# Comparative and Cost Analysis of a Novel Predictive Power Ramp Rate Control Method: A Case Study in a PV Power Plant in Puerto Rico

^{*}

## Abstract

**:**

## 1. Introduction

_{out}, and the depth-of-discharge (DoD) of the ESS through a day may vary drastically depending on the PRRC method and the type of battery used. These factors directly impact battery degradation and the levelized cost of storage (LCOS) [9,10,11]. Thus, LSSPP may incur extra costs in ESS depending on the implemented PRRC method. The ramp-saturation (RS) is the simplest PRRC method [12,13]. In this method, the battery absorbs or injects power when the PRR at the point of interconnection (POI) exceeds the requirement. The Simple Moving Average (SMA) and the Exponential Moving Average (EMA) are also two popular methods due to their low computational cost and ease of implementation [14,15,16,17]. However, the RS, MA, and EMA methods require a large ESS storage capacity [13,18,19]. This implies an increase in costs and battery degradation. PRRC methods such as the Enhanced Linear Exponential Smoothing (ELES) [20,21,22,23], the First Order Low-Pass filter (FOLPF) [24,25,26,27], and the second-order LPF (SOLPF) have been proposed to reduce power fluctuations in the ESS [28]. A solution to avoid the use of ESS is the Active Power Curtailment (APC) method [5,29,30,31,32,33,34]. This method moves the power converter away from the maximum power point to reduce the power injection to the main grid. Though, the APC is only valid for ramp-up events. For this purpose, the Forecasted APC (FAPC) method has been proposed in [35,36]. This method determines whether a ramp-down event will occur and reduces the injected power by moving the power reference away from the maximum power point. However, as both APC and FAPC are aimed to avoid the use of ESS, their reliability is highly affected by the accuracy of the forecast.

## 2. Overview of the Power Ramp-Rate Control Methods

_{s}is represented by:

#### 2.1. Ramp Saturation (RS) Method

#### 2.2. Simple Moving Average (SMA) Method

#### 2.3. Exponential Moving Average (EMA) Method

#### 2.4. First Order Low-Pass Filter (FOLPF) Method

#### 2.5. Second Order Low-Pass Filter (SOLPF) Method

#### 2.6. Enhanced Linear Exponential Smoothing (ELES)

## 3. Proposed Predictive Dynamic Smoothing PRRC Method

_{pv}. The output power of the ESS is then defined as ${\mathrm{P}}_{\mathrm{ess}}[\mathrm{k}]={\stackrel{~}{\mathrm{P}}}_{\mathrm{out}}\left[\mathrm{k}\right]-{\mathrm{P}}_{\mathrm{pv}}\left[\mathrm{k}\right]$. A flowchart that describes the PDS algorithm is presented in Figure 5. The proposed PDS method can be used to reduce the ESS capacity requirements and battery degradation, reducing equipment costs and increasing the lifetime of the ESS. Simulation results are presented in the results section of this manuscript.

## 4. Methodology for the Levelized Cost of Storage Estimation

#### 4.1. Battery Degradation Estimation for PRRC

#### 4.2. Levelized Cost of Storage (LCOS) Estimation

#### 4.3. Ramp Violations

## 5. Coto Laurel Case Study

#### 5.1. General Description of Coto Laurel Solar Power Plant

#### 5.2. Environmental Characteristics of Coto Laurel Solar Power Plant

#### 5.3. Proposed Model

#### 5.4. Model Validation

## 6. Simulation Results

#### 6.1. First Stage: One Day Evaluation

#### 6.1.1. Ramp Saturation Method

#### 6.1.2. Simple Moving Average (SMA) Method

_{out}for W = 10 is more than three times less than W = 5.

#### 6.1.3. Exponential Moving Average (EMA) Method

#### 6.1.4. First Order Low-Pass Filter (FOLPF) Method

#### 6.1.5. Second Order Low-Pass Filter (SOLPF) Method

#### 6.1.6. Enhanced Linear Exponential Smoothing (ELES) Method

#### 6.1.7. Proposed Predictive Dynamic Smoothing (PDS)

#### 6.2. Economic Analysis through One Year

- RS with a PRR
_{max}of 10%. - SMA with a window size W = 10.
- EMA with a window size W = 30 and a smoothing factor α = 0.123.
- FOLPF with a sampling period T
_{s}= 60 s and a T_{f}= 500 s. - SOLPF with a sampling period of T
_{s}= 60 s, a damping ratio ζ = 0.707, and a natural frequency ω_{n}= 1/25 rad/s. - ELES with a smoothing factor α = 0.06.
- Proposed PDS with a window size W = 5 and a disturbance coefficient µ = 10%. This coefficient was selected since it represented errors in estimations of about 1 MW, which is reasonable according to the literature presented in Section 3.

#### 6.2.1. Battery Degradation

#### 6.2.2. LCOS

#### 6.2.3. Violations

_{max}. It is noted that most of the PRR violations in Coto Laurel occurred during the summer, which is characterized for having the highest solar radiation profiles according to Figure 8. The main cause of these violations over the year was because the ESS reached its minimum (30%) or maximum capacity (100%). This implied that the ESS was unable to support the PRRC. However, the PRR violations were relatively small, considering that the RS was the PRRC method with the most violations throughout the year (84 min). The PDS and the SOLPF were the PRRC methods that did not show any PRR violations throughout the year.

## 7. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Puerto Rico Electrical Power Authority. Generation, Consumption, Cost, Income and Customers of the Puerto Rico Electrical System; indicadores.pr: San Juan, PR, USA, 2020. [Google Scholar]
- Puerto Rico Electric Power Authority. SB 1121 Puerto Rico Energy Public Policy Act; Government of Puerto Rico: San Juan, PR, USA, 2020; p. 23.
- Government of Puerto Rico. PREPA Hydroelectric Power Plants Revitalization Project (PRQ2019-2)—Questions and Responses Log; Government of Puerto Rico: San Juan, PR, USA, 2020.
- Puerto Rico Energy Bureau. Final Resolution and Order on the Puerto Rico Electric Power Authority’s Integrated Resource Plan (CEPR-AP-2018-0001); Puerto Rico’s Electric Energy Bureau: San Juan, PR, USA, 2020; p. 179.
- Crǎciun, B.I.; Kerekes, T.; Séra, D.; Teodorescu, R.; Annakkage, U.D. Power Ramp Limitation Capabilities of Large PV Power Plants With Active Power Reserves. IEEE Trans. Sustain. Energy
**2017**, 8, 573–581. [Google Scholar] [CrossRef] - Martins, J.; Spataru, S.; Sera, D.; Stroe, D.I.; Lashab, A. Comparative study of ramp-rate control algorithms for PV with energy storage systems. Energies
**2019**, 12, 1342. [Google Scholar] [CrossRef] [Green Version] - Elwakil, E.; Hegab, M. Risk Management for Power Purchase Agreements. In Proceedings of the 2018 IEEE Conference on Technologies for Sustainability (SusTech), Long Beach, CA, USA, 11–13 November 2018. [Google Scholar] [CrossRef]
- Puerto Rico Electric Power Authority. Minimum Technical Requirements For Interconnection Of Photovoltaic (Pv) Facilities; Energia.pr.gov: San Juan, PR, USA, 2020; pp. 1–11.
- Beltran, H.; Tomas Garcia, I.; Alfonso-Gil, J.C.; Perez, E. Levelized Cost of Storage for Li-Ion Batteries Used in PV Power Plants for Ramp-Rate Control. IEEE Trans. Energy Convers.
**2019**, 34, 554–561. [Google Scholar] [CrossRef] - Belderbos, A.; Delarue, E.; D’haeseleer, W. Calculating the levelized cost of storage? Energy Expect. In Proceedings of the Uncertainty, 39th IAEE International Conference, Beren, Norway, 19–22 November 2016; pp. 1–2. [Google Scholar]
- Hoff, M.; Lin, R. Development and Practical Use of a Levelized Cost of Storage (LCOS) Metric. Available online: https://www.neces.com/wp-content/uploads/2019/08/Development_and_practical_use_of_a_LCOS_031619.pdf (accessed on 27 January 2021).
- Alam, M.J.E.; Muttaqi, K.M.; Sutanto, D. A novel approach for ramp-rate control of solar PV using energy storage to mitigate output fluctuations caused by cloud passing. IEEE Trans. Energy Convers.
**2014**, 29, 507–518. [Google Scholar] [CrossRef] [Green Version] - Marcos, J.; de La Parra, I.; García, M.; Marroyo, L. Control strategies to smooth short-term power fluctuations in large photovoltaic plants using battery storage systems. Energies
**2014**, 7, 6593–6619. [Google Scholar] [CrossRef] - Solanki, S.G.; Ramachandaramurthy, V.K.; Shing, N.Y.K.; Tan, R.H.G.; Tariq, M.; Thanikanti, S.B. Power smoothing techniques to mitigate solar intermittency. In Proceedings of the 2019 International Conference on Electrical, Electronics and Computer Engineering, UPCON 2019, Aligarh, India, 8–10 November 2019. [Google Scholar]
- Tesfahunegn, S.G.; Ulleberg, Ø.; Vie, P.J.S.; Undeland, T.M. PV fluctuation balancing using hydrogen storage—A smoothing method for integration of PV generation into the utility grid. Energy Procedia
**2011**, 12, 1015–1022. [Google Scholar] [CrossRef] [Green Version] - Ellis, A.; Schoenwald, D.; Hawkins, J.; Willard, S.; Arellano, B. PV output smoothing with energy storage. In Proceedings of the Conference Record of the IEEE Photovoltaic Specialists Conference, Austin, TX, USA, 3–8 June 2012; pp. 1523–1528. [Google Scholar]
- Hund, T.D.; Gonzalez, S.; Barrett, K. Grid-tied PV system energy smoothing. In Proceedings of the Conference Record of the IEEE Photovoltaic Specialists Conference, Honolulu, HI, USA, 20–25 June 2010; pp. 2762–2766. [Google Scholar]
- Addisu, A.; George, L.; Courbin, P.; Sciandra, V. Smoothing of renewable energy generation using Gaussian-based method with power constraints. Energy Procedia
**2017**, 134, 171–180. [Google Scholar] [CrossRef] - Lin, D. Strategy Comparison of Power Ramp Rate Control for Photovoltaic Systems. CPSS Trans. Power Electron. Appl.
**2020**, 5, 329–341. [Google Scholar] [CrossRef] - Jamroen, C.; Usaratniwart, E.; Sirisukprasert, S. PV power smoothing strategy based on HELES using energy storage system application: A simulation analysis in microgrids. IET Renew. Power Gener.
**2019**, 13, 2298–2308. [Google Scholar] [CrossRef] - Chanhom, P.; Sirisukprasert, S.; Hatti, N. Enhanced linear exponential smoothing technique with minimum energy storage capacity for PV distributed generations. Int. Rev. Electr. Eng.
**2014**, 9, 1190–1196. [Google Scholar] [CrossRef] - Usaratniwart, E.; Sirisukprasert, S.; Hatti, N.; Hagiwara, M. A case study in micro grid using adaptive enhanced linear exponential smoothing technique. In Proceedings of the 2017 8th International Conference on Information and Communication Technology for Embedded Systems, IC-ICTES 2017—Proceedings, Chonburi, Thailand, 7–9 May 2017. [Google Scholar]
- Usaratniwart, E.; Sirisukprasert, S. Adaptive enhanced linear exponential smoothing technique to mitigate photovoltaic power fluctuation. In Proceedings of the IEEE PES Innovative Smart Grid Technologies Conference Europe, Melbourne, VIC, Australia, 28 November–1 December 2016; pp. 712–717. [Google Scholar]
- Liu, H.; Peng, J.; Zang, Q.; Yang, K. Control Strategy of Energy Storage for Smoothing Photovoltaic Power Fluctuations. IFAC-PapersOnLine
**2015**, 48, 162–165. [Google Scholar] [CrossRef] - Datta, M.; Senjyu, T.; Yona, A.; Funabashi, T.; Kim, C.H. Photovoltaic output power fluctuations smoothing methods for single and multiple PV generators. Curr. Appl. Phys.
**2010**, 10, S265–S270. [Google Scholar] [CrossRef] - Koiwa, K.; Liu, K.Z.; Tamura, J. Analysis and Design of Filters for the Energy Storage System: Optimal Tradeoff between Frequency Guarantee and Energy Capacity/Power Rating. IEEE Trans. Ind. Electron.
**2018**, 65, 6560–6570. [Google Scholar] [CrossRef] - Lin, Z.; Qiu, G.; Wang, G.; Jiang, R. Improved wind power and storage system smoothing control strategy based on RE reinforcement learning and low pass filtering algorithms. In Proceedings of the POWERCON 2014–2014 International Conference on Power System Technology: Towards Green, Efficient and Smart Power System, Chengdu, China, 20–22 October 2014; pp. 1749–1753. [Google Scholar]
- Nikolov, D. Power Ramp Rate Reduction in Photovoltaic Power Plants Using Energy Storage. Master’s Thesis, Aalborg University, Aalborg Øst, Denmark, 2017. [Google Scholar]
- Blaabjerg, F.; Yang, Y.; Ma, K.; Wang, X. Power electronics-the key technology for renewable energy system integration. In Proceedings of the 2015 International Conference on Renewable Energy Research and Applications, ICRERA 2015, Palermo, Italy, 22–25 November 2015; pp. 1618–1626. [Google Scholar]
- Yang, Y.; Wang, H.; Blaabjerg, F.; Kerekes, T. A hybrid power control concept for PV inverters with reduced thermal loading. IEEE Trans. Power Electron.
**2014**, 29, 6271–6275. [Google Scholar] [CrossRef] [Green Version] - Sangwongwanich, A.; Yang, Y.; Blaabjerg, F. High-performance constant power generation in grid-connected PV systems. IEEE Trans. Power Electron.
**2016**, 31, 1822–1825. [Google Scholar] [CrossRef] [Green Version] - Omran, W.A.; Kazerani, M.; Salama, M.M.A. Investigation of methods for reduction of power fluctuations generated from large grid-connected photovoltaic systems. IEEE Trans. Energy Convers.
**2011**, 26, 318–327. [Google Scholar] [CrossRef] - Ina, N.; Yanagawa, S.; Kato, T.; Suzuoki, Y. Smoothing of PV system output by tuning MPPT control. Electr. Eng. Jpn.
**2005**, 152, 10–17. [Google Scholar] [CrossRef] - Zarina, P.P.; Mishra, S.; Sekhar, P.C. Exploring frequency control capability of a PV system in a hybrid PV-rotating machine-without storage system. Int. J. Electr. Power Energy Syst.
**2014**, 60, 258–267. [Google Scholar] [CrossRef] - Chen, X.; Du, Y.; Wen, H.; Jiang, L.; Xiao, W. Forecasting-Based Power Ramp-Rate Control Strategies for Utility-Scale PV Systems. IEEE Trans. Ind. Electron.
**2019**, 66, 1862–1871. [Google Scholar] [CrossRef] - Chen, X.; Du, Y.; Xiao, W.; Lu, S. Power ramp-rate control based on power forecasting for PV grid-Tied systems with minimum energy storage. In Proceedings of the IECON 2017—43rd Annual Conference of the IEEE Industrial Electronics Society, Beijing, China, 29 October–1 November 2017; pp. 2647–2652. [Google Scholar] [CrossRef]
- Lave, M.; Kleissl, J.; Ellis, A.; Mejia, F. Simulated PV power plant variability: Impact of utility-imposed ramp limitations in Puerto Rico. In Proceedings of the 2013 IEEE 39th Photovoltaic Specialists Conference (PVSC), Tampa, FL, USA, 16–21 June 2013; pp. 1817–1821. [Google Scholar] [CrossRef]
- Cormode, D.; Cronin, A.D.; Richardson, W.; Lorenzo, A.T.; Brooks, A.E.; Dellagiustina, D.N. Comparing ramp rates from large and small PV systems, and selection of batteries for ramp rate control. In Proceedings of the 2013 IEEE 39th Photovoltaic Specialists Conference (PVSC), Tampa, FL, USA, 16–21 June 2013; pp. 1805–1810. [Google Scholar] [CrossRef]
- Marquez, R.; Pedro, H.T.C.; Coimbra, C.F.M. Hybrid solar forecasting method uses satellite imaging and ground telemetry as inputs to ANNs. Sol. Energy
**2013**, 92, 176–188. [Google Scholar] [CrossRef] - Salehi, V.; Radibratovic, B. Ramp rate control of photovoltaic power plant output using energy storage devices. In Proceedings of the 2014 IEEE PES General Meeting|Conference & Exposition, National Harbor, MD, USA, 27–31 July 2014. [Google Scholar] [CrossRef]
- Stroe, D.I.; Swierczynski, M.; Stan, A.I.; Teodorescu, R.; Andreasen, S.J. Accelerated lifetime testing methodology for lifetime estimation of lithium-ion batteries used in augmented wind power plants. IEEE Trans. Ind. Appl.
**2014**, 50, 4006–4017. [Google Scholar] [CrossRef] - Downing, S.D.; Socie, D.F. Simple rainflow counting algorithms. Int. J. Fatigue
**1982**, 4, 31–40. [Google Scholar] [CrossRef] - Safari, M.; Morcrette, M.; Teyssot, A.; Delacourt, C. Life-Prediction Methods for Lithium-Ion Batteries Derived from a Fatigue Approach. J. Electrochem. Soc.
**2010**, 157, A713. [Google Scholar] [CrossRef] - Adarme-Mejia, L.M.; Irizarry-Rivera, A.A. Feasibility study of a linear Fresnel Concentrating Solar Power plant located in Ponce, Puerto Rico. In Proceedings of the 2015 North American Power Symposium (NAPS), Charlotte, NC, USA, 4–6 October 2015. [Google Scholar] [CrossRef]

**Figure 6.**Maximum number of cycles to achieve EOL for different DoD values for LFP batteries. The EOL capacity is defined by the manufacturer to be 70% of the initial capacity.

**Figure 8.**Average day global horizontal irradiance (GHI) in Ponce, Puerto Rico, for each month of the year.

**Figure 11.**Simulation results for the RS method. (

**a**) One-day data results showing the total output power (P

_{out}), the ESS output power (P

_{ess}), the PRR at the output (PRR

_{out}), and the state of charge (SOC). (

**b**) Zoomed figures of the corresponding black squares.

**Figure 12.**Simulation results for the SMA method. (

**a**) One-day data results showing the total output power (P

_{out}), the ESS output power (P

_{ess}), the PRR at the output (PRR

_{out}), and the state of charge (SOC). (

**b**) Zoomed figures of the corresponding black squares.

**Figure 13.**Simulation results for the EMA method. (

**a**) One-day data results showing the total output power (P

_{out}), the ESS output power (P

_{ess}), the PRR at the output (PRR

_{out}), and the state of charge (SOC). (

**b**) Zoomed figures of the corresponding black squares.

**Figure 14.**Simulation results for the FOLPF method. (

**a**) One-day data results showing the total output power (P

_{out}), the ESS output power (P

_{ess}), the PRR at the output (PRR

_{out}), and the state of charge (SOC). (

**b**) Zoomed figures of the corresponding black squares.

**Figure 15.**Simulation results for the SOLPF method. (

**a**) One-day data results showing the total output power (P

_{out}), the ESS output power (P

_{ess}), the PRR at the output (PRR

_{out}), and the state of charge (SOC). (

**b**) Zoomed figures of the corresponding black squares.

**Figure 16.**Simulation results for the ELES method. (

**a**) One-day data results showing the total output power (P

_{out}), the ESS output power (P

_{ess}), the PRR at the output (PRR

_{out}), and the state of charge (SOC). (

**b**) Zoomed figures of the corresponding black squares.

**Figure 17.**Simulation results for the proposed PDS method. (

**a**) One day data results showing the total output power (P

_{out}), the ESS output power (P

_{ess}), the PRR at the output (PRR

_{out}), and the state of charge (SOC). (

**b**) Zoomed figures of the corresponding black squares.

**Figure 18.**Simulation results for the proposed PDS method. (

**a**) One-day data results showing the total output power (P

_{out}), the ESS output power (P

_{ess}), the PRR at the output (PRR

_{out}), and the state of charge (SOC). (

**b**) Zoomed figures of the corresponding black squares.

**Figure 20.**Histogram representing the number of cycles per each DoD during an entire year for the Coto Laurel plant under different PRRC methods using the rainflow algorithm. The DoDs were accumulated in intervals of 10%.

**Figure 21.**ESS capacity degradation estimation using a whole year data from Coto Laurel simulations under different PRRC methods.

**Figure 22.**Comparison of the LCOS for each PRRC method. This analysis was based on data from an entire year in the Coto Laurel power plant.

Battery | Output | DC Power [MW] | Inverter Capacity [kWac] | Feeder | Transf. Capacity [kVA] | Primary-Delta [kV] | Secondary-Yn [V] |
---|---|---|---|---|---|---|---|

1 | 1 | 1 | 880 | 3 | 1800 | 13.2 | 360 |

2 | 880 | ||||||

2 | 1 | 1 | 880 | 3 | 1800 | 13.2 | 360 |

2 | 880 | ||||||

3 | 1 | 1 | 880 | 3 | 1800 | 13.2 | 360 |

2 | 880 |

Group | PV Capacity [W] | PV Quantity | DC Power [kW] | PowerLimit [kW] | Feeder ID | Transf. Capacity [kVA] | Primary-Delta [kV] | Secondary-Yn [V] |
---|---|---|---|---|---|---|---|---|

A1 | 235 | 3408 | 800.88 | 575 | 1 | 1800 | 13.2 | 360 |

A2 | 235 | 3312 | 778.32 | 555 | 1 | |||

B1 | 235 | 3480 | 817.8 | 585 | 1 | 1800 | 13.2 | 360 |

B2 | 235 | 3240 | 761.4 | 545 | 1 | |||

D | 275 | 3744 | 1029.6 | 695 | 2 | 1800 | 13.2 | 360 |

G | 275 | 3744 | 1029.6 | 695 | 2 | |||

E | 275 | 3720 | 1023 | 705 | 2 | 1800 | 13.2 | 360 |

H | 275 | 3744 | 1029.6 | 705 | 2 | |||

D-G | 275 | 3864 | 1062.6 | 710 | 2 | 1800 | 13.2 | 360 |

E-H | 275 | 3864 | 1062.6 | 735 | 2 | |||

F | 260 | 3720 | 967.2 | 695 | 1 | 800 | 13.2 | 360 |

J | 260 | 3744 | 973.44 | 695 | 1 | 1800 | 13.2 | 360 |

F-J | 260 | 3864 | 1004.64 | 710 | 1 | |||

K | 280 | 3984 | 1115.52 | 790 | 2 | 1800 | 13.2 | 360 |

L | 280 | 3984 | 1115.52 | 790 | 2 | |||

= | 55,416 | 14,571.72 | 10,185 |

Measurement | PRR_{max} = 8% | PRR_{max} = 10% | PRR_{max} = 12% |
---|---|---|---|

$\mathrm{D}$(%) | 0.0023 | 0.0021 | 0.0014 |

$\mathrm{NC}(80\%)$ | 0.2349 | 0.2097 | 0.1405 |

Violations (mins) | 0 | 0 | 161 |

SOC (end of the day)-SOC(ref) | −4.5307 | −9.0051 | −3.5554 |

${\sigma}^{2}{(\mathrm{PRR}}_{\mathrm{out}})$ | 22.7312 | 31.9882 | 41.9434 |

Measurement | W = 5 | W = 10 | W = 20 |
---|---|---|---|

$\mathrm{D}$(%) | 0.0019 | 0.0052 | 0.0107 |

$\mathrm{NC}(80\%)$ | 0.1864 | 0.5201 | 1.0685 |

Violations (mins) | 64 | 0 | 0 |

SOC (end of the day) -SOC(ref) | −13.6058 | −27.1991 | −24.6659 |

${\sigma}^{2}{(\mathrm{PRR}}_{\mathrm{out}})$ | 25.3416 | 7.7530 | 2.6601 |

Measurement | $\mathsf{\alpha}$ | $\mathsf{\alpha}=0.123$ | $\mathsf{\alpha}=0.133$ |
---|---|---|---|

$\mathrm{D}$(%) | 0.0048 | 0.0053 | 0.0049 |

$\mathrm{NC}(80\%)$ | 0.4823 | 0.5315 | 0.4927 |

Violations (mins) | 13 | 0 | 1 |

SOC (end of the day) -SOC(ref) | 28.215 | 15.3441 | 6.2242 |

${\sigma}^{2}{(\mathrm{PRR}}_{\mathrm{out}})$ | 25.9067 | 5.3813 | 6.1433 |

Measurement | ${\mathbf{T}}_{\mathbf{f}}=450$ | ${\mathbf{T}}_{\mathbf{f}}=500$ | ${\mathbf{T}}_{\mathbf{f}}=550$ |
---|---|---|---|

$\mathrm{D}$(%) | 0.0071 | 0.0081 | 0.0085 |

$\mathrm{NC}(80\%)$ | 0.7117 | 0.8127 | 0.8485 |

Violations (mins) | 1 | 0 | 0 |

SOC (end of the day) -SOC(ref) | −21.6426 | −22.8112 | −21.7886 |

${\sigma}^{2}{(\mathrm{PRR}}_{\mathrm{out}})$ | 6.1622 | 5.1486 | 4.3769 |

Measurement | ${\mathsf{\omega}}_{\mathbf{n}}=1/15$ | ${\mathsf{\omega}}_{\mathbf{n}}=1/25$ | ${\mathsf{\omega}}_{\mathbf{n}}=1/35$ |
---|---|---|---|

$\mathrm{D}$(%) | 0.0063 | 0.0101 | 0.0136 |

$\mathrm{NC}(80\%)$ | 0.6286 | 1.0117 | 1.3634 |

Violations (mins) | 18 | 0 | 0 |

SOC (end of the day) -SOC(ref) | −29.9978 | −34.8233 | −32.3034 |

${\sigma}^{2}{(\mathrm{PRR}}_{\mathrm{out}})$ | 14.4757 | 4.6293 | 2.4287 |

Measurement | $\mathsf{\alpha}=0.05$ | $\mathsf{\alpha}=0.06$ | $\mathsf{\alpha}=0.07$ |
---|---|---|---|

$\mathrm{D}$(%) | 0.0072 | 0.0057 | 0.0046 |

$\mathrm{NC}(80\%)$ | 0.7206 | 0.5709 | 0.4599 |

Violations (mins) | 0 | 0 | 1 |

SOC (end of the day) -SOC(ref) | −31.949 | −22.593 | −20.975 |

${\sigma}^{2}{(\mathrm{PRR}}_{\mathrm{out}})$ | 3.9163 | 5.3242 | 6.8792 |

Measurement | $\mathit{\mu}=0\%$ | $\mathit{\mu}=10\%$ | $\mathit{\mu}=20\%$ |
---|---|---|---|

$\mathrm{D}$(%) | 0.0016 | 0.0020 | 0.0026 |

$\mathrm{NC}(80\%)$ | 0.1591 | 0.1990 | 0.2621 |

Violations (mins) | 0 | 0 | 0 |

SOC (end of the day) -SOC(ref) | −1.5788 | 14.4696 | 29.9847 |

${\sigma}^{2}{(\mathrm{PRR}}_{\mathrm{out}})$ | 14.2955 | 14.1632 | 15.9081 |

Measurement | $\mathit{\mu}=0\%$ | $\mathit{\mu}=10\%$ | $\mathit{\mu}=20\%$ |
---|---|---|---|

$\mathrm{D}$(%) | 0.0043 | 0.0041 | 0.0042 |

$\mathrm{NC}(80\%)$ | 0.4340 | 0.4115 | 0.4245 |

Violations (mins) | 0 | 0 | 0 |

SOC (end of the day) -SOC(ref) | −18.594 | 3.8675 | −10.287 |

${\sigma}^{2}{(\mathrm{PRR}}_{\mathrm{out}})$ | 5.1573 | 4.7417 | 6.1070 |

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**MDPI and ACS Style**

Patarroyo-Montenegro, J.F.; Vasquez-Plaza, J.D.; Rodriguez-Martinez, O.F.; Garcia, Y.V.; Andrade, F.
Comparative and Cost Analysis of a Novel Predictive Power Ramp Rate Control Method: A Case Study in a PV Power Plant in Puerto Rico. *Appl. Sci.* **2021**, *11*, 5766.
https://doi.org/10.3390/app11135766

**AMA Style**

Patarroyo-Montenegro JF, Vasquez-Plaza JD, Rodriguez-Martinez OF, Garcia YV, Andrade F.
Comparative and Cost Analysis of a Novel Predictive Power Ramp Rate Control Method: A Case Study in a PV Power Plant in Puerto Rico. *Applied Sciences*. 2021; 11(13):5766.
https://doi.org/10.3390/app11135766

**Chicago/Turabian Style**

Patarroyo-Montenegro, Juan F., Jesus D. Vasquez-Plaza, Omar F. Rodriguez-Martinez, Yuly V. Garcia, and Fabio Andrade.
2021. "Comparative and Cost Analysis of a Novel Predictive Power Ramp Rate Control Method: A Case Study in a PV Power Plant in Puerto Rico" *Applied Sciences* 11, no. 13: 5766.
https://doi.org/10.3390/app11135766