Droop-I Control

• Droop-I control is a decentralized primary-control method in power-electronic systems that uses local feedback from current, voltage, or frequency to regulate shared bus variables.
• It encompasses variations like current-based VI droop, I–V droop, and dynamic controllers such as iDroop to balance steady-state power sharing with transient performance.
• Researchers emphasize passivity-based stability assessments, including low-pass filtering and distributed PI control, to ensure robust performance under varying load conditions.

Searching arXiv for recent and foundational papers on “Droop-I control,” including DC microgrid droop, iDroop, and droop-based inertia control. “Droop-I control” denotes a family of decentralized primary-control mechanisms in power-electronic energy systems, but the term is not used uniformly across the literature. In DC microgrids it commonly refers to current-based droop, most often the classical voltage–current law $v_{\mathrm{ref}} = V_0 - d\,i_o$ applied to converter-interfaced sources, while related DC work also uses the label for current–voltage droop that generates a current reference from DC-bus voltage deviation (Anees et al., 2024, Krajacic et al., 29 Apr 2026). In low-inertia AC power systems, closely related usage includes only-droop-based equivalent inertia control for fast frequency regulation resources and the dynamic droop controller iDroop, both of which preserve droop-like steady-state sharing while reshaping transient behavior (Liu et al., 2022, Mallada, 2016). Across these settings, the unifying principle is local feedback from electrical variables—current, power, voltage, or frequency—to regulate shared bus variables without fast communication. The main distinctions lie in which variable is drooped, whether the droop law is static or dynamic, and whether stability is analyzed through passivity, small-signal network models, or frequency-domain performance metrics.

1. Terminological scope and principal meanings

The literature represented here attaches “Droop-I control” to several nearby but non-identical constructions. In one DC-microgrid convention, it denotes the canonical current-based VI droop; in another, it denotes DC I–V droop; in AC frequency-control work, the same label is associated with only-droop inertia emulation or with iDroop, a dynamic droop controller (Anees et al., 2024, Liu et al., 2022, Krajacic et al., 29 Apr 2026, Mallada, 2016).

Context	Representative law	Meaning of “Droop-I”
DC microgrids, boost converters	$v_{\mathrm{ref}} = V_0 - d\, i_o$	Current-based VI droop
DC source converters, duality view	$$\hat i_f^{\mathrm{dc}} = i_{f,\mathrm{set}}^{\mathrm{dc}} + K_d^{\mathrm{dc}}(v_{o,\mathrm{set}}^{\mathrm{dc}} - v_o^{\mathrm{dc}})$$	I–V droop
Fast frequency regulation resources	$\Delta P_r = -k^r \omega$	Only-droop inertia control
Low-inertia AC systems	$q_i = q_i^{r,0} + x_i$, with dynamic $x_i$	iDroop / dynamic droop

This variation reflects genuine subfield differences rather than mere notation. One paper explicitly states that “Droop-I” refers to current-based droops and most commonly to the VI law $v_{\mathrm{ref}}=V_0-d\,i_o$ in DC microgrids (Anees et al., 2024). Another uses “Droop-I control” for DC I–V droop, where voltage deviation produces a current reference (Krajacic et al., 29 Apr 2026). This suggests that the label often emphasizes the current-mediated character of the primary loop rather than a universally fixed input–output pairing.

2. Current-based Droop-I in DC microgrids

For boost-converter DC microgrids, the most explicit “Droop-I” definition is the current-based primary droop family. The four implementations compared in “Passivity based Stability Assessment for Four types of Droops for DC Microgrids” are VI, VP, IV, and PV droop, grouped by feedback variable into current-based droops (VI and IV, coefficient $d$) and power-based droops (VP and PV, coefficient $k$) (Anees et al., 2024). Within that taxonomy, the canonical Droop-I law is the VI relation

$v = v_o - d\, i,$

or, equivalently in the paper’s notation,

$v_{\mathrm{ref}} = V_0 - d\, i_o$0

In this form, each source reduces its voltage reference linearly with measured output current. The intended effect is decentralized power sharing on a common DC bus: if one converter increases its current, its effective voltage reference drops, which discourages monopolization of the load and invites the other sources to participate. The implementation is hierarchical. The paper describes an inner current loop with bandwidth about $v_{\mathrm{ref}} = V_0 - d\, i_o$1, an outer voltage loop with bandwidth about $v_{\mathrm{ref}} = V_0 - d\, i_o$2, and a slower droop loop whose bandwidth is an order of magnitude below the outer loop (Anees et al., 2024).

The same work contrasts VI Droop-I with the current-reference form IV droop,

$v_{\mathrm{ref}} = V_0 - d\, i_o$3

and with the power-based alternatives

$v_{\mathrm{ref}} = V_0 - d\, i_o$4

These comparisons are important because the advantages of Droop-I are conditional. For the studied setup, VI and VP show better stability and smaller oscillations than IV and PV at higher constant-power-load levels, whereas IV and PV are more suitable on longer or more inductive lines (Anees et al., 2024).

A second DC interpretation appears in the converter-duality literature, where Droop-I denotes I–V droop: $v_{\mathrm{ref}} = V_0 - d\, i_o$5 Here the droop controller does not directly regulate the voltage with a PI loop; instead, it uses measured DC-bus voltage to adjust the converter current reference. The resulting dynamics are governed by

$v_{\mathrm{ref}} = V_0 - d\, i_o$6

which the paper interprets as a DC analog of the AC swing equation (Krajacic et al., 29 Apr 2026).

3. Passivity-based design and stability assessment in DC systems

The most detailed stability treatment for DC Droop-I in the supplied literature is passivity-based. For each droop type, the converter plus its controller is represented by a small-signal output impedance $v_{\mathrm{ref}} = V_0 - d\, i_o$7, and converter passivity is imposed through

$v_{\mathrm{ref}} = V_0 - d\, i_o$8

At system level, the aggregate bus impedance is formed as the parallel interconnection of the source and load impedances, and the paper uses the condition

$v_{\mathrm{ref}} = V_0 - d\, i_o$9

as a passivity-based stability test (Anees et al., 2024).

A low-pass filter in the droop feedback path is central to this construction. For VI Droop-I, the filtered-current implementation is

$$\hat i_f^{\mathrm{dc}} = i_{f,\mathrm{set}}^{\mathrm{dc}} + K_d^{\mathrm{dc}}(v_{o,\mathrm{set}}^{\mathrm{dc}} - v_o^{\mathrm{dc}})$$0

so that

$$\hat i_f^{\mathrm{dc}} = i_{f,\mathrm{set}}^{\mathrm{dc}} + K_d^{\mathrm{dc}}(v_{o,\mathrm{set}}^{\mathrm{dc}} - v_o^{\mathrm{dc}})$$1

The filter slows the droop action and attenuates high-frequency interaction between the converter loops and the constant-power load. The paper reports that without an LPF, or with too high a cutoff such as $$\hat i_f^{\mathrm{dc}} = i_{f,\mathrm{set}}^{\mathrm{dc}} + K_d^{\mathrm{dc}}(v_{o,\mathrm{set}}^{\mathrm{dc}} - v_o^{\mathrm{dc}})$$2 and above, the converter impedance shows non-passive regions near the current-loop bandwidth around $$\hat i_f^{\mathrm{dc}} = i_{f,\mathrm{set}}^{\mathrm{dc}} + K_d^{\mathrm{dc}}(v_{o,\mathrm{set}}^{\mathrm{dc}} - v_o^{\mathrm{dc}})$$3; suitable cutoffs such as $$\hat i_f^{\mathrm{dc}} = i_{f,\mathrm{set}}^{\mathrm{dc}} + K_d^{\mathrm{dc}}(v_{o,\mathrm{set}}^{\mathrm{dc}} - v_o^{\mathrm{dc}})$$4 or $$\hat i_f^{\mathrm{dc}} = i_{f,\mathrm{set}}^{\mathrm{dc}} + K_d^{\mathrm{dc}}(v_{o,\mathrm{set}}^{\mathrm{dc}} - v_o^{\mathrm{dc}})$$5, depending on operating point and line conditions, restore passivity (Anees et al., 2024).

The constant-power-load mechanism is modeled through a negative incremental resistance approximation,

$$\hat i_f^{\mathrm{dc}} = i_{f,\mathrm{set}}^{\mathrm{dc}} + K_d^{\mathrm{dc}}(v_{o,\mathrm{set}}^{\mathrm{dc}} - v_o^{\mathrm{dc}})$$6

so the bus must remain sufficiently resistive or passive to avoid oscillatory interaction. Time-domain simulations in the case study show the limits of this strategy. At rated power, a $$\hat i_f^{\mathrm{dc}} = i_{f,\mathrm{set}}^{\mathrm{dc}} + K_d^{\mathrm{dc}}(v_{o,\mathrm{set}}^{\mathrm{dc}} - v_o^{\mathrm{dc}})$$7 LPF makes all four droops fully passive. At $$\hat i_f^{\mathrm{dc}} = i_{f,\mathrm{set}}^{\mathrm{dc}} + K_d^{\mathrm{dc}}(v_{o,\mathrm{set}}^{\mathrm{dc}} - v_o^{\mathrm{dc}})$$8, IV and PV exhibit minor oscillations while VI and VP do not. At $$\hat i_f^{\mathrm{dc}} = i_{f,\mathrm{set}}^{\mathrm{dc}} + K_d^{\mathrm{dc}}(v_{o,\mathrm{set}}^{\mathrm{dc}} - v_o^{\mathrm{dc}})$$9, the $\Delta P_r = -k^r \omega$0 LPF largely removes non-passive regions and VI stabilizes the bus, albeit with noticeable voltage droop and moderate oscillations. At $\Delta P_r = -k^r \omega$1, all four droops become unstable even with the $\Delta P_r = -k^r \omega$2 LPF, indicating a load-power limit beyond which the constant-power load overwhelms the passive margins (Anees et al., 2024).

The same paper imports the EN 50388-2 philosophy from railway systems: converter manufacturers should ensure converter impedance is strictly passive above a threshold frequency, while infrastructure operators should avoid weakly damped passive resonances below that threshold. In the DC-microgrid adaptation, converter passivity and bus-impedance passivity together guide the selection of droop gain $\Delta P_r = -k^r \omega$3 and LPF cutoff $\Delta P_r = -k^r \omega$4 (Anees et al., 2024).

4. Droop-I as droop-based inertia and dynamic frequency control

In low-inertia AC systems, “Droop-I” is also used for only-droop-based inertial support. The relevant model starts from the aggregate swing equation

$\Delta P_r = -k^r \omega$5

and defines fast frequency regulation resources with droop response

$\Delta P_r = -k^r \omega$6

Equating this with a hypothetical scenario of increased physical inertia yields an equivalent inertia coefficient

$\Delta P_r = -k^r \omega$7

For constant droop $\Delta P_r = -k^r \omega$8, the resulting equivalent inertia is time-varying: $\Delta P_r = -k^r \omega$9 The paper therefore proposes the time-variant-droop-based equivalent inertia control (VDIC) law

$q_i = q_i^{r,0} + x_i$0

with practical upper and lower bounds, so that only-droop control provides a prescribed constant equivalent inertia without introducing generator-like control dynamics (Liu et al., 2022).

A distinct but related dynamic-droop line is iDroop. In one formulation, inverter power is

$q_i = q_i^{r,0} + x_i$1

At steady state, $q_i = q_i^{r,0} + x_i$2, so iDroop preserves the same droop-based power sharing as classical droop while introducing extra degrees of freedom $q_i = q_i^{r,0} + x_i$3 and $q_i = q_i^{r,0} + x_i$4 for transient shaping (Mallada, 2016). A frequency-domain realization used in later work is

$q_i = q_i^{r,0} + x_i$5

which keeps the DC gain equal to $q_i = q_i^{r,0} + x_i$6 but changes the high-frequency behavior, thereby decoupling steady-state control effort share from dynamic performance (Jiang et al., 2019).

This dynamic-droop idea is developed further in two directions. First, iDroop can be tuned to achieve high noise rejection, fast system-wide synchronization, or Nadir elimination without affecting the steady-state control effort share (Jiang et al., 2019). Second, a distinct “dynamic droop approach” for storage-based frequency control chooses

$q_i = q_i^{r,0} + x_i$7

and under the tuning

$q_i = q_i^{r,0} + x_i$8

obtains

$q_i = q_i^{r,0} + x_i$9

which cancels turbine dynamics and renders the disturbance-to-frequency map effectively first order, thereby eliminating the frequency Nadir in the studied aggregate model (Jiang et al., 2019).

5. Stability, filtering, and secondary augmentation in AC inverter networks

The AC droop literature in the supplied corpus emphasizes that measurement filtering, network losses, and topology fundamentally shape the stability of droop-controlled inverter networks. One small-signal model writes filtered real-power droop as

$x_i$0

so the low-pass filter time constant $x_i$1 acts mathematically as an inertial term. For lossless networks, stability is governed by the positive semidefiniteness of an active-power-flow Laplacian and is independent of filter lag, though larger lag worsens damping and settling time. For lossy mesh networks, by contrast, sufficiently large filter time constants can destabilize the system if the Laplacian has complex eigenvalues with positive real parts; radial lossy networks are more forgiving when the operating point has no critical lines (Maruf et al., 2019).

Another secondary-control interpretation of “Droop-I” appears in distributed PI frequency regulation. There, standard droop dynamics

$x_i$2

are augmented by a distributed integral state $x_i$3: $x_i$4

$x_i$5

This distributed averaging proportional-integral controller restores frequency to nominal and, in the paper’s $x_i$6-based performance analysis, can also reduce transient resistive power losses relative to standard droop. The improvement is larger in loosely interconnected networks than in highly interconnected ones (Tegling et al., 2016).

Taken together, these results show that “dynamic” or “integral” Droop-I variants are not merely add-ons to a static droop curve. They alter modal damping, sensitivity to measurement noise, and the relationship between local control action and network-wide synchronization. The practical consequence is that droop-gain selection cannot be separated from filtering, topology, and secondary-control architecture.

6. Duality, generalized droop, and advanced formulations

A notable contemporary perspective is converter-control duality between AC grid-forming and DC droop control. The duality paper shows that AC power–frequency droop with virtual inertia and DC I–V droop have isomorphic outer-loop dynamics under the mapping

$x_i$7

In this interpretation, DC bus capacitance plays the role of inertia, DC voltage plays the role of frequency, and current disturbance plays the role of active-power disturbance (Krajacic et al., 29 Apr 2026). This provides a unifying lens for the otherwise disparate AC and DC uses of Droop-I.

Beyond classical linear droop, HVDC work embeds droop laws into a generalized ZIP structure. The primary-control term

$x_i$8

induces a DC-side power injection

$x_i$9

so conventional voltage droop appears as a specific choice of $v_{\mathrm{ref}}=V_0-d\,i_o$0. The paper derives LMI-based non-existence conditions for equilibria, additional LMI conditions for equilibria satisfying power-sharing constraints, and Jacobian-based local stability tests (Zonetti et al., 2016).

At a more abstract level, complex droop control identifies dVOC as a droop law on complex frequency. In complex-angle coordinates,

$v_{\mathrm{ref}}=V_0-d\,i_o$1

which augments standard $v_{\mathrm{ref}}=V_0-d\,i_o$2-$v_{\mathrm{ref}}=V_0-d\,i_o$3 droop and admits almost-global asymptotic stability results for non-nominal synchronous steady states under explicit parametric conditions (He et al., 2022).

The cumulative picture is therefore not of a single control law, but of a control family. In its narrowest and most standard DC meaning, Droop-I is current-based primary droop, particularly the VI law $v_{\mathrm{ref}}=V_0-d\,i_o$4 with passivity-oriented LPF shaping under constant-power loads (Anees et al., 2024). In AC low-inertia studies, closely related meanings emphasize only-droop inertia provision and dynamic droop controllers such as iDroop that preserve droop-optimal steady-state sharing while improving transient behavior and noise robustness (Liu et al., 2022, Mallada, 2016, Jiang et al., 2019). The coexistence of these meanings is now a stable feature of the literature rather than an anomaly.