Thesis
Optimal black-start restoration of low-inertia networks enabled by innovative estimation and control methods for grid-forming converters
- Creator
- Rights statement
- Awarding institution
- University of Strathclyde
- Date of award
- 2026
- Thesis identifier
- T18087
- Person Identifier (Local)
- 202250583
- Qualification Level
- Qualification Name
- Department, School or Faculty
- Abstract
- The progressive displacement of synchronous generation by converter-interfaced resources is fundamentally transforming the dynamic behaviour of modern power systems. As conventional synchronous generators are decommissioned, the rotational inertia, electromechanical damping, fault current contribution, and inherent synchronising capability that have historically underpinned grid stability are systematically diminished. Grid-forming converters have emerged as the foremost enabling technology for sustaining stable operation under these conditions. However, a critical gap persists in understanding how converter-level estimation and control capabilities can be formally embedded within system-level operational decision-making. This challenge is particularly pronounced during black-start restoration following a complete or partial blackout. This thesis addresses this gap by developing novel estimation and control methods for grid-forming converters and demonstrating their integration within an optimal black-start restoration framework for converter-dominated low inertia distribution networks. In the estimation domain, this thesis addresses the two most critical parameters governing the dynamic security of low-inertia power systems, namely inertia and frequency. For inertia estimation, the first method introduces a wavelet transform-based approach operating in the time-frequency domain. A closed-form relationship between wavelet coefficient magnitudes and the physical inertia constant is established and validated through hardware-in-the-loop experiments under realistic noisy measurement conditions. The second method introduces an integral-based reformulation of the swing equation that simultaneously captures aggregate and spatially distributed inertia. This formulation accurately identifies inertially weak zones across the network. For frequency estimation, two novel methods are proposed. The first exploits the oscillatory behaviour of the ParkâClarke transformation under frequency deviation conditions. A cross-product formulation of normalised voltage components is developed that enables near-instantaneous frequency extraction. The second method extends this principle through fractional-order derivative calculus. The amplitude of the fractional derivative encodes the frequency deviation in a manner that permits direct algebraic recovery of the system frequency. Experimental validation demonstrates superior dynamic response and improved estimation accuracy compared with leading phase-locked loop (PLL) methods. In the control domain, this thesis addresses two fundamental challenges facing grid-forming converters in low-inertia networks, namely transient damping performance and voltage quality under unbalanced conditions. The first contribution introduces a fractional-order derivative-based feedforward damping loop that augments the conventional droop controller. The auxiliary loop provides continuously tuneable transient damping while remaining inherently inactive at steady state. Significant reductions in active power overshoot and settling time are achieved under step load conditions. The second contribution addresses voltage unbalance through a novel Expectation-Maximisation algorithm integrated with a Kalman filter. A new time-varying measurement matrix is derived that represents the second order harmonic coupling between sequence components. An integrated controller simultaneously suppresses negative-sequence and zero-sequence voltages within the positive-sequence grid-forming architecture. The unbalance suppression framework is complemented by a data-driven Prony-based stability assessment method that evaluates system stability directly from time-domain measurements. Experimental validation on a laboratory-scale converter confirms that the proposed controller effectively reduces the voltage unbalance factor to within the limits mandated by the GB Grid Code. To bridge the gap between converter-level intelligence and system-level operational decision-making, a mixed-integer linear programming formulation is developed for optimal black-start restoration in converter-dominated distribution networks. The objective function minimises the total customer damage cost, which inherently drives the restoration towards the shortest feasible makespan. The optimisation is applied to a standard distribution test system with multiple grid-forming and grid-following converters. Estimation and control outputs from all preceding contributions are embedded within the optimisation through confidence factors that parameterise the usable value of each physical quantity as perceived by the restoration optimiser. Inertia estimation scales the available system kinetic energy at each restoration step and enforces a RoCoF ceiling that limits the permissible load pickup. Frequency estimation accuracy narrows the guard margin on frequency constraints and unlocks additional feasible load pickup capacity. Effective damping relaxes the frequency nadir constraint and permits larger load increments within the same frequency headroom. Unbalance suppression efficiency prevents derating of available sources and makes more power available for load pickup. The formulation demonstrates that the proposed estimation and control enhancements yield measurable improvements in restoration speed, transient security, and economic efficiency compared with conventional methods. Collectively, these results confirm that grid-forming converters equipped with the proposed estimation and control methods can serve as the primary enablers of black-start restoration
- Advisor / supervisor
- Ahmed, Khaled
- Resource Type
- DOI
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PDF of thesis T18087 | 2026-09-22 | Public | Download |