Traditionally black-start service has been provided mainly by coal- or gas-fired generators and pumped-hydro storage due to their capability to meet all the technical requirements . However, due to the societal decarbonization aims, rising fuel costs coupled with ageing assets, and decreasing load factors, large conventional generation plants are being phased out in favour of renewables and non-traditional technologies, which increases the cost of warming up large generators, and consequently of black-start services . Since maintaining the status quo for black start and restoration is not an option, considerable changes are required to facilitate the participation of alternate sources like renewable energy and non-traditional technologies in the black-start market given the modern evolving energy landscape. and , for example, have recently confirmed that there is a potential to open up the delivery of black-start service to interconnectors, sites with trip-to-house load operation, and aggregated units including variable generation (like wind, solar), especially with support from energy storage systems.

Black start and islanding operation requirements have been included as options for WPPs in the ENTSO-E network codes, where the relevant system operator is allowed to request these functions to support grid recovery . Driven by grid codes, state-of-the-art wind turbines (WTs) are already capable of providing some services that are a part of the restoration process – e.g. fast frequency response and low-voltage ride-through (LVRT) – and are expected to deliver more advanced requirements like inertia emulation, power oscillation damping, and reactive current injection, which are increasingly being demanded by grid codes . This is possible due to the advanced functionalities of the full-scale PEC interface of modern WTs, as mentioned in . show that WTs owing to their fast start-up times can be included earlier in the restoration process to provide reactive-power support and pickup load, thus decreasing the impact of a blackout event by reducing the restoration time and unserved load. However, connection of the currently prevalent grid-following (GFL) WTs in the beginning of the restoration procedure can cause a recurrence of blackout as the grid is generally not stable enough . The early participation of WPPs in successful bottom-up network energization can be facilitated instead by grid-forming (GFM) control of WTs, allowing them to operate together as an AC voltage source without relying on an external grid, and supply load in a power island.

GFM control of converters to integrate renewables at the distribution level has been extensively researched for microgrids. However, only recently has it begun being applied to high-power applications. To the authors' knowledge, there are not enough in-depth studies addressing black-start energization by high-power GFM renewable sources connected at the transmission level. Even at the distribution level, it is only recently – due to risks of uncontrolled islanding – that research has been conducted on microgrid islanding capabilities provided by GFM converters, for defence against blackouts in future power systems . Moreover, most existing microgrids are AC systems, with DC systems only now gaining momentum as they allow higher operational and control flexibility of the microgrid, enhancing its role in maintaining the reliability of future power grids .

This study investigates the black-start capability of a GFM OWPP, connected via high voltage, direct current – a challenging scenario due to not only faster energization transients but also more active components – and controlled with different grid-forming schemes, to compare their transient behaviour in such a challenging black-start setup. The aim is to characterize the different techniques and compare their capability to deal with the energization transients in a controlled manner while maintaining stable voltage and frequency at the offshore terminal. There exist only a handful of such studies – on black start by high-voltage-AC/DC-connected GFM OWPPs – however, they choose one GFM method and focus on different aspects of the restoration process. In general, this paper aims at covering the lack of literature comparing the different grid-forming control strategies – typically developed for general purposes and driven by microgrid research – in a specific and demanding task such as a wind power plant providing black-start services. While non-exhaustive, we think that this comparison can help direct future research in this area. To the authors' knowledge, such a study has not been done before.

In the next section of the paper, the state of the art of the role of wind energy in power system restoration has been reviewed. This is followed by an explanation of the general working principle of GFM control, along with a conceptual comparison of the four different control strategies considered for this study – on the energization of onshore load by an HVDC-connected GFM OWPP. Then the PSCAD model of the point-to-point HVDC-connected OWPP is described along with the different stages in the simulation of the energization sequence. Finally the transient behaviour of the different control techniques during the various stages of energization are presented and discussed.

Traditional GFL WTs can be used with an external power supply (e.g. diesel generator or energy storage) and a synchronous var generator (SVG) or STATCOM, combining services into a joint/hybrid black-start unit to facilitate WT participation in black-start procedure as proposed in . The external supply provides startup power and sets the reference voltage and frequency for the isolated system, the SVG/STATCOM supports the var requirement of the cables and transformers and stabilizes the voltage, after which the WTs connect to meet the load power demand. show that earlier participation of WTs in the restoration procedure is feasible as GFM control allows black-start and stand-alone island operation with better inherent synchronous-machine-like inertial response during a transient that can help absorb the initial impact of energization and ensure smooth load pickup, thus mitigating large voltage/frequency excursions that might occur during restoration. However, only the transients during load pickup and resynchronization to the grid have been studied, while energization of collector lines, export cables, and transformers, which present more challenges to transient stability during energization, are not shown. Additionally the major energization transients are dealt by the energy storage system and SVG, while the WTs behave only as passive GFL power sources to meet the load demand during the last stages of restoration.

Recent studies by and demonstrate the potential capability of high-voltage alternating current (HVAC)-connected OWPPs to black-start the onshore grid using GFM controls in less than 25 % WTs and assuming adequate wind resource. The results show that it is possible to do sequential energization of the array cables and WT transformers, starting with one WT energizing its string followed by others synchronizing to it and then sharing the control of voltage and frequency. Shorter cable sections are energized first until enough WTs are connected to absorb the var generated by subsequent cable sections. However, according to and , a large gap to bridge is the energization of the export link while meeting grid code requirements.

HVDC with voltage source converters (VSCs) can also be used as a standby facility for black start and restoration of the onshore AC grid, as demonstrated by the excellent voltage and frequency control performance in real system tests done by , proving for the first time that VSC-HVDC helps reduce restoration time while facilitating a safer and smoother restoration process with lower investment and maintenance cost. With HVDC transmission gaining momentum as the preferred choice for longer distance connections to larger OWPPs, show that the Skagerrak-4 VSC-HVDC link between Norway and Denmark (DK) can be successfully used to ramp up the voltage of an islanded 400/150 kV DK network to energize overhead transmission lines, transformers, and block load, followed by synchronization to the continental EU. Additionally, a top-down restoration test of the NEMO link between Belgium and the UK also demonstrates the capability of the VSC-HVDC interconnector to energize a dead Belgian grid from the live UK side .

Simulation results by show, although without any details of the transformer–cable energization transients, that a VSC-HVDC-connected OWPP can respond to onshore load changes and participate in load restoration. analyse the inrush current of transformers and cables (HVAC and HVDC) using electromagnetic transient simulations, but with a diesel generator to pre-charge the offshore converter that then energizes the offshore collector grid and the onshore converter pre-charged by the onshore AC grid, contrary to what is expected from an OWPP to provide black-start service. Simulation results presented by demonstrate, for the first time, an HVDC-connected OWPP with GFM control, sequentially energizing the offshore AC network including transformer, cables, and converter through a pre-insertion resistor, followed by HVDC link energization and onshore converter pre-charging and de-blocking for picking up block load, successfully participating in restoration as a black-start unit. However, the energy imbalance in the HVDC link during the DC-side uncontrolled pre-charging of the onshore converter leads to a significant dip in HVDC voltage and large transients in the offshore and onshore converter cell voltages and valve currents.

In addition to enabling black-start and islanding capabilities of WTs, GFM control can also allow the use of hybrid HVDC connection with a diode rectifier unit (DRU) instead of the offshore VSC. The application of controls proposed in for an OWPP to ramp up the offshore AC grid voltage and control frequency, considering it to be an inverter-based microgrid, has shown improved steady-state regulation during islanding when the DRU-HVDC is not conducting and smooth transition to current-control mode during grid-connected operation. This significantly reduces the cost vs. performance, due to lower losses (especially for higher power levels) and lesser capital cost, along with increasing efficiency and reliability due to a lower probability of commutation failure than a VSC .

According to the definition in , GFM converters are controlled in closed loop to work as ideal AC voltage sources (low-output impedance), while GFL converters are controlled as current sources with high parallel output impedance and cannot operate in islanding or stand-alone mode as they require a GFM converter or local synchronous generator to set the bus voltage and frequency.

The structure of GFM control consists of different functional blocks, as shown in Fig. . The main objective of GFM control is to operate the VSC as an ideal AC voltage source of a given amplitude V0 and frequency ω0. This requires most importantly a voltage control loop CV. The shortcomings of the single-loop approach, explained in , are already known from switch-mode power supplies and electrical machine drives as overcurrents during transients, and faults cannot be limited due to the lack of an explicit closed-loop current controller. Additionally sensitivity to disturbances and plant-parameter fluctuations eliminates open-loop control as a good choice. The most commonly used alternative is thus the nested or cascaded voltage–current controller, in which a faster inner current control loop CI is added . CI is designed to have a relatively smaller time constant than CV for decoupling the control loops. The controllers are in the synchronous reference frame that uses an angle θ* (for abc⇌dq transformation) obtained from the synchronization block .

While grid-feeding converters require perfect synchronism with the voltage at the point of connection to accurately regulate the power exchange with the grid, in the case of GFM converters the synchronization system must provide precise signals for both islanded and grid-connected modes of operation. It works as a fixed-frequency oscillator in the former case, while it slowly varies the phase angle and frequency of the island voltage during the reconnection transient to resynchronize with the grid voltage, in the latter. The most extended method used in grid-connected operation is a phase-locked loop (PLL), also called voltage-based synchronization as the frequency and phase angle of the grid voltage vector is used for control. However, enhancements are needed to ensure stability under unbalanced and distorted voltage conditions as voltage sag, weak grids, or off-grid operation can lead to instabilities. Alternatively power-based synchronization can also be used as the structure of the swing equation that governs synchronous machine dynamics and can be equated to that of a PLL, in the sense that the PLL structure can be modified to extract the derivative term of the frequency (∼inertia) and the speed variation (∼damping), as shown in . This presents a more stable solution and allows the power controller to also act as the synchronization block.

The outer power control loops CP,Q are required to regulate the real (P) and reactive (Q) powers exchanged with the grid (in grid-connected mode) or meet the demand set by the load (in islanded mode), while ensuring communication-less power sharing between the multiple paralleled inverters. The simplest method for this, by only relying on local measurements, is the droop control scheme, which was initially introduced for synchronous generators in utility scale grids, and now is well incorporated into microgrids . The primary level of the three-level hierarchical control, explained in , employs droop control equations, based on interconnecting impedance X/R ratio, to mimic the self-regulation capability of a grid-connected synchronous generators and allow power sharing in microgrids without using critical communication links .

Although easy to implement with high reliability and flexibility, traditional droop control suffers from an inherent trade-off between load sharing and voltage regulation, load-dependent frequency deviation, slow dynamic response due to filters for power measurement, and non-linear load-sharing issues due to harmonics. A variable virtual impedance ZV can be used to add harmonic droop characteristics with additional damping and improve trade-off between current harmonic sharing and voltage total harmonic distortion by adjusting the output impedance seen at different frequencies. Additionally this allows intelligent mode switching with soft start to take advantage of the fast converter response while avoiding large transients . In the last decade, several different GFM control schemes have been proposed in literature, of which four have been chosen for this study and explained in the next section.

The traditional droop-based power controllers can be replaced with more complex controls to replicate the system-level functionalities of synchronous generators like inertia and damping characteristics, frequency and voltage droop, self-organizing parallel operation, and automatic power sharing. The virtual synchronous machine (VISMA) concept, introduced by , uses power-based synchronization with a detailed implementation of the electromechanical model of a synchronous machine in its power control loop. This eliminates the need for PLL and allows conventional and proven grid operation with the usual static and dynamic properties that are characteristic to synchronous generators (both desired and undesired). Different detail levels of the VISMA implementation are listed in , while give a review of different control methods that mimic the operation of a rotating synchronous machine, for example Synchronverter , and PLL-based swing-equation emulation . Moreover, improvements have been made to the VISMA concept; for example recently, non-linear control-based GFM strategies relying on the duality between PECs and synchronous machines have been proposed. This includes machine matching and virtual oscillator control , which provide steady-state droop-like behaviour with a faster and better damped response during transients.

Several simplifications have been made, mainly removing modelling details deemed not relevant for this study.

Firstly, the WT rotor-side converter (RSC) and changes to the turbine controller that are required for GFM operation have not been modelled. In conventional GFL operation of the WT, the RSC is controlled to extract maximum power from the generator while the GSC maintains power balance to control the DC link voltage of the back-to-back PEC interface of the WT and the reactive power output at the AC terminal. However, in GFM mode, the GSC cannot control the WT–DC link and reactive power anymore with the required generator torque and real power being set by the AC load, not the turbine controller, which now has to regulate the speed using pitch control (and especially avoid overspeeding during low AC-load and high winds). Hence the RSC control requires changes to be able to maintain the DC link voltage constant by ensuring real power balance . Since the WT rotor and DC link dynamics are outside the scope of this study, the model assumes a constant WT–DC link voltage. Additionally an average voltage source model is used for the GSC with focus on dynamics not faster than the bandwidth of the inner current control loop. Moreover, the WT transformer is modelled as a pure electrical impedance r+jx without any magnetic characteristics as it can be soft-started along with the WT voltage ramp-up, to avoid magnetic inrush and saturation effects.

Secondly, for this study, although power sharing between the WTs inside the WPP is controlled by including the outer power control loops, the WTs are started up simultaneously as opposed to a more realistic sequential energization, e.g. in , as the study mainly focuses on the capabilities of the GFM OWPP as a whole, to provide black-start services to the onshore grid while dealing with offshore network transients due to energization of the large converter transformer, HVDC converters, and export cable – in a controlled manner. This puts any synchronization dynamics of multiple GFM PEC-interfaced WTs out of the scope of this study.

In this section, the tuning criteria for the control parameters of the different control schemes are presented. In a cascaded control structure, the inner loops are designed to achieve a fast response while the outer loops are tuned for regulation and stability.

Assuming a switching frequency of the wind turbine converter of 1 kHz, and with the main objective of the current controller to have a fast response, a bandwidth (α) of 200 Hz has been selected . A proportional controller has been used as any steady-state error can be taken care of by the outer voltage controller. This results in the same value (αLf) of the proportional gain for VSG and dPLL, as that already used in the current control Eq. () for the PSC scheme.

The voltage controller on the other hand is tuned to provide zero steady-state error with a bandwidth of 40 Hz and a phase margin of 45∘ .

The outer power control loops are tuned to be sufficiently slower than the voltage and current controls to avoid coupling between the control levels. Since the WPP is operating in islanded mode, there is no grid to exchange power with based on a set reference; rather the real and reactive power demands are set by the load.

For the DPC, the power control loops take the form of standard vector current control, as shown in . Since p∝id and q∝iq, tuning the DPC power controller is equivalent to tuning a slower current controller – a natural frequency of 4 Hz with damping ratio of 0.74 has been chosen.

A unique control loop in the dPLL scheme is the frequency control loop that includes the cascaded voltage–current controller dynamics along with PLL, as shown in . This requires tuning of the PLL and the controller gain kf of Eq. (). The PLL has been tuned to be critically damped with a bandwidth of 0.5 Hz – slow enough for the slow voltage controller which significantly reduces damping (∼ phase margin) in the system, moving it closer to instability. While increasing kf leads to a faster response but with reduced damping , a low value was found to result in oscillations in the shared powers. As a trade-off, kf has been tuned for the frequency control loop to have a bandwidth of 0.5 Hz. Overall, these values ensure a high phase margin (82∘) for stable operation.

Similar to the dPLL, the cascaded voltage–current controller of the VSG moves the system closer to instability at low bandwidths, due to a significant reduction in system damping (∼ phase margin). This is justified by , who show that certain eigenvalues close to the imaginary axis are sensitive to the proportional gain of the voltage controller kpv, with higher values improving the stability of the system. Moreover, lower switching frequencies seem to shift the root locus closer to imaginary axis, restricting the range of stable operating points. show the complexity associated with tuning VSG for damping the different oscillations, implicitly caused due to coupling terms in the state-space matrix. While virtual resistance helps damp the intrinsic synchronous mode of a single droop-controlled VSC, it introduces coupling between active and reactive powers, especially for multiple paralleled VSCs. The inertia term J can then be tuned to provide further attenuation, but this introduces sub-synchronous oscillations which deteriorate with increased inertia. Finally according to , since smaller droop gains reduce the inter-oscillations, values for D and kq from have been taken as initial estimates and then fine-tuned for stable operation. It is important to note that improving one oscillation mode can trigger another and that the tuning strategy used for a single VSG might not be applicable to multiple VSGs . Consequently the VSG control strategy implemented here – with a swing equation – has been found to be limited in its damping of oscillations. With a slow voltage controller – smaller kpv – the sub-synchronous mode moves closer to origin, while the synchronous mode improves in damping . So the voltage controller has been set to the lowest possible bandwidth (∼150 Hz) while ensuring good damping and stable operation, with appropriately tuned outer loops.

The complete set of tuned parameter values are listed in Table .