# Optimal Operation of Isolated Microgrids Considering Frequency Constraints

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## Abstract

**:**

## 1. Introduction

#### 1.1. Literature Review

#### 1.2. Required Improvements in the EMS Development for Isolated Microgrids

#### 1.3. Paper Contributions

- The parameters that, being available by the EMS, may influence the frequency deviations are analyzed.
- The the maximum frequency deviation in front of the maximum power imbalance is formulated. This formulation uses the above-mentioned parameters.
- An EMS including a frequency constraint is formulated.
- The validation of the proposed EMS using dynamic simulation and laboratory platform is presented.

## 2. System Description

_{pv-nom}; and a battery with rated power and capacity P

_{bat-nom}and ${C}_{bat}$, respectively. Finally, all these generation and storage units feed the total power demanded by the loads (${P}_{c}$). The layout is based on a real stand alone system. It has the particularity that all generation and storage units (controllable units) are connected to the same bus. Thus, the load side can be treated as a single aggregated load. Each controllable unit has its local controller (LC) which is in charge of managing each resource separately:

- LC for diesel generation power plant: The local controller is in charge of controlling the frequency of the grid. A proportional–integral (PI) controller, where the input is the frequency error (filtered by a low pass filter), computes the mechanical torque setpoint of each diesel generator. This local controller also receives the required number of connected diesel generators and accordingly sends orders of connection/disconnection to each diesel unit. Each diesel generator has its internal controller in charge of reaching the torque setpoint and to perform its connection and disconnection according to the LC requirements. A similar control architecture is found in [23]. The main difference is that in the present paper the PI is a central controller that coordinates all the diesel units, while in [23] a single unit is considered.
- LC for the PV power plant: This LC implements a power–frequency droop curve to provide support to the grid. Reducing the active power will always be possible, but increasing it (under frequency events) will depend on the available active power. The controller can perform power curtailments. A maximum PV power setpoint is received externally and a PI controller computes the active power setpoint of each PV inverter. This controller is defined in [24], but the ramp rate limitation is not taken into account.
- LC for the battery: This controller receives externally an active power sepoint and applies a power–frequency droop curve to provide grid support. The output is the droop modified setpoint. The inner control loops will be in charge of reaching this value of active power. The dynamic model is simplified as in [25], but the local frequency droop has been included.

## 3. Methodology

#### 3.1. EMS Design Requirements

#### 3.2. EMS Performance

#### 3.3. Execution Cycle

#### 3.4. Modeling Frequency Deviations

_{2}emissions) solution. Accordingly, the optimal solution is to connect the minimum number of rotating machines that ensures that, after a maximum power imbalance, the grid frequency will be kept in the required range.

#### 3.5. Scenarios Generation

#### 3.6. Stochastic Formulation Approach

#### 3.7. Formulation of the Optimization Algorithm

#### 3.7.1. Sets

#### 3.7.2. Decision Variables

#### 3.7.3. Parameters

#### 3.7.4. Objective Function

#### 3.7.5. Constraints

## 4. Case Study

## 5. Experimental Validation

#### 5.1. Platform Description

#### 5.2. Emulation Results

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Box plot showing the relation between the minimum frequency reached and the decision variables of the EMS.

**Figure 5.**Linear regression results for the coefficients of the minimum frequency equation. Caption from R software.

**Figure 10.**Laboratory emulation results for the first scenario (high PV power variability after the midday.

Parameter | Value | Parameter | Value | Parameter | Value |
---|---|---|---|---|---|

${n}_{TEMS}$ | 288 | $Ca{p}^{bat}$ | 1120 kWh | ${P}^{mnB}$ | −2200 kW |

${n}_{Tintra}$ | 10 | $SO{C}^{i}$ | 0.9 | ${P}^{mnD}$ | 0.3·1100 kW |

${N}_{d}$ | 9 | ${\eta}^{bat}$ | 0.9 | ${P}^{mxD}$ | 1100 kW |

${N}_{s}$ | 5 | ${P}^{mxB}$ | 2200 kW | $marg{e}_{dies}$ | 2000 kW |

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**MDPI and ACS Style**

Vidal-Clos, J.-A.; Bullich-Massagué, E.; Aragüés-Peñalba, M.; Vinyals-Canal, G.; Chillón-Antón, C.; Prieto-Araujo, E.; Gomis-Bellmunt, O.; Galceran-Arellano, S.
Optimal Operation of Isolated Microgrids Considering Frequency Constraints. *Appl. Sci.* **2019**, *9*, 223.
https://doi.org/10.3390/app9020223

**AMA Style**

Vidal-Clos J-A, Bullich-Massagué E, Aragüés-Peñalba M, Vinyals-Canal G, Chillón-Antón C, Prieto-Araujo E, Gomis-Bellmunt O, Galceran-Arellano S.
Optimal Operation of Isolated Microgrids Considering Frequency Constraints. *Applied Sciences*. 2019; 9(2):223.
https://doi.org/10.3390/app9020223

**Chicago/Turabian Style**

Vidal-Clos, Josep-Andreu, Eduard Bullich-Massagué, Mònica Aragüés-Peñalba, Guillem Vinyals-Canal, Cristian Chillón-Antón, Eduardo Prieto-Araujo, Oriol Gomis-Bellmunt, and Samuel Galceran-Arellano.
2019. "Optimal Operation of Isolated Microgrids Considering Frequency Constraints" *Applied Sciences* 9, no. 2: 223.
https://doi.org/10.3390/app9020223