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Investigation and Enhancement of Stability in Grid-Connected Converter-Based Distributed Generation Units With Dynamic Loads

Medium-voltage distributed generation (DG) units can be subjected to a high penetration level of dynamic loads, such as induction motor (IM) loads. The highly nonlinear IM dynamics that couple active power, reactive power, voltage, and supply frequency dynamics can affect the stability of MV grid-connected converter (GCC)-based DG units. However, detailed dynamic analysis and, more importantly, stabilization approaches of GCC-based DG units with IM loads when subjected to the grid faults, are not reported in the current literature. In addition, the literature lacks a thorough study on the effect of the grid strength on the low-voltage ride-through (LVRT) performance of such practical systems. To fill in this gap, this paper presents comprehensive integrated modeling, stability analysis, and LVRT performance improvement methods for GCC-based DG units in the presence of an IM load considering different grid strengths. A detailed multi-stage small-signal model of the complete system is obtained, and the eigenvalue analysis is conducted considering both static and dynamic load modeling. Furthermore, a sensitivity analysis is performed to investigate the effect of the length of the power line between the DG unit and the IM on the stability and LVRT performance of the entire system. Finally, the LVRT performance of the DG unit under an unbalanced grid fault is investigated using three different reference current generation strategies to determine the best strategy to provide a stable and efficient LVRT performance under strong and weak grid conditions. The time-domain simulation and experimental results are also presented to validate the effectiveness of the proposed methods.


I. INTRODUCTION
Distributed generation (DG) units have gained high momentum as an enabling structure to integrate renewable energy resources in power networks [1]- [3]. Most of DG units are interfaced to the network by voltage-source converters, known as grid-connected converter (GCC)-based DG units. With the expected high penetration level of DG units in future power systems and recent progress in power converter topologies and ratings, medium voltage DG units will be subjected to a wide range of both static and dynamic loads [4]. The electromechanical rotor oscillation phenomenon occurs in motors with large megawatt ratings [5], which are directly connected to medium voltage (MV) systems (1.0 kV to 30 kV). Typically, motors consume 60% to 70% of the total energy The associate editor coordinating the review of this manuscript and approving it for publication was Fengjiang Wu .
provided by a power system [6]. Ignoring this type of load in stability analysis of GCC-based DG units results in large stability operating region, which is unrealistic due to the highly nonlinear load dynamics. These dynamics couple the active power, reactive power, voltage, and supply frequency responses in the system. Therefore, severe stability problems may arise because of neglecting the load dynamics in systems with a high penetration level of MV-DG units [6]- [10].
Several studies are reported in conventional power system analysis to study the impact of large IM loads on power system dynamics [7]- [12]. In small-signal studies of power systems with IMs, since the use of soft-starters only limits motor starting inrush current, it does not change the final steady-state operating conditions of the motor. Therefore, the small-signal stability analysis will not be affected, and the motor performance will be mainly determined by the motor dynamics [15]. The linearized state-space model of the IM is obtained in [5], [6], [13], [15], where a system eigenvalue spectrum is derived for stability analysis. In the context of microgrids, the impact of IMs on load margins is studied in [15]. An integrated modeling and stabilization method for MV droop-controlled microgrids with IM load is studied in [13] where a small-signal model of a typical MV microgrid system with dynamic loads is presented, and a wide range of droop parameters is studied to keep the system stable and yield the expected control performance. Another study in [16] investigated the impacts of dynamic interaction between doubly-fed induction generator (DFIG)based wind farms and IM loads on system voltage stability using a modal coupling. The dynamic performance of a grid-connected dc distribution system with a high penetration level of dynamic loads is studied in [17] considering the power system instability issues. However, a literature survey indicates that detailed analysis and, more importantly, improved stabilization of MV GCC-based DG unit with IM loads under grid code conditions, are not reported yet and need special attention. Therefore, this paper develops comprehensive integrated modeling, stability analysis, and LVRT performance improvement methods for GCC-based DG systems in the presence of dynamic loads.
The static load modeling method is addressed in [6] and [18]- [20], which is suitable for low-voltage applications with small IMs. For small IMs, the rotor-circuit time-constant is small, which represents the fast decay of rotor electrical dynamics as compared with rotor mechanical dynamics [21]. Therefore, the electromechanical rotor dynamics are decoupled, and small IM loads can be modeled by their equivalent steady-state RL circuit or active and reactive power demand. This justifies the use of static load models in the existing low-voltage low-power grid stability studies. However, with the increasing penetration level of DG units in future power networks, it is not reasonable anymore to model large IM loads with static load equivalents. In fact, electromechanical rotor oscillations in large IMs couple the rotor speed oscillations, which are directly coupled to the rotor flux dynamics and the supply frequency. The time-constant of the rotorcircuit is large, and both electrical and mechanical dynamics of the rotor are coupled. Because rotor oscillations cause the mechanical and electrical power oscillations, the output power of DG units feeding an IM contains the frequency modes of these oscillations [13].
Another missing but essentially important point is the study of the low-voltage ride-through (LVRT) capability of the GCC-based DG units with large IM loads. Recently, the LVRT requirement has been an important mandate for DG units [22]- [24]. This is particularly important when considering the effect of the grid strength on the system performance considering the dynamic loads. The interactions of GCC-based DG units and the power system are highly dependent on the strength of the ac system. Therefore, it is essential to consider this phenomenon in LVRT studies. Furthermore, the system operators have imposed new grid codes requiring large DG units to remain connected and improve the voltage profile by reactive current injection (RCI) during short-term grid faults [24], [25]. Very recently, the multi-sequence RCI has also been mandated in the German code of VDE-AR-N [26], [27], which presents regulations for the injection of both positive and negative sequences of the reactive current. Reference [27] further offers to include two controlling parameters in the future standards of GCC-based DG units to support the connection voltage with a combination of boosting the positive-sequence voltage and reducing the unbalance factor. However, the literature still lacks a study on the LVRT capability of GCC-based DG units with the IM loads considering both the stiffness of the host grid and the new multi-sequence RCI requirements.
Motivated by the aforementioned shortcomings in the literature, this paper presents integrated modeling, analysis, and stabilization approach of GCC-based DG units in connection with an IM load. A detailed multi-stage small-signal model of an MV GCC-based DG unit with both dynamic and static loads is developed in the decoupled double synchronous reference frame (DDSRF). The DDSRF is used to enable the implementation of the newly imposed grid codes. The model includes the exact 10th order model of the IM load and the 25 th order model of the GCC-based DG unit along with the network dynamics. The comprehensive multi-stage small-signal model is used to provide the possibility of the grid fault studies for three different operating states of the system: before-fault (BF), during-fault (DF), and after-fault (AF) stages. This model is then used to assess the impact of the IM dynamics on the overall system stability as compared with the static load model and under different grid strength conditions. The participation factor analysis (PFA) is also conducted to identify the contribution of different states to the dominant eigenvalues of the GCC-based DG system with a dynamic load. The model-based controller design method is proposed in this paper based on the small-signal stability analysis to improve the LVRT performance of the DG system in the presence of the IM dynamics under the strong and weak grid condition. In the proposed design method, the newly imposed multi-sequence RCI grid code requirement has also been considered. The proposed method can identify the optimum value for the control parameters of the system to improve its LVRT performance under different grid conditions and, at the same time, maintain its ability to retrieve the stable condition considering its relative stability margins. Finally, a sensitivity analysis is conducted to characterize the effect of the length of the power line between the IM and DG unit. Theoretical analysis, time-domain simulation results, and experimental results are used to validate the effectiveness of the proposed method.
The research in this paper is developed as part of the first author's Ph.D. research work [38].   DG unit and a typical MV 2240 hP, 2.4 kV IM connected to the middle feeder. The DG unit is connected to the MV feeder via a step-up Y/ transformer. The term PCC on bus4 stands for the point of common coupling. The system parameters are given in 0. The grid frequency synchronization, and active/reactive current control functions are performed at the low-voltage side of the GCC. The DG current controller is designed in the DDSRF on the dq coordinates, with the rotating frequencies in the positive and the negative directions with respect to the fundamental grid frequency; hence, it controls the positive-and negative-sequence current components.
There are three strategies used in this paper to implement the RCG unit in the GCC control system. The first one is the traditional RCG, which is still being used in GCC implementations in the distribution system [28]- [30]. The second one is known as the balanced positive-sequence control (BPSC) strategy which is a well-known RCG method in the study of LVRT performance of the GCCs [3], [14], [22]. Finally, the recently introduced RCG method known as the flexible multi-sequence reactive current injection (FMS-RCI) [27] to satisfy the newly imposed grid codes on the LVRT requirements to inject the reactive current in both positive and negative sequences to support the PCC voltage during a grid fault [24], [25]. The main equations for each RCG method in the DDSRF are presented in 0.
Without loss of generality, the system presented in Fig. 1 is used to investigate the effect of the dynamic load on the GCC-based DG unit small-signal stability. A small-signal state-space model of the overall system components is developed and presented in the following subsections. The modeling approach can be easily extended to include additional DG units and load models.

A. STATE-SPACE MODEL OF GCC-BASED DG UNIT
The control system of a typical GCC-based DG unit consists of 1) phase-locked loop (PLL) system which performs the grid frequency synchronization and provides the frequency signal to the dq transformation blocks implemented in the DDSRF; and 2) the inner current control loop to regulate the filter inductor current (i 1 ), and damp the resonance peak of the output LC filter [14].
The PLL and current control loop equations including the conventional proportional and integral (PI) compensators and the feedforward PCC voltage signal are listed (1)-(5), where the positive and negative dq reference frames are assumed to be rotating at the positive and negative directions of the angular frequency (ω), respectively, provided by the PLL. The superscripts ''+'' and ''-'' represent the positive and negative components, respectively.
where i +,− 1d and i +,− 1q are the filter current components, V +,− cd and V +,− cq are the inverter output voltages, and V +,− pd and V +,− pq are the PCC voltage values, all in the DDSRF; and the superscript '' * '' represents a reference value. These signals are also demonstrated in Fig 1. K p and K i are the current controller PI compensator gains and, K p2 and K i2 stand for the same gains for the PLL. L f is the inductance of the LC filter. The current and voltage dynamics for the PCC are already given in many available references [3], [32].

B. STATE-SPACE MODEL OF IM
The relation between the IM's stator and rotor voltages and currents in the common synchronous rotating reference frame can be stated by (6)- (9). Because the IM fluxes and currents are not independent, the IM equations can be written using either of them as state variables. However, for the integration of IM state equations into the GCC-based DG unit state-space model, the voltage equations with currents as state variables are more suitable [13]. Therefore, the relation between the voltage and currents of the stator and the rotor can be given in the DDSRF frame as follows: where L ls and R s are the stator inductance and resistance; L lr and R r are the corresponding rotor parameters; L m , s, and ω are the linkage inductance, rotor slip, and the angular frequency of the stator supply, respectively. i M stands for the stator current, and i r is the rotor current. The electromagnetic torque in terms of stator and rotor currents can be expressed as The relation between torque and the mechanical speed can be obtained in terms of the motor slip and stator angular speed as In (10) and (11), ρ, J , and T L are the number of magnetic poles, combined motor and load inertia, and the load torque, respectively. Note that since the rotor circuit of the IM is shorted, the V r values are set to zero. The machine parameters are given in 0.
By linearizing the dynamic equations of (1) to (11) and the RCG equations of 0, the state and input variables for the complete system can be derived in (12) and (13), as shown at the bottom of the next page, where (12) and (13) demonstrate the related 25 states and six input variables of the GCC-based DG unit and the connected power system and ten states and six input variables related to the IM dynamics. The obtained state matrix of the system considering the BPSC RCG method is presented in the Appendix. Further modeling details for the GCC-based DG unit can be found in [3] and [14].

C. THREE-STAGES MODELING METHOD
Considering the low-voltage conditions, a DG unit will be subjected to different operating states; therefore, it is not reasonable to develop only one linearized model for these various conditions [31]. Hence, the three-stage modeling method, presented in [14], [31] and [36], is adopted in this paper to overcome this limitation. This method adopts the segmental multi-point linearization [31] over three stages (before fault, during fault, and after fault) to represent the system dynamics at these central conditions.
The first stage characterizes the DG unit dynamics before any fault occurrence. In this model, the initial condition is obtained from the normal operating condition of the DG unit. This stage is called the before-fault (BF) stage. The second stage reflects the DG unit dynamics during the fault period, where the steady-state condition is obtained from the system status during the fault. Finally, the third stage represents VOLUME 8, 2020 the system dynamics after fault clearance and is called the after-fault (AF) stage. More details on this modeling method can be found in [14] and [36]. This model also provides the possibility of studying the system performance on fault occurrence and clearance transients.

III. STABILITY ANALYSIS
To demonstrate the importance of using the complete dynamic model of the IM and not to simplify it with a static load model (i.e., the ZIP model), the complete small-signal model of the GCC-based DG unit is obtained with the consideration of the mentioned two load modeling approaches: static and dynamic. The IM load model adds six more states to the complete state-space model of the system, comparing to the static load model. The eigenvalue spectrum for both models is obtained and shown in Fig 2 separated based on their influence on the system stability (the static load model has four additional non-dominant modes with real values around −3.6 × 10 5 , which are not shown in Fig 2). The most dominant modes are the most fundamental modes for system stability analysis. As illustrated, for the static load model, the 29 system modes are distributed in the most-, lest-and the least-dominant ranges, with only seven modes located in the range of most dominant (i.e., 0 to 50 Hz), shown in Fig 2(b). However, for the IM load modeling, all 35 modes are distributed in a more dominant range, which represents an overall shift towards lower relative stability. Besides, as shown in Fig 2(b), there are 26 modes of the IM load modeling located in the most dominant range, which FIGURE 2. Eigenvalues of the GCC-based DG unit system with static and dynamic load models. denotes 19 more dominant modes compared to the static load model. Therefore, considering the transient stability of the system, the system with IM load modeling demonstrates considerably higher sensitivity and lower relative stability compared to the static load model.
It should be noted that rotor oscillations are characterized by their low-frequencies, and they cannot be effectively filtered by the average low-pass filters in the DG unit control system [34]. Due to the lightly-damped nature of rotor oscillations in large IMs, the feedback system can be subjected to power oscillations and even system instability, especially in the case of a fault occurrence. Therefore, as revealed by Fig 2, although equations (6)-(11) add more complexity to the dynamic model of the system, considering them is essential for accurate stability analysis of the GCC-based DG unit system.
93430 VOLUME 8, 2020 Another study, based on the PFA [6], demonstrated the relative participation of each state variable to the mentioned 26 most dominant modes of the IM dynamic model, shown in Fig 2(b). The normalized participation factors greater than zero are obtained for all 26 modes. Amongst them, there are nine modes that are highly related to the IM dynamics state variables (i.e., has non-zero participation in the IM related dynamics). The PFA results for these nine modes are listed in 0. Note that the stator flux is composed of both the stator and rotor current components, and therefore, they highly participate to the demonstrated eigenvalues when using the dynamic load modeling. It is observed that these nine modes are related to the IM dynamics state variables, and their participation factor in all other variables are zero. Therefore, system stability can be remarkably affected in the presence of such a load.
The eigenvalue and PFA analysis results demonstrate that there are nine dominant poles in total, which are associated with the IM state variables and according to their location (i.e., less-damped modes resulting in more oscillatory system responses), they have a high impact on the overall GCC-based DG unit system stability. In fact, these modes can be regarded as the source of added oscillatory response to the system, and therefore, they should be considered in stability studies. Furthermore, the participation factors obtained in 0 imply that all the dominant eigenvalue pairs shown in Fig 2(b) are very sensitive to the stator and rotor current components. This leads to the fact that the dominant system modes are mainly influenced by the active power component drawn by the motor. This is in agreement with the familiar fact that controlling the stator currents is an effective way to reshape the open-loop IM dynamics, which is the case in IM drive systems [33]. However, in the system under study with the direct connection of the IM, the motor currents may not be available for stabilization. In this case, the motor power is shared among the DG unit and the grid. Therefore, some methods are proposed in this paper to improve the during-fault voltage support by the DG unit. In this way, the injected active and reactive current components of the DG unit result in an improved power supply to the IM and boost its functionality to ride through the fault condition.

IV. PROPOSED STABILITY AND LVRT IMPROVEMENT METHODS
Before 2003, no requirements were imposed from utility grids for LVRT performance of wind turbine generator systems (WTGSs). However, in that year, E.ON-Netz of Germany was the first to implement those requisites into their grid code [28]. According to the guideline of the grid code, WTGS needs to stay connected and provide reactive power into the grid. Only when the grid voltage drops below the guideline of the grid code, a WTGS is allowed for disconnection from the grid [24]. Also, LVRT for photovoltaic (PV) plants was mentioned in the German grid code from January 2011 to provide uninterrupted service in the case of grid disturbances. However, to the best of authors' knowledge, the LVRT performance of a GCC-based DG unit in the presence of an IM load is not reported in the literature yet. On the other hand, based on [6], the IMs typically consume 60% to 70% of the total energy provided by a power system. Therefore, the dynamics related to motors are usually the most important aspects in dynamic analysis of system loads and, therefore, in the analysis of modern power systems it is also crucial to consider the IM dynamics with respect to the mandated LVRT requirements in the grid codes [24]- [26]. The shortcircuit ratio (SCR) is used in this paper as a measure of the grid strength. The SCR is a standard definition to quantify the strength of an ac system as compared to the rating of the connected DG unit. If the ac network impedance at the fundamental frequency is considered as Z s , and the rated ac voltage and power of the converter are V rated and P rated , respectively, then the SCR is defined as Typically, an ac system with SCR higher than three is known as a strong grid, and an SCR lower than three represents a weak grid condition [6]. Therefore, the LVRT performance of the presented system of Fig 1 under a short-term unbalanced grid fault is investigated in this section. For the time-domain simulation studies, the aforementioned system is implemented in MATLAB/Simulink environment. Three different RCG methods of 0 are implemented, and the system performance is monitored for a satisfactory LVRT. The location of the fault is also shown in Fig 1. It is an unbalanced two-phase to ground grid fault happened at t = 1.8 s and lasted for 200 ms.

A. LVRT UNDER STRONG GRID CONDITION
To investigate the LVRT performance of the system under study when connected to a strong grid, the above mentioned unbalanced fault scenario is studied when the DG unit is connected to a grid with SCR∼ 10 ∼ = 10. The three RCG methods of 0 are implemented and tested under the same condition. The results revealed that all three strategies are able to maintain the DG unit connected during and after the fault when the connected grid is strong. Fig 3 compares the results of employing the traditional and BPSC RCG strategies. These two methods perform almost in the same way without any negative-sequence reactivecurrent compensation. Between them, the BPSC delivers the balanced current with lower maximum-phase value during the fault, and shorter settling-time after the fault. Besides, assuming a protection limit for the three-phase DG unit current value at 2 p.u. , Fig 3(a) shows that employing the traditional RCG may trigger the protection devices. If the fault duration passes the adjusted time of the over-current protection system, it can result in DG unit disconnection and LVRT failure.
Because the BPSC and the traditional RCG methods have no specific rule on the reactive-current injection according to the voltage drop value, during the fault, they cannot be chosen to provide the LVRT requirements considering the grid codes [24]- [26]. However, the FMS-RCI method improves the voltage profile during the fault by injecting the reactive current in both positive and negative sequences.
Therefore, in the next test, the LVRT performance of the system is studied while employing the FMS-RCI strategy with the K + and K − parameters set to 2. This value is chosen to be compatible with the regulated value of the reactivecurrent injection under the balanced fault condition presented in [24]. Fig 4 shows the FMS-RCI strategy results compared to the BPSC method to demonstrate their difference in supporting the IM bus voltage and improving the active and reactive power profiles of the DG unit and the IM. Fig 4(b) reveals that the FMS-RCI generates a higher average power in the DG unit during the fault. With the IM, the FMS-RCI strategy provides a smoother recovery on the active/reactive power after the fault. The only possible problem in the application of the FMS-RCI with the injection of the flexible reactive-current during the fault is that the maximum phase value of i 1 stays over the reasonably assumed 2 p.u. limit (Fig 4(a)). Therefore, to find a remedy, a modelbased current controller design method is utilized in the next section using the small-signal stability analysis of the system for the BF and DF stages.

1) LVRT PERFORMANCE IMPROVEMENT USING MODEL-BASED CONTROLLER DESIGN
In this method, the initially designed current controller parameters, i.e., K p and K i of the PI compensator, are changed, and the eigenvalue locus of the complete system is obtained. The initial design of these parameters is obtained based on the pole-zero cancellation method described in [32].
In the mentioned model-based controller design, the controller parameters are changed, and the eigenvalue locus of the system is monitored for the best relative stability condition. Fig 5 shows the eigenvalue locus of the system when the K p and K i parameters are increasing for the DF and BF stages. As demonstrated, for the DF stage, there are three pole-pairs moving farther from the imaginary axis to a specific point, from which they return their path towards the imaginary axis. This point is when the value of the K p and K i parameters are increased to 17 times their initial value. Therefore, there is a limitation in increasing the K p and K i parameters to improve the relative stability of the system. However, considering the BF stage, which has the same RCG method as the AF stage, it is observed that by increasing the K p and K i parameters, two dominant poles move towards the imaginary axis. Therefore, there is another limitation on increasing the current controller parameters to keep the system stability for the normal operation of the DG unit, before and after the fault. Further investigation revealed that by increasing the K p and K i parameters more than four times, the system would show unstable poles for the BF stage. From now on, this method is called the current controller improved design or the CCID method.
Also, it is worth mentioning that by comparing the results of Fig 5 with those of Fig 2(b), it is inferred that these affected poles by the CCID are amongst those which are added to the most dominant range by considering the dynamic load. Again, it demonstrates the importance of using the detailed dynamic load model instead of simplifying it with the static load model.
To investigate the effectiveness of this improved model-based CCID method in preventing the DG unit over-current problem, while keeping the same control parameters value (K + and K − ) for the FMS-RCI strategy, the timedomain simulation results of the system are obtained. Fig 6 shows the results for the case of K p and K i parameters increased to 2.5 times their initially designed values.   Fig 4(a). However, the system is acting slower in returning to its steady-state after the fault clearance, which was predictable by considering the results of Fig 5(b). In fact, the speed of decay of the transient response depends on the value of the time constant of the most dominant poles [35].
By representing a complex pole by −σ ± ω, the time constant is defined by 1/σ , which justifies the slower transient response or higher settling for the system after the fault. The IM bus voltage, active and reactive powers have not experienced any remarkable change. Therefore, the CCID could effectively reduce the possibility of the LVRT failure due to the potential DG unit over-current.

B. LVRT UNDER WEAK GRID CONDITION
As mentioned above, the strength of the ac system plays an important role in the interactions between the DG unit and the power system. Considering the LVRT requirements, because a weak grid has a lower ability to support the load during the fault, it is more probable to get a DG unit disconnection and failure of the LVRT. In this subsection, the results are presented for the case of a system with SCR∼2 (weak grid) and the same fault scenario of Section A, considering three RCG methods. Fig 7 shows the system performance with the traditional RCG method. As demonstrated, after the fault clearance, the DG current value has elevated and passed the DG current limit. In fact, the PCC voltage cannot return to its normal value after the fault clearance. Therefore, the DG current is increased to deliver the required power. It ultimately results in the DG unit disconnection, due to the protection system function, and the LVRT failure. The motor torque and speed are also dropped down. To find the best RCG method to satisfy the LVRT requirements, the other two RCG methods, i.e., the BPSC and FMS-RCI, are used and evaluated. These strategies are also advised and studied in many LVRT-related studies [3], [14], [27]. The same fault scenario occurred, and the results are obtained and presented in Fig 8. In this test, the initial design of the FMS-RCI controlling parameters, K + and K − , are based on what is imposed in the German grid code of [24]  for the symmetrical faults and what is presented in [27] for the application of the FMS-RCI. Therefore, the initial values of K + and K − are set to 2.
As shown in Fig 8, despite the strong grid condition, the BPSC method has wholly failed in retrieving to its normal condition after the fault clearance when the connected grid is weak. The positive-sequence of the PCC voltage profile has remained low, and the DG unit has not been able to generate the expected amount of the active and reactive power after the fault. However, because the FMS-RCI method can better support the PCC voltage by injecting the reactive current during the fault in both positive and negative sequences, it has been able to boost up the PCC voltage faster than the BPSC after the fault clearance. Besides, Fig 8(c) and (d) show that the FMS-RCI has clearly improved the system transient performance during and after the fault. Therefore, in the case of a weak grid condition, choosing the FMS-RCI method seems the only reasonable choice for the LVRT studies on a GCC-based DG unit system connected to an IM load. However, because the connected grid is weak and the DG unit is mainly providing the required power for the IM load, Fig 8 results show that the existing system is not fast enough in recovering after the fault clearance. As illustrated in Fig 8(a), the DG unit current stays high for a long period after the fault, which can result in the DG unit disconnection. Also, the PCC voltage finally fails in getting back to its normal value. Therefore, the obtained results imply that it is necessary to improve the system response to let the DG satisfy the LVRT requirements and remain connected during and after the fault occurrence.

1) PROPOSED MODEL-BASED LVRT PERFORMANCE IMPROVEMENT METHODS
As the first step, the proposed CCID method presented in Section A is studied for the weak grid condition in both DF and BF stages. The eigenvalue locus of the system is obtained when the K + and K − are set to 2, and the current controller parameters are increasing. The trend is completely similar to what is presented in Fig 5 for the strong grid condition. Therefore, due to space limitation, it is not shown here again. According to the mentioned small-signal stability analysis, the current controller parameters, i.e., K p and K i , are increased to 2.5 times their initial values. One other possible and reasonable solution to improve the LVRT performance of the DG unit in the presence of the IM load and under a weak grid condition can be increasing the PCC voltage support during the fault in the FMS-RCI strategy. This can be obtained by choosing higher RCG controlling parameters, i.e., higher K + and K − values . In this way, the PCC and, therefore, the IM bus voltages will experience lower voltage drop (due to the injection of more positive-sequence reactive current) and lower unbalance (due to the injection of more negative-sequence reactive current) during the fault. Therefore, although the value of K + and K − parameters is different from what is suggested in [27], based on the abovepresented results, it seems mandatory in the case of a weak grid condition to keep the DG unit connected to the grid and satisfy the LVRT requirements. However, to the date, there is no study presented in the literature to investigate the limitation on selecting the value of the K + and K − parameters considering the grid strength, the depth of the voltage dip, and the DG unit constraints. To find this threshold, first, the smallsignal stability analysis is carried out on the complete linear model of the system using the DF-stage modeling. In fact, changing the value of the K + and K − parameters is only valid when the DF-stage modeling is being used. The result is shown in Fig 9 when increasing the K + and K − values from 2 to 5. There are four dominant pole pairs affected by changing the value of K + and K − , amongst them two pairs start moving towards the right-half plane (RHP), denoting lower transient stability in the system. The interesting point is that these two pairs are the same, which were moving towards left by using the CCID method for the DF stage (refer to Fig 5(a)). Therefore, although increasing the K + and K − parameters move these poles towards lower relative stability, the combination of this tuning method with the CCID method can compensate for this undesirable effect to some extent. Therefore, the limitation on increasing the value of K + and K − parameters is applied by the consideration of maintaining the relative stability of the system. This lower stability threshold can be effective on the fault clearance where the system will experience a significant transient in the voltage and current values and, therefore, in the system states. Further investigation demonstrated that increasing the K + and K − parameters up to 13 will still keep the system stable with all poles on the left-half plane (LHP). After that point, the system will experience unstable poles. However, even for setting K + and K − close to 13, the system will have a high sensitivity to sudden changes such as an unexpected fault. Consequently, by conservatively choosing the value of K + and K − parameters as five, the system is supposed to represent a faster response, higher voltage support, and ultimately a successful LVRT performance while keeping a reasonable stability margin on the transients.
To verify the effectiveness of the proposed methods, the time-domain simulation results of the system are obtained under the same fault scenario and connection to the same weak grid with SCR∼2. The results are shown in Fig 10. It represents a successful LVRT performance in which the value of the DG unit current, i 1 , remained below the limit, during and after the fault. Compared to Fig 8, the apparent improvement in the voltage profile of the PCC and the IM bus is observed in Fig 10(b) and (d). Besides, all presented system values illustrate the faster recovery on the fault clearance.  It should be noted that, because the DG unit is mostly in charge of providing the IM power demand, the quality of the provided active and reactive power (P and Q) by the DG unit is remarkable from the IM point of view. As demonstrated, the injected P and Q during and after the fault is improved, compared to Fig 8(c). This enhancement is also observable on the IM rotor speed and electromagnetic torque profiles of Fig 10(d).
To investigate the effectiveness of the inferred conclusion of the eigenvalue analyses presented in Fig 9 about the limitation on increasing the FMS-RCI controlling parameters, another test case is studied while the values of K + and K − parameters are set to 7 under the same fault and grid condition. The results are presented in Fig 11. Although the value of the voltage support during the fault is improved, the system is not able to retrieve its balanced condition after the fault. It should be noted that neither the positive-nor the negative-sequence values of the PCC voltage have not passed the defined boundaries of 0 for the FMS-RCI strategy from where the reference reactive currents should be set to 1 p.u. However, due to the reduced stability margin of the whole system, as observed in the small-signal stability analysis of Fig 8, the RCG system is unable to rapidly follow the sudden change in |V − P | on the fault clearance. Therefore, the injection of the negative-sequence reactive current is continued even after the fault is cleared, and the system is failed in satisfying the LVRT requirements.
To illustrate the eigenvalue spectrum of each test case considering the related DF-stage values, Fig 12 is presented for the most dominant system poles. It is observed that for the case of K + = K − = 7, two system modes have moved to the unstable condition for the DF state values. These results confirm the illustrated time-domain simulation results and validate the developed analytical model.

V. SENSITIVITY ANALYSIS OF THE IM LOCATION RELATIVE TO THE DG UNIT
Another missing but significant study on the stability performance of a GCC-based DG unit in the presence of an IM load is an investigation on the effect of the distance between the DG unit and the IM load and how it can affect the relative stability of the entire system. To perform this study, in the obtained linear state-space model of the system, the length of the power line between the DG unit and the IM, presented by Z 2 (refer to Fig 1), is increased by increasing its magnitude (starting from 0.01 p.u.) whereas its angle, presented by the X /R ratio, is kept constant at 12.0 shows the obtained eigenvalue locus for both strong and weak grid conditions. For both cases, although the most dominant pole of the system is slowly moving towards left, there are two other poles quickly moving to the right. More investigations revealed that by increasing the magnitude of Z 2 more than 0.4 p.u. for the strong grid and more than 0.1 p.u. for the weak grid condition, the system represents unstable poles in the RHP. Therefore, it should be considered that there is a limitation on the length of the power line when installing a DG unit close to an IM load. Although longer distance decreases the interactions of the machine dynamics and the DG unit, it presents a higher voltage drop, which reduces the capability of the DG unit in providing active and reactive powers to the IM load.
This outcome is also investigated in the time-domain simulation model of the system. Results are shown in Fig 14 where the DG active power is presented for the case of the initial length of Z 2 (i.e., 0.01 p.u.) and when it is increased to FIGURE 11. LVRT performance of the system under weak grid condition using the FMS-RCI strategy with higher controlling parameters (K + = K − = 7). 0.1 p.u., which still represents stable system modes. The implemented RCG strategy is the FMS-RCI with K + = K − = 5. The same fault scenario of Section IV is studied  at t = 1.8 s. It is observed that, although the system is experiencing a stable performance before the fault, the power system, including the IM load, cannot retrieve its stable mode after fault clearance. The IM rotor lost its speed and the electromagnetic torque. The maximum value of i 1 on all phases stays high, which finally leads to the DG unit disconnection and the LVRT failure. This result verifies what is realized in Fig 13. Therefore, in the case of installing a DG unit to support an IM load, an efficient length of the power line between them should be considered to prevent future system collapse.

VI. EXPERIMENTAL RESULTS
The results of the time-domain and the state-space stability analyses are validated using a scaled-down 1.0 kVA laboratory prototype, as shown in Fig 15. The key components  for the laboratory setup are a dSPACE DS1104 real-time control systems, a three-leg voltage source converter (VSC) (Semistack intelligent power modules, each includes gate drives, six insulated gate bipolar transistors, and protection circuit), 60-Hz three-phase grid (phase-phase voltage 208 V), interfacing transformers, and sensor boxes to sample voltages and currents. The converter is interfaced with a control card using an interfacing circuit.
The pulse-width modulation and the converter controllers are implemented on the dSPACE control card supported with a coprocessor structure for switching signal generation. An induction motor is also connected between the grid and the VSC unit, as demonstrated in Fig 15, to represent the dynamic load effect. A three-phase, 4-pole, 208/230 V, 1725 rpm induction motor is used. The grid stiffness is changed by connecting series inductors to the ac grid so that the SCR of the studied system can be varied. For the strong grid condition, the SCR is considered 6.6, and for the weak grid condition, the SCR is set to be 3. In all test cases, an unbalanced fault is occurred at the same location as the simulation test cases, i.e., on the line between the grid and the IM.

A. STRONG GRID CONDITION
First, the DG unit is connected to the strong grid, and the LVRT performance of the system is monitored using the traditional and the FMS-RCI strategies. The results are shown in Fig 16, representing a successful LVRT performance when employing the traditional RCG and the FMS-RCI with the initially selected parameters as K + = K − = 2. However, the FMS-RCI strategy is clearly able to reduce the positivesequence voltage drop and the negative-sequence voltage value during the same fault condition, compared to the traditional RCG (see Fig 16(a) and (b)). Also, to show the system limitation in increasing the K + and K − parameters, another test case is studied when K + = K − = 7, shown in Fig 17. In this case, the injected current during the fault is greater than the protection setting (20 A) and causes the DG unit trip.  These results verify the small-signal and the time-domain simulation results of Section IV-A.

B. WEAK GRID CONDITION
In this test, the system is connected to the weak grid with SCR= 3, and the same fault scenario is studied. The results revealed that by employing the traditional RCG and the same initial design of the FMS-RCI which was used in the strong grid case, the system fails in providing the LVRT requirements and the DG unit gets disconnected. Fig 18 illustrates the results of the initial FMS-RCI method. Therefore, based on the obtained results of Section IV-B, the FMS-RCI parameters are increased to provide more voltage support on the PCC. The results are shown in Fig 19 which verify the aforementioned time-domain results. In addition, to find the maximum FMS-RCI parameters value for the case of weak grid condition, the value of K + and K − increased and the same fault scenario is observed. The results revealed that in this case, the maximum value of these parameters is K + = K − = 5 which is lower than what is observed for the strong grid condition. This result is also in agreement with the small-signal and the simulation results. The obtained waveforms are presented in Fig 20.

VII. DISCUSSION
According to a recent requirement by the German code of VDE-AR-N, the multi-sequence RCI has been mandated in the GCC-based DG units in which the injection of both positive and negative sequences of the reactive current is required for the LVRT.
Since the rotor oscillations cause mechanical and electrical power oscillations, the output power of DG units feeding an IM load contains the dynamic modes of these oscillations. This fact is demonstrated in Figure 2. Therefore, a thorough analysis of the dynamic behavior of GCC-based DG systems is essential for LVRT studies. This study attains more importance when the connected grid is not strong enough to support the IM load during a fault. To the best of the authors'  knowledge, the existing literature lacks an analytical and experimental study under the stated conditions. Therefore, the main contributions of this paper are as follows.
1) Modeling and dynamic analysis of the DG units connected to a large IM load and equipped with the RCG controllers based on the new LVRT standards [26], [27] have not been studied so far in the existing literature.
The new LVRT standards, require the DG units not only to stay connected to the grid but also to inject both positive and negative sequence reactive currents proportional to the unbalanced voltage sag characteristics under severe short-term unbalanced grid faults. In this paper, this newly-imposed important requirement is referred to as a flexible multi-sequence reactive current injection (FMS-RCI). Since the rotor oscillations cause the mechanical and electrical power oscillations, the output power of DG units feeding an IM load contains the dynamic modes of these oscillations. IM load contains the dynamic modes of these oscillations. This fact is demonstrated in Figure 2. Therefore, a thorough analysis of the dynamic behavior of GCC-based DG systems is essential for LVRT studies.
2) The flexible multi-sequence reactive current injection (FMS-RCI) technique is utilized in this paper to meet the mentioned grid code requirement, which uses two control parameters (i.e., K + and K − ) to simultaneously inject the required positive-and negative-sequence reactive currents, respectively, proportional to the amount of the positive-sequence voltage drop and negative-sequence voltage rise. 3) A multi-stage linearized state-space model (i.e., before, during, and after the fault) is developed for an IM-loadconnected DG unit with the consideration of all dynamics added to the system by the IM load/ This detailed model is the used to analyze the dynamic performance and stability of the system under the FMS-RCI requirement. This method provides the possibility of studying the imposed RCG methods before and during the unbalanced faults with different operating points. 4) The impact of two coefficients, K + and K − , in the FMS-RCI technique, on the dynamic performance and the transient stability of the IM-load-connected DG control system is studied. A model-based control parameter design is proposed to find suitable values of K + and K − in weak grid conditions for stability purposes under FMS-RCI requirements. 5) The impact of the grid strength on the stability and LVRT performance of the system in the decoupled double synchronous reference frame (DDSRF) is studied and analyzed using the participation factor analysis and the small-signal stability analysis. The parameters of the current controller are also designed based on the developed state-space model to have improved LVRT capability. 6) The proposed analytical design of the parameters in the FMS-RCI controller, as well as the current control loop, is also tested by several detailed nonlinear time-domain simulation and experimental test cases. The results are promising and demonstrate the effectiveness of the developed model and the proposed approach to improve the stability of the IM-load-connected DG system under severe unbalanced faults when the new LVRT standard is required by the grid code. 7) A sensitivity analysis based on eigenvalue analysis is performed on the location of the IM load relative to the DG unit. The results could reveal the limitation on the AC line length, considering the dynamics of the whole system.

VIII. CONCLUSION
This paper presented the dynamic analysis and performance improvement methods for the GCC-based DG unit system in the presence of an IM load. To assess the impact of utilizing the dynamic load on the integrated system stability, a detailed multi-stage small-signal model of the complete system was obtained, and the eigenvalue analysis was conducted considering both static and dynamic load modeling. The results showed that the dynamic load modeling adds 19 highly dominant less-damped modes to the studied DG unit system, which result in a lower relative stability margin and could effectively change the shaping of the system eigenvalues. Furthermore, considering the critical effect of the grid stiffness on the LVRT performance of the DG unit system connected to the IM load, the performance of the system was investigated under an unbalanced grid fault using three different reference current generation strategies to indicate the best strategy to provide a stable and efficient LVRT performance in the GCC-based DG unit system under strong and weak grid conditions. The model-based control system improvement method was used in both strong and weak grid conditions using the small-signal stability analysis to implement a stable and efficient system to ride through the grid fault considering the LVRT requirements. Besides, in the case of the weak grid condition, a maximum boundary for selecting the control parameters of the FMS-RCI strategy was obtained to satisfy the LVRT requirement and maintain the system stability margins. Finally, the sensitivity analysis was also performed to investigate the effect of the length of the power line between the DG unit and the IM on the stability and LVRT performance of the whole system. The time-domain simulation and experimental results were also presented to validate the effectiveness of the proposed methods.

APPENDIX
The standard linearized form of the state -space equations, Ẋ = A X + B U , is used in obtaining the complete system model, including the GCC-based DG unit, IM load, and the power system. Besides, to keep the final model equations less complicated, the state and input matrices are obtained using the following equations: Additional details on the linearization process can be found in [3]. The BPSC strategy (with the related equations presented in 0) is selected as the RCG method in obtaining the following state-space matrices. Also, the following auxiliary variables are defined to facilitate compact representation: pd,ss ) 2 +( v + pq,ss ) 2 ] 2 , den 2 = (v + pd,ss ) 2 + ( v + pq,ss ) 2 where the subscript ss stands for the steady-state values. The A 1 matrix is divided into smaller sections as follows: The non-zero elements of each sub-matrix are as follows: