Enabling 100 % Renewable Power Systems Through Power Electronic Grid-Forming Converter and Control: System Integration for Security, Stability, and Application to Europe

| In accordance with European plans, dynamic controls are developed to allow for system-wide integration of 100% renewable energy sources (RESs) interfaced through power electronic converters while maintaining security. At the heart of the development is the concept of the grid-forming resource (GFR) which brings together both the technologies of renewable energy resource and grid-forming converter. Extending on an extensive review, a grid-forming converter


B. List of Symbols
Angle-related signal path. ω Frequency-related signal path.

I. I N T R O D U C T I O N
The ambition of accomplishing an emission-free renewable power system in Europe by 2050 relies on the large-scale integration of renewable energy sources (RESs), with photovoltaics (PV) and wind power being among the most dominant ones [1]. Such an extensive penetration of renewables is affiliated with an increasing share of power generation interfaced by power electronic converters [2]. The latter can efficiently adjust the characteristics of the RESs to the requirements of the grid for meeting voltage and frequency specifications [3]. This involves a conversion from direct current (dc) to alternating current (ac) for PV [4]. For wind energy conversion systems (WECSs), ac-dc-ac power electronic conversion stages are popular [3], facilitating a wide range of variable-speed operations [3], [5]. As of today, the involved power electronic converters predominantly make use of the grid-following control scheme [6]. The latter involves a phase-locked loop (PLL) for the synchronization with the ac grid voltage [4]. When employing grid-following control schemes, the powerelectronic-interfaced RESs typically behave as controlled current sources and rely on an ac grid voltage to be available, thus they can not operate in an islanded mode by themselves [7], [8].
The grid-following converters are not capable to operate in an islanded mode because they are not capable of establishing the ac grid voltage by themselves [7] and must be shut down if their control loses synchronism with the grid [9]. Moreover, small-signal stability problems can be observed when multiple grid-following converters are operated in proximity to each other [10]. These problems are associated with the interactions of the PLLs employed by the grid-following converters and with low short circuit ratios in the grid [10]. Additionally, wideband frequency oscillation problems have been reported in the context of grid-following converters operated in weak power grids [6], [11].
The grid-forming converter is said to have the potential to overcome the aforementioned issues associated with grid-following converters [2], [12]. When driving toward an emission-free renewable power system with converterdominated generation, attention will therefore be directed especially to the grid-forming converters. Resources connected to grid-forming converters are expected to establish and support the ac grid voltage [7], [10]-a fundamental role that has been adopted by synchronous generators. Voltage sources connected to grid-forming converters have been shown to allow for instantaneous power provision to sudden power changes in the grid. Thus, the grid-forming converter is considered a technology to deal with the challenge of diminishing system inertia that is associated with the increasing penetration of converter-interfaced generation [2], [9], [13]. An intrinsic voltage source characteristic along with a self-synchronization ability have shown to be beneficial for the application of grid-forming converters in weak grids [10].
Important is further the requirement for accurate synchronization with the grid voltage if multiple gridforming converters are to be operated in parallel. For this purpose, the power-synchronization control is widely used [6], [10]. With the latter integrated, the grid-forming converter connected to an ideal dc voltage source enables an instantaneous response to disturbances [9], [10], [14] thanks to the provision of inertia. On the other hand, the grid-forming converter has been shown to support load-frequency control by means of a droop characteristic [6], [9], [15]. This possibility to design controls that allow for power balancing over diverse time scales makes the grid-forming converters promising candidates when phasing out power generation based on synchronous machinery while striving to maintain a secure operation of the power system.
Beyond the small-signal changes to be dealt with by load-frequency control, the secure grid of the future must also be fault tolerant. Thus, it is also critical to design protection algorithms and controls to enhance transient stability when faults occur in the presence of resources connected to grid-forming converters [16]. Such algorithms and controls should be capable to support compliance with low-voltage ride-through standards [17], to limit fault currents to acceptable values, as well as to enhance the quick recovery and resynchronization of the grid-forming converters after large-signal transient disturbances. Therefore, with the purpose of maintaining the system stability and security in power systems dominated by converter-interfaced generation, the design of suitable power electronic control methods for grid-forming converters deserves attention.
However, the fluctuating nature of an RES and its power supply limitation were not accounted for. In [21], a lack of power of a given PV converter was overcome by a second PV converter. In general, fluctuations can be compensated through the usage of diverse types of energy storage [22], [23]. When it comes to WECSs realized through type-4 wind turbines [24], a suitable location for connecting additional energy storage is the dc link [25], [26], and short-term storage, in particular, was shown to support the control of grid-forming converters integrated with WECSs [27]. Without such dedicated energy storage units available, fast response times can still be realized by accessing the energy stored in the capacitor of the dc link [28]- [30]. But while the capacitor is an access-oriented type of storage, the rapid depletion of the energy stored can compromise stability. For the purpose of obtaining an enhanced inertial response capability, it is therefore desirable to avoid too high a reduction of the energy stored in the dc-link capacitor and also to make use of the kinetic energy stored in the rotating turbines.
In this article, when considering the perspective of a 100 % renewable power system in Europe, the focus moves toward a wide-area level. In this context, the following three questions need to be answered. Among the variety of different grid-forming control schemes proposed so far, which ones are practical at the wide-area level while supporting ancillary power system services? What kind of protection and control approaches are effective in supporting transient stability of converter-interfaced generation? How can grid-forming converters turn wind parks into resources offering functions that are consistent with the secure operation of power systems? Those questions will be answered in the following. The claims made are being validated by the study of a 100 % renewable power system that only comprises converter-interfaced generation. The study comprises 2204 wind turbines that are grouped into 49 grid-forming and grid-following wind parks.
In Section II, the principles of grid-forming converter controls are developed step by step and compared with one another. A suitable scheme that integrates the functionalities of inertia emulation, frequency droop characteristic, and reactive power droop characteristic is retained. In Section III, the control scheme of Section II is extended in functionality from the small-signal level to the large-signal level to address the aspect of transient stability. Section IV in turn builds upon the knowledge acquired in Sections II and III in developing the concept of the grid-forming resource. The grid-forming resource brings together renewable energy technology and gridforming converter technology so that the virtues of the grid-forming converter controls can be made available even when nonideal renewable power sources are connected to the dc side of the power electronic converter. At the heart of the concept is the idea to apply suitable controls such that the behavior of an ideal voltage source is approximated on the dc-side terminal of the grid-forming converter. Validations are performed based on the detailed scenario of the Irish power transmission system in Section V. Conclusions are drawn in Section VI.

II. P R I N C I P L E S O F G R I D -F O R M I N G C O N V E R T E R S I N P O W E R S Y S T E M S
Power electronic converters connected to a voltage source at the dc side can be controlled via grid-forming control schemes to emulate an alternating voltage on the ac side. In such configurations, power electronic converters are referred to as grid-forming converters. Among the commonly used methods for synchronization of the ac side of the grid-forming converter with the ac grid voltage is the power-synchronization control, which enables selfsynchronization of the grid-forming converter without a PLL [6], [7], [31]. Such synchronization is a main functionality of the grid-forming control scheme. It can be realized by controlling the voltage amplitudes and angles at the ac-side terminal of the respective converter [31].
In what follows, the basics of the grid-forming control scheme are elaborated upon by consideration of a voltagesourced converter (VSC) connected to a power grid. For the purpose of illustration, in a first step, the overall structure of a VSC connected to the power grid including the gridforming control scheme are introduced. In a further step, the principle of active power exchange is described. The principle relies on controlling the voltage angle at the ac side terminal of the grid-forming converter. Then, the development of ancillary services that are affiliated with the active power exchange is discussed for the grid-forming control scheme. Finally, the reactive power exchange that is associated with controlling the voltage amplitude of the grid-forming converter is addressed in this section.

A. Overview of Voltage-Sourced Converter With Grid-Forming Control Scheme
A VSC with a grid-forming control scheme connected to the grid is depicted in Fig. 1. The family of the VSC technology can be categorized into the two-level and multilevel converters [32], [33]. Among the multilevel converters is the MMC, which has drawn much attention in medium and high-power applications, especially for high-voltage power systems [34], [35].
The VSC in Fig. 1 is connected to the point of common coupling (PCC) through a transformer and an optional LC filter that is not needed when using VSCs of type MMC with the significant number of levels used at high-voltage installations. The transformer is represented by its series resistance Rt and leakage inductance Lt. The LC filter can be used to reduce the undesired harmonics in the output voltage of the grid-forming converter and comprises an inductor of inductance L f and a capacitor of capacitance C f . The ac grid is modeled as a Thévenin equivalent, composed of a three-phase equivalent voltage source v e,abc as well as a series resistor of resistance Re and an inductor of inductance Le. An ideal dc voltage source is connected to the terminals of the dc side of the VSC. The lower part of Fig. 1 shows the grid-forming control scheme in the generic dq reference frame [4], [36]. At the input of the depicted measurement processing block, the three-phase measurements of the current i c,abc from the VSC to the capacitor of the LC filter, the three-phase output voltage v o,abc across the capacitor of the LC filter, the three-phase output current i o,abc , and the phase angle θo affiliated with phase a of v o,abc are received. If the LC filter is omitted, then the currents i c,abc and i o,abc coincide. The measured voltages and currents are filtered as appropriate and transformed into dq variables. The angle of the d-axis is equal to θo, while the q-axis leads the d-axis by 90 electrical degrees. In the per unit system of Appendix A, the instantaneous active output power and reactive output power can be expressed by The measured active power and reactive power are fed to the active and reactive power control blocks, which are part of the high-level control of the grid-forming converter. The active power control regulates the angular frequency ωo of the grid-forming converter and the active output power Po  In addition to the regulation of the active power and the reactive power, the high-level control can be used to enable grid-forming converters to provide ancillary services. The ancillary services, as offered by appropriate settings, comprise the provision of inertia emulation [9] and frequency droop characteristics [37].
Furthermore, Fig. 1 includes the virtual impedance block, which issues the signal Δv ref o,dq . The virtual impedance (VI) concept has been used to dampen active power oscillations that might occur due to the transmission line properties during transient disturbances and to limit fault currents [38]. For the damping of active power oscillations, a virtual impedance that comprises a resistance R do and a high-pass filter is formulated in Appendix B according to [31], [39]. For the limitation of fault currents, the block also incorporates a virtual impedance for current limitation as shown in Section III.
The output signal The low-level control of the grid-forming control scheme is detailed in Fig. 2. It comprises voltage and current controls in a cascaded structure, and PI-controllers are typically employed [40]- [42]. At the output of the current control, vector m abc comprises the individual scalar modulation signals referring to the three phases. Those serve as a basis in the generation of switching pulses [4]. The voltage and current controls aim at compensating the impact of the filter on the dynamic behavior of the measured currents and voltages. If the filter is not applied, then the voltage reference v ref o,dq at the input of the voltage control can be directly used to create the modulation signals after division through v dc , omitting the voltage and current control blocks bordered by the dashed-dotted lines. Since the voltage reference v ref o,dq incorporates the effect of the virtual impedance for current limitation, overcurrent protection is accounted for as such.
In accordance with the configuration in Fig. 1, for the purpose of illustration and the development of control schemes, several assumptions are made for practical consideration at the large-scale power system level.
• The grid side of the PCC is supposed to be at the high-voltage transmission system level, where the reactances of the transformer and the line are much higher than the resistances. Therefore, Rt and Re may be neglected in power flow calculus. • The angle differences between complex nodal voltages are such that errors in describing power flows through linear equations can be neglected. • The focus will be on realizing the VSC as an MMC connected to the transmission system level, where the MMC is known to be practical [32], [35]. As a consequence, a sinusoidal waveform at the ac-side terminal of the VSC is well approximated.

Fig. 2. Grid-forming control scheme, including details of low-level voltage and current controls.
• Since MMCs with a significant number of levels barely produce harmonics, LC filters are not needed and will be disregarded [32]. Details pertaining to the harmonic filter are not in the scope of this work. Thus, v o,abc and i o,abc of Fig. 1 become the VSC output voltage and current on the ac-side terminal, respectively. With i c,abc = i o,abc , the extra measurement of i c,abc is not applicable. • Only balanced three-phase voltage and current conditions are assumed. This causes the zero sequence component of the dq0 variables to disappear. • The deviations of the electrical angular frequency relative to its steady-state value are small. • Most quantities are given in per unit. Exceptions are noted. Examples include angles, time, and time constants, inertia constant, length, density, translational speed, as well as base, rated, and nominal values of quantities. The per unit system employed is described in Appendix A.

B. Active Power Control
In what follows, the principle of active power regulation is derived as part of the grid-forming control scheme. Considering small perturbations around a steady-state operating point, a small-signal formulation of the power injection ΔPo from the grid-forming converter over its terminal toward the transformer in Fig. 1 can be expressed in the time domain by the convolution operation where g δ (t) is the impulse response of the system relating the change of ΔPo and the change of angle Δδ expressed in the unit rad. Here, δ is the difference of θo and θe that are, respectively, the phase angles of phase a of the grid-forming converter output voltage vo,a and the grid equivalent voltage ve,a. The complex transfer function G δ (s) of the impulse response g δ (t) is derived in Appendix B. In Appendix B, it is shown that the two poles of G δ (s) indicate poor damping as a consequence of the small resistive components of the transformer and the line between the grid-forming converter and the grid equivalent voltage. With the appropriate control of the virtual impedance for damping oscillations, these poles can be shifted to achieve a desired damping ratio so that the network transients decay very rapidly. The action of the virtual impedance for this purpose is mathematically given by (79) and (80) of Appendix B.
Thanks to the addition of the virtual impedance, the active and reactive power controls do not just see G δ (s) but a well-damped counterpart. The latter is well approximated through a static relationship, as evidenced by (83) of Appendix B. Considering the aforementioned assumptions and this static relationship, the output power Po injected into the grid via the VSC can be determined from where Vo is the root-mean-square (rms) output voltage at the ac-side terminal of the VSC, Ve is the rms grid equivalent voltage, Xt and Xe are the transformer and grid equivalent reactances, respectively. Thus, with the impact of the virtual impedance for damping oscillations of Appendix B together with the assumption of the approximate validity of linear lossless power flow relationships of Section II-A, the large-signal static equation (5) is consistent with the small-signal dynamic relation (3) for the development of the active power control. Based on this relationship, the voltage angle θo can be used to adjust the active power output of the VSC. Fig. 3 illustrates the closed-loop active power output control. Here, Vo and Ve may be obtained as steady-state values based on measurements of the output voltage vo as well as and the grid impedance comprising Re and Xe. The grid impedance may be approximated based on impedance measurement techniques [43], [44]. As mentioned earlier, P ref o is defined as the reference input for the active output power injected into the grid, and θe adopts the role of a disturbance input.
For a given P ref o , the active power control aims at regulating the active power Po injected by the VSC such that the difference between θo and θe is also given in the steady state. This specified difference then indicates that the VSC is synchronized to the power grid. Such a synchronization mechanism is usually referred to as power-synchronization control [6], [10], [31].
With the purpose of providing an inertial response ability, the active power control in Fig. 3 can be designed to mimic the inertial response of a synchronous machine connected to a power grid. The inertial response of a synchronous machine can be derived by using the rotor swing equation [45]. When neglecting losses and damper winding effects, the swing equation can be formulated as where Ps,m and P s,el are, respectively, the mechanical power input and electrical power output of the synchronous machine, Hs is its inertia constant with the unit second, θs is the electrical rotor angle of the synchronous machine, and ωs,n is the nominal electrical angular frequency of the synchronous machine expressed in the unit rad per second. Given the used per unit system of Appendix A, the latter is taken as the base angular frequency. In order to mimic the inertial response of the synchronous machine as part of the active power control, (6) may be emulated by where H is a corresponding virtual inertia constant with the unit second and ω b is the base angular frequency with the unit rad per second. Based on (7), the controller in Fig. 3 is developed with two integrators to mimic the inertial response, as illustrated in Fig. 4. The double integrator is able to cancel the steady-state error between the active power Po and its reference P ref o , despite of the disturbance introduced by the grid equivalent voltage angle θe. Therefore, a PLL is not required for the synchronization process. However, it should be noted that the closed-loop control in Fig. 4 represents a pure oscillator. Therefore, a damping effect has to be added.
A possible approach for achieving a damping effect is by feeding back a signal −kω(ωo −ωg) to the controller input, where the damping effect is realized by the damping gain kω and the difference between ωo andωg as the estimate of the grid angular frequency ωg. The resulting control scheme is referred to as a virtual synchronous machine (VSM) [40], [46], which employs a PLL to estimate the angular frequency at the PCC. If insteadωg is replaced by Given that ω ref o remains unchanged, an alternative representation of the control scheme in Fig. 5 is the droop control in Fig. 6 [7], [46], [47]. A correspondence between Figs. 5 and 6 can then be observed through the following relations: where Dω is the frequency droop coefficient, and τH is the time constant of the first-order lag element. The frequency droop coefficient emulates the frequency droop characteristic known from speed governors of synchronous machines. The lag element is necessary to introduce the inertial response effect, as determined by the setting of the inertia constant in (10). From (9) and (10), it can be seen that in the control designs of Figs. 5 and 6, the inertial response effect and the frequency droop characteristic cannot be set independently.
With the purpose of avoiding additional measurement devices and inaccurate frequency measurements under distorted grid conditions, a further PLL-free control scheme is proposed in [39]. The control scheme provides a pure inertial effect. It may be modified by a frequency droop characteristic in order to provide load-frequency control. The resulting overall control scheme is presented in Fig. 7, which consists of a frequency droop characteristic and an integral-proportional controller (IP-controller). In the latter, the integral part lies in the forward path, and the proportional gain is applied to the feedback signal Po. Instead of estimating the grid frequency via a PLL for the damping effect, the active power is weighted by the gain kP. The resulting overall control scheme allows for flexible choices of the inertia constant H and the frequency droop coefficient Dω. This makes the IP-droop control scheme superior to the standard droop control in Fig. 6 and also to the VSM control scheme, as a PLL function is avoided.
In the Laplace domain, the transfer function of the resulting IP-droop control scheme in Fig. 7 is expressed by with k δ = VoVe Xt + Xe . (12) As stated in the description of Fig. 3, Ve and Vo are taken as steady-state values. From (11), the damping ratio ζ can be determined as follows: According to (13), the desired damping effect can be achieved by appropriate tuning of the gain kP with respect to the predefined frequency droop coefficient Dω, where Dω enables a desired frequency droop characteristic.

C. Reactive Power Control
As depicted in Fig  The presented control structure in Fig. 1 gives gridforming converters the ability to establish and regulate the grid voltage and frequency. The reactive power control complements the active power control of Section II-B for allowing the provision of ancillary services such as inertial response effect and frequency droop characteristic. The grid-forming converter so establishes and supports the ac voltage and contributes to maintaining the power balance in the grid.

III. T R A N S I E N T S T A B I L I T Y O F G R I D -F O R M I N G C O N V E R T E R S I N P O W E R S Y S T E M S
The grid-forming converters must be able to withstand severe transient disturbances and to maintain synchronism during the latter. Transient stability is a precondition for good levels of power system security. Associated with the transient stability of the grid-forming converter in power systems is the dynamic response of the voltage angle θo to transient disturbances [13], such as large voltage sags or short circuits in the grid.
In what follows, solutions for the grid-forming control scheme are proposed to mitigate the effect of transient disturbances on the voltage angle of the gridforming converter. First, it is shown how the virtual impedance for current limitation, which was briefly introduced in Section II-A, can be exploited for protecting the grid-forming converter during transients as a precondition for transient stability. For this purpose, the virtual impedance for current limitation, as discussed in [49]- [51], is to be integrated into the grid-forming control together with the virtual impedance for damping oscillations. The idea behind the virtual impedance for current limitation is to emulate the effect of a physical impedance at the terminal of the grid-forming converter when the output current of the latter exceeds a threshold value. Con-sequently, fault currents are limited to acceptable ranges while power and current oscillations are reduced. Second, further developments in the grid-forming control are introduced for limiting the impact of transient disturbances on the voltage angle and improving the resynchronization after a fault. This is achieved by adaptively adjusting the virtual inertia constant of the grid-forming converter and by adjusting the output voltage angle signal of the gridforming converter in case of too high an angle deviation.

A. Virtual Impedance Control for Current Limitation as Precondition of Transient Stability
The capability of grid-forming converters to provide high currents during transient disturbances is limited by the current-carrying capacity of the semiconductor power switches [52]. For example, during short circuits a fault current of a converter may be limited to about 120 % of the nominal current value [53]. The possibility to withstand higher fault currents comparable to those of synchronous machines would require greatly oversized semiconductor components at high additional costs.
The protection of grid-forming converters during largesignal transients is crucial for transient stability and for the ability to facilitate system recovery by means of the gridforming control scheme. In order to protect the converters from high fault currents through the virtual impedance of Fig. 1, a part of this virtual impedance is to serve for current limitation.
For the purpose of illustration, a symmetrical fault at the PCC of Fig. 1 will be considered hereafter. The output current of the grid-forming converter is influenced by the impedance between the converter terminal and the fault location. Assuming that the voltage control of the grid-forming converter retains its reference value during a transient disturbance, a considerable deviation between the voltage v o,abc of the converter and the voltage v g,abc at the fault location is expected. As a consequence of this voltage deviation, the output currents of the grid-forming converter increase significantly. With the purpose of limiting the fault currents, the virtual impedance for current limitation incorporates a detection algorithm to identify the increased output currents and to adapt an emulated virtual impedance between the gridforming converter and the fault location. Subsequently, the output voltages, as offered by an appropriate setting of the virtual impedance for current limitation, can be decreased to limit the output currents to acceptable values.
The setting of the virtual impedance for current limitation in dependence of the dq components i o,d and io,q of the output currents of the grid-forming converter is described by where X cl,max is the maximum value of the reactive component of the virtual impedance for current limitation, i o,th,max is a given maximum threshold value of the output current magnitude, Δio is the deviation between the output current magnitude and its maximum threshold value, and Δio,max is the maximum permissible value of Δio. The resistive component of the virtual impedance for current limitation is obtained from where σ cl defines the ratio between the reactive and resistive components of the virtual impedance for current limitation. Further details on the choice of σ cl may be consulted via [49]. As depicted in Fig. 1 where where τ do is the time constant of the high-pass filter in the virtual impedance for damping oscillations, making the resistive component R do only effective during transients.
In what follows, the effectiveness of the virtual impedance for the current limitation in limiting the current to acceptable values is verified by simulation. The parameters of the virtual impedance are selected as Δio,max = 0.25 pu, X cl,max = 1 pu, i o,th,max = 1 pu, σ cl = 4 and R do = 0.18 pu. A voltage sag of 0.85 pu is assumed at the PCC in Fig. 1. The simulation results are depicted in Fig. 9. The voltage sag of 100 ms duration and starting at time instant 0.5 s is shown to cause a significant drop in active power. By enabling the virtual impedance for current limitation, the output current of the grid-forming converter can be limited to an acceptable maximum value

B. Enhancement of Transient Stability by Adaptive Inertia Control With Voltage Angle Estimation and Modification
To ensure transient stability during large-signal disturbances, it is crucial to avoid large variations between the grid-forming converter output voltage angle and the grid voltage angle in the transient time frame. Moreover, to facilitate a fast resynchronization with the grid after the disturbance, it is important that the voltage angle difference reaches its post-disturbance value quickly.
For the purpose of illustration, the general principles of the transient stability of grid-forming converters in power systems are elaborated upon. In order to examine the relationship between changes in power and the voltage angle difference as well as the process of resynchronization with the grid, it is assumed that the grid-forming converter is subject to a symmetrical fault at the PCC. Then, the development of an effective grid-forming control scheme that enhances transient stability and allows for fast resynchronization is introduced.  in the analysis of the transient stability of grid-connected synchronous generators [54] and also of voltage-sourced converters [13], [55], [56]. Those descriptions serve as a good starting point for the consideration of the following relationship, which is derived in Appendix C: where δtr represents the transient angle by which the voltage of the grid-forming converter leads the voltage at the fault location at the PCC; R cl is much smaller than X cl and can therefore be neglected. The blue curve in Fig. 10 illustrates (20) when X cl equals zero, which would result in a maximum Po of Po,max. The yellow curve represents the power-angle curve with X cl = X cl,max , leading to a maximum Po of P o,cl,max . Since an operation within the restricted area is to be prevented, the value of the virtual impedance for the current limitation is selected such that the output current of the grid-forming converter is limited to acceptable values.
Point A in Fig. 10 denotes the initial operating point before the fault occurs. A solid three-phase symmetrical short circuit to ground results in a zero voltage at the fault location. Large fault currents are to be expected, triggering the application of the virtual impedance for current limitation. The zero voltage at the PCC causes the active power output of the grid-forming converter to drop to zero, leading to a positive power error, i.e., P ref o − Po > 0 in the grid-forming control of Fig. 7. Affiliated with the positive power error is an increase in the output frequency of the grid-forming converter, as determined by the design of the grid-forming control scheme. Such increase in the output frequency causes δtr to continuously increase dur-ing phase 1 up to point B in Fig. 10, as it can be recognized from (88) in Appendix C.
The transition from points B to C in phase 2 of Fig. 10 describes the time period in which the voltage at the PCC recovers after the fault. In this phase, the active power output of the grid-forming converter is expected to start exceeding the active power reference value, since δtr has risen from δA to the higher value δC. Thus, the resulting negative power error in the active power control of Fig. 7 would in turn cause the output frequency ωo to decrease. In phase 3, δtr continues to rise from δC until ωo equals ωg. Notably, if δtr overshoots the maximum value at δ cl,max , δtr would further increase and lead to a loss of synchronism.
Starting from point C* during phase 4, ωo keeps on decreasing as long as a negative power error persists in the active power control. The decrease in ωo is affiliated with a reduction of δtr. According to (20), this would appear to lead to a reduction of the active power output, as described by the yellow curve in Fig. 10. However, as the output current of the grid-forming converter starts to decrease, according to (14), the value of X cl decreases, too. Thus, the parallel reduction of δtr and X cl can cause a transition from points C to D as described by phase 4 of Fig. 10. The final transition from points D to A in phase 5 represents the time period in which the active power control of the grid-forming converter regulates the power error to zero.

2) Adaptive Inertia Constant and Phase Shift Compensation Scheme:
While an adaptive virtual inertia may also support load-frequency control [57], the design described hereafter introduces the adaptive adjustment of the virtual inertia H as a control parameter to support transient stability. As described in Section III-B1, during phase 1 of Fig. 10, the positive active power error in the active power control of Fig. 7 is expected to be affiliated with considerable variations of the output frequency and in turn of the output voltage angle of the grid-forming converter during a transient disturbance. A possible solution to avoid such large voltage angle variation is given by increasing the emulated inertia of the grid-forming control scheme of Fig. 7. This is achieved by adaptively adjusting the control parameter H during transient disturbances. As a result, the sensitivity of the output frequency toward changes in the active power error can be reduced significantly.
A suitable indicator for transient disturbances is the output voltage magnitude at the terminal of the gridforming converter. As seen from (17) where H 0 is the virtual inertia constant in a steady state. According to (21), the value of the emulated inertia during transients will increase with decreasing reference voltage magnitude. But even with the adaptive inertia implemented to restrict too high of an increase in δtr at phase 1 of Fig. 10, the loss of synchronism may still ensue in the subsequent phases if δtr does exceed δ cl,max . Moreover, from the discussion in Section III-B1, it can be concluded that it is of particular interest to accelerate the resynchronization process during phase 3 and phase 4 of Fig. 10. In this sense, a supplementary control is useful to be added to the adaptive inertia constant scheme for the enhancement of the resynchronization process of the grid-forming converter. The supplementary control is a phase shift compensation scheme. It estimates the post-disturbance value of θo and uses this estimate to reset the latter after the disturbance.
The estimation of the post-disturbance output voltage angle of the grid-forming converter considers the linear power flow relation between the grid-forming converter and the fault location at the PCC as follows: where θ o,pd and θ g,pd give, respectively, the postdisturbance voltage phase angles at the grid-forming converter terminal and at the PCC in steady state. Assuming that P o,pd would match its reference P ref o in steady state and that the rms voltages Vo and Vg be very close to 1 pu, (22) can be recast into During the voltage recovery, the voltage angle θg at the PCC may be estimated by a PLL. Based on the obtained estimateθg, an estimateθ o,pd of the post-disturbance angle of the grid-forming converter output voltage is readily derived based on (23) as During the transient disturbance, the value of the output voltage angle θo of the grid-forming converter may well exceed the value θ o,pd due to the positive power error in the active power control. Thus, θo andθ o,pd are expected to be significantly different. If this difference exceeds a predefined maximum value Δθo,max, then the angle θo will be reset to its post-disturbance estimateθ o,pd , which is very close to θ o,pd . The reset happens at the time instant where the voltage magnitude at the PCC exceeds a minimum threshold v g,th,min during the voltage recovery.
The proposed extensions, including the virtual impedance control, were tested for the voltage sag scenario of Section III-A. The simulation results are presented in Fig. 11. For the purpose of illustration, the virtual impedance, comprising the virtual impedance for current limitation and damping oscillations is referred to as virtual impedance, and the proposed developments are denoted by AICS for adaptive inertia constant scheme and PSCS for phase shift compensation scheme in Fig. 11(d).
Thanks to the presented virtual impedance, the current is limited to an acceptable maximum value of 1.18 pu, and power as well as current oscillations are damped. Fig. 11(d) illustrates the transient angle δtr by which the output voltage of the grid-forming converter leads the voltage at the fault location at the PCC. The fast performance is explained by the combined effect of the adaptive inertia constant scheme and the phase shift compensation scheme. The adaptively adjusted inertia constant shown in Fig. 11(e) reaches a maximum value of 17.1 s and then moves to values of around 16 s, i.e., to about 3.2 times the value of H 0 at 5 s. The curve of the adaptive inertia constant is consistent with an initial drop of the output voltage magnitude reference to 0.29 pu before moving to around 0.31 pu in accordance with (21). Such an increased virtual inertia can significantly restrict the increase of δtr until the voltage recovery occurs at 0.6 s.
After the voltage recovery, the resynchronization process is considerably shortened with the proposed methodology. This can be observed in Fig. 11(d), when δtr quickly returns close to its steady-state pre-disturbance value thanks to the resetting of the voltage angle of the grid-forming converter. The reset is performed after a short delay following the voltage recovery to avoid the transients in the angle measurement performed by a PLL scheme.

IV. I N T E G R A T I O N O F G R I D -F O R M I N G C O N V E R T E R S W I T H W I N D T U R B I N E S
The control schemes introduced in Sections II and III were developed for the grid-forming converter. The controls allow for establishing and maintaining the grid voltage and frequency during normal operation as well as during transient disturbances. Nonetheless, in those developments of the previous sections, it was assumed that the grid-forming converter was connected to an ideal dc voltage source that by definition is able to provide any amount of the power as requested by the grid-forming control scheme.
In what follows, however, the power system integration of WECSs through grid-forming converters is elaborated upon. As for other nonideal sources, the availability of electric power that can be drawn from a WECS is limited. The limitation needs to be taken care of in the design of grid-forming controls for interfacing such a constrained resource, which is referred to as a grid-forming resource (GFR) hereafter. This is done in preparation of a power system operation at 100 % power-electronic-interfaced renewable energy resources. Such integration requires suitable control methods for the WECSs in order to supply the power consistent with the grid-forming control scheme. Furthermore, the original grid-forming control scheme is to be modified to account for WECS power supply limitations.
The section is organized as follows. For the purpose of illustration, in a first step, an overview of the system configuration that comprises a wind park of multiple WECSs interfaced to the grid by a single grid-forming converter is given. In a second step, the characteristics of the WECS power response are designed in order to supply the power to the grid in terms of an inertial response and frequency droop properties.
In accordance with the frequency droop characteristic, the GFR control system is to provide power reserve so that flexibility is given in terms of meeting requested power schedules. To allow for the quasi-instantaneous reaction needed for an inertial response, the kinetic energy stored in the WECS rotating masses can be made use of. At the same time, the control of the grid-forming converter is extended to avoid excessive energy depletion from the dc bus capacitor.

A. Overall System Configuration
An overview of the wind park system configuration is depicted in Fig. 12. The system comprises multiple WECSs in a back-to-back configuration with a single grid-forming converter, building a GFR. Among the widely used configurations for the integration of WECSs into the power system, there is the type-4 wind turbine [24] whose generator is connected to a full-scale back-to-back frequency converter. The latter consists of a grid-and a generatorside converter, both being interconnected through a dc bus. The fact that the rotating generator is only accessible through power electronic converters makes the type-4 wind turbine particularly suitable for investigations of power systems with 100 % converter-interfaced generation. In the configuration of Fig. 12 of multiple WECSs, there is a cumulative equivalent dc bus capacitor, which is directly connected with the grid-forming converter. Such dc collector networks are said to offer significant potential [24].
The different elements of a WECS, including its control scheme, are depicted on the left of Fig. 12. The WECSs are shown to include a turbine, a permanent magnet synchronous generator (PMSG), and an ac-dc converter. The speed Vw,i of the wind acting on the turbine generates a mechanical accelerating torque Ttur,i on the drive train. The electromagnetic torque T el,i coming from the PMSG creates a decelerating effect on the drive train as long as the PMSG delivers electric power P w,el,i toward the ac-dc converter. At the input of the torque reference processor, the measured electric power P w,el,i is compared with the power reference P ref w,el,i , issued by the power reference processor. To support a quasi-instantaneous reaction for the inertial response, the torque reference processor also receives a feedforward signal that readily relates to the power Po delivered by the grid-forming converter.
The torque reference processor block determines the electrical torque reference T ref el,i , which is converted into current references for the WECS inner-loop current control. Further details on the modeling of the different stages of the WECS may be consulted via [58].
The lower right part of Fig. 12 shows the coordinated grid-forming control scheme. The shown block of coordinated active power control extends the IP-droop control of Fig. 7 as discussed below. The reactive power control operates according to Fig. 8, and the virtual impedance block makes use of processes described in (18) and (19).

B. Inertial Response and Frequency Droop Control of Grid-Forming Converters Integrated With WECS
As can be seen in Fig. 12, the voltage v dc across the capacitor C e,dc serves as an indicator of interaction between the WECS and the grid-forming converter. Using the per unit system of Appendix A and as also described in [4], this interaction can be expressed by the power balance between the WECSs and the grid-forming converter considering the voltage v dc by with where ω b is the base angular frequency in rad per second, P wp,el is the sum of the power generations P w,el,i of the WECSs, P loss gives the electric power losses occurring in the grid-forming converter, Po is the output power injected into the grid by the grid-forming converter, and S w,b,i is the base apparent power of the ith WECS expressed in unit VA and being equal to the rated apparent power of the ith WECS. The power Po is to be supplied by the grid-forming converter with the purpose of meeting an active power request P ref o and is to allow for participation in load-frequency control. The latter includes the possibility of offering an inertial response to support the balance of power supply and demand even in the wake of fast disturbances. While an ideal dc voltage source at the location of the dc bus could deliver any amount of power at any time, there is no such ideal voltage source available in the real world. Various types of storage could be connected to the dc bus to at least approximate the behavior of an ideal dc voltage source. In this overall configuration of Fig. 12, the capacitor is assumed to be present as the only form of storage at the dc bus. To approximate the behavior of an ideal dc voltage source at the dc bus nonetheless, two objectives are to be met. First, the dc voltage is to be controlled. Second, electric power is to be made available at a quasi-instantaneous response rate as requested. It is obvious that practical limits are to be respected when striving to meet such objectives.

1) WECS Control Scheme:
The WECS control is to consider the finite availability of wind power while aiming at keeping the balance with the power flow through the gridforming converter. This calls for adjusting the power reference signal P ref w,el,i through the power reference processor depicted in Fig. 13 accordingly. As shown, the power reference processor takes in signal Po. By appropriate setting of the gain kP,x,i, the desired fraction of Po to be allocated to the ith WECS is defined. Inputs and outputs of the blocks kP,x,i are subject to different base values of the per unit system. Thus, kP,x,i = 1 would imply that per unit inputs and outputs of this block are unchanged. Furthermore,  In the output path of the power reference processor of Fig. 13, there is a limiter block. The limiter ensures that P ref w,el,i is positive and does not exceed the power of the maximum power point PMPP,i of the WECS or its rated apparent power. The calculation of PMPP,i relates to the wind speed Vw,i, given in meters per second and is shown in Appendix D. The control will support the WECS to operate in deloaded operation, as long as the power requested for injection into the grid by the grid-forming converter control remains inferior to the maximum available power of the ith WECS.
As shown in Fig. 12, the output P ref w,el,i of the power reference processor as well as Po are forwarded to the WECS torque reference processor. In Fig. 14, it is shown how the torque reference T ref el,i is obtained. The upper part concerns the outer electric power control loop and involves an integrator and a lead-lag block for the generation of T ref el,P,i . The integrator together with the leadlag compensator represents the power controller proposed in [58], which can be described by the following transfer function: The lower part of Fig. 14  As shown in [58], for example, the inner current control loop has a time constant of the order of just a few milliseconds. Since a step in the electric torque leads to an instantaneous change of the stator current, an instantaneous change of the electric power P w,el,i of the WECS is also observed. This way an inertial response capability is realized to counter the change of the energy stored in the dc bus capacitor. The degree to which such an inertial response is desired can be adjusted through the gain kP,y,i. For the setting, it is to be considered that different base values of the per unit system do apply to the input and output of this proportional element. where P max w,el,i is forwarded from the power reference processor, N is the number of WECSs in a GFR, and P loss gives the estimated electric power losses occurring in the grid-forming converter. The active power control of the grid-forming converter should not exclusively rely on the limitation of the power reference to prevent Po from exceeding the maximum available power that could be supplied by the WECSs. Inaccurate estimation of P max o or the power ΔP requested by the frequency droop control may cause Po to exceed the WECS power available. For example, if P set o equals P max o and if the output of the frequency droop control ΔP is larger than zero, ΔP would naturally be drawn from the energy stored in the dc bus capacitor. This could lead to excessive depletion of the energy stored in the dc bus capacitor.
The issue of excessive depletion of the energy stored may be tackled by using additional energy storage systems connected in parallel to the dc bus capacitor. The installation of additional energy storage systems is sensible from the engineering standpoint [23], [27], but it also comes at an additional cost. The added value should be studied for the particular installation case considered. As an alternative, [21] suggests the modification of the grid-forming control scheme by adaptively restricting the amount of power Po injected into the grid to prevent too high a drop in the dc bus voltage. Such an adaptive restriction of the power injected into the grid was realized by a supplementary dc voltage droop control that adjusts the output angular frequency of the gridforming converter based on a deviation in the dc bus voltage.
Here, a supplementary dc voltage droop control is proposed and integrated into the active power control block of Fig. 7 of the grid-forming control scheme. A comparison of Fig. 15 and Fig. 7 shows that IP-controller and frequency droop characteristics are retained, while the dc voltage droop function is added. With the support of this dc voltage droop control, the power Po is modified by adding an offset Δω dc for obtaining the output angular frequency ωo of the grid-forming converter. The offset is only enabled if the dc voltage drops below its reference value v ref dc as described by The higher the droop coefficient Dv is set, the higher is the reduction of power injected into the grid in case of a drop in the dc bus voltage. The resulting drop in the dc bus voltage causes the offset Δω dc , according to (29). In steady state, the combined impact of the frequency droop control and the dc voltage droop control on the output angular frequency of the gridforming converter becomes in accordance with Fig. 15 for

C. Coordination of WECS and Grid-Forming Control Schemes
The proposed coordinated WECS and grid-forming control schemes facilitate the integration of grid-forming converters with WECSs as GFRs into the power system. For the purpose of enabling the GFR to rapidly and securely respond to scheduled and unscheduled changes in the active power exchange with the grid, while considering the maximum available power of the WECSs, dedicated control and communication signals are deemed necessary. Those communication signals are highlighted in Fig. 12 in blue and comprise the dc bus voltage v dc , the power Po injected into the grid by the grid-forming converter, and the maximum available power P max o of all WECSs in a GFR. The dc bus voltage serves as an implicit means of status communication and builds a backbone for the coordination within the overall control scheme. However, by its own, the dc bus voltage as a state variable is not subject to instantaneous changes. Therefore, a high-performance solution in terms of a quasi-instantaneous reaction is made possible by the fast communication of the signal of the power Po to all WECSs in the GFR. As shown in Fig. 13, the signal Po serves as a supplement to the regulation of the square of the dc voltage, where the latter preserves the security of the GFRs in case of internal communication failures. As futher depicted in a Fig. 14, a high-frequency component of Po is also applied as a feedforward signal to modify the torque reference, which also implicates an immediate change of the current reference of the WECS generator. An inertial response making use of kinetic energy in the rotor is so enabled for the GFR thanks to the coordination of WECS power and grid-forming control schemes. With the quasi-instantaneous access to electric power, an important hallmark of an ideal voltage source is approximated on the dc-side terminal of the grid-forming converter.
In order to ensure that the setpoint P ref o for the power to be injected into the grid does not exceed the maximum available power generated by the WECSs, the signal P max o is made available to the grid-forming converter control. But even in the case of an inaccurate estimate of P max o , the dc voltage droop control exploits the dc bus voltage signal to keep the power balance at the dc bus.

V. 1 0 0 % R E N E W A B L E P O W E R S Y S T E M S T H R O U G H G R I D -F O R M I N G C O N V E R T E R C O N T R O L
Within the European research and development project MIGRATE [20], the electric power transmission system of the Republic of Ireland and Northern Ireland served as an important role model in showcasing the integration of power-electronic-interfaced resources. The following two hallmarks characterize the overall model. First, interconnections to other parts of Europe have exclusively been realized through high voltage direct current (HVDC) links. Thus, the Irish power system is a well-defined ac power system on its own. The proposed operating scenario considers a situation of high load in winter at nighttime where wind parks by far dominate power generation and where only grid-forming resources participate in offering the load-frequency control including the inertial response capability. The challenges that come along with converterinterfaced generation and the applicability of the gridforming resource can so be put into evidence. Second, the overall power system model offers a real-world context. Together, those two hallmarks support the transferability of the results to other systems of Europe and beyond where large-scale penetration of converter-interfaced renewable power generation is of interest.
A geographic interpretation of the electric power transmission system is shown in Fig. 16. For the future scenario of a 100 % renewable power system that is entirely realized with converter-interfaced resources, a total of 2204 wind turbine models have been considered. All have been modeled individually and grouped into 49 wind parks. Ten of those are grid-forming resources as discussed in Section IV and are marked in Fig. 16. The entire system was implemented in the DIgSILENT PowerFactory program. Dynamic phasor calculus was performed as dynamic phasors have been shown to be well suited for accurate simulation of the transients of power systems dominated by converterinterfaced generation [60].

A. Power System
The implemented model of the grid is adopted from [59] as it meets the specifications of a future energy scenario. The transmission grid model contains 6840 nodes at voltage levels of 400 kV, 220 kV, and 110 kV. For the sake of clarity, the 110-kV voltage level is not entirely represented in Fig. 16.
The element models comprise loads, power-electronicinterfaced generation units, and HVDC interconnectors, as well as synchronous generators. The loads, the converterinterfaced generation units, and the synchronous generators are connected at lower voltage levels of 10.5 kV and 20 kV and are linked to the transmission grid via transformers. More information on the element models is given in Appendix E.
The simulation comprises 1786 wind turbine models for the case of 60 % converter-interfaced generation and 2204 wind turbine models for the case of 100 % converterinterfaced generation. All wind turbine models are represented by a nonlinear type-4 model of [58] and are driven by individual wind speed profiles. The wind turbine models are grouped into 49 wind parks in the 100-% case and 39 wind parks in the 60-% case. The wind parks are of different sizes. The ten extra wind farms in the 100-% case are interfaced to the grid by grid-forming converters, leading to GFRs, as described in Section IV.
The coupling of each of the remaining 39 wind park models in both study cases is realized with grid-following control schemes. The control loops of these schemes are represented in the dq reference frame and include the inner current control loop and the PLL scheme [4]. In a higher control layer, the reference of reactive power to be delivered is adjusted to enable the grid-following wind parks to participate in the control of the ac voltage amplitude at the PCC [4]. The active power reference of the grid-following converters is obtained by adding up the output power values of all wind turbine units, which are operated at maximum power point in a wind park. The maximum power point operation of a wind turbine is obtained by replacing the power reference processor of Section IV-B1 with the one of [58].

B. Operating Scenario
The operating points of the Irish grid model are listed in Table 1. The operating scenario represents a winter peak situation at night with an aggregated active power demand of 5.9 GW.
In the 100-% case, on average 85 % of the power generated is supplied by wind parks, of which 10 % are operated as GFRs. This fraction was considered in accordance with the MIGRATE project, where 10 % of power injected by grid-connected synchronous generators turned out to be  Fig. 17. Frequency responses. (a) GFRs at Hsys 2.9 s in 100-% case. (b) Synchronous machines in 60-% case. a minimum requirement for stable operation of the implemented grid models with GFRs absent. The remaining 15 % is supplied by power-electronic-interfaced wave and tidal power plants and batteries, as mentioned in Appendix E. In the 60-% case, the power-electronic-interfaced generation comprises contributions by wind parks at a level of 54 %. Those values are averages that are subject to variation along with changes in weather conditions.
The parameters of the WECS are summarized in Appendix E. As described in [60], the system inertia can be calculated from where M is the number of power generation units connected to the system, Hj and Sr,j are, respectively, the inertia constant and the rated apparent power of the jth generation unit in the power system, where generation interfaced by grid-following converters is assumed to not contribute to system inertia. In the case of GFRs, the virtual inertia constants Hj of their grid-forming controls are considered for calculating the system inertia.
The system inertia from synchronous generators in the present-day scenario with 60 % converter-interfaced generation was defined as 2.9 s in accordance with findings in [20]. By appropriate setting of the virtual inertia constants in the GFRs, the same value of 2.9 s for Hsys was emulated in the 100-% case according to (31).

C. Simulation Results
The secure operation of the power system of the future is set to rely on the capability of the grid-connected resources to maintain the power balance in the system during normal operation and during disturbances. This includes the ability of a GFR to deliver the power requested as offered by the appropriate setting of the emulated inertia and frequency droop characteristic at diverse time scales, while ensuring that each GFR contributes to the power demanded as long as the availability of input power is given. As such, the simulation of a realistic contingency is to be studied. Therefore, a loss of 185 MW of power generation is considered by disconnecting a grid-following wind park. This contingency corresponds to a loss of 3 % of power generation. Fig. 17(a) and (b) show the frequencies of the GFRs and the synchronous machines for the 100-% case and the 60-% case, respectively, over a four-minute interval. Both figures highlight that the change in frequencies caused by the contingencies can be limited effectively such that the changes remain within a predefined frequency operation limit of ±0.2 Hz [61].
The frequency responses in Fig. 17(a) and (b) in the time frame immediately after the disturbance are primarily determined by the inertial responses of the GFRs and of the synchronous machines, respectively. The further courses of the frequencies are impacted by the active power controls with emulated inertias and frequency droop characteristics.
In order to facilitate an in-depth investigation of the changes in the frequencies immediately following the contingency, the rates of change of frequencies (RoCoFs) are illustrated in Fig. 18. For the purpose of further analyzing the impact of different emulated system inertias on the frequency response of the GFRs, the 100-% case was simulated at different system inertia constants. To account for the relevance of the RoCoF in future converterdominated power systems, here, a sliding window of 10 ms was chosen, which is considerably narrower than the sliding windows of several hundred milliseconds indicated in the current RoCoF standards [62], [63]. Fig. 18 includes simulation results with the predefined system inertia of Hsys = 2.9 s as well as system inertia with a lower value of 1.5 s. During the time interval immediately following the contingency, the power demanded for the inertial response is implicitly and initially withdrawn from the energy stored in the dc capacitors of the GFRs of the wind parks. Thanks to the quasi-instantaneous inertial response by direct modification of the WECS torque reference through the feedforward signal Po representing the output power as explained in Fig. 14, rapid energy depletion of the dc capacitor is avoided. There are of course practical limits to the inertial response that makes use of the kinetic energy stored in the rotors. The setting of the inertial characteristic must, therefore, honor the limited amount of energy that is stored and readily accessible. While a hypothetical reduction of the system inertia constant from

Fig. 19. Active power feed-ins of GFRs at Hsys 2.9 s.
2.9 s to 1.5 s at the same amount of energy available in the dc capacitor leads to considerable deterioration of the RoCoF, a hypothetical increase would need to be matched by the energy rapidly accessible in the GFRs. Beyond the contingency, the frequencies in Fig. 17 settle around the same operating point in both study cases, as a result of their identical composite frequency response characteristics.
The active power outputs for each of the ten GFR wind parks in the 100-% case are shown in Fig. 19. The power responses following the disturbance are similar for all GFRs except for the two at the bottom of the figure, refering to the two Cathaleen's Fall wind parks in Fig. 16. The similar responses are associated with the same settings for the emulated inertias and the frequency droop coefficients of all GFRs. For the two Cathaleen's Fall wind parks, drops in the dc bus voltages are observed in Fig. 20. These drops are associated with a lack of power reserve as the grid-forming controls initially request more than the power available. The lack of power reserve is affiliated with the assumption of a presently lower wind speed at the north-western coast of Ireland, where the two GFRs in Cathaleen's Fall are located. Thanks to the dc voltage droop control of Fig. 15, a further drop of the dc bus voltages was prevented through decreases in the output frequency signals. Thus, the developed control succeeded in bridging the lack of power of the two GFRs in Cathaleen's Fall via the remaining GFRs that have sufficient power reserves.

Fig. 21. Average rotor angular speeds and their optimal setpoints
for all WECSs of GFRs at Hsys 2.9 s. Fig. 21 illustrates the average mechanical rotor angular speed Ωw,avg as well as the optimal average mechanical rotor angular speed Ωw,avg,opt of the 418 wind turbines interfaced through grid-forming converters. The course of the optimal average mechanical rotor angular speed Ωw,avg,opt is directly related to the average wind speed seen by those 418 wind turbines. The course of the average mechanical rotor angular speed Ωw,avg, however, is not only dependent on the average wind speed but also on the operating points of the 418 wind turbines. The operation of the wind turbines at suboptimal points leads to a higher average angular speed.
With the contingency occurring at 1 min, the average angular speed of the turbines decreases toward their average optimal value, as the wind turbines support the frequency by shifting their operation toward the optimal operating point, i.e., the maximum power point.

VI. C O N C L U S I O N
With the ambition of the European Union to become climate neutral, technology solutions on how to integrate renewable energy sources into the electric power grid at a large scale are in high demand. Moreover, further attention is to be paid to reach a successful systemic integration of those technologies to maintain high levels of system security. This is also where the scope of the discussions in this article comes in. In this context, three contributions offer insight.
First, the grid-forming converter and its control and protection schemes were analyzed and further developed for implementation in a European power system. On the one hand, these comprise load-frequency control including the inertial response capability and reactive power control for voltage support. While those control functions consider small-signal variations, two further control functions were proposed for large-signal variations in case of faults to enhance transient stability: a virtual impedance control serves to protect against overcurrent, and an adaptive inertia control scheme supports continued connection of the converter to the grid. Second, the grid-forming converter controls were combined with the controls of a wind energy conversion system to create a wind park as a gridforming resource. The scheme involves an inertial response capability by feedforwarding measurements from the grid side to readily modify the torque reference of the WECS control.
Third, based on findings of the European Union s MIGRATE project, a model of the Irish power system was developed and presented here. Today, wind power in Ireland is allowed to reach a share on total generation of 60 %. The presented model goes further and allows for a renewable converter-interfaced generation of 100 %. This model covers 6840 nodes at the highvoltage transmission level and 2204 wind turbines, all of which were represented individually. The simulation results confirm that the transient performance obtained at 100 % converter-interfaced generation including the proposed grid-forming wind park resources benefits from the fast controls developed. A comparison case with a 60-% share of converter-interfaced generation confirms the competitive performance.
In sum, the analysis and the modeling of the power system of Ireland as a role model of Europe have put into evidence that the technology to deal with load-frequency transients in power systems with 100 % converter-interfaced generation is largely available. It should be kept in mind that the situations encountered in different countries and regions typically differ. Security requirements should always be considered on a case-bycase basis in research and development. Fundamental insight, however, is transferrable in general. As such, the presented controls and protections centered on the concept of the grid-forming resource appear suitable and practical for the consideration of solutions for the large-scale integration of renewable energy in general.

A P P E N D I X A. Per Unit System for Grid-Forming Converter and WECS
Both ac-side base apparent power S ac,b and dc-side base power P dc,b of the grid-forming converter adopt the values of their rated three-phase apparent power Sc,r: Within a wind park of N wind turbines, the base apparent power S w,b,i of the ith WECS is set equal to its rated apparent power Sw,r,i, with the sum of the N rated apparent power and base values being equal to S ac,b = P dc,b = Sc,r: The base peak ac voltagev ac,b of the grid-forming converter is selected as the amplitude of the line-to-neutral nominal voltage at the converter output terminal. Only for representing rms quantities, further bases are applied. In this context, the base rms ac voltage V ac,b is given by the corresponding rms line-to-neutral nominal voltage Vo,n. The base dc voltage V dc,b of the grid-forming converter and of the ith WECS are defined to be twicev ac,b : The base peak and rms ac currentsî ac,b and I ac,b as well as the base dc current I dc,b are obtained by rearranging the following relations: The base impedance is The ac-side base angular frequency ω b is set equal to the nominal angular frequency of the ac power system: Other base values follow from the above equations (32)- (42). For example, the ac-side base capacitance is Further details may be found in [4].

B. Dynamic Relation of Power Flow and Angle Deviation
In accordance with the convention in Fig. 1 of Section II-A, the active power equation (1) can be linearized about a steady-state operating point marked by subscript 0 to obtain the following small-signal deviation: The objective here is to express all small-signal quantities in terms of a small-signal change of the angle affiliated with the output voltage and then to obtain a transfer function for small-signal changes of the active output power.
In the dq reference frame [4], the dynamics on the ac side of the grid-forming converter can be expressed by Lt+e with where ω b is the base angular frequency in rad per second, and ωe is the angular frequency of the grid equivalent voltage source. Given the made assumption of small deviations of the angular frequency, the latter can be approximated by a constant value. By selecting the angle of the d-axis equal to the angle of phase a of the three-phase equivalent voltage source v e,abc , the following applies: where, according to (4), δ represents the angle by which vo,a leads ve,a. To distinguish the chosen dq reference frame used from the grid-forming control scheme introduced in Fig. 1, the superscript ω b is added here to denote the constant rotating angular frequency of the dq reference frame. Thus, ωe = 1 pu for the purpose of deriving the transfer function. Amplitudesvo andve are also considered to be constant here. Together, those considerations allow for the focus on the small-signal changes Δδ. Then, (44) and (45) can be rewritten as Lt+e o,q are subject to small-signal deviations around their steady-state operating points, then they can be described by Sine and cosine functions are linearized as follows: sin(δ0 + Δδ) ≈ sin δ 0 + cos δ 0 Δδ (59) From (50), (51), (54)- (56), (59), and (60), it follows that Insertion of (54) and (57)- (62) into (52) and (53), while considering only the small-signal parts: By applying the Laplace transform to (65) and (66) Δδ.
The transfer function G δ (s) contains poles that point to poor damping due to the low resistance of the transformer and the transmission line. The complex conjugate poles s δ,1,2 which reveal a poor damping are given by Damping can be enhanced by applying a virtual impedance for damping oscillations as a function of the grid-forming control scheme. By applying the virtual damping oscillation resistance R do , (44) and (45) can be modified as Lt+e Following the steps described from (53) to (74) considering (76) and (77), the complex conjugate poles can be reformulated as In order to eliminate the effect of R do in a steady state, a high-pass filter is integrated into the virtual impedance for damping oscillations. For this purpose, the virtual impedance is then realized as follows: where Δv ref o,d and Δv ref o,q are the output signals of the virtual impedance control, and τ do is the time constant of the high-pass filter. By appropriate setting of R do , oscillations become well damped. Thus, a static representation of (71) may be employed. Further considering the assumptions of Section II-A that resistances are here neglected in power flow calculus and that angle differences are sufficiently small so that cos δ 0 ≈ 1, then it follows from (71): with Xt + Xe = ωe(Lt + Le).
Expressed in terms of the base rms ac voltage V ac,b instead of the base peak ac voltagev ac,b , (81) is alternatively expressed as

C. Transient Angle Difference Between Converter Output Terminal and PCC
The relationship between the output terminal voltage phase angle θo and ϑo as its phase angle with respect to the time origin is given by Likewise, the relationship between the phase angle θg of the grid voltage at the PCC and ϑg as its phase angle with respect to the time origin is obtained by Considering an additional virtual reactance X cl , the power flow from the grid-forming converter terminal to the PCC in Section III-B1 can be described based on the nonlinear power-angle relationship [54] Po = VoVg X cl + Xt sin θo − θg .
By inserting (84) and (85) into (86), an expression of the power flow with respect to the phase angles ϑo and ϑg as well as the angular frequencies ωo and ωg is given by as the transient difference between θo and θg.

D. Calculation of Maximum Power Point of WECS
At the maximum power point, the WECS power PMPP in per unit can be calculated with the help of the wind speed measurement Vw, given in meters per second, by PMPP = 1 2 where ρ is the air density expressed in unit kg/m 3 ; r is the rotor blade length with the unit meter; CP is the power coefficient, which has its maximum at λopt; λopt is the optimal tip speed ratio, and Sw,r is the rated apparent power of the WECS in VA.

E. Grid Element Models
Loads are modeled as 14 % power-electronic-interfaced load elements and 86 % conventional load elements. The latter elements are assumed as a combination of 50 % static load elements represented by constant impedance and 50 % dynamic load elements represented by nonlinear impedance models [59]. The converter-interfaced generation units comprise wind parks, wave and tidal power plants, and battery storage units. All units except the wind parks are modeled as constant power sources using static generators [59].
Two HVDC interconnectors are modeled using a VSCbased back-to-back HVDC average model. The two HVDC interconnectors have a combined power transmission capacity of 1200 MW and represent the East-West HVDC interconnector between Ireland and Great Britain and a foreseen HVDC interconnector linking Ireland to France [64].
The power-electronic-interfaced loads, wave and tidal power plants, and battery storage units utilize gridfollowing control schemes. The same applies to the HVDC interconnectors.
The synchronous generator model is based on the sixthorder model. The synchronous generator is equipped with  [65]. Furthermore, synchronous generators with steam turbines include speed governors of type IEEEG2, while those with hydraulic turbines employ HYGOV speed governors. Table 2 lists the parameters of the WECS models developed in [58]. The rated three-phase apparent power of the GFR is calculated by summing up the rated apparent power values of the individual WECSs. The equivalent capacitance C e,dc can be obtained by summing up the dclink capacitances of each WECS in a GFR and converting it to a per unit value. She is a power systems technical expert with over 25 years of experience in the industry. She has been with EirGrid (transmission system operator), Dublin, Ireland, since 2007, working in different roles in planning, innovation, and future operations. Her main areas of expertise include integration of renewable energy technologies, power system modeling and analysis, system stability, power quality, electromagnetic transients analysis, protection coordination, and design of earthing electrodes. Her current areas of responsibility involve the development and integration of innovative control centers' decision support tools to enable the operation of the Irish power system with increasing levels of renewable generation. Her other areas of interest include the integration of grid-forming controls and green hydrogen.
Xavier Guillaud received the Ph.D. degree from the University of Lille, Lille, France, in 1992.
He joined the Laboratory of Electrical Engineering and Power Electronic (L2EP), Lille, in 1993. He has been a Professor with the École Centrale, Lille, since 2002. First, he worked on modeling and control of power electronic systems. Then, he studied the integration of distributed generation and especially renewable energy in the power system. Nowadays, he is more focused on the integration of high-voltage power electronic converters in the transmission system. He is leading the development of an experimental facility composed of actual power electronic converters interacting with virtual real-time simulated grids. He is involved in several projects about power electronics on the grid within European projects and a large number of projects with French electrical utilities.