Dynamic Ancillary Services: From Grid Codes to Transfer Function-Based Converter Control

—Conventional grid-code specifications for dynamic ancillary services provision such as fast frequency and voltage regulation are typically defined by means of piece-wise linear step-response capability curves in the time domain. However, although the specification of such time-domain curves is straightforward, their practical implementation in a converter-based generation system is not immediate, and no customary methods have been developed yet. In this paper, we thus propose a systematic approach for the practical implementation of piece-wise linear time-domain curves to provide dynamic ancillary services by converter-based generation systems, while ensuring grid-code and device-level requirements to be reliably satisfied. Namely, we translate the piece-wise linear time-domain curves for active and reactive power provision in response to a frequency and voltage step change into a desired rational parametric transfer function in the frequency domain, which defines a dynamic response behavior to be realized by the converter. The obtained transfer function can be easily implemented e.g. via a proportional-integral (PI)-based matching control in the power loop of standard converter control architectures. We demonstrate the performance of our method in numerical grid-code compliance tests, and reveal its superiority over classical droop and virtual inertia schemes which may not satisfy the grid codes due to their structural limitations.


I. INTRODUCTION
Today's grid-code specifications for dynamic ancillary services provision such as fast frequency and voltage control are typically defined by means of a prescribed time-domain stepresponse characteristic [1]- [3].As an example, the European network code [1], which is adopted in most European national grid codes, specifies the active power provision for frequency containment reserve (FCR) in response to a frequency step change by a piece-wise linear time-domain capability curve, where the required active power response should be satisfied at or above the curve.Likewise, the dynamic response of reactive power for voltage control is defined via time specifications in response to a voltage step change.Recently, also modern grid codes (e.g., Finland [2], Ireland [3]) define the activation of fast frequency reserves (FFR) or synthetic inertia via piece-wise linear active power capability curves in the time domain.
Although the specification of the piece-wise linear timedomain curves in today's grid codes is straightforward, their practical implementation in a converter-based generation system is not immediate, and there is a lack of systematic approaches.In particular, the classical droop and virtual inertia control may This work was supported by the European Union's Horizon 2020 and 2023 research and innovation programs (Grant Agreement Numbers 883985 and 101096197).Corresponding author's email address: verenhae@ethz.ch.not be able to achieve the required specifications due to their fixed controller structure (therefore may not pass the grid-code compliance tests), or would require a cumbersome trial-anderror tuning procedure by adding filters to approximately satisfy the requirements and the local device-level constraints.In this regard, today's industrial practice to implement the piece-wise linear time-domain grid-code curves is usually very ad-hoc, e.g., often relying on open-loop trajectory commands [4], varyinggain [5], [6], or look-up table schemes.
In this work, we propose a systematic way to provide dynamic ancillary services with converter-based generation systems, which ensures that desired grid-code and device-level requirements are reliably satisfied.In particular, we translate the piece-wise linear time-domain grid-code curves for active and reactive power provision into a desired rational transfer function matrix in the frequency domain, which defines a tractable response behavior to be realized by the converter.Since the conventional cascaded control structure of power converters is typically designed for tracking active and reactive power reference signals, it is well-suited to further include a reference model as given by the desired transfer function, and thus enables a simple matching control implementation.
Finally, the proposed method is versatile to match any piecewise linear time-domain capability curve, and thus also allows for more complex grid-code specifications in the future, e.g., to address grid-forming requirements.Beyond that, our results might even inspire a change of perspective in such a way that there will be an immediate transfer function-based formulation of future grid codes specified in the frequency domain.

II. PRELIMINARIES: GRID-CODE SPECIFICATIONS
We consider conventional grid-code specifications for dynamic frequency and voltage regulation in grid-following converters (i.e., reserve units), which are typically defined by means of a prescribed time-domain step-response characteristic [1]- [3].Different schematic examples of such grid-code specifications are depicted in Fig. 1 and presented in the following.
Example 1 -FCR Provision: The first example in Fig. 1a is extracted from the European network code [1], which is adopted in most European national grid codes, and the plotted piece-wise linear time-domain capability curve is used to specify the active power provision for frequency containment reserve (FCR) in response to a frequency step change.In particular, the FCRproviding reserve unit has to deliver a certain Dp .The time parameters t fcr i and t fcr a , in turn, allow for some flexibility of the reserve unit, as they are not fixed to a particular value, but only have to satisfy the following grid-code and device-level requirements [1], i.e., where T fcr i,max and T fcr a,max are the maximum admissible FCR initial delay and activation times, and R p max is the normalized maximal active power ramping rate of the reserve unit.
Example 2 -Voltage Control: Likewise, as illustrated in Fig. 1b, the European network code defines the dynamic activation of a certain reactive power capacity in response to a voltage step change, where the normalized reactive power capacity levels |∆q 90 | of 90% and |∆q 100 | of 100% have to be achieved in accordance with the times t vq 90 and t vq 100 , respectively.The normalized reactive power capacity levels are conventionally given by the allocated reactive power droop gain D q during a unit voltage step change ∆v = 1 p.u. as |∆q n 100 | := where T vq 90,max and T vq 100,max are the maximum admissible 90% and 100% activation times for the reactive power capacity provision, respectively, and R q max is the normalized maximum reactive power ramping rate of the reserve unit.
Example 3 -FFR Provision: To ensure frequency regulation on faster time scales to counteract the effect of reduced inertial response in future power systems, modern grid codes (e.g., Finland [2], Ireland [3]) recently also specify the activation of fast frequency reserves (FFR) or synthetic inertia via piecewise linear active power capability curves in the time domain.An example of such a normalized active power capability curve for FFR provision after a unit step change in frequency is shown in Fig. 1c.More specifically, the FFR-providing reserve unit has to deliver a certain normalized active power FFR capacity |∆p n ffr | after an activation time t ffr a , which has to remain activated for a particular support duration t ffr d − t ffr a .The reserve unit can return to recovery at time t ffr r after the support duration has elapsed.The FFR capacity |∆p n ffr | is usually specified during prequalification tests of the reserve unit [2], where a unit step change in frequency 1 To introduce the formalism of the grid-code specifications and translate them into rational parametric transfer functions in Sections II and III, we consider normalized active and reactive power capability curves in response to (practically unrealistic) unit step changes in frequency and voltage, i.e., |∆f | = 1 p.u. and |∆v| = 1 p.u., respectively.In a practical implementation setup, however, the capability curves are scaled with a non-unity frequency and voltage step input in order to obtain reasonable power capacities which are realizable by a converter-based generation system (cf.Sections IV and V).| are subject to constraints from grid-code and device-level requirements as [2], [3] where T ffr a,max is the maximum admissible full activation time for the FFR provision.The FFR support duration t ffr d − t ffr a is lower and upper bounded by the minimum and maximum support duration T ffr d,min and T ffr d,max , respectively.Likewise, the minimum and maximum return-to-recovery times are given by T ffr r,min and T ffr r,max , respectively.The FFR overdelivery |∆p peak,n ffr | must not exceed the reserve unit's normalized maximum active power peak capacity M p max , as well as the maximum tolerable overdelivery x ffr peak • |∆p n ffr |, where x ffr peak is specified in the grid code.Finally, R p max is again the reserve unit's normalized maximum active power ramping rate.
Example 4 -Superimposed FFR-FCR Provision: Although the FCR and FFR time-domain capability curves are typically specified separately as in Figures 1a and 1c, a single reserve unit can also provide both frequency regulation services simultaneously.However, depending on the future market situation, one might only be able to participate with the same amount of active power at one reserve market at a time (see, e.g., [2]), i.e., the power sold to the FFR market cannot be sold to the FCR market.In respect thereof, a simple and pragmatic solution is to superimpose the FFR and FCR time-domain capability curves, where the time and capacity parameters can be maintained.A graphical illustration is exemplarily given in Fig. 1d, where the FFR capacity |∆p n ffr | is larger than the FCR capacity |∆p n fcr |.However, also equivalent or reversed capacity sizes can be superimposed.For the superimposed FFR-FCR time-domain curve in Fig. 1d, we extend the device-level requirements in (1) and ( 3) accordingly as In addition to the requirements in ( 1) to ( 4), we assume that the services-providing reserve unit is able to supply the normalized FCR, FFR, and reactive power capacities |∆p n fcr |, |∆p n ffr |, and |∆q n 100 | when scaled with a non-unity frequency and voltage deviation ∆f and ∆v up to a certain threshold, while at the same time being able to satisfy the minimum grid-code requirements.Typical parameter values for the grid-code specifications are provided in Table I.Beyond that, notice that the active and reactive power time-domain capability curves in Fig. 1 represent simplified schematic examples of grid-code capability curves, which in practice are often more complex and sophisticated, while deviating for different grid codes and system operators.Furthermore, depending on the grid code, the capability curves can be superimposed or combined in various ways.

III. FROM GRID-CODE SPECIFICATIONS TO RATIONAL
TRANSFER FUNCTIONS Although the specification of the previous piece-wise linear time-domain curves in the grid-code examples is straightforward, their practical implementation in a converter-based generation system is not immediate, and no systematic methods have been developed yet.In particular, as we will demonstrate later in our numerical experiments in Section V, the well-known droop and virtual inertia control may not be able to achieve the required grid-code specifications due to their fixed controller structure (therefore may not pass the grid-code compliance tests), or would require a cumbersome trial-and-error tuning by adding filters to approximately satisfy the grid-code and devicelevel requirements.In this regard, today's industrial practice how to implement the required piece-wise linear time-domain gridcode curves is usually very ad-hoc and highly customized, e.g., relying on open-loop trajectory commands [4], varying-gain [5], [6], or look-up table schemes.
In this work, we thus propose a more systematic and versatile approach for the practical implementation of piece-wise linear time-domain curves to provide dynamic ancillary services by converter-based generation systems, while ensuring grid-code and device-level requirements to be reliably satisfied.More specifically, we aim to translate generic piece-wise linear timedomain curves for active and reactive power injection (∆p and ∆q, respectively) after a unit frequency and voltage step change (∆f and ∆v, respectively) into a desired rational 2 × 2 transfer function matrix T des (s, α) in the frequency domain, i.e., which specifies a decoupled grid-following frequency and voltage control behavior of a reserve unit via T fp des (s, α) and T vq des (s, α), respectively.These two transfer functions are parametric in the vector α that contains the time-domain curve related parameters to be selected by the reserve unit, while ensuring that the grid-code and device-level requirements are satisfied.More specifically, when translating the previous gridcode example for the superimposed FFR-FCR provision in Fig. 1d into T fp des (s, α) = T fp des,fcr (s, α) + T fp des,ffr (s, α), as well as the example for the voltage control in Fig. 1b into T vq des (s, α), the parameter vector α would be assembled as and has to satisfy the grid-code and device-level requirements in (1) to (4).In the following, we present in detail how to obtain the parametric frequency-domain transfer functions T fp des (s, α) and T vq des (s, α) from any piece-wise linear time-domain grid-code curves.Afterwards, in Section IV, we show how these transfer functions can be easily implemented in standard converter control architectures.
Remark 1.In this work, we consider the active and reactive power time-domain capability curves in response to a general frequency and voltage step change ∆f and ∆v.However, in practice, grid codes often consider different piece-wise linear time-domain response patterns for different operating ranges of ∆f and ∆v.Also deadband or saturation thresholds for a particular range of ∆f and ∆v are usually defined [1].Although we omit these features in this paper, they can be easily realized in the reserve unit's converter control setup.

A. Translating Piece-wise Linear Time-Domain Grid-Code Curves into Rational Parametric Transfer Functions
In this section, we present a general procedure on how to translate a piece-wise linear step-response capability curve which is specified in the time domain into a rational parametric transfer function in the frequency domain.Our approach is based on the assumption that the time-domain curve reflects a stable step-response behavior y(t) under a unit step input u(t) = u step = 1.Moreover, each curve kink is assumed to be characterized by a time-capacity parameter pair (t i , y i ), i ∈ N, where the normalized capacity y i = K i u step = K i is scaled by the unit step input via some gain K i ∈ R (cf. the droop gains introduced in Section II).For ease of translation, we consider a unit-step response (u step = 1).A general representation of a normalized piece-wise linear time-domain response curve with a similar shape as the one in Fig. 1d is illustrated in Fig. 2a.
The procedure to obtain a rational transfer function representation of such a piece-wise linear time-domain response curve, consists of four steps: In a first step, we decompose the overall piece-wise linear time-domain response curve y(t) in Fig. 2a into linear curve segments y ij (t), i, j ∈ N as indicated in Fig. 2b.Each unit step response curve segment y ij (t) is characterized by two time-capacity parameter pairs (t i , y i ) and (t j , y j ), where j > i and thus t j > t i , such that the curve segment can be described in the time domain as where we define d = yj −yi tj −ti as the slope of the curve segment.Obviously, depending on the capacities y i and y j , the curve segment is either increasing for y j > y i (i.e., d > 0), decreasing for y j < y i (i.e., d < 0), or flat for y j = y i (i.e., d = 0).
Next, in a second step, we apply the Laplace transformation to each time-domain curve segment y ij (t) in ( 7) and obtain the unit step response of a curve segment in the s-domain as where we have used the time-shift property of the Laplace transformation [7].The actual transfer function or impulse response of the curve segment can be computed by multiplying the unit step response in (8) by s as T uy ij (s) = sY ij (s), i.e., which corresponds to a non-rational transfer function.From a practical point of view, however, such a non-rational transfer function is not easily interpretable and implementable, e.g., when using standard discretization and micro-controller interfaces.On top of that, most methods for analysis and synthesis of control systems, are developed for rational transfer functions [7] (e.g., to determine stability, assess passivity, Nyquist and Root Locus methods, robust and optimal control methods).In this regard, as a third step, we need to approximate (9) by a rational transfer function.To do so, we apply the commonly used Padé-approximation with numerator and denominator degree n ∈ N to every exponential as [8] e which approximates (9) as a rational transfer function, i.e., Alternatively, one might also resort to more general types of Padé-approximations or other rational series expansions.Finally, in a fourth step, the overall rational transfer function of the normalized piece-wise linear time-domain unit step response capability curve in Fig. 2a    in Fig. 2b, i.e., T uy des (s) = T uy ij (s).Notice that the obtained transfer function T uy des (s) is parametric in the time and capacity parameters t i and y i , respectively, which are either directly fixed by the grid-code or can be appropriately selected by the reserve unit.In accordance with the notation introduced in (5), one might therefore equivalently write T uy des (s) = T uy des (s, α) with α = [..., t i , ..., y i , ...] ⊤ , to indicate the parametric dependence.
Coming back to the grid-code examples in Section II, we translate the superimposed FFR-FCR time-domain capability curve in Fig. 1d and the reactive power time-domain capability curve in Fig. 1b into rational parametric transfer functions T fp des (s, α) = T fp des,fcr (s, α) + T fp des,ffr (s, α) and T vq des (s, α), respectively.For a feasible choice of α in ( 6) satisfying (1) to (4) with the grid-code specifications in Table I, and for a sufficiently flexible reserve unit as in Section V, the unit step response of the latter transfer functions for different orders n of the Padéapproximation is shown in Fig. 3.We can see how a higher order improves the approximation accuracy of the piece-wise linear time-domain curve.However, since a too large order typically becomes numerically intractable, and, additionally, might not be realizable in a practical power converter control architecture, we recommend to choose orders n ≤ 10.To gain some insights on the structure of T des (s, α), the transfer functions for n = 2 in Fig. 3 Finally, our approach to translate a piece-wise linear timedomain curve into a rational transfer function always results in a stable transfer function T uy des (s, α) for any order n of the Padéapproximation.Indeed, the rational transfer function T uy ij (s, α) in ( 11) of one curve segment can be rewritten as in (13), where the stability of the last term follows from the fact that the numerator has a zero at s = 0 which cancels with the pole at s = 0 in the denominator, i.e., We can thus conclude that the rational transfer function T uy ij (s, α) of one curve segment is stable, and with this the sum T uy des (s, α) = T uy ij (s, α).Next, we provide insights on how to select the time-domaincurve related parameters α.For the sake of consistency, we stick to the grid-code examples for frequency and voltage control in Figures 1d and 1b for the remainder of this paper.

B. Parameter Selection
Given the grid-code and device-level requirements in ( 1) to ( 4), it follows that the time-domain-curve related parameters α in (6) allow for a set of feasible rational transfer functions T des (s, α) in ( 5) to provide a decoupled frequency and voltage regulation.Among the various options on how to select the parameters α, we can consider two boundary scenarios: One, where the parameters α satisfy the minimum grid-code requirements, and one, where the parameters α are selected such that the maximum device-level limitations are exploited.In case of the former, we select the parameters α as where typical values for the grid-code specifications are given in Table I.On the other hand, for the latter, we specify where R p max , R q max , T ffr d,max , T ffr r,max , and M p max are device-level specifications of the ancillary services providing reserve unit.In this regard, for an exemplary reserve unit as in Section V, we obtain the unit step responses of the two boundary scenarios for the superimposed FFR-FCR provision, as well as the voltage control as in Fig. 4. The first scenario which encodes the minimum grid-code requirements, offers a cheap and robust (i.e., with smaller gain) version to provide dynamic ancillary  services.In contrast, the second scenario encodes a response behavior that reaches the limit of the reserve unit, but offers the possibility to improve the overall frequency response of the grid in closed loop.All remaining feasible choices of α are located in between these two boundary scenarios.
Ideally, the choice of α should be based on some stability and/or performance criteria when considering T des (s, α) in closed-loop with the grid.In particular, future ancillary service markets might provide some incentives on providing grid services beyond the minimum grid-code requirements, i.e., by rewarding additional effort in improving the overall grid response behavior, while taking local device-level limitations into account.This might also motivate for a parameter-varying ancillary services specification T des (s, α) which is adapted online during different grid conditions.Making these considerations more concrete is part of our ongoing research.

IV. TRANSFER FUNCTION-BASED CONTROL OF CONVERTER-INTERFACED GENERATION SYSTEMS
The desired rational transfer function matrix T des (s, α) defines a grid-following frequency and voltage control behavior in the frequency domain which can be realized in a converter-based generation system, while ensuring grid-code and device-level requirements are satisfied.The proposed grid-side converter model used for dynamic simulation represents an aggregation of multiple commercial converter modules, and is based on a state-of-the-art converter control scheme [9], into which we can easily incorporate the required transfer-function matching control (Fig. 5).While Fig. 5 shows only one exemplary converter control architecture, our method is compatible with any architecture that accepts active and reactive power references.
Similar to [10], we assume the dc current i dc to be supplied by a controllable dc current source, e.g., schematically representing the machine-side converter of a direct-drive wind power plant, a PV system, etc.In particular, we consider a generic coarsegrain model of the primary source technology and model its response time by a first-order delay with time constant τ dc [10], e.g.representing the resource associated dynamics as well as communication and/or actuation delays.Moreover, we limit the primary source input by a saturation limit, which, e.g., corresponds to current limits of a machine-side converter or an energy storage system, or PV/wind power generation limits.In case of a wind or PV generation system, we assume they are operated under deloaded conditions with respect to their maximum power point, allowing them to put an active power reserve aside for participating in frequency regulation.While we stick to such an abstract representation of the primary source, one could of course consider more detailed models tailored to the specific application at hand.
The ac-side control of the grid-side converter is used to control the network current magnitudes.It is implemented in a dq-coordinate frame oriented via a phase-locked loop (PLL), which tracks the system frequency, while keeping the converter synchronized with the grid voltage [9].
Given the cascaded controller structure of the converterinterfaced generation system, we can directly incorporate the transfer function matching control in the outer control loops of the dc and ac side of the converter via simple PI controllers to track the desired dynamic response behavior for frequency and voltage regulation specified by T fp des (s, α) and T vq des (s, α), respectively.Likewise, as indicated in light gray in Fig. 5, also classical (filtered) virtual inertia and droop specifications can be implemented in the same way.Notice that alternatively, more robust and optimal matching controllers can be obtained by replacing the cascaded PI-loops with a multivariable linear      parameter-varying (LPV) H ∞ controller (see [11], [12]), which can accomplish superior matching behavior especially in case of a parameter-varying T des (s, α) specification.

V. CASE STUDIES
To demonstrate the performance of the proposed transferfunction based converter control, we consider a common setup for practical grid-code compliance tests, where the converterinterfaced reserve unit is connected to an infinite bus (Fig. 5).The parameters of the test setup used for the EMT simulations with MATLAB/Simulink are provided in Table II.To evaluate the ability of the reserve unit in providing grid-following dynamic ancillary services for frequency and voltage regulation according to the active and reactive power time-domain capability curves specified in the grid-code, it is tested under some step change scenarios in frequency and voltage.Depending on the particular grid-code, the size of such step changes can be different.We thus consider a test frequency and voltage step change of 0.5 Hz and 0.05 p.u..However, our methods can also be generalized to other step change amplitudes.

A. Tailored Transfer-Function Based Converter Control
The test results of the two boundary scenarios presented in Section III-B are illustrated in Figures 6 and 7. We can see how the measured active and reactive power deviations ∆p and ∆q accurately match their desired behaviors as specified by T fp des (s, α) and T vq des (s, α), respectively (dotted lines).Moreover, given the deliberate choice of α, both grid-code and device-level requirements are reliably satisfied (dashed lines).

B. Conventional Virtual Inertia & Droop Control
Next, we perform the same grid-code compliance tests for a classical virtual inertia and droop control strategy with a simple first-order filter.For the converter-interfaced generation system in Fig. 5, we can resort to the same PI-based matching control   Reactive power response.Figure 9: System response of a filtered virtual inertia and droop control with filter time constant τ f = 2s during a test frequency and voltage step input.implementation as before, where, however, the desired dynamic response behavior is now described by the filtered virtual inertia and droop control (cf.light gray boxes in Fig. 5) accordingly as τ f s+1 ∆v(s), (16) where M = 4, D p = 0.06 are the virtual inertia and droop coefficients for the frequency regulation, D q = 0.06 is a droop gain for the voltage regulation, and τ f ∈ {0.1s, 2s} is the filter time constant.Notice that we use the same droop gains as encoded in T des (s, α) before (cf.Table I), since they are typically directly given by the system operator.
By considering the desired active power response behavior in Figures 8a and 9a (dotted lines), we can observe how the dynamic ancillary services provision via filtered virtual inertia and droop control is not able to satisfy the minimum grid-code requirements (dashed lines).Namely, in contrast to T fp des (s, α) which allows for more structural flexibility to accomplish the grid-code requirements (see, e.g., the transfer function structure in (12)), the demanded filtered virtual inertia and droop specifications in (16) are limited in their fixed dynamic structure and thus often fail during grid-code compliance tests.In particular, this cannot be fixed by a proper tuning of the virtual inertia, droop or filter parameters.Instead, to overcome this problem, one would therefore require more sophisticated filters, which are aiming to replicate the structure of T fp des (s, α).On the other hand, due to the particular shape of the considered reactive power time-domain capability curve, the desired reactive power response of the filtered droop control (dotted lines) does satisfy the minimum grid-code requirements (dashed lines) (Figures 8b  and 9b).However, this is not guaranteed for other types of gridcode specifications.
Finally, aside from violating grid-code requirements with the filtered virtual inertia and droop control, also device-level limitations can be hit (dc-current saturation) if the filter time constant is not chosen appropriately.This results in a mismatch of the actually obtained (solid line) and the desired power injection (dotted lines) in Fig. 8a.Hence, the virtual inertia and droop control has to be deliberately slowed down, to ensure the device-level limitations are not violated (Fig. 9a).

VI. CONCLUSION
We have presented a systematic approach on how to translate piece-wise linear time-domain grid-code curves into desired rational parametric transfer functions in the frequency domain.The latter can be easily realized in standard converter control architectures to provide dynamic ancillary services, while ensuring grid-code and device-level requirements to be satisfied.Our numerical experiments verified the effectiveness of our proposed transfer function-based converter control, and especially revealed its superiority over classical droop and virtual inertia schemes, which are limited by their fixed controller structure and thus not able to satisfy a given grid-code requirement.
Finally, our proposed method is versatile to match any given piece-wise linear time-domain response curve, and thus also allows for more complex grid-code specifications in the future, e.g., also grid-forming grid-code requirements.On top of that, it might even inspire an immediate transfer-function based formulation of future grid-code requirements. |∆p| Approximation of the normalized piece-wise linear time-domain curve for voltage control in Fig.1b.

Figure 3 :
Figure 3: Unit step response of the rational transfer functions (a) T fp des (s, α) and (b) T vq des (s, α) for different orders n of the Padé-approximation.
Approximation of the normalized piece-wise linear time-domain curve for FFR-FCR provision in Fig.1d.Approximation of the normalized piece-wise linear time-domain reactive power curve for voltage control in Fig.1b.

Figure 4 :
Figure 4: Unit step responses of (a) T fp des (s, α) and (b) T vq des (s, α) for the two boundary scenarios of the parameter choice α: satisfying minimum grid-code requirements vs. exploiting maximum device-level limitations.

Figure 5 :
Figure 5: Converter-interfaced generation system with matching control implementation to provide the desired dynamic behavior specified by T des (s, α).

Figure 6 :
System response of the T des (s, α)-based converter control during a frequency and voltage step, where α satisfies the min.grid-code requirements.
Reactive power response.

Figure 7 :
System response of the T des (s, α)-based converter control during a frequency and voltage step, where α exploits the max.device-level limitations.

Figure 8 :
System response of a filtered virtual inertia and droop control with filter time constant τ f = 0.1s during a test frequency and voltage step input.
can be established as the sum of the rational transfer functions of the linear curve segments are exemplarily given as

Table II :
Parameters for the converter-interfaced generation system.