Intentional Islanding of Active Distribution Networks by GenSets: An Analysis of Technical Constraints and Opportunities

. Te willingness to improve the security and reliability of power supply to end-users, often pushed by prescriptions of national regulatory authorities, is bringing considerable challenges for distribution system operators. Islanding a portion of the public distribution network after a fault is considered a measure to mitigate the efects of service interruptions. Tis procedure is usually carried out by counterfeeding the grid through a generator set (GenSet). Even if this approach is widely adopted around the world, reenergizing the grid and keeping the electric island stable is not a trivial task. In this framework, the scope of this paper is to provide a set of technical guidelines for the usage of GenSets to supply public grids in emergency conditions. Te goal is to highlight the static and dynamic limits of the GenSet operations and simplify their exploitation for the grid operators. Te numerical analyses, which have been carried out through the RMS simulation tool of the DigSilent PowerFactory software, also aim to evaluate the technical constraints in the case of active networks, which involve distributed generation implementing regulations according to ENTSO-E and Italian technical standards.


Introduction
In recent years, the global GenSets' (GSs) market size has constantly increased. In 2019, it was valued at USD 23.9 billion, and it is expected to progress at a compound annual growth rate of 8.1% over the next ten years [1]. Tis positive trend is supported by the growing demand for reliable and uninterrupted power supply from end-use sectors, such as construction, manufacturing, telecommunication, and power generation. In public distribution networks, GSs are adopted as an emergency power supply when a fault occurs and the main grid is unavailable. In recent years, the usage of GSs as backup generators on public distribution grids increased due to the fast spreading in the EU and worldwide of more and more challenging prescriptions for distribution system operators (DSOs) in terms of a better continuity of service, both during single fault events and in case of large accidents afecting the grid (e.g., force majeure events). Following the emergency operating practices of DSOs, this paper investigates how intentionally islanding a portion of the public distribution network supplied by a backup diesel GS could improve the continuity and quality of the electric service in a radially arranged system. In particular, the technical aspects afecting the island operation are evaluated and proper technical criteria are formulated to support the DSO in creating and managing the network supplied by the GS.
Te introduction is organized as follows: in Subsection 1.1, the main motivations of the paper are explained, while in Subsection 1.2, an overview of the relevant literature, including key theoretical frameworks and relevant studies, is provided; fnally, in Subsection 1.3, the innovations and original contributions of the study are outlined.

Motivation and Incitement.
Tis paper evaluates the static and dynamic stability of a diesel GS used to supply a medium voltage (MV) distribution grid to mitigate the efects of service interruptions and guarantee a better continuity of power supply. Te need for a better quality of service is also a consequence of the regulatory schemes applied to network operators in many countries in the EU, which reward or penalize the DSO according to the level of continuity of service provided to users, measured according to the indicators defned by the technical standard EN 50160 [2]. Tese schemes are usually applied by defning service continuity standards ("target levels") [3], which establish a maximum number and duration of interruptions that each DSO must guarantee to its customers over a year. In general, this approach has shown in the past good results in pushing continuity of service toward better quality levels [4] and promoting the adoption of more advanced protection and automation schemes, especially over MV distribution networks. However, in grids with a purely radial layout without the possibility of reverse feeding, or in case of multiple faults, the emergency supply by a GS can be considered the only solution capable of limiting the interruption duration for the involved customers.
Moreover, in some countries, additional measures have been taken to deal with exceptional events, like those caused by large weather accidents: snowfalls, waterfoods, and windstorms. In Italy, for example, the DSOs must prepare a three-year horizon plan (so-called resilience plan) and send it to ARERA, the national energy regulatory authority, for approval [5,6]. Tis plan must include a set of actions selected by the DSO to contain the risk of power outages against the main critical factors that may impact the distribution network. Te efectiveness of the interventions in improving the grid operation is assessed based on their ability to increase the network robustness or to mitigate the efects of a contingency; the latter can be addressed by increasing the readiness of restoration actions using GSs as an emergency power supply. In this context, the adoption of GSs to counterfeed a portion of the distribution network working as an intentional electric island shows signifcant benefts; because by reducing the outage period, the customers can experience a better continuity of service. In addition, also people's safety increases, especially in environments such as mountains or rural areas, where most public networks are radially arranged, and outages could last more than a day [7]. Terefore, one of the main goals of the present paper is to investigate if following the current emergency procedures put in place by the DSOs, the intentionally islanded portion of the public distribution network is dynamically stable if supplied by a mobile GS.
Furthermore, distribution networks are undergoing a phase of deep transformation due to global drivers related to environmental issues [8]. In this new energy scenario, DSOs must face a wide difusion of small-sized power plants [9], the so-called dispersed generation (DG), supported by a legislative framework strongly oriented toward incentives for renewables. In the near future, distributed energy resources (DERs) on MV and LV grids could also be used to manage contingencies and backup plans, especially if connected through grid-forming inverters [10][11][12]: by adopting a suitable control logic, they can emulate the behavior and inertia of synchronous machines, even with better performance, providing a voltage and frequency reference to the entire system. However, nowadays, a black start scheme from DG units still requires reliable power supplies and stable voltage references, which fuel-driven rotating machines (e.g., GSs) can only ofer. In this scenario, the goal of the work is to carefully evaluate the interaction between the GS and DG units within an electric island. Tis investigation is of particular interest also because, in recent years, technical connection rules for DG units in many countries have been updated to include a minimum set of active and reactive power control functions to support the grid in contingency conditions. Tis is the case in Italy of technical standards CEI 0-16 and 0-21 [13,14], which provided a set of prescriptions concerning the DG connection to the MV/ LV grid, harmonized with the relevant ENTSO-E network code [15,16].

Literature Review.
In the literature, the study of the behavior of GSs as backup power supply on distribution systems is of particular interest due to their wide use motivated by the relevant robustness and reliability; for this reason, several papers study the optimal design of GSs in diferent operating conditions. In general, the GS must be properly sized for supplying large and varying loads, such as motors; if not so, signifcant stability issues (e.g., frequency and voltage fuctuations) may occur, especially during sudden load changes (e.g., motors startup) [17]. To avoid these problems, the main research and development efort by GS manufacturers is related to the design of highperformance speed governors and voltage excitation systems [18]. Concerning frequency control, the GS regulates its mechanical torque according to the power required by the load. In [19], several confgurations of speed governors are presented, and their benefts on the stability of the islanded portion of the distribution network are highlighted. In [20], the authors investigate the frequency stability of the island with GSs that work both in isochronous and droop conditions; the proposed frequency control could ensure the stability of the electric grid after a major generation outage. Te stability of the electric island may also be threatened by other factors, for example, according to [21], in extreme load conditions, when the electrical load torque exceeds the mechanical torque limits of the prime mover, the stalling of the GS occurs and the integrity of the island is compromised.
Even if this is not the focus of this work, it is worth mentioning that a signifcant area of the research related to the islanded operation of public networks aims to study unintentional electric islands. In particular, several papers defne new protection strategies to avoid the unintentional islanding operation of portions of public distribution networks with high penetration of DG, for example, adopting governor signal clustering [22], fuzzy classifer or inference systems [23,24], deep learning techniques [25,26], rate of change of reactive power criteria [27], and Gibbs phenomenon-based hybrid methods [28]. Authors in [29,30] propose an innovative machine learning-based antiislanding method tested on a microgrid with a real-existing PV plant, which is compared to other islanding detention methods. All these studies highlight a strong interest from the scientifc community in avoiding unwanted operating conditions that could jeopardize the distribution grid's reliability and safety. However, this paper approaches the problem of how to guarantee a better continuity of service of the MV/LV network from a diferent point of view, that is, by facilitating the use of GSs to supply portions of public grids during outages and emergency conditions, manage the network as an intentional electric island.
Regarding the intentional islanding operation supported by DG units, the optimal location and sizing of a set of DG units designed to operate in a stand-alone grid in emergency conditions are studied in [31]. New approaches aiming at promoting DG units as the only power supply are also evaluated in [32][33][34], especially exploiting grid-forming inverters. However, as already introduced, black start schemes nowadays cannot rely yet on DG only, due to its typical uncontrollability and still limited difusion, at least in some areas of the territory. Indeed, in the literature, some works investigate the stability of the island when both rotating machines and inverter-based dispersed generators are powering the system. For instance, in [35], the load sharing and the consequent electromechanical transients are analyzed. Moreover, the authors provide a detailed examination of the diferences between the frequency-regulation characteristics of inverters and generators to explain the cause of the poor transient power sharing. Similarly, [36] studies the interaction between synchronous generator and inverterbased DG in a stand-alone grid: a modifed droop control technique is proposed to improve their transient behavior during active and reactive power sharing. However, this paper does not consider the reconnection process of the DG to the island and its possible efects on its stability. In [19], the power losses calculation and short-circuits' analysis have been performed on an intentional island with GSs and wind power plants. Finally, the benefts for the stability of the system of the load sharing between diferent DG units, having diferent technology and primary source, are analyzed in [37].
As far as the authors know, a complete understanding of the interactions between the GS power controls and the DG regulation logics for grid service-related purposes is not present in the literature. Moreover, at present, there is a lack of literature studying the impact of diferent grid confgurations on the repowering ability of commercially available GSs. Tis shortfall represents a signifcant knowledge gap that this paper wants to address to better understand the behavior of intentionally islanded grids. Hence, this study provides valuable insights into the impact of DG units on the islanded grid and can help to identify the optimal control strategies for ensuring system stability and reliability.

Goals, Contribution to the State of the Art, and Paper
Organization. In the outlined framework, this paper aims to further extend the knowledge on the topic, providing a set of technical guidelines for the proper usage of backup diesel GenSets on public grids in emergency conditions. Te main contributions of this paper are summarized as follows: (i) Te identifcation, modeling, and optimal tuning of all the components needed to faithfully reproduce the real behavior of an emergency GS during its operation, in particular concerning the speed governor and voltage excitation systems, which are crucial elements for ensuring the stability of the system, particularly when disconnected from the main grid (ii) Te development of realistic numeric models of inverter-based DG units that incorporate active and reactive power control logics for grid-purpose services aligned with both ENTSO-E and Italian technical standards (iii) Te evaluation of the static and dynamic operational limits of the GS on a wide set of electric island grid confgurations to highlight the backup generator's capability and limitations It is worth noticing that, in this paper, the variability of the input parameters, such as the characteristics of the GS or of the distribution grid, is addressed by adopting the technical characteristics of network components most widely used in real-existing applications and, when possible, by performing parametric analyses testing how diferent values of the same parameter change the behavior of the system. Moreover, in order to give more generality to the approach, we identifed the limit conditions under which the GenSet can safely supply a portion of the isolated distribution grid. Tis way, the results obtained can be applied across a wide range of scenarios and electrical networks, as long as the parameters fall within those considered in the study. For these reasons, despite the variation in the numerical results, the robustness of the developed technical guidelines remains valid.
In the following, an in-depth description of the models developed for the GS components (Section 2) and of DG control laws is provided (Section 3). Te case study considered to evaluate the stability limits of the electric island, and the relevant results are presented in Section 4. Ten, a case study involving an active public grid is analyzed in Section 5 to understand the limits and benefts of DG in the electric island. Finally, conclusions are provided.

Generator Set Modeling
In the present work, a model has been developed in DigSilent PowerFactory to simulate the operation of a GS by employing the information available in the literature or provided by manufacturers (e.g., datasheets). Te implemented model consists of a prime mover (i.e., a diesel motor), an alternator (i.e., a three-phase synchronous generator), a speed governor, and a voltage excitation system ( Figure 1).
Te diesel engine and alternator protections have not been implemented in the software environment, but they have been considered during the evaluation of the results in the diferent case studies.
International Transactions on Electrical Energy Systems 2.1. Te Alternator. In general, the alternators coupled with prime movers can be synchronous or asynchronous generators, or dynamos. In this work, a three-phase synchronous generator is considered, which is the most widely adopted solution for GSs used as emergency power supply. Te static limits of operation of the GS are described by the capability curve shown in Figure 2.
In particular, the capability curve is bounded by the following limits [38]: (i) Te stator limit, defned by the maximum stator current (usually, the nominal one) to avoid overheating in the stator windings. (ii) Te rotor limit, function of the maximum excitation current to avoid overheating in the rotor windings. (iii) Te turbine limit, given by the maximum mechanical torque that can be applied to the alternator shaft. (iv) Te stability limit, corresponding to the maximum load angle allowed to avoid the loss of synchronism of the generator. Even if the loss of synchronism occurs when the load angle reaches 90°, in practice, a safety margin of 10% of the nominal power is considered, reducing this limit to 65/70° [38].
Usually, to prevent generator damage, the GS is equipped with protections that detect if the capability limits are overcome, i.e., if the operating point is outside the capability curve, and consequently trip.

Te Speed Governor.
Te selected speed governor is a diesel Woodward model (Figure 3), used in most dieseldriven GSs [39]. It is a speed droop governor that can work both in isochronous and droop conditions, depending on the parameter D of the "droop" feedback block. In the intentional islanding operation, the isochronous condition (D � 0) is usually preferable because the frequency is maintained at the reference value (50 Hz). However, in some cases, a droop behavior can be preferable, especially to prevent issues in the power sharing, when more than one generator supplies the island. Terefore, in the next case studies, both control laws will be analyzed to investigate the stability of the electric island.
Te "electric control box" block takes in input the speed error and provides as an output an electric signal that oscillates with a damped motion around the value of the speed error. According to the electric signal delivered, the electromechanical "actuator" block provides the output throttle, which controls the fuel injection of the diesel engine; this signal is saturated by T max /T min to avoid over/under fueling conditions. Finally, the "combustion delay" block represents the diesel engine's response to a variation of the throttle. Te output of the model is a mechanical torque that, multiplied by the instantaneous value of the speed, provides the mechanical power P m applied to the alternator.

Te Voltage Excitation
System. Regarding the voltage excitation system, the selected one is a static IEEE model ( Figure 4). Te choice of a static model is related to the fast time response of this exciter, the reduced axial dimensions, high reliability, and efciency [40].
Te "input flter" works as a frst-order lag in which the output signal reaches the input steady-state voltage value at the generator terminals V c after a small transient, avoiding any step change. Given the voltage error between the fltered voltage input and the reference value V ref , the "regulation" block behaves as a frst-order lag with a multiplication factor at the numerator. Tus, it works as an amplifer, intensifying the input signal and damping out any abrupt change within the range V min -V max . Ten, the "excitation" block operates as a pure integrator: the input regulation voltage is converted into the excitation voltage EFD of the synchronous generator. When the maximum excitation voltage is reached, it is limited to EFD max , which represents the physical limit on the excitation voltage due to the saturation of the magnetic components. Te time constant TE is associated with the inductance of the control windings. Te "feedback control" block works as a frst-order lag diferentiator: the output voltage signal V f is the frst derivative with respect to the time of the input voltage signal EFD. Tis derivative feedback is used to improve the dynamic response of the system. Indeed, it works as a compensation feedback signal.
All the parameters that characterize the alternator, the speed governor, and the voltage excitation system are reported in the case study description (Section 4).

DG Unit Modeling
Concerning the DG, today most of the dispersed units on MV/LV networks, especially from PV/wind generation, are coupled to the grid by inverters. Hence, in this work, DG has been modeled into the DigSilent PowerFactory environment as a current-controlled static generator, normally working at a unitary power factor ( Figure 5). In this confguration, the "per unit" values of the direct (id ref ) and quadrature (iq ref ) axes current correspond, respectively, to the active and reactive power exchanges of the DG unit. Instead, the cosine (cos ref ) and sine (sin ref ) input signals generated by the phaselocked loop (PLL) provide the reference values to perform the park's transformation between the phasor and time domains.
Te additional measurements required for proper modeling of the DG unit are provided by the "voltage measurement," and the "PQ measurement" blocks. Tese blocks provide the instantaneous value of voltage u, and active and reactive power, respectively, p and q; while the frequency f is given in output to the PLL. In particular, f and     In addition, the reconnection process must be gradual, performing for the active power a soft start ramp-up with a slope that should not exceed 20% of the maximum power (P max ) of the DG unit over a minute; therefore, the complete reconnection process should last at least 300 s. Te soft start aims to avoid possible disturbances and detrimental efects on the stability of the electrical grid caused by the DG.
In addition, in order to limit the extent of overfrequency events, the ENTSO-E grid code introduced a P(f ) control logic that modulates the active power injected into the grid by the DG unit, as reported in Figure 6. Te active power is decreased linearly when the frequency exceeds a specifc frequency threshold (LIf ), while it is zeroed when the frequency reaches Lf max . Tis control logic is only activated if DG active power is greater than a lock-in value (LIp).
Tis work implements the soft start ramp-up DG reconnection process and the P(f ) control logic inside DigSilent PowerFactory according to the block diagram in Figure 7. It takes as inputs: (i) Te DG bus frequency acquired by the PLL block f (Hz) (ii) Te DG active power acquired by the measurement power block p (p.u.) (iii) Te input step change of the direct axes current yi_id (-) It outputs the direct axes current id ref (p.u.). Te frst two inputs, f and p, are processed in the "comparator" block: in order to activate the P(f ) regulation by the switch signal, both f and p must be respectively greater than LIf and LIp. p_reg is the active power provided by the DG unit according to the P(f ) characteristic ( Figure 6), which is implemented through the linear "P(f ) lookup table." Te inputs of the "P(f ) lookup table" are f and pimax; pimax is equal to the maximum power delivered by the DG unit when LIf is reached. o_id (and the integrator block 1/sT) is responsible for the soft start ramp-up process, which is performed by varying as a ramp signal id ref .

Te Q(V) Control
Logic. Te reconnection process of a DG unit could reverse the power fow over the grid, increasing the voltage at the DG connection point. In order to cope with this issue, a Q(V) control logic has been introduced in the technical connection rules for DG units, which adjust the local reactive power exchange as a function of the voltage measured at the point of common coupling with the grid, as Figure 8 shows. Te reactive power regulation is activated if the voltage amplitude is outside the range V1i ÷ V1s. Instead, if the voltage value is outside the range V2i ÷ V2s, the regulation saturates at ±Q max . According to technical standards, a rectangular-shaped capability curve has been considered, where Q max is defned as 0.4843 of P max .
Te Q(V) control logic has been modeled in DigSilent PowerFactory according to the block diagram shown in Figure 9, taking as inputs: (i) Te voltage amplitude at the DG bus u (p.u.) (ii) Te active power exchanged by the DG p (p.u.) Te output of the transfer function is the quadrature axis current iq ref (p.u.).
Te Q(V) control logic is activated when the active power p is greater than the lock-in value LI. Tis check is performed by the "comparator" block. If so, the switch shifts its input position from Q_nr_pu, which is a constant value equal to zero with a unitary power factor, to Q_ref. Te latter value is defned by the "Q(V) lookup table" block, which models the Q(V) characteristic and returns as output the corresponding value of reactive power Q_ref defned according to the measured voltage amplitude u ( Figure 8).
All the parameters that characterize both the P(f ) and Q(V) control logics are reported in Section 5.

Intentional Islanding Operation: Case Study Definition and Numerical Results
Te case study under investigation is introduced by looking at the emergency operating practice of DSOs in a radiallyarranged distribution system ( Figure 10). After the occurrence of a fault on the network, e.g., on a MV line or in a MV/LV substation, the following operations are performed (as shown in Figure 10): (i) In order to isolate the fault, the DSO usually opens the circuit breaker in the primary substation and a sectionalizing switch along the MV line (ii) A portion of the public distribution network remains deenergized; being it radially arranged, no other paths are supposed to exist to feed MV/ LV loads (iii) In the meantime that the fault is repaired, the DSO resupplies the isolated grid by a GS connected to the  International Transactions on Electrical Energy Systems LV side of a secondary substation, thus performing an intentional islanding of the grid [41] In DigSilent PowerFactory, this procedure has been implemented by means of the following simulation events: (i) Te test grid is deenergized at the beginning of the numerical simulation (t � 0 s) (ii) At t � 5 s, the isolated portion of the distribution network is reenergized through the GS connected at the LV side of a secondary substation Furthermore, the elements and parameters of the distribution test grid have been defned to recall the structure of a real-existing network. In particular, in the software environment, the islanded system consists of a 630 kVA MV/LV transformer (Table 1), a MV line, and a MV load.
For broader considerations on the stability of the electric island, a wide set of analyses have been performed, varying the typology (see Table 2) and length of the MV line (0 ÷ 15 km, with a step of 0.5 km), as well as the amount of load supplied, from no-load to full-load condition, with a step of 3% the nominal active power of the GS.
In Table 2, naked conductors are often used for overhead lines especially in rural areas, while cables can be used both in underground or overhead laying conditions. Te 25 mm 2 cross section has been selected because it is widely adopted for terminal sections of MV lines, the most likely to be supplied through GSs.
Concerning the load behavior, a hybrid model has been considered with 50% static and 50% PQ load. Tis assumption has been introduced to mimic the actual load behavior in real-existing distribution networks [42].
(i) Te static model considers the load as a constant impedance; therefore, active and reactive powers vary with the square of the voltage magnitude [43], as the next formulas suggest: where P load /Q load represent the actual active/reactive power required by the load, P rated /Q rated represent their rated values, V load and V n , respectively, the voltage measured at the connection point and its nominal value. (ii) Te PQ model represents the load as a constant power bus; thus, its active and reactive powers do not depend on voltage magnitude variations as, for example, inverter-supplied loads.
Te electrical and mechanical parameters adopted for the alternator are reported in Table 3.
A common size for GSs adopted in emergency conditions by DSOs has been selected for this purpose. In Table 3, the impedance values are expressed as a percentage of the reference impedance Z ref :

International Transactions on Electrical Energy Systems
Te parameters selected for the speed governor and voltage excitation system are reported in Tables 4 and 5.
Te dynamic stability of the electric island was verifed through the RMS simulation tool of the DigSilent PowerFactory software, employing a variable step size of 0.01 s. In the software environment, the electric grid was modeled as a set of diferential and algebraic equations describing the behavior of the system components, including generators, transformers, lines, and loads; by solving these equations over a selected simulation period, the dynamic behavior of the islanded system was evaluated. Te simulation parameters used in the analyzed case study (Table 6) were set to observe the complete electromechanical transient of all the electrical quantities. Te total number of simulations performed was 3842, with a computational time for each simulation of around 0.5 s. Simulations were performed on a 12th Generation Intel(R) Core(TM) i7-1255U, CPU 1.70 GHz, RAM 16 GB computer.

Numerical Results: Dynamic Stability in No-Load
Condition. In this section, the aim is to analyze the stability of the electric island during the power supply restoration process. A frst set of simulations has been carried out assuming that no MV/LV loads are supplied. Tis assumption is coherent with the procedures carried out by DSOs: after a fault, the DSO usually fnds it convenient to reenergize the grid by the GS initially in no-load conditions. Tis procedure is performed by powering the distribution feeder up to the MV side of the MV/LV substations and, only after, by    International Transactions on Electrical Energy Systems gradually reconnecting the underlying loads. In this scenario, a main problem is represented by the capacitive contribution of MV line susceptance, which is not compensated by any inductive load. Indeed, by increasing the length of the feeder, the operating point of the GS moves to the underexcited region of the capability curve toward the stability limit Q min (see Figure 2), defned as follows: where Vc represents the voltage at the GS terminals and X d is the direct axes synchronous reactance. From data reported in Table 3, the value of Q min obtained is equal to −0.12 Mvar. Te capacitive contribution is much higher for cable lines than for overhead ones (see Table 2). For this reason, they show a very diferent behavior when energized by a GS. In particular, naked conductor lines did not face stability issues in the whole range of the lengths considered (i.e., 0 ÷ 15 km) because their capacitive contribution is low and Q min is never reached over a given length. On the contrary, cable lines can cause the operating point of the GS to exceed the stability limit defned by the capability curve. If this occurs, protections trip and the electric island is deenergized. In Figure 11, the stability limit Q min (red vertical line) and the operating points for diferent cable lengths and sections are represented. For a 25 mm 2 cable line, when the length overcomes 5 km, the reactive power produced by the feeder exceeds Q min , the GS is no longer able to work in stable conditions, and the system diverges. In addition, also the operating points of 95 mm 2 and 185 mm 2 cable lines are represented; their electrical parameters are reported in Table 7. It has been observed that, by increasing the section of the cable, the capacitive contribution increases as well, and the stability limit Q min is reached for lower lengths; in particular, the stable length is reduced to 4 km for the 95 mm 2 and 3 km for the 185 mm 2 cable line. When the length is zero, the losses of the 630 kVA MV/LV transformer are responsible for the small amount of active power (1.09 kW) produced by the GS.
For example, Figure 12 reports the frequency and voltage measured at the GS terminals for an MV cable line (6 km long, 25 mm 2 ); in real-existing networks, the voltage/frequency protections mounted on the GS would immediately trip, disconnecting the GS and deenergizing the entire grid.

Numerical Results: Dynamic Stability Close to the Full-Load Condition.
Tis scenario aims at studying the intentional island stability when the GS supplies a feeder of the public distribution network and the relative MV/LV loads. Te power required by the hybrid load is such that the GS is working near the full-load condition (87 ÷ 100% P n ). Unlike the previous scenario, the inductive contribution of the load, which operates at a power factor equal to 0.9, compensates the line capacitance, increasing the length of the lines that can be energized both in isochronous and droop conditions, as shown in Table 8: Regarding the isochronous condition, Table 8 shows that if the active power required by the load does not exceed 93% of the GS nominal one, the cable length that can be reenergized is more than 10 km. In this case, the intentional island stability is limited by the practical stability angle: as for the no-load scenario, when the grid extension increases, the capacitive contribution increases as well, and the operating point moves toward the underexcited region of the capability curve. Consequently, the load angle increases, getting closer to the practical stability limit (65/70°), as shown in Figure 13.
On the other hand, Table 8 shows a severe length reduction when the active power required by the load exceeds 93% of the GS nominal one. In full-load conditions, the energy losses over the MV line can bring the speed governor to work close to its saturation limits. In particular, if the frequency error is high enough to saturate the throttle signal at T max (1.25 p.u.), the mechanical torque cannot compensate for the frequency deviation and the electric island frequency diverges. Figure 14 shows the MV line lengths that allow operating the network in a stable condition in the case of a 100% P n load: the load angle is much lower than the practical stability limit, while the throttle is close to the reference value in p.u. An additional increase in the line length would saturate the throttle signal at T max .   International Transactions on Electrical Energy Systems For a complete understanding of possible issues afecting the stability of the electric island, a droop characteristic is also implemented on the speed governor. In particular, a 4% droop is selected (see Figure 15), assuming that the nominal frequency value (50 Hz) is reached when the GS delivers half the nominal power (0.5 p.u.). In real life, the slope and the initial frequency value of the droop characteristic can be set by the manufacturer or user of the GS.      According to the characteristic selected, in full-load condition, the frequency of the system reaches values around 49 Hz (0.98 p.u.), far below the nominal value, as shown in Figure 16.
Te numerical simulations performed show that the droop characteristic reduces the maximum extension of the MV grid that can be supplied without stability issues compared to the isochronous case (Table 8, right column).
Tis behavior can be explained by the expression of the mechanical power P m in output to the speed governor, which in steady-state conditions must be equal to the active power absorbed by the load: With the droop characteristic, being the frequency lower than the nominal value, the mechanical torque Tm must increase to provide the same mechanical power P m . Tus, T m saturates, creating stability issues for smaller lengths of MV lines. In Figure 17, the diferent trend of the mechanical torque T m is represented for the isochronous and droop conditions for the same line length (8 km).
In conclusion, the analyses performed showed that, if the distribution power system is made by cable lines, additional attention must be paid to not exceeding the maximum line length allowed by the GS capability limit. Tis aspect can become critical especially if the rating of the generator is similar to the active power required by loads. In this case, the admissible extension of the intentional island to prevent stability issues is drastically reduced. Finally, the adoption of a droop characteristic for the speed governor can negatively afect the maximum network extension that can be safely supplied.

. Active Network: Case Study Definition and Numerical Results
Te intentionally islanded portion of the public distribution network repowered by the GS may also contain DG units (Figure 18). When a fault occurs on the grid, in order not to interfere with the procedures put in place by the DSO to reenergize the faulted portion of line, the DG units are promptly disconnected. Ten, once the electric island is steadily resupplied by the GS, the DG units reconnect, usually automatically. Tis in Italy is carried out according to the soft start ramp-up reconnection prescriptions reported in Section 3.1.
In the numerical simulations performed in the present paper, the reconnection process has been modeled by means of the following events: (i) At t � 0 s: the GS is assumed to be stably counterfeeding the electric island (ii) At t � 100 s: since both voltage and frequency at the terminals of the DG unit are inside the selected reconnection ranges (85%V n < V < 110%V n ;  Te DG unit is assumed to reconnect following a rampup of active power with a slope equal to +20% P max /min. Terefore, the complete reconnection process lasts 300 s, as shown in Figure 19.
In this case study, the DG unit is supposed to inject a maximum power P max equal to 200 kW with a unitary power factor. It is connected to the LV busbar through a LV cable line having the parameters described in Table 9 and a length equal to 0.3 km. All the other elements and the confguration of the test grid are the same as in the previous case study.
In addition, the MV load has the characteristics in Table 10.
After the reconnection of the DG unit, if voltage and frequency overcome the thresholds reported in Tables 11  and 12, the P(f ) and Q(V) control laws are switched on, and their efects on the electric island stability must be evaluated. By setting LIp in Table 11 equal to zero, the P(f ) regulation is activated regardless of the value of active power delivered by the DG unit.
As for the case study discussed in Section 4, the dynamic stability of the electric island during the reconnection process of a DG unit was investigated through the RMS simulation tool of DigSilent PowerFactory software. Te simulation parameters are the same reported in Table 6, except for the simulation period, which was set equal to 500 s to observe the complete electromechanical transient of all the electrical quantities and the ramp-up process of the DG. Te computational time for each simulation was around 5 s.

Numerical Results: Dynamic Stability during the DG Unit
Reconnection Process. Te frst objective of the numerical simulation in this section was to evaluate if the automatic DG reconnection process can compromise the stability of the electric island. Te most obvious efect of the DG injections concerns the active power balance. Indeed, if the active power provided by DG overcomes the load demand, instability will occur (Figure 20), and the active power in excess must be absorbed by the GS, causing the alternator to work as a motor. Usually, a directional relay protection is adopted on the GS to avoid this condition [39].

Numerical Results: Efects of the P(f ) Control Logic.
Usually, no particular issues can emerge when the P(f ) control logic is enabled on the DG if an isochronous speed control characteristic is adopted for the GS. In fact, the GS regulates the frequency on the grid at 50 Hz, preventing the DG from performing the P(f ) regulation. However, problems can arise if a droop characteristic is adopted for the GS because the frequency variation can trigger the activation of the P(f ) control logic. Tis situation is analyzed in the following simulations, where the droop characteristic reported in Figure 15 is adopted.
As described above, the GS is assumed to supply the electric island in a steady-state condition at the beginning of the simulation. According to the power requested by the load in Table 10, the frequency is equal to 49.36 Hz (Figure 21(a)). When the DG is reconnected to the grid (t � 100 s), the frequency increases due to the load-sharing efect between the GS and DG: the active power provided by the DG unit increases as a ramp, progressively reducing the active power that the GS supplies to the load. Consequently, the GS detects a gradual load reduction and the frequency increases following the droop characteristic of the speed governor.

International Transactions on Electrical Energy Systems
If the P(f ) control logic is switched of, the active power provided by the DG unit increases according to the soft start ramp-up characteristic in Figure 19, reaching its maximum value (0.2 MW) at 400 s (blue characteristic in Figure 21(b)). At the end of the transient, the frequency is equal to 50.6 Hz (blue characteristic in Figure 21(a)).
On the contrary, if the P(f ) control logic is switched on, when the LIf threshold (50.2 Hz) is reached (t � 300 s), the control logic modulates the DG active power, reducing the overfrequency variation. Te overlapping of this regulation with the ramp-up reconnection one results in the active power injected by the GS, which remains constant at 0.135 MW (t � 300 s) (orange curve in Figure 21(b)). Similarly, the frequency is also kept constant at 50.2 Hz, according to the P(f ) control logic shown in Figure 6.
Regarding the GS, Figure 22 shows that the active power produced by the diesel GenSet is reduced by the same amount provided by the DG unit (in this case, 0.135 MW), while the reactive power is almost constant because the DG unit is working at a unitary power factor.
Terefore, from the analyses carried out, it emerges that the P(f ) control logic has no detrimental efects on the proper operation of the electric island and indeed it is benefcial in mitigating possible overfrequencies: once activated, the DG active power modulation helps to keep the frequency of the system at LIf (50.2 Hz), avoiding further increases that could lead to protections tripping. Nevertheless, the P(f ) control logic has also an economic drawback for DG owners, given by the production curtailment during its activation.

Numerical Results: Efects of the Q(V) Control Logic.
Te DG reconnection at t � 100 s causes the reverse power fow over the LV line, thus increasing the voltage at the DG terminals with a trend similar to the reconnection ramp. When the Q(V) control logic is switched of, the steady-state voltage value at the DG unit terminals reaches 1.064 p.u., as represented by the blue curve in Figure 23(a), on the left. Instead, if the Q(V) control logic is activated, as expected, the fnal voltage value is closer to the reference one. According to Figure 8, when voltage overcomes V2i (t � 320 s), the DG unit starts absorbing reactive power from the grid to compensate the voltage increase. As a result, the voltage keeps increasing but with a lower slope, which is shown by the orange curve in Figure 23(a), until that the reconnection process (t � 400 s) is accomplished. Te steadystate voltage value is 1.058 p.u, reduced by 0.06 p.u. compared to the previous case.
Tis fnding is confrmed by Figure 23(b): when the V2i threshold is exceeded, the DG starts exchanging an amount of reactive power that is a function of the Q(V) characteristic ( Figure 8). Te fnal value of reactive power absorbed by the DG unit is 0.015 Mvar. In the simulations performed, this control logic showed to have benefcial efects on the GS operation. Indeed, the reactive power provided by the GS approaches zero, moving the operating point away from the     Figure 20: Frequency trend in case of active power provided by the DG unit higher than the power requested by the load. stability limit of the capability curve. A similar behavior is seen on the active power profle ( Figure 24): with the reconnection ramp, the active power of the DG unit reaches its nominal value (0.2 MW), reducing by the same amount, the active power produced by the GS.
Tus, numerical simulations demonstrated that the Q(V) control logic provides two benefts for the stability of the intentional electric island: frstly, the control logic brings the voltage value closer to the reference one for over/ undervoltage events. Secondly, in overvoltage conditions,  the GS operating point moves away from the stability limits toward the overexcited region of its capability curve.

Conclusions
Te study carried out confrmed that the emergency supply of a portion of a public distribution grid with commercially available diesel-driven GenSets is, in most cases, practically feasible, thus improving the quality of service and reducing the outage periods. In particular, in areas in which most of the MV distribution grid is made by naked conductors, as rural or mountain areas, GSs can energize overhead lines even longer than 15 km without stability issues in any load condition. In urban environments, where usually the majority of lines are cables, the portion of the network that can be reenergized should not exceed a specifc length (usually a few kilometers), depending on the size of the GS, the cross section of the cable line, the required power, and typology of the load. For this reason, other counterfeeding methods should be identifed for these situations: for example, by changing the confguration of the system through the opening and closing control of MV disconnectors. Unstable conditions are more likely to emerge when loads are supplied close to the rated power of the GS (>90% P n ), especially if a droop characteristic is adopted for the speed governor.    Regarding the active network case study, particular attention must be paid to the amount of active power injected by the DG on the electric island, which must never exceed the one requested by the load. However, the control laws currently prescribed to DG units by ENTSO-E and Italian technical standards concerning the soft start ramp-up reconnection, P(f ) and Q(V), have shown not to interfere with the speed and voltage regulation of the GS. Indeed, they help the GS maintain the frequency and voltage inside the operating ranges, avoiding protection tripping.
Finally, although the current study has provided valuable guidelines for using GSs as emergency power supplies for improving the reliability and resilience of public distribution grids, even in the presence of DG units, there are still open questions that could motivate further research on the topic. Indeed, in addition to evaluating the efect on the island stability of diferent control laws of DG units and load typologies, future studies should focus on validating the results currently obtained by numerical models through experimental tests, also taking advantage of possible collaborations with DSOs.