# A Method for Reducing the Instability of Negawatts Considering Changes in the Behavior of Consumers

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Related Research

#### 2.2. Definition

#### 2.2.1. Market Players and Times for Power-Saving Requests

#### 2.2.2. A Target Amount of Power Saving and Requirement of Power Saving

#### 2.2.3. Behavioral Models of Consumers Considering Weather

- An average amount of demand: the average amount of electricity consumption in the most recent 49 days within the same time period;
- Deviation of demand at a forecasting period: the difference between the average electricity consumption and the record of demands during a forecasting time period;
- A dummy variable for Saturday: a variable to which 1 is substituted if the forecasting day is a Saturday, which is not a holiday, and to which 0 is substituted if the day is not a Saturday or the day is a holiday;
- A dummy variable for Sunday or a holiday: a variable that is 1 if the forecasting day is a Sunday or a holiday, and it is 0 if the day is not a Sunday nor a holiday;
- A variable of the air conditioner effect: the variable is set to reflect the effect of temperatures toward the behaviors of consumers. The value is calculated using the equation below.$$max(d-20,18-d,0),$$d denotes the record of temperature during a forecasting period. A variable of the air conditioner effect is assigned a value using a particular function. When d is higher than 293.15 Kelvin, the variable increases in proportion to the temperature to reflect the effect of coolers. In this weather, consumers may use coolers in their homes. When d is lower than 291.15 Kelvin, the variable exhibits an inverse relation relative to the temperature to reflect the effect of heaters. In this weather, consumers use heaters to retain comfort. To simplify the formula, the variables related to temperatures are dealt with as degree Celsius.
- A variable of solar irradiance: the value is calculated from the equation below.$$\omega \xb7(\mathrm{Global}\phantom{\rule{4.pt}{0ex}}\mathrm{Horizontal}\phantom{\rule{4.pt}{0ex}}\mathrm{Irradiance}\phantom{\rule{4.pt}{0ex}}\mathrm{at}\phantom{\rule{4.pt}{0ex}}\mathrm{the}\phantom{\rule{4.pt}{0ex}}\mathrm{forecasting}\phantom{\rule{4.pt}{0ex}}\mathrm{period}),$$Here, Global horizontal irradiance is the amount of energy obtained from the sun. $\omega $ is a coefficient for correcting the difference in solar insolation effects due to the difference in the amount photovoltaic systems installed each year. When a large number of photovoltaic systems are installed by many consumers, the effects of solar irradiance will be high.
- A dummy variable for one year before: a variable that takes 1 if the record for using the coefficient in a regression equation comprises data from one year before a forecasting year, and it takes 0 if not.
- A dummy variable for two years before: A variable that takes 1 if the record for using the coefficient in a regression equation comprises data from two years before a forecasting year, and it takes 0 if not.

#### 2.2.4. Estimated Achievement Rate

#### 2.2.5. The Estimated Amount of Saved Power and the Maximum Estimated Amount of Saved Power

#### 2.2.6. The Error in the Amount of Saved Power

#### 2.3. Formulation of Problems

#### 2.3.1. The Minimization Problem of the Gap between the Sum of the Estimated Amount of Saved Power and the Target Amount of Saved Power

#### 2.3.2. The Minimization Problem of the Error in the Sum of the Amount of Power Saved by All Consumers

#### 2.3.3. The Algorithm to Request Power Saving

Algorithm 1 The algorithm for requesting power saving |

Require:${T}^{t}$$\left|B\right|$${I}^{t}t-1$${d}_{j}$${E}_{j}^{t}$ |

Ensure:${x}_{j}^{t}$ |

${I}^{t}$ ← $sort\left({I}^{t-1}\right)$ |

$rest\leftarrow {T}^{t}$ |

for $i\leftarrow 1$$\left|B\right|$do |

$request\leftarrow 0$ |

if $rest>0$ then |

for $n\leftarrow 1$ to ${d}_{{I}^{t}\left[i\right]}$ do |

if $rest\ge n*$${E}_{{I}^{t}\left[i\right]}^{t}$ then |

$request\leftarrow request+1$ |

else |

break |

end if |

end for |

${x}_{{I}^{t}\left[i\right]}^{t}$$\leftarrow request$ |

$rest\leftarrow rest-request\ast $${E}_{{I}^{t}\left[i\right]}^{t}$ |

end if |

end for |

return ${x}_{j}^{t}$ |

#### 2.4. Simulation

#### 2.4.1. Simulation Overview

#### 2.4.2. Evaluation Function

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Programming Codes

## References

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Tendency | m | Range of ${\mathit{CU}}_{\mathit{m}}$ |
---|---|---|

shortage | 1 | $0.1\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\le \phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}C{U}_{1}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\le \phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}0.3$ |

negative | 2 | $0.6\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\le \phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}C{U}_{2}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\le \phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}0.8$ |

standard | 3 | $0.9\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\le \phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}C{U}_{3}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\le \phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}1.1$ |

accurate | 4 | $0.95\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\le \phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}C{U}_{4}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\le \phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}1.05$ |

positive | 5 | $1.2\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\le \phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}C{U}_{5}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\le \phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}1.4$ |

excess | 6 | $1.7\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\le \phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}C{U}_{6}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\le \phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}1.9$ |

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

Target amount ${T}^{t}$ | ${\sum}_{j=1}^{\left|B\right|}0.06{c}_{j}^{t}$ |

Number of consumers $\left|B\right|$ | 300 |

Contracted amount to save ${d}_{j}$ | 100 |

Type | Number | ||
---|---|---|---|

Equable Market | Majority Positive | Majority Negative | |

Shortage | 50 | 0 | 75 |

Negative | 50 | 0 | 75 |

Standard | 50 | 75 | 75 |

Accurate | 50 | 75 | 75 |

Positive | 50 | 75 | 0 |

Excess | 50 | 75 | 0 |

Market | RMSE for A | RMSE for B | |
---|---|---|---|

Method I | equable market | 1,076,482.02 | 419.18 |

negative market | 1,529,869.49 | 453,806.65 | |

positive market | 622,671.29 | 453,391.55 | |

Method II | equable market | 1,076,842.45 | 779.60 |

negative market | 1,076,842.45 | 779.60 | |

positive market | 1,075,252.26 | 810.59 | |

Method III | equable market | 1,074,627.82 | 1435.02 |

negative market | 1,077,474.046 | 1411.20 | |

positive market | 1,073,341.63 | 2721.21 |

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## Share and Cite

**MDPI and ACS Style**

Takai, K.; Tamura, Y.; Shinomiya, N.
A Method for Reducing the Instability of Negawatts Considering Changes in the Behavior of Consumers. *Energies* **2023**, *16*, 1072.
https://doi.org/10.3390/en16031072

**AMA Style**

Takai K, Tamura Y, Shinomiya N.
A Method for Reducing the Instability of Negawatts Considering Changes in the Behavior of Consumers. *Energies*. 2023; 16(3):1072.
https://doi.org/10.3390/en16031072

**Chicago/Turabian Style**

Takai, Koichi, Yuto Tamura, and Norihiko Shinomiya.
2023. "A Method for Reducing the Instability of Negawatts Considering Changes in the Behavior of Consumers" *Energies* 16, no. 3: 1072.
https://doi.org/10.3390/en16031072