Emulated Synchronous Condenser (ESC)

Updated 18 February 2026

ESC is a grid-forming power-electronic system that emulates the dynamic and steady-state properties of a synchronous condenser using software-based models of inertia, damping, and voltage regulation.
Its advanced control architecture integrates a swing-equation emulator, virtual impedance synthesis, and high-bandwidth current controllers to achieve robust frequency stability, voltage regulation, and grid-code compliance.
ESC implementations have demonstrated effective fault ride-through, rapid grid support, and seamless operation under extreme transients in inverter-dominated power systems.

An Emulated Synchronous Condenser (ESC) is a grid-forming, power-electronic system whose control structure is specifically designed to reproduce—in the electrical network context—the dynamic and steady-state properties of a rotating synchronous condenser (SC) but without any physical rotating mass. Implemented via an advanced voltage source converter (VSC) coupled to an energy buffer (e.g., battery, supercapacitor), the ESC embeds software-based models of inertia, electromechanical damping, voltage regulation, and fault-current limitation, enabling it to support system inertia, frequency stability, voltage regulation, and grid-code compliance under extreme transient and fault conditions. The ESC concept is central to the integration of high penetrations of inverter-based resources in modern power grids, where traditional sources of inertia and voltage support are being displaced.

1. Core Principles and Dynamic Model

The ESC architecture merges two control branches: (1) a swing-equation-based emulation of synchronous condenser dynamics and (2) a controlled current-source branch ensuring rapid enforcement of active power setpoints. The swing equation provides explicit virtual inertia ( $H$ ) and damping ( $K_D$ ) dynamics in software, yielding angle and frequency dynamics:

$\frac{d\omega_s}{dt} = \frac{1}{2H}\left( -P_{ESC} - K_D\omega_s(1-\mathrm{LPF}(s))\right)$

where $P_{ESC}$ is the virtual machine power and the high-pass washout filter $\mathrm{LPF}(s)$ ensures proper frequency response. The virtual impedance module models both positive and negative sequence behaviors, and an elliptical current limiter protects semiconductor hardware by restricting the magnitude of the synthesized grid current vector in the $d_p,q_p,d_n,q_n$ space. This structure results in a continuous, non-mode-switching control that imposes swing-emulator constraints even during severe grid events such as black start, main grid disconnection, extreme phase-angle jumps, and fault ride-through (FRT) scenarios (Freytes et al., 2023).

ESCs thus fundamentally couple the following emulation components:

Virtual inertia and damping: Software-tuned counterparts to rotational inertia and damper windings in an SC, realized in the outer-loop grid-forming controller (Lepour et al., 2021, Vu et al., 2015, Tzounas et al., 2023).
Automatic voltage regulation (AVR): Q-droop-based or explicit PI-based AVR in analogy to the field-excitation control of synchronous machines.
Fault-current limitation: Threshold virtual impedance or explicit current-limiting blocks ensure current does not exceed semiconductor capabilities, replacing subtransient reactance limitations of real machines.

2. Control Architecture and Implementation

A prototypical ESC controller includes:

Swing Equation Emulator: Implements the core inertia and damping behaviors.
Virtual Impedance Synthesis: Models grid interconnection reactances and provides both positive- and negative-sequence handling for FRT.
Active and Reactive Power Controllers: Instantaneously tracks power setpoints via current-source control, including frequency and voltage droop laws.
Current Limiting: Elliptical (multi-phase) or threshold-based logic that enforces hardware constraints during extreme events.
Inner-Loop Current Controllers: High-bandwidth PI plus resonant controllers achieve sub-millisecond tracking, thereby ensuring decoupling between swing and current loops (Freytes et al., 2023, Lepour et al., 2021).

Holistic designs often utilize explicit representation of the swing equation, possibly augmented by virtual oscillators and passivity-based control (PBC) schemes for global asymptotic stability and plug-and-play capability in multi-inverter grids (Jouini, 2022, Arghir et al., 2017).

3. Performance Characteristics and Grid-Code Compliance

ESCs have been found to:

Replicate inertia response: Providing inertial power injection $\Delta P = -2H\Delta \omega$ and maintaining rate-of-change-of-frequency (RoCoF) on par with SCs, provided energy buffers are adequately sized (Lepour et al., 2021, Tzounas et al., 2023).
Achieve robust frequency and voltage control: Unified controllers pass all grid-code requirements (e.g., frequency-droop, voltage-droop, black start, main-grid disconnection) with a single, mode-independent architecture. High bandwidths on inner loops ( $\sim$ 1–2 kHz) ensure tight current and voltage regulation (Freytes et al., 2023).
Handle severe transients: Time-domain studies on a 2 MW BESS demonstrate seamless transition through large power steps, black start within 250 ms, islanding, phase jumps, and unbalanced or multi-phase faults without loss of synchronism or the need for fault logic switching (Freytes et al., 2023).
Current-limited fault ride-through: While classical synchronous machines deliver subtransient currents $>$ 4 pu, ESCs are constrained by overcurrent settings (typically $1.1$–$1.5$ pu) but maintain grid support and rapid post-fault resynchronization (Jiang et al., 2023, Tzounas et al., 2023).

4. Comparison to Physical Synchronous Condensers

ESCs emulate (but do not physically duplicate) key properties of rotating SCs:

Property	Synchronous Condenser (SC)	Emulated Synchronous Condenser (ESC)
Inertia	Rotor mass, kinetic energy $E = H S_n$	Software-tuned via energy buffer, $E = H_{virt} S_{esc}$
Voltage regulation	Field-excitation AVR	Q-droop, PI AVRs (software)
Fault current	$4$–$6$ pu via subtransient reactance $X''$	$1$–$1.5$ pu via current limits/TVI
Damping	Mechanical, damper windings	Virtual damper, software-tunable $K_D$
Settling after fault	100–200 ms	50–200 ms depending on control bandwidth
Headroom/tuning	Fixed by machine design	Fully software-configurable
Hardware risk	No semiconductors; inertia prevents trip	Risk of overcurrent—must limit with protection logic

While SCs retain an edge in sub-cycle voltage stiffness, ESCs offer faster programmable tunability, resynchronization, and scalability (Lepour et al., 2021, Jiang et al., 2023).

5. Controller Design, Tuning, and Practical Considerations

Practical ESC design requires:

Energy buffer sizing: For virtual inertia $H=2$ –$10$ s and power rating $S_{esc}$ (MW), $E_{esc} \geq H S_{esc}$ must be satisfied. Batteries are typically oversized 10–20% to ensure multi-second ride-through capacity (Jiang et al., 2023, Tzounas et al., 2023).
Bandwidth allocation:
- Inner current loops: $1$–$2$ kHz
- Swing (inertia) loop: $5$–$10$ Hz
- Droop (primary) loops: $0.2$–$1$ Hz
- Excessively high inertia-loop bandwidths reduce the inertia-to-damping energy ratio, impairing SM emulation (Tzounas et al., 2023).
Parameter examples: Inertia $H=2$ s, Damping $K_D=100$ s $^{-1}$ , LPF $\tau=1$ ms, $k_{droop}=1/0.05$ , $L_v=0.2$ pu, $R_v=0.05$ pu, $k_q=0.1$ pu, current limiter $I_{lim}=1.1$ pu (Freytes et al., 2023).
Grid-forming support: ESCs inherently maintain synchronization, voltage, and frequency under all tested grid events without logic mode switching (Freytes et al., 2023).

6. Software-Defined and Hybrid Virtual Approaches

Recent advancements extend ESC realizations into software-defined and distributed control for multi-inverter systems and wind farms. The Software-Defined Virtual Synchronous Condenser (SDViSC) approaches virtualize the ESC control stack, deploying discretized swing, AVR, and current loops via event-driven software networks (SDN/OpenFlow) with Tustin-discretized controllers to reduce communication bandwidth without compromising dynamic performance (Jiang et al., 2023).

Validation on 500 MW wind farm digital twins shows that SDViSCs maintain voltage recovery, frequency nadir, and FRT nearly matching a 40 MVAR hardware SC, with deterministic event-driven failover and plug-and-play multi-unit scaling. Current hardware remains the limiting factor for FRT currents and weak-grid support, requiring parallelization or converter overrating (Jiang et al., 2023).

7. Stability, Passivity, and Multibus Operation

ESC controllers are commonly designed to guarantee strict incremental passivity and global asymptotic stability over a wide operating range. Analysis in rotating dq frames shows that Lyapunov functions incorporating energy in the DC buffer, AC filter, and modulation vector ensure robust voltage and frequency regulation even under large disturbances. Plug-and-play connectability is enabled by this passivity property, simplifying network expansions without destabilizing the system (Arghir et al., 2017, Jouini, 2022).

Multi-converter ESC networks achieve proportional power sharing and droop-based frequency and voltage regulation, provided controller parameters are coordinated. Numerical simulations confirm stability and sharing under dynamic islanding, black-start, and severe load/line switching events.

In summary, the Emulated Synchronous Condenser paradigm, grounded in grid-forming VSC control with explicit swing-equation and passivity-based inner structure, enables power-electronics-based resources to provide system-strength, inertia, and voltage/reactive-power support analogous to conventional SCs—meeting the evolving requirements of low-inertia, inverter-dominated power systems (Freytes et al., 2023, Lepour et al., 2021, Vu et al., 2015, Tzounas et al., 2023, Arghir et al., 2017, Jiang et al., 2023, Jouini, 2022).