# Load shedding strategy coordinated with storage device and D-STATCOM to enhance the microgrid stability

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## Abstract

Recently microgrids have drawn a potential attraction by fulfilling the environmental demands and the increasing energy demands of the end-users. It is necessary to focus on various protection and control aspects of a microgrid. During the transition between the grid-following and grid-forming modes, the voltage and the frequency instability due to the power mismatch condition becomes the major point of concern. Therefore, the paper executes a frequency-active power and voltage-reactive power drooping control strategy for the precise power-sharing among the distributed power generators. Furthermore, to handle the power deficit scenarios and to maintain the system stability, a system independent and priority-based adaptive three-stage load shedding strategy is proposed. The sensitivity of the strategy depends on the system inertia and is computed according to the varying absolute rate-of-change-of-frequency. The strategy incorporates the operation of battery storage system and distributed static compensator (D-STATCOM) in the microgrid, to provide a reliable power supply to the customers for a considerable time instead of a sudden load shedding. The effectiveness of the proposed strategies is investigated on a scaled-down modified IEEE 13-bus microgrid system on the podium of MATLAB 2015b through the time-domain simulation.

## Keywords

Microgrid Power-sharing Load shedding High inertia distributed generators Inertia-less distributed generators Battery storage system D-STATCOM## Abbreviations

- AVR
Automated voltage regulator

- BES
Battery energy storage

- DG
Distributed generators

- D-STATCOM
Distributed static compensator

- ESS
Energy storage system

- MPPT
Maximum power point tracking

- PCC
Point of common coupling

- PI
Proportional-integral

- PV
Photovoltaic

- ROD
Rate of discharge

- SOC
State of charge

- SPWM
Sinusoidal pulse width modulator

- UFLS
Under-frequency load shedding

- VSC
Voltage source converter

## 1 Introduction

The incorporation of renewable power sources with the power utilities has been a promising solution towards the uninterrupted eco-friendly power demand. As a consequence, the installation and integration of distributed generators (DG) with the utilities appear as a major source of developing the small and medium-size microgrids [1]. Since the DGs in the conventional microgrid are operationally similar, the effects of disturbance and the amount of power to be shared are equally distributed without overloading any particular DG in the microgrid. But the voltage and the frequency at the point of common coupling (PCC) between the microgrid and utility undergo high distortion [2]. However, with the increased research efforts, the microgrids successively integrate the very differently operating DG (i.e., synchronous machine and inverter-based power sources). This incorporation of high inertia synchronous machines in an inertia-less dominated microgrid environment supports the system to ride through during the transient [3].

At the occurrence of any disturbance in the operationally diversified DG integrated microgrid, the power-sharing challenge arises. The inertia-less inverter-based DG can instantly respond to the fluctuation and vary the voltage according to the power required. Conversely, the sudden changes in the power are not feasible for high inertia based DG (synchronous machine). Further, the issue turns out to be critical, when the power generation of the operating DG reduces significantly due to the climatic condition [4]. Thus, the conjunction of high inertia power sources with the inertia-less sources challenges the operational stability. In order to address these issues, power-sharing integrated load shedding strategy is executed to enhance the performance of the microgrid [5, 6]. A two-phase droop based frequency control and a load shedding strategy are analyzed in [5] to maintain the stability of an autonomous microgrid.

To attain a stable electric system, various researchers have proposed several under-frequency load shedding (UFLS) schemes [7, 8, 9]. The conventional UFLS technique employs the strategy of shedding a fixed amount of load according to the predefined frequency limits. This conventional strategy uses a trial and error approach to calculate the number and the amount of load to be shed in each step. The strategy possesses a major drawback of shedding either the excessive or insufficient load amount, to attain the system stability [10]. Thus to shed an exact amount of load from an appropriate location brings into the adaptive UFLS scheme. The adaptive load shedding strategy sheds the load by measuring the frequency derivatives [11]. As a result, the load is shed based on the power deficit in each step.

Extensive work has been done in the field of adaptive UFLS. A comparison among the conventional, semi adaptive and adaptive UFLS is presented in [12]. The adaptive load shedding scheme implements rate-of-change-of-frequency in [11, 12, 13] and disturbance magnitude in [14] to shed the load. Further to enhance the shedding strategy, [13, 15] use voltage dependency of the load to shed the loads. In [16, 17] the frequency deviation is monitored in accordance with the inertia constant and follows a pattern of response based event approach. A strategy proposed in [18] implements shedding at the location where the voltage reduction and the frequency deviation is maximum. Integer programming and genetic algorithm are executed in load shedding strategies by [19, 20]. Moreover, certain smart-grid load shedding strategies are introduced by [21, 22]. The strategies proposed till now need to be explored further to achieve efficient performance in a microgrid environment. The microgrid system with multiple numbers and multiple types of power sources, storage devices, and loads, challenges the calculation of exact values for the load shedding parameters. Furthermore, the slightest interruption in an isolated microgrid can affect system stability. A reactive power deficit during the autonomous mode of operation may lead the system towards voltage sag. Subsequently, the voltage sags vary the amount of power drawn by the load. As a result, delay in the measurements of frequency and its derivative may mislead the shedding strategy, because the estimated power shortage will be lesser than the actual deficit. Further, an additional drawback of this strategy is the non-linear relationship between the amount of load shed and the power deficit.

In order to further enhance the adaptive UFLS scheme in accordance with the transient stability, storage elements like ultracapacitor are incorporated to impart dynamic frequency support by [23]. Further to compensate for the frequency variations until the governor response comes into action, the super-conducting storage devices are implemented by [24]. The super magnetic energy storage device to enhance transient stability while shedding the loads are also employed in [25]. However, the implementation of fast-responding storage devices cannot be imposed with the frequency limit and their energy recovery factor. Further, the presence of slow-responding storage devices in the microgrid is yet to be considered while designing the UFLS.

The energy storage system has been an indispensable part of the microgrid. The addition of a storage system is a smart way to curb the power fluctuations and counteract the power imbalances [26]. Besides that, the storage system plays a significant task in improving the system reliability and stability in a microgrid (comprising a major share of renewable sources). Its integration could set-back the cost of improving the transmission and distribution capacity to address the increasing power demand [27]. Thus, a battery energy storage (BES) device is integrated into the microgrid system to counteract the power deficits. The operation of BES is incorporated with the load shedding strategy to support the local loads from the instantaneous power cut-off during the unstable system operation.

However, the incorporation of the battery storage devices cannot always ensure a robust transient support system because these storage elements offer low power density with respect to their storage volume. Though these kinds of storage devices increase the relative inertia of the microgrid, but fail during the transient period. In other words, the microgrid lacks the required amount of inertia to withstand the transient fluctuations due to the system disturbances. Therefore, considerable attention has been drawn towards the integration of distributed static compensator (D-STATCOM) in the microgrids.

D-STATCOMs solely perform to improve the load balancing and power factor of a system [28]. The incorporation of D-STATCOMs in the distribution structure has drawn a significant interest because of its novel characteristic of compensating either PCC voltage or the line current [29]. Thus in this paper, the D-STATCOM performs to avoid the instantaneous conflict of power-sharing between the two different types of inertial DG by compensating the voltage. The paper also highlights that the D-STATCOM and the high inertia system can efficiently control the system stability for a few cycles until the load shedding is initialized.

A detailed analysis of a P-f and Q-V droop control strategy to attain an efficient power-sharing among the different inertial DGs.

The paper proposes an independent and priority-based adaptive three-stage load shedding strategy.

To enhance the system stability, the performance of the battery and D-STATCOM present in the microgrid is closely analyzed while executing the load shedding algorithm.

The manuscript is organized as follows: Section II introduces the test system undertaken. Section III describes the controller design for each power source incorporated in the microgrid. The proposed control method for power-sharing and load shedding is extensively described in Section IV. The test results of the proposed strategy are analyzed in Section V. A brief discussion and conclusion obtained from the result analysis are discussed in Section VI and Section VII respectively.

## 2 Microgrid structure

The system parameters are presented in the Appendix. The microgrid covers a distance of 8200 ft. length. The designed microgrid is integrated with the utility via a 115 kV(delta)/25 kV(grounded wye) substation transformer. The Simulink platform of MATLAB 2015b is used to replicate and test the designed microgrid system.

## 3 Controllers of power sources

### 3.1 Micro-sources

^{2}solar irradiance. The maximum power point tracking (MPPT) uses the Incremental Conductance method. The duty cycle controlled by the MPPT varies according to the voltage required to maximize the power extraction [30]. The DC-AC inverter converts the maximum extracted DC power to AC power using the control based on the dq reference frame. The control is designed such that it varies the DC link voltage according to the voltage variations at the PCC. The extracted power from the PV system is fed to the DC link [31]. Therefore, the

*V*

_{dc}controller in the inverter, controls the voltage variations by specifying the d-axis current (\( {I}_{d_{ref}} \)) values to balance the power flow in the DC link [32]. Since the system is considered to be operating at unity power factor, the reactive reference current (\( {I}_{q_{ref}} \)) is considered to be zero. Further, the control system implements the phase-locked loop to maintain the inverter voltage in phase with the grid voltage. The d-q axis currents when fed to the proportional-integral (PI) controllers, it helps in obtaining the reference voltages for the sinusoidal pulse width modulator (SPWM). The control design for the inertia-less inverter-based DG is shown in Fig. 2a.

*i*and

*v*terms represent the instantaneous current and voltage respectively.

*R*

_{f}and

*L*

_{f}signify the resistance and the inductance of the filter respectively.

*v*

_{dconv}and

*v*

_{qconv}, the magnitude and the angle for the SPWM are generated. Hence, the inverter’s switching pattern is signalled using (4).

- 1)
It provides protection against the over-current.

- 2)
It reduces the contribution of fault currents by the unit.

- 3)
It limits the converter output current during fault conditions.

On the other hand, the design of a high inertia synchronous system regulates the voltage and the frequency by a different approach. The frequency of the generator is regulated by adjusting the torque on the basis of speed error. Simultaneously the reference speed is adjusted according to the active power measured. Further, the automated voltage regulator (AVR) integral action regulates the voltage when the voltage reference error becomes zero [33]. The control strategy of the generator is presented in Fig. 2b.

The synchronous generator feeds both the active and the reactive power simultaneously up to certain limits of MVA rating according to the prime mover’s capability. These limits can be obtained from the capability curve of the synchronous generator. The curve in Fig. 2c defines the inter-relation between the active and the reactive power to be generated by the generator. The shaded portion under the capability curve in Fig. 2c represents the required quantity of reactive power to be generated by the generator. Further, the point of intersection between the armature heating limits and field heating limits specifies the MW and MVAR rating of synchronous generators [34]. In Fig. 2c, it can be analyzed that intersecting point ‘A’ sets the generator active power as \( {P}_{SG}^{rated} \) and reactive power at \( {Q}_{SG}^{rated} \). The reactive power can be fed until it reaches the heating limits (i.e., \( {Q}_{SG}^{rated} \)). However, if the reactive power to be fed is further increased to \( {Q}_{SG}^B \) at point B in Fig. 2c, it is delivered by reducing the active power generation as \( {P}_{SG}^B \) (where \( {P}_{SG}^B \) < \( {P}_{SG}^{rated} \)). The limits on the reactive power generation are set by either the armature heating limits as in point ‘B’ or by the field heating limits as in point ‘C’ [35].

### 3.2 D-STATCOM

The major role of D-STATCOM is to perform a conversion of input DC voltage to an output three-phase AC voltage. The instantaneous input and output power have to be balanced properly. Therefore, the input terminal of VSC is connected to a capacitor, which acts as a passive voltage source. On the other hand, the output of the VSC is connected to a coupling transformer, which acts as a passive current source.

*V*

_{stat}and

*E*represent the voltage at D-STATCOM and bus respectively,

*X*signifies the system reactance and

*I*

_{stat}presents the current fed by the D-STATCOM. On using eq.(5), the reactive power compensated by the D-STATCOM can be stated as:

Analyzing (6), it can be clearly stated that the voltage fed by the D-STATCOM regulates the reactive power of the system [38]. The control over reactive power is attained by keeping the D-STATCOM voltage in phase with the system voltage. Moreover, these in phase voltages do not allow the charged capacitor to supply active power into the system. Further, at zero frequency of the DC capacitor, the reactive power of D-STATCOM is zero. Thus, it can be concluded that the DC capacitor does not play a role in reactive power generation. It proves that the VSC of D-STATCOM is capable of facilitating the free flow of reactive power among the three AC terminals [39]. The DC capacitor only enables the compensation for the instantaneous power mismatch in the system.

### 3.3 Storage device

The storage system considered in this study is the Lithium-Ion battery model acquired from the Matlab *SimPowerSystems* library. The battery parameters are set to support the P-f and Q-V control within the system. In-depth analysis regarding the storage devices presented in [40]. Due to the uncertain fluctuations in renewable power generation and load demands, lithium-ion batteries are highly preferable in microgrids. This is due to the fact that these batteries can be exploited up to their maximum capacity [41]. Therefore, to achieve a deep cycle operation, the lithium-ion batteries have been modelled with the proper selection of parameters.

*E*

_{battery}) can be expressed as:

The analytical battery model can be presented by (8) and (9) for charging and discharging respectively.

#### 3.3.1 Charge

#### 3.3.2 Discharge

*V*

_{battery}and

*I*

_{battery}represent the battery voltage and current respectively.

*K*signifies the polarisation constant and

*R*

_{int}signifies the internal battery resistance. The battery capacity is represented by

*Q*whereas the actual charge of the battery is presented by

*Q*

_{actual}. The constant voltage and the filtered current of the battery are stated as

*E*

_{0}and

*i*

_{filtered}respectively. To address the exponential zone of amplitude and time constant inverse, under the characteristic curve of the battery are termed as A and B respectively [42].

The assumption made for the undertaken battery system is that it can discharge up to State-of-Charge (SoC) being 30%. The battery parameters are set to reduce the rate of discharge after 50% of SoC is attained.

## 4 Proposed control method for microgrid

In order to attain a balanced voltage profile and a reduced system loss, efficient power-sharing is crucial. Power-sharing can be controlled either by implementing a communication-based centralized control strategy or by decentralized droop strategy. In recent times, communication strategies are avoided because of their economic limitations. Moreover, the interruptions and break-down in communication are few added up limitations to the communication-based control strategy. Hence, decentralized droop control strategies have drawn major attention. The droop control facilitates faster stability and an efficient power-sharing among the distributed generations in a microgrid.

*V*

_{1}∠

*δ*and

*V*

_{2}∠ 0) connected by reactance (

*X*) dominated impedance line. The power transfer between the two sources can be termed as:

*δ*, as the angle tends to be small during the normal operation of the system. The reactive power transferred also varies proportionally with the difference between the voltage magnitudes at the two ends [43]. Thus, the droop characteristics can be framed as in (12) and (13), and are graphically shown in Fig. 4.

Therefore, the control strategy of DGs present in an inductance-dominated microgrid implements active power-frequency (P-f) and reactive power-voltage (Q-V) droop control characteristics [44]. The strategy aims to maintain the voltage and the frequency of the microgrid within its limit, along with a precise power-sharing between the multiple power generators present in the microgrid.

In spite of an efficient power-sharing strategy, the microgrid may undergo an instability while experiencing an overloading condition. In an autonomous mode, the distributed power generators sacrifice their frequency and voltage to increase the power generation. This leads to a reduction in voltage and frequency, which may go beyond the specified threshold limits and cause a system blackout. A self-governing microgrid manages the power shortage either by increasing the power generation or by shedding the increased power demand. As a result, the system response due to the increased generation or reduced load demand is incorporated to restore the voltage and frequency stability. Thus, the paper proposes a load shedding strategy along with power-sharing.

A system independent and priority-based adaptive three-stage load shedding strategy is proposed. It deals with the power inequality in a microgrid after the occurrence of an islanding event. The rate-of-change-of-frequency is considered to compute the amount of load to be shed. At the beginning of the load shedding algorithm, it verifies the presence of a storage system. The stored battery power supports to prolong the load for a certain time. The first stage of the strategy controls the rapid frequency drop by shedding large loads. It also causes the system frequency to settle within the specified operational lower limit (*f* ≥ 59.3).

As the grid-forming microgrid possesses minimum inertial stability, it becomes highly sensitive to the dynamic load demand. This sensitivity increases the system instability with the increment in the frequency deviation. Therefore, in the second and third stages of the proposed load shedding algorithm, it has been observed that the operating frequency tends to maintain the nominal frequency (60 Hz). Thus, to reach the predetermined operating value of the system frequency, the second stage of load shedding strategy triggers and sheds small load in iterative steps. Subsequently, the third stage of load shedding tends the difference between the operating frequency and the nominal frequency to approximately zero by shedding the very small loads. The algorithm for the proposed load shedding scheme is presented in Fig. 6 and each shedding stage is analyzed in the section as follows:

### 4.1 Proposed load shed amount

*Δf*respectively. However, the amount of shed load differs in each stage. The proposed scheme ensures an iterative shedding process and the sheddable loads from busses are decided using the strategy presented in [45]. The iteration continues until it satisfies the individual criterion. The scheme computes the shedding amount concerning the instantaneous rate of change of frequency measured. From Fig. 5 it can be observed that the rate-of-change-of-frequency varies significantly during the transition between the stages. The load to be shed during an iteration is computed using (14).

Here, *P*_{Load − shed} is the amount of load shed in each iteration, and *K* denotes the shedding constant obtained from the swing equation of the system. *H*_{equivalent} denotes the normalized inertia constant.

### 4.2 Battery and DSTATCOM performance simultaneously with the proposed load shedding strategy

The presence of a storage system in a microgrid adds to the advantages of the proposed load shedding strategy. It provides a certain amount of power to the extra loads by a certain period of time. The battery storage element supports during the islanded microgrid and compensates for the steady part of the power deficit. Conversely, the D-STATCOM compensates the system disturbances during the transients. The batteries supply a steady power at a specified nominal rate of discharge (RoD_{1}) till they reach 50% and at RoD_{2} till they reach 30% of their state-of-charge (SoC). The SoC of a battery is a time-scaled factor with respect to the rate of power delivery. In other words, the instantaneous change in power supply does not change the SoC instantaneously. Therefore, considering the deep discharge limit of the battery, the power supplied by the battery is intentionally reduced to RoD_{2} at a specified SoC condition of 50%. It can be observed from Fig. 6 that the algorithm clearly shows the operational performance of the storage device.

### 4.3 Stage-I of load shedding

The first stage of the proposed load shedding scheme functions with the objective to hold back the normal operating conditions of the microgrid after facing a severe power deficit. In Fig. 6, load shedding steps involved in each stage are highlighted. From the conventional strategy of power networks, it is observed that the rate of decrement of the frequency inversely depends on the cumulative short-circuit MVA of the entire integrated system [46]. However, in the microgrid the short-circuit MVA dramatically falls down due to the power electronic interfaces present in the system. Therefore, the microgrid fails to withstand the extra load demand. As a result, at the instant of islanding, system frequency drops down in proportion to the surplus load demand. The analyzed microgrid characteristic can be observed in Fig. 5. From Fig. 5 it can be clearly observed that the rate-of-change-of-frequency is proportional to the microgrid demand. So, to regain the rate-of-change-of-frequency, a large load is shed using eq.(14) in an iterative process. Thus, the load shedding starts when the system frequency goes beyond 59.3 Hz. The iterative process continues until the frequency regains to the given threshold set value *f* ≥ 59.3. The instant, when the microgrid reaches the set frequency limit for operational stability, the stage-II triggers.

### 4.4 Stage-II of load shedding

The loads in this stage are shed by considering the rate-of-change-of-frequency \( \left(\raisebox{1ex}{$ df$}\!\left/ \!\raisebox{-1ex}{$ dt$}\right.\right) \). Smaller values of load shed in each step tends the frequency towards the operating nominal frequency of 60 Hz. The proposed algorithm in Fig. 6 illustrates that the iterative shedding process in this stage continues until the rate-of-change-of-frequency is less than 0.03.

### 4.5 Stage-III of load shedding

Now, as soon as the rate-of-change-of-frequency attains its 0.03 limit, the third stage of load shedding starts. In this stage, the *Δf* (i.e., difference between the operating frequency and the nominal frequency (60 Hz)) is calculated to shed small loads. The intention of this stage is to make *Δf* = ± 0.05, by shedding small load iteratively. The stage-III of the load shedding strategy sheds the loads in a very small amount and makes the system stable. The stage reaches an end on achieving the *Δf* to be approximately zero.

The amount of load shed in each iteration and in each stage of the algorithm is based on the absolute rate-of-change-of-frequency of the microgrid. Hence, the shedding scheme is independent of the power generation. As a result, the climatic challenges or the operational challenges will not affect the load shedding strategy. Thus, the load shedding controls the microgrid to attain stability during the grid-forming mode of the microgrid. Further, the power-sharing scheme subsequent to load shedding strategy also operates to maintain a stiff system synchronization.

## 5 Result analysis

This section presents the efficacy of the proposed approach under the system undertaken. About four different cases are simulated to analyze the performance of the system. Initially, the performance of the compensating devices present in the test system is analyzed individually and subsequently the proposed load shedding approach. Case-1 highlights the power-sharing performance within the microgrid integrated only with a battery storage device under 5% of overloading. Case-2 is an extension of the first case. It integrates D-STATCOM into the system and analyses its effect on the distributed generators present in the system. Highlighting the power-sharing strategy in Case-1 and Case-2, an emphasis has been given to investigate the power-sharing and load shedding strategy together in the subsequent cases. Case-3 verifies the system stability using load shedding strategy under 30% of active power and 10% of reactive power overloading condition. Further, in Case-4 the load shedding strategy is examined under a power deficit scenario, where the power generation at the DG end reduces significantly.

### 5.1 Case-1

At time 4.55 s, when the battery attains 50% of SoC, the power to be fed is reduced. On attaining the 30% of SoC at 7.49 s, the power fed by the battery is approximately zero. The active power fed by a battery based on the SoC can be studied in Fig. 7b. In the meantime, when the battery power reduces, the microgrid load demand is compensated by the synchronous generator of the microgrid. The photovoltaics do not increase its power generation as it is an MPPT based system and always supplies the maximum power in the system. The DG-2 increments the power in two steps at time 4.55 s and 7.49 s as illustrated in Fig. 7c. The reactive power fluctuations are negligible, as only the active power of the battery is compensated by the DG-2 in this case study. This negligible reactive power variation of DG-2 is presented in Fig. 7d. The increase in power generation by DG-2 is attained by reducing the DG voltage and frequency. Thus, the drop in voltage and frequency corresponding to the power increment can be analyzed from Fig. 7e and f respectively.

### 5.2 Case-2

Case-2 is an extension of the case-1. The system is considered with a similar overloading condition of 5% with the integrated power sources, storage device and a D-STATCOM. The power-sharing is efficient in Case-1 but the reactive power overloading is solely controlled by the synchronous generator from the instance of islanding. In order to support the reactive power compensation, the D-STATCOM is integrated and its effect on the system is examined in Case-2. The D-STATCOM is assumed to be triggered at the detection of an autonomous mode of operation.

A comparative analysis of DG power generated with and without D-STATCOM

D-STATCOM | Peak overshoot (in p.u) | Rise time (in seconds) | Settling time (in seconds) | ||
---|---|---|---|---|---|

DG-1 | P | Without | 0.7326 | 0.006 | 0.192 |

With | 0.7184 | 0.044 | 0.148 | ||

Q | Without | 0.002998 | 0.015 | 0.191 | |

With | 0.001992 | 0.024 | 0.132 | ||

DG-2 | P | Without | 0.7477 | 0.046 | 0.328 |

With | 0.5853 | 0.054 | 0.245 | ||

Q | Without | 0.3274 | 0.045 | 0.278 | |

With | 0.2542 | 0.064 | 0.186 |

The integration of D-STATCOM suppresses the transient peak overshoot in active power by 1.938% and 21.71% in DG-1 and DG-2 respectively. It can be observed that the suppression in DG-1 is negligible, as it operates at the maximum power point. The reactive power transient fluctuation is suppressed by 21.71% and 22.35% in both DG-1 and DG-2 respectively.

### 5.3 Case-3

The location and amount of the load shed

Load No. | L1 | L2 | L3 | L4 | L5 | L6 | L7 | L8 | L9 | L10 | L11 | L12 | L13 | L14 | L15 | L16 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Bus no. | 1 | 8 | 7 | 12 | 7 | 13 | 9 | 11 | 10 | 2 | 5 | 3 | 4 | 6 | 6 | 10 |

Load(kW) | 13.2 | 50 | 10 | 12.8 | 4.5 | 22.5 | 2.3 | 4.7 | 15 | 7.5 | 17.2 | 5.5 | 7 | 4.2 | 2.4 | 6.4 |

Priority | ✓ | ✓ | ✓ | ✓ | ||||||||||||

Stage-I of LS | i = 2 | i = 1 | i = 3 | |||||||||||||

Stage-II of LS | i = 1 | |||||||||||||||

Stage-III of LS | i = 1 |

The proposed load shedding strategy initializes the stage-I of the strategy and sheds the load in three iterations at time 1.4 s, 1.8 s, and 2.2 s. The effects of the load shedding on voltage and frequency are illustrated in Fig. 12a and b respectively. The MPP controlled DG-1 being an inertia-less power source responds with an insignificant time delay to the load shed. Whereas the DG-2 being a high inertia system shows a sluggish response and consumes a certain time to retain itself within the stability zone. The time consumed to retain the stability is compensated by the D-STATCOM present in the microgrid. The stage-I of the load shedding strategy tends the microgrid to attain the voltage and the frequency within the operating limits as shown in Fig. 12a and b.

Further, when the \( \frac{df}{dt} \) condition satisfies, the stage-II of the load shedding strategy is triggered. Though the system parameters are operating within the stability limit, but to achieve the system to be operating at a standard operating point, a small load is shed at a time about 3.2 s and the stage-III of the load shedding scheme sheds another small load at 3.9 s. The variations in active and reactive power generation of DG-1 and DG-2, corresponding to the load shed can be analyzed from Fig. 12c and Fig. 12d.

### 5.4 Case-4

The location and amount of the load shed

Load No. | L1 | L2 | L3 | L4 | L5 | L6 | L7 | L8 | L9 | L10 |
---|---|---|---|---|---|---|---|---|---|---|

Bus no. | 1 | 8 | 7 | 12 | 7 | 13 | 9 | 11 | 10 | 2 |

Load(kW) | 13.2 | 50 | 10 | 12.8 | 4.5 | 22.5 | 2.3 | 4.7 | 15 | 7.5 |

Priority | ✓ | ✓ | ✓ | ✓ | ||||||

Stage-I of LS | ||||||||||

Stage-II of LS | i = 1 | |||||||||

Stage-III of LS | i = 1 | i = 2 |

## 6 Discussion

A comparative study of the proposed load shedding strategy with the state-of-art

Ref | System undertaken | The efficiency of the load shedding strategy | Overall system frequency drop (in Hz) | Remarks |
---|---|---|---|---|

[17] | Microgrid (50 Hz) | 98.36% | 48.92 | The system with synchronous and asynchronous generators |

[18] | Microgrid (50 Hz) | 96.82% | 48.8 | Implementation of an adaptive controller to maintain stability. |

[21] | IEEE 14 Bus System (60 Hz) | 94.50% | 59.6 | Load shedding without any supporting device. |

[22] | Power system with interconnected power districts (50 Hz) | 98.20% | 49.72 | Application of smart metering system for emergency shedding |

[23] | Distribution system (Guadeloupean Power System) (50 Hz) | 97.45% | 48.5 | Ultracapacitor storage to support the dynamic frequency. |

[24] | Distribution system (23 bus sample system) (60 Hz) | 98.34% | 59.46 | Super-conducting storage devices compensate the frequency variations until the governor response |

[25] | Distribution System (China Steel Corporation) (60 Hz) | 97.89% | 58.10 | Super magnetic energy storage device to enhance transient stability while shedding the loads |

Proposed Approach | Modified IEEE 13-bus microgrid system (60 Hz) | 99.25% | 58.92 | Three-stage adaptive load shedding strategy supported by battery and D-STATCOM to maintain system stability. |

## 7 Conclusion

The article aims to address the microgrid stability while operating in an autonomous mode of operation. The microgrid system undertaken integrates both inertia-less and high inertia power sources along with the storage system and the reactive power compensating device. The control strategy for each unit is elaborated in Section III of the manuscript. Each operating unit uses the P-f and Q-V power-sharing control strategy to maintain system stability. To deal with the worst-power deficit scenario, a load shedding strategy is proposed. The shedding strategy incorporates the microgrid storage system to prolong the loads for a certain time after attaining the frequency within the operational stability and limit. The D-STATCOM present in the system helps to avoid the instantaneous conflict of power-sharing between the two different types of inertial DG by compensating the voltage, and efficiently control the system stability for few cycles until the load shedding is initialized. The designed droop based load shedding strategy is only dependent on the system inertia. The strategy sheds load to control the reducing rate-of-change-of-frequency. The precise shedding process is faster compared to the conventional schemes and confirms the difference between the operating frequency and nominal frequency to be approximately zero proving its robustness to act under a wide range of operating conditions.

## Notes

### Acknowledgments

The authors acknowledge the financial support provided by the Council of Scientific and Industrial Research (CSIR), Government of India.

### Authors’ contributions

SC and PB carried out the design of the proposed study and performed the statistical analysis. PKR perceived the study, and participated in its design and coordination and helped to draft the manuscript. All authors read and approved the final manuscript.

### Funding

Financial funding by Council of Scientific and Industrial Research (CSIR), Government of India.

### Ethics approval and consent to participate

Not applicable.

### Consent for publication

The Authors grants the Publisher the sole and exclusive license of the full copyright in the Contribution, which license the Publisher hereby accepts.

### Competing interests

The authors declare that they have no competing interests.

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