goal: The goal isn't just to keep the lights on now; it's to make sure that by the end of the day, every battery has used roughly the same amount of energy. This keeps the whole neighborhood healthy for the long haul.

How They Tested It

The researchers didn't just write this on paper; they built a digital twin of a real neighborhood (based on a standard test model called the IEEE 13 bus system) and even connected real Arduino microcontrollers to it (a "Controller Hardware-In-the-Loop" test).

They ran three main scenarios:

The Standard Neighbors: Using traditional rules. Result: One battery drained faster.
The Fair Neighbors: Using their new "Fairness Team" rules. Result: Everyone shared the work equally, and the batteries lasted longer.
The Mixed Neighborhood: A mix of different types of batteries and generators. Result: The system still managed to keep things fair, even with the differences.

The Big Picture

Why does this matter?
As we move toward a future powered by solar, wind, and batteries, we can't rely on giant power plants anymore. We need these small, local grids to be smart and resilient.

This paper provides the rulebook for making sure that when a storm hits or the sun sets, the local batteries don't burn out because one of them did all the work. It ensures that the "energy reserves" (the backup power) are managed fairly, keeping the lights on for everyone, for longer.

In short: It's about making sure that in the race to keep the lights on, no single battery gets left behind or worn out before its time.

1. Problem Statement

The increasing integration of Renewable Energy Sources (RES) and Distributed Energy Resources (DERs) has shifted power grids from centralized structures to distributed Microgrids (MGs) and Networks of MGs (NMGs). While Grid-Forming (GFM) inverters (using Droop or Virtual Synchronous Machine - VSM control) are essential for stability in these systems, existing distributed secondary control strategies (like Distributed-Averaging Proportional-Integral or DAPI) face a critical limitation:

Inadvertent Energy Exchange: Although DAPI control successfully achieves frequency/voltage regulation and active power sharing, it often results in unequal energy discharge/charge among Battery Energy Storage Systems (BESS). This occurs because load changes and network topology variations cause inverters to deviate from their power setpoints for varying durations.
Lack of Tertiary Linkage: Current distributed control schemes focus on primary and secondary levels but lack a clear link to tertiary-level energy management. They do not explicitly quantify "energy reserves" (headroom) required for long-term resource adequacy.
Consequence: Unequal energy usage leads to State of Charge (SoC) imbalances and reduces the available headroom for future regulation, potentially requiring costly tertiary-level interventions to restore reserves.

2. Methodology

The authors propose a framework to quantify and regulate energy reserves within a hierarchical control structure, integrating them into the secondary control layer.

A. Energy Reserve Formulation

The paper redefines energy reserves based on the deviation from power setpoints ( $P^*, Q^*$ ) rather than just static capacity.

Active Energy Reserve ( $E_i$ ): Defined as the total unused capacity minus the accumulated energy imbalance ( $\Delta E_i$ ) caused by the integral of power deviations over time:
$E_i(t) = \bar{E}_{c,i} - \int_0^t \Delta P_i(\tau) d\tau$
Reactive Energy Reserve ( $F_i$ ): Since reactive power does not directly deplete BESS SoC, it is linked to the available reactive power headroom (based on inverter apparent power limits $S_{max}$ ) rather than battery chemistry.

B. Modified DAPI Control with Energy Consensus

The authors modify the standard DAPI controller to include energy reserve consensus terms.

Frequency Control: The frequency consensus dynamics ( $\Omega_i$ ) are updated to include a term that drives the active energy imbalances ( $\Delta E_i$ ) toward consensus:
$k_i \dot{\Omega}_i = -\Delta \omega_i - \sum a_{ij}(\Omega_i - \Omega_j) - \sum e_{ij}(m_i \Delta E_i - m_j \Delta E_j)$
Voltage Control: Similarly, the voltage consensus dynamics ( $e_i$ ) are updated to balance reactive energy reserves ( $\Delta F_i$ ), introducing a trade-off between voltage regulation, reactive power sharing, and reactive energy sharing.
Goal: By driving the energy imbalance terms to zero across the network, the system ensures equitable energy expenditure (discharge/charge) among inverters.

C. Stability Analysis

The authors perform a small-signal stability analysis using modal analysis and the Routh-Hurwitz criterion.

They decompose the system into "agreement" (power sharing) and "disagreement" (deviation) subspaces.
They prove that the proposed composite system (combining droop/VSM dynamics with the new energy consensus terms) remains stable in the disagreement space, provided specific bounds on integral gains and droop parameters are met.

3. Key Contributions

Quantification Framework: Proposes a real-time metric for quantifying active and reactive energy reserves based on inadvertent energy exchange, bridging the gap between secondary control and tertiary-level resource adequacy.
Modified DAPI Controller: Introduces a novel consensus-based control scheme that regulates energy reserves alongside frequency and voltage, ensuring equitable energy sharing among heterogeneous inverters (Droop and VSM).
Stability Guarantees: Provides a rigorous mathematical proof of stability for the proposed energy-consensus scheme under simplified assumptions (lossless lines, homogeneous parameters).
Hardware Validation: Validates the control strategy using Controller Hardware-In-the-Loop (CHIL) simulations with Arduino microcontrollers and an OPAL-RT test bench, demonstrating real-time feasibility.

4. Simulation Results

The proposed scheme was tested on an islanded Microgrid based on the IEEE 13-bus test feeder with three BESS-based inverters under three scenarios:

Scenario 1 (Droop Control, Active Energy): In a load pickup scenario, the proposed scheme successfully achieved consensus on active energy reserves while maintaining frequency regulation and power sharing, unlike the base DAPI which showed divergent energy discharge.
Scenario 2 (VSM Control, Reactive Energy): For reactive power, the scheme achieved consensus on reactive energy reserves. The authors note a trade-off: achieving perfect reactive energy consensus slightly compromises voltage regulation and reactive power sharing, but the result is deemed acceptable for distribution-level applications.
Scenario 3 (Heterogeneous Inverters): The scheme was tested with a mix of Droop and VSM inverters with different capacities (1:2:2 ratio). The results confirmed that the system could achieve active and reactive power sharing and energy reserve consensus even with heterogeneous dynamics and capacities.
Observations: The introduction of the integral energy consensus term can induce slight "hunting" oscillations during transients, requiring careful tuning of the consensus gains ( $e_{ij}, f_{ij}$ ).

5. Significance

This paper addresses a critical gap in the control of future distributed power grids. By explicitly quantifying and regulating energy reserves at the secondary level, the proposed method:

Prevents Premature Depletion: Ensures that BESS units do not unevenly deplete their reserves, thereby extending the operational life of the storage assets.
Enables Tertiary Planning: Provides a clear metric for "headroom" that tertiary-level controllers can use for long-term energy management and market services (e.g., ancillary services).
Supports High RES Penetration: Offers a robust control strategy for Microgrids and NMGs where traditional centralized AGC is insufficient due to the fast-varying nature of inverter-based resources.
Hardware Feasibility: The CHIL validation proves that these complex consensus algorithms can run on low-cost hardware (Arduino) in real-time, making the solution scalable for practical deployment.