# Dynamic Modeling and Simulation of Non-Interconnected Systems under High-RES Penetration: The Madeira Island Case

^{1}

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^{*}

## Abstract

**:**

## 1. Introduction

^{®}E, etc., offer automated calculations with closed “black box” models. On the contrary, a more transparent approach can be implemented using the Modelica language [29], allowing the simulators to customize real operating parameters and strategies in more detail. Modelica is an object-oriented, declarative, multidomain modeling language for the component-oriented modeling of complex systems. Users can define custom models utilizing its acausal equation-based nature. Modelica environments include open-source environments like OpenModelica [30] and proprietary environments like Dymola, SystemModeler, SimulationX, etc. Several open-source power system libraries have been developed, and a review can be found in [31]. The main noteworthy Modelica libraries for electric power systems modeling studies are PowerSystems [32] and OpenIPSL [33]. However, few simulation studies dedicated to islanded high-RES systems problems have been conducted using Modelica so far.

_{e}and incorporates various renewable sources in its energy mix. Furthermore, the island belongs to the innovator islands in terms of energy transition, and, in the near future, there are extension plans for the introduction of a high percentage of intermittent generation capacities into the HV/MV grid, supported by energy storage units [34,35,36]. For all these characteristics, Madeira’s power system is a considerably valuable case study.

- The transient modeling of a complex NII power system with a wide range of renewable and conventional power generation units, utilizing exclusively open-source software. This feature enhances the innovative character of the current work, as the value of open-source software for power systems’ simulations has already been emphasized by the research community [37]. There are no publications of such complex real systems without using a commercial package, making this paper innovative.
- A novel methodological approach for the impact assessment of high-RES penetration on the island’s frequency stability. This approach involves examining both the current and future states in terms of stability and considering all the additional RES capacities with the simultaneous reduction of fossil-based plant capacity. Furthermore, power flow analysis is incorporated as an ancillary step in the scenario determination procedure to identify extreme cases in terms of the online inertia and primary frequency reserves. The final part of the methodological approach regards the conduction of transient simulations for disturbances such as rapid load changes and the tripping of generation units and short-circuits. The comparative analysis of the results reveals the impact of increased vRES capacities, decreased inertia and limited primary frequency reserves on the system’s stability.
- The consideration of energy storage technologies (BESS, FESS) to address the revealed instabilities in future low-inertia scenarios.

## 2. Theoretical Background

#### 2.1. Frequency Control Ancillary Services

_{m}) is aligned with the angular velocity of the electromagnetic field (i.e., ω

_{e}). When a disturbance occurs leading to an imbalance between the two opposing torques, their sum on the rotor is nonzero, resulting in acceleration or deceleration according to the electromechanical swing equation (Equation (1)):

^{2}), T

_{m}and T

_{e}represent mechanical and electrical torque, respectively (N·m) and T

_{a}represents acceleration/deceleration torque (N·m). From the above equation, it can be deduced that mitigating the effect of power imbalances in terms of the rate of change of frequency (RoCoF) can be realized by enhancing the system’s rotational inertia, utilizing fast reserves with RoCoF-based control.

_{0}the nominal frequency, r

_{p}the droop gain, P is the active power of the unit and P

_{0}to the initial active power.

#### 2.2. BESS Primary Frequency Ancillary Services

_{ref}), the control also receives a signal for the system frequency (f), which is compared with the nominal value (f

_{0}) to compute the error. The error signal is routed through proportional and derivative sides, implementing droop and synthetic inertia control, respectively. For parameters, it receives two gains: one for the droop control (R) and one for the inertia response (k) [43], as well as the limits for the rated power exchange (P

_{max}and P

_{min}).

## 3. Methodology

_{e}with a step of 2 MW

_{e}),” “short-circuit (SC)” of a transmission line 60 kV with the requirement of a 100 ms clearance time and “loss of the island’s second-largest production unit online.” After the evaluation and comparison of the results, a third scenario is considered, which corresponds to the future scenario with the additional integration of a BESS to mitigate the frequency stability issues that are revealed in the high-RES case. Lastly, the results are thoroughly assessed and taken into account in the decision-making process in the context of the long-term planning of the island’s power system.

## 4. System Description and Scenarios Definition

_{e}. Its generation fleet is composed of two thermal plants, nine hydro plants, one pump-hydro plant, one solid-waste plant and a number of wind turbines (WTs) and photovoltaic (PV) parks, as well as some distributed PV generation rooftop-mounted systems [48]. Table 1 summarizes the installed power for all generation units per type, along with the number of generating units for conventional power plants.

- A set of 11 busses at the 60 kV level, 35 at the 30 kV level and 27 at the 6.6 kV level (73 in total).
- A set of 57 transmission lines (or cables) with their appropriate parameters, 13 at the 60 kV and 44 at the 30 kV level (114 in total).
- Forty-six transformers: 6: 60 kV/30 kV, 6: 60 kV/6.6 kV, 21: 30 kV/6.6 kV, 4: 6.6 kV/60 kV and 9: 6.6 kV/30 kV.

_{e}and 15 MW

_{e}. In this study, the future scenario is investigated considering the inclusion and nonuse of the BESS, aiming to examine the battery’s impact on the grid. Although the battery’s location has been indicated by EMM, this option was further examined with the conduction of several simulations with the BESS installed in different busses. The simulations proved that the location of the BESS was irrelevant to its performance during disturbances. Table 2 gathers the new total installed capacities per technology.

## 5. Case Definition

_{e}minimum thermal production to ensure the system’s stability, which translates into a considerable RES curtailment mainly during the night hours. This restriction is not present in the future scenario, as the BESS is responsible for securing the power system operation. Figure 4 and Figure 5 depict the resulting operation for the two scenarios and highlight the extreme points that form the basis for the transient simulations.

_{e}to 11.33 MW

_{e}and 1.36 pu to 0.65 pu, respectively) is substantial and renders the system particularly sensitive under disturbances. It is mentioned that due to an increase in the installed hydropower plants’ capacity, the power system base is 250.17 MW

_{e}and 289.95 MW

_{e}for the reference and future cases, respectively.

## 6. Dynamic Simulations Results and Discussion

#### 6.1. Disturbances

#### 6.1.1. Load Step-Change

_{e}, 4 MW

_{e}, 6 MW

_{e}and 8 MW

_{e}. Figure 7 and Figure 8 show the frequency response and RoCoF for the best and worst cases of the reference scenario, respectively. It can be observed that the system responded successfully to this disturbance and no load-shedding relay activation was required as the load-shedding criteria were not met. Of course, the higher the load increase, the greater the steady-state error of frequency and RoCoF fluctuations. Even if load-shedding actions are avoided, frequency and RoCoF could reach extremely low values of 48.93 Hz and 1.14 Hz/s, respectively. This new low steady-state frequency will negatively affect the power quality provided to all customers, especially industries, as the operation of grid-coupled induction motors present in industrial environments is highly affected by the power system’s frequency.

_{e}load step-changes. The frequency rapidly reaches 46 Hz where generators have to be disconnected and the system collapses. In addition, in the RoCoF diagrams, it can be observed that the frequency drops sharply due to the presence of reduced inertia.

_{e}). At the moment when the disturbance event occurs, the power of the BESS increases rapidly due to virtual inertia control and, due to the droop control, follows a pattern inversely proportional to the frequency.

_{e}, in the future with BESS scenario, the resulting RoCoF oscillates in the interval [−0.18, −0.015] Hz/s. The corresponding interval for the reference scenario is constrained between [−0.3, −0.03] Hz/s, demonstrating a strong advancement over the current operational mode, also considering the reduction of the physical system inertia from 1.36 pu to 0.65 pu.

#### 6.1.2. Generation Loss

_{e}. According to the future case, the second-largest unit is a solar power plant with a 14.22 MW

_{e}maximum power output. Although the system maintained its stability in the best case of the future scenario as depicted in Figure 14, it collapsed in the corresponding worst case of Figure 15. Furthermore, load-shedding relays activated before system collapse as the load-shedding criteria were met. Additionally, BESS installation leads to secure system operation without load-shedding relay activation, even after the complete loss of a significant production unit.

#### 6.1.3. Three-Phase Short-Circuit (3ph SC) in a 60 kV Line

#### 6.2. BESS/FESS Comparison

^{7}kg∙m

^{2}, which were selected to be analogous to the BESS characteristics.

## 7. Conclusions

_{e}, 10 MWh

_{e}) to provide frequency support under severe disturbances. In island systems, the location of a BESS is of minor importance, and in the context of the present study, the battery is considered to be installed in one of the major nodes of the system.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

BESS | Battery energy storage system |

DFIG | Double-fed induction generator |

FESS | Flywheel energy storage system |

GHG | Greenhouse gas |

IC | Internal combustion engine |

LCOE | Levelized cost of energy |

NII | Non-interconnected island |

OPF | Optimal power flow |

PV | Photovoltaic |

RES | Renewable energy source |

RMS | Root mean square |

RoCoF | Rate of change of frequency |

SG | Synchronous generator |

SOH | State of health |

ST | Steam turbine |

TSO | Transmission system operator |

vRES | Variable renewable energy source |

WT | Wind turbine |

## Appendix A. Dynamic Models Description

**Figure A4.**Hydro turbine governor type GovHydroIEEE0 (adopted by [57]).

**Figure A5.**Steam turbine governor (adopted by [58]).

**Figure A6.**Diesel turbine governor (adopted by [57]).

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**Figure 4.**Resulting best and worst cases from the yearly optimal power flow (OPF) of the reference scenario.

**Figure 7.**Load step-change frequency response and rate of change of frequency (RoCoF) for the best case of the reference scenario.

**Figure 8.**Load step-change frequency response and RoCoF for the worst case of the reference scenario.

**Figure 11.**Load step-change frequency response and RoCoF for the future best case with the BESS installation.

**Figure 12.**Load step-change frequency response and RoCoF for the future worst case with the BESS installation.

**Figure 13.**Contribution of the BESS to the system response of a load step-change for the best and worst cases.

**Figure 14.**Generation loss frequency response and RoCoF for the best cases of the reference, future and future with BESS scenarios.

**Figure 15.**Generation loss frequency response and RoCoF for the worst cases for the reference, future and future with BESS scenarios.

**Figure 16.**Short-circuit frequency response and RoCoF for the best cases of the reference, future and future with BESS scenarios.

**Figure 17.**Short-circuit frequency response and RoCoF for the worst cases of the reference, future and future with BESS scenarios.

**Figure 18.**Short-circuit frequency response of the hydro generation unit for the best case of the reference scenario.

Type | Inst. Power (MW_{e}) | Generator Units | Description/Comments |
---|---|---|---|

Thermal | 136.00 | 12 IC | Diesel |

54.40 | 3 IC—1 ST | Combined-cycle natural gas | |

Hydro | 47.17 | 18 | - |

Solid waste | 8.00 | 1 ST | - |

Wind | 45.11 | - | - |

Solar | 19.10 | - | - |

Type | Ins. Power (MW_{e}) | Generator Units | Description/Comments |
---|---|---|---|

Thermal | 136 | 12 IC | Diesel |

54.4 | 3 IC—1 ST | Combined-cycle natural gas | |

Hydro | 88.25 | 18 | - |

Solid waste | 8 | 1 ST | - |

Wind | 70.11 | - | - |

Solar | 69.1 | - | - |

Storage | 15 | - | 10 MWh_{e} |

Type | Description/Comments | Best Case (Instantaneous vRES Penetration 0.35%) (MW_{e}) | Generator Units (-) | Worst Case (Instantaneous vRES Penetration 35.5%) (MW_{e}) | Generator Units (-) |
---|---|---|---|---|---|

Conventional units | Combined-cycle natural gas | 29.19 | 4 | - | - |

Diesel | 68.85 | 10 | 30.61 | 5 | |

Hydro | 24.02 | 16 | 3.28 | 2 | |

Solid waste | 5.23 | 1 | 5.42 | 1 | |

Inverter-based units | PV | - | - | - | - |

Wind | 0.42 | - | 21.62 | - |

Type | Description/Comments | Best Case (Instantaneous vRES Penetration 0.1%) (MW_{e}) | Generator Units (-) | Worst Case (Instantaneous vRES Penetration 78.8%) (MW_{e}) | Generator Units (-) |
---|---|---|---|---|---|

Conventional units | Combined-cycle natural gas | 28.55 | 4 | - | - |

Diesel | 69.39 | 11 | 11.25 | 2 | |

Hydro | 42.92 | 13 | 6.64 | 1 | |

Solid waste | 1.56 | 1 | 5.21 | 1 | |

Inverter-based units | PV | - | - | 50.65 | - |

Wind | 0.14 | - | 35.13 | - |

Reference Case | Future Case | |||
---|---|---|---|---|

Best | Worst | Best | Worst | |

Primary reserve (thermal) (MW_{e}) | 54.42 | 24.95 | 65.58 | 10.97 |

Primary reserve (hydro) (MW_{e}) | 18.6 | 1.92 | 31.98 | 0.36 |

Primary reserve (total) (MW_{e}) | 73.02 | 26.87 | 97.56 | 11.33 |

Total inertia (pu) | 4.86 | 4.86 | 4.85 | 4.85 |

Online inertia (pu) | 4.00 | 1.36 | 4.17 | 0.65 |

Load Step-Change | Reference/Future/Future with BESS Scenarios | |||
---|---|---|---|---|

2 MW_{e} | 4 MW_{e} | 6 MW_{e} | 8 MW_{e} | |

Min. RoCoF (Hz/s) | −0.08/−0.064/−0.005 | −0.16/−0.12/−0.1 | −0.23/−0.18/−0.14 | −0.3/−0.23/−0.18 |

Max. RoCoF (Hz/s) | 0.008/0.006/0.003 | 0.016/0.013/0.007 | 0.024/0.02/0.011 | 0.03/0.027/0.015 |

Min. frequency (Hz) | 49.95/49.95/49.96 | 49.90/49.91/49.93 | 49.86/49.87/49.89 | 49.82/49.84/49.87 |

Max. frequency (Hz) | 50/50/50 | 50/50/50 | 50/50/50 | 50/50/50 |

New steady-state frequency (Hz) | 49.96/49.96/49.97 | 49.93/46.92/49.93 | 49.88/49.88/49.90 | 49.85/49.85/49.87 |

Resulting issues | NONE/NONE/NONE | NONE/NONE/NONE | NONE/NONE/NONE | NONE/NONE/NONE |

Load Step-Change | Reference/Future/Future with BESS Scenarios | |||
---|---|---|---|---|

2 MW_{e} | 4 MW_{e} | 6 MW_{e} | 8 MW_{e} | |

Min. RoCoF (Hz/s) | −0.31/−0.54/−0.18 | −0.61/−1.07/−0.35 | −0.88/−1.56/−0.53 | −1.14/−2.02/−0.68 |

Max. RoCoF (Hz/s) | 0.037/0.1/0.008 | 0.07/0.19/0.009 | 0.10/0.28/0.015 | 0.14/0.38/0.02 |

Min. frequency (Hz) | 49.78/48.4/49.82 | 49.55/46.51/49.64 | 49.26/0/49.46 | 48.93/0/49.30 |

Max. frequency (Hz) | 50/50/50 | 50/50/50 | 50/50/50 | 50/50/50 |

New steady-state frequency (Hz) | 49.78/48.4/49.85 | 49.57/46.51/49.67 | 49.26/0/49.50 | 48.93/0/49.37 |

Resulting issues | NONE/NONE/NONE | NONE/NONE/NONE | NONE/system collapse/NONE | NONE/load-shedding-system Collapse/NONE |

Reference Case | Future Case | Future Case BESS | ||||
---|---|---|---|---|---|---|

Best Case | Worst Case | Best Case | Worst Case | Best Case | Worst Case | |

Min. RoCoF (Hz/s) | −1.00 | −1.25 | −0.73 | −3.69 | −0.64 | −0.98 |

Max. RoCoF (Hz/s) | 0.15 | 0.17 | 0.11 | 0 | 0.04 | 0.09 |

Min. frequency (Hz) | 49.18 | 48.92 | 49.36 | 0 | 49.40 | 48.87 |

Max. frequency (Hz) | 50 | 50 | 50 | 50 | 50 | 50 |

New steady-state frequency (Hz) | 49.18 | 48.92 | 49.36 | 0 | 49.40 | 49.03 |

Resulting issues | NONE | NONE | NONE | Load-shedding/system collapse | NONE | NONE |

Reference Case | Future Case | Future Case BESS | ||||
---|---|---|---|---|---|---|

Best Case | Worst Case | Best Case | Worst Case | Best Case | Worst Case | |

Min. RoCoF (Hz/s) | −2.73 | −3.08 | −2.79 | −6.69 | −3.11 | −4.27 |

Max. RoCoF (Hz/s) | 3.60 | 6.12 | 3.09 | 4.32 | 3.53 | 3.22 |

Min. frequency (Hz) | 49.82 | 49.69 | 49.89 | 49.18 | 49.91 | 49.82 |

Max. frequency (Hz) | 50.39 | 50.91 | 50.32 | 50.99 | 50.35 | 50.24 |

New steady-state frequency (Hz) | 49.99 | 50 | 50 | 50 | 50 | 50 |

Resulting issues | NONE | NONE | NONE | NONE | NONE | NONE |

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## Share and Cite

**MDPI and ACS Style**

Ntomalis, S.; Iliadis, P.; Atsonios, K.; Nesiadis, A.; Nikolopoulos, N.; Grammelis, P.
Dynamic Modeling and Simulation of Non-Interconnected Systems under High-RES Penetration: The Madeira Island Case. *Energies* **2020**, *13*, 5786.
https://doi.org/10.3390/en13215786

**AMA Style**

Ntomalis S, Iliadis P, Atsonios K, Nesiadis A, Nikolopoulos N, Grammelis P.
Dynamic Modeling and Simulation of Non-Interconnected Systems under High-RES Penetration: The Madeira Island Case. *Energies*. 2020; 13(21):5786.
https://doi.org/10.3390/en13215786

**Chicago/Turabian Style**

Ntomalis, Stefanos, Petros Iliadis, Konstantinos Atsonios, Athanasios Nesiadis, Nikos Nikolopoulos, and Panagiotis Grammelis.
2020. "Dynamic Modeling and Simulation of Non-Interconnected Systems under High-RES Penetration: The Madeira Island Case" *Energies* 13, no. 21: 5786.
https://doi.org/10.3390/en13215786