# A Heuristics-Based Policy to Reduce the Curtailment of Solar-Power Generation Empowered by Energy-Storage Systems

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## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

#### 2.1. Technical Terms

#### 2.1.1. Photovoltaic System

#### 2.1.2. Energy-Storage System

#### 2.1.3. Power Grid

#### 2.1.4. Energy-Management Systems

#### 2.2. Methodological Terms

#### 2.2.1. Artificial Neural Networks (ANN)

#### 2.2.1.1. Feed-Forward Neural Network (FFNN)

#### 2.2.1.2. Radial Basis Function Network (RBFN)

#### 2.2.1.3. NeuroEvolution of Augmenting Topologies (NEAT)

#### 2.2.2. Statistical Methods

#### 2.2.2.1. Mean Absolute Error (MAE)

#### 2.2.2.2. Mean Square Error (MSE)

#### 2.2.2.3. Root Mean Square Error (RMSE)

#### 2.2.3. Pearson’s Correlation

## 3. Related Work

#### 3.1. PV Power-Generation Forecasts

#### 3.2. Energy-Management Optimization

## 4. Forecasting of Power Generation

#### 4.1. Proposed Methodology

- Information of the consolidated dataset fetched from three different data sources (PV power generation, weather, and irradiation) is considered.
- The set of correlated and causally related attributes are identified using Pearson’s correlation on all the attributes of the consolidated dataset of Step 1.
- The corresponding network under study is trained using three different neural networks while altering attribute sets to identify those with the highest impact on prediction precision. Those types are compared against each other in order to identify the most accurate solution.

#### 4.2. Correlation Analysis

#### 4.3. Neural-Network Analysis

#### 4.3.1. Adopted Training Technique

#### 4.3.2. Evaluation and Results

## 5. Heuristics-Based Optimization

- Photovoltaic System: The system under study is equipped with an array of 36 panels, each generating 280 Wp with a total overall peak generation of 10.08 kWp.
- Energy-Storage System: The system under study is equipped with a BYD PRO Hybrid 9–10 energy-storage system. It provides a usable storage capacity of 9 kWh with a guaranteed number of 6000 cycles until a remaining capacity of 80%. This equates to an average of 300 cycles per year for an expected life span of 20 years. The ESS degree of efficiency for charging and discharging taken from the data sheet is 93%.
- Feed-in Grid: In this work, we consider the feed-in maximum power constraint to be 50% of the installed panels’ peak power generation (e.g., 5 kWp).

#### 5.1. Considered Policies

#### 5.1.1. Naive Policy

Algorithm 1: Naive Policy |

#### 5.1.2. Loss Avoidance

Algorithm 2: Loss Avoidance Policy |

- Find the maximum amount of charge reduction dependant on the intermediate timeslots: For each intermediate timeslot i where $c<i<t$, obtain the amount of energy drawable from ESS, then take the minimum of those, call it minDelta (since we move in a backward direction/from t to c/from hour 23 to hour 0, planning for the intermediate steps is already settled and we must not do modifications that would deplete the ESS during these slots; these slots count on the fact that there is enough energy in the ESS since, during the Planning phase, this was the case).
- Compute how much we can increase feed-in in theory. This is calculated by subtracting maximum feed-in constraint (5 kW in our case) from $feed\_i{n}_{c}$, and we call this maxAdditionalFeed${}_{c}$.
- The minimum of minDelta and maxAdditionalFeed${}_{c}$ is the amount of energy we can shift from timeslot t to c.

#### 5.2. Obtained Results

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

GHI | Global Horizontal Irradiation |

RES | Renewable-Energy Sources |

DSO | Distribution-System Operator |

EMS | Energy-Management System |

ANN | Artificial Neural Network |

RBFN | Radial Basis Function Neural Network |

FFNN | Feed Forward Neural Network |

NEAT | NeuroEvolution of Augmenting Topologies |

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**Figure 1.**A sample system consisting of photovoltaics (PV), an energy-storage system (ESS), power grid, and household load, which is managed by an EMS.

**Table 1.**Electricity prices for households in Germany from 2014 to 2017, semiannually (in euro cents per kilowatt-hour).

2014 S1 | 2014 S2 | 2015 S1 | 2015 S2 | 2016 S1 | 2016 S2 | 2017 S1 | 2017 S2 | |
---|---|---|---|---|---|---|---|---|

Price | 29.81 | 29.74 | 29.51 | 29.46 | 29.69 | 29.77 | 30.48 | 30.48 |

**Table 2.**Pearson’s correlation of different attributes over the whole observation time presented in percent. For the symbols and their definition, see Table 3.

CSG | CSD | GHI | DHI | MT | TP | CC | HM | PP | PI | PR | VS | WB | WS | MP | HD | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

CSG | 100 | 91 | 93 | 91 | 6 | 43 | 37 | 54 | 8 | 3 | 2 | 28 | 3 | 11 | 80 | 9 |

CSD | 91 | 100 | 82 | 89 | 3 | 46 | 42 | 50 | 7 | 2 | 2 | 26 | 6 | 9 | 70 | 10 |

GHI | 93 | 81 | 100 | 80 | 8 | 48 | 23 | 63 | 16 | 10 | 0 | 33 | 4 | 5 | 82 | 7 |

DHI | 91 | 89 | 80 | 100 | 6 | 38 | 42 | 46 | 8 | 4 | 3 | 25 | 6 | 12 | 70 | 8 |

MT | 6 | 3 | 8 | 6 | 100 | 14 | 2 | 15 | 7 | 4 | 7 | 4 | 27 | 2 | 7 | 0 |

TP | 43 | 46 | 48 | 38 | 14 | 100 | 3 | 61 | 11 | 1 | 5 | 53 | 12 | 20 | 42 | 11 |

CC | 37 | 42 | 23 | 42 | 2 | 3 | 100 | 8 | 19 | 12 | 3 | 6 | 11 | 27 | 23 | 16 |

HM | 54 | 50 | 63 | 46 | 15 | 61 | 8 | 100 | 29 | 18 | 5 | 62 | 10 | 7 | 60 | 23 |

PP | 8 | 7 | 16 | 8 | 7 | 11 | 19 | 29 | 100 | 72 | 9 | 31 | 20 | 24 | 14 | 0 |

PI | 3 | 2 | 10 | 4 | 4 | 1 | 12 | 18 | 72 | 100 | 7 | 16 | 14 | 13 | 8 | 3 |

PR | 2 | 2 | 0 | 3 | 7 | 5 | 3 | 5 | 9 | 7 | 100 | 2 | 1 | 6 | 1 | 2 |

VS | 28 | 26 | 33 | 25 | 4 | 53 | 6 | 62 | 31 | 16 | 2 | 100 | 7 | 1 | 30 | 17 |

WB | 3 | 6 | 4 | 6 | 27 | 12 | 11 | 10 | 20 | 14 | 1 | 7 | 100 | 19 | 0 | 3 |

WS | 11 | 9 | 5 | 12 | 2 | 20 | 27 | 7 | 24 | 13 | 6 | 1 | 19 | 100 | 6 | 4 |

MP | 80 | 70 | 82 | 70 | 7 | 42 | 23 | 60 | 14 | 8 | 1 | 30 | 0 | 6 | 100 | 0 |

HD | 9 | 10 | 7 | 8 | 0 | 11 | 16 | 23 | 0 | 3 | 2 | 17 | 3 | 4 | 0 | 100 |

**Table 3.**Abbreviations, definitions, and explanations of the symbols used in Table 2.

Abbreviation | Definition | Explanation and Unit |
---|---|---|

CSG | Clear-Sky GHI | Clear-sky global irradiation on horizontal plane (Wh/m${}^{2}$) |

CSD | Clear-Sky DHI | Clear-sky diffuse irradiation on horizontal plane (Wh/m${}^{2}$) |

GHI | Global Horiz.Irradiance | Global irradiation on horizontal plane (Wh/m${}^{2}$) |

DHI | Diffuse Horiz. Irradiance | Diffuse irradiation on horizontal plane (Wh/m${}^{2}$) |

MT | Month | Month of the year |

TP | Temperature | Temperature (°C) |

CC | Cloud Cover | Amount of eighths of the sky covered in cloud (oktas) |

HM | Humidity | Ratio of masses of vapor in air to vapor in saturated air (%) |

PP | Precipitation Probability | The probability of rain (value between 0 and 100%) |

PI | Precipitation Intensity | Depth of precipitation occurring over a unit area (mm/m${}^{2}$) |

PR | Pressure | The pressure applied by air on the unit area (mb) |

VS | Visibility | Distance at which an object or light can be clearly discerned (m) |

WB | Wind Bearing | |

WS | Wind Speed | The speed of the wind (Km/h) |

MP | Mean Power | Average power generated by the solar-panel system (W) |

HD | Hour of Day |

**Table 4.**Results of training by taking into account GHI and temperature and considering three different neural-network methods.

FFNN | RBFN | NEAT | |
---|---|---|---|

Cross-validation score | 0.05880 | 0.01561 | 0.01520 |

Training error | 0.05845 | 0.01558 | 0.01479 |

Validation error | 0.06130 | 0.01596 | 0.01539 |

Elapsed time (ms) | 1988 | 466 | 560311 |

MAE | MSE | RMSE | |
---|---|---|---|

FFNN | 253.32 | 240,239 | 490.14 |

RBFN | 272.48 | 259,542 | 509.45 |

NEAT | 252.29 | 226,397 | 475.81 |

**Table 6.**Obtained statistical values of Figure 7.

Naive Policy | Loss Avoidance Policy | |
---|---|---|

Min (W) | −500 | −500 |

Max (W) | 4907.717 | 4629.152 |

Median (W) | 0 | 0 |

Lower Quartile (W) | −500 | −500 |

Upper Quartile (W) | 0 | 168.391 |

Arithmetic Mean (W) | 35.837 | 122.392 |

Lower Whisker (W) | −500 | −500 |

Upper Whisker (W) | 2710.65 | 2775.828 |

Number of Zero Values | 2119 | 1387 |

Total Energy (Wh) | 311,743.771 | 1,064,690.65 |

**Table 7.**Obtained statistical values of Figure 8.

Naive Policy | Loss Avoidance Policy | |
---|---|---|

Min (W) | −500 | −500 |

Max (W) | 5000 | 5000 |

Median (W) | 0 | 0 |

Lower Quartile (W) | 0 | 0 |

Upper Quartile (W) | 699.488 | 1185.535 |

Arithmetic Mean (W) | 904.476 | 1023.229 |

Lower Whisker (W) | −500 | −500 |

Upper Whisker (W) | 5000 | 5000 |

Number of Zero Values | 5480 | 5262 |

Total Energy (Wh) | 7,868,036.043 | 8,901,068.92 |

**Table 8.**Obtained statistical values of Figure 9.

Naive Policy | Loss Avoidance Policy | |
---|---|---|

Min (W) | 0 | 0 |

Max (W) | 5638.856 | 5638.856 |

Median (W) | 0 | 0 |

Lower Quartile (W) | 0 | 0 |

Upper Quartile (W) | 0 | 0 |

Arithmetic Mean (W) | 270.719 | 146.495 |

Lower Whisker (W) | 0 | 0 |

Upper Whisker (W) | 3572.09 | 2899.652 |

Number of Zero Values | 7677 | 8209 |

Total Energy (Wh) | 2,354,983.92 | 1,274,357.15 |

Prediction Type: | No | Optimal | Overestimated | Underestimated | Deviation |
---|---|---|---|---|---|

Draw from the grid | −363,201 | −363,201 | −418,437 | −312,850 | −363,983 |

Feed into the grid | 8,231,237 | 9,264,270 | 9,084,403 | 9,107,617 | 9,133,862 |

Net value | 7,868,036 | 8,901,069 | 8,665,966 | 8,794,767 | 8,769,879 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Basmadjian, R.; De Meer, H.
A Heuristics-Based Policy to Reduce the Curtailment of Solar-Power Generation Empowered by Energy-Storage Systems. *Electronics* **2018**, *7*, 349.
https://doi.org/10.3390/electronics7120349

**AMA Style**

Basmadjian R, De Meer H.
A Heuristics-Based Policy to Reduce the Curtailment of Solar-Power Generation Empowered by Energy-Storage Systems. *Electronics*. 2018; 7(12):349.
https://doi.org/10.3390/electronics7120349

**Chicago/Turabian Style**

Basmadjian, Robert, and Hermann De Meer.
2018. "A Heuristics-Based Policy to Reduce the Curtailment of Solar-Power Generation Empowered by Energy-Storage Systems" *Electronics* 7, no. 12: 349.
https://doi.org/10.3390/electronics7120349