# Increasing the Benefit from Cost-Minimizing Loads via Centralized Adjustments

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## Abstract

**:**

## 1. Introduction

## 2. General Framework

#### 2.1. Market Environment

#### 2.2. Aggregator and Consumers

#### 2.3. Control Strategy

## 3. Problem Formulation

#### 3.1. Local Optimization

#### 3.2. Aggregators’ Decision-Making

## 4. Simulations

#### 4.1. Simulation Setup

- Base: Loads optimize locally but they cannot be centrally controlled. However, the aggregator is able to bid in the DA market but without the heating load flexibility.
- Base+RT: RT optimization and control are possible but the flexibility is not considered in the DA optimization.
- DA+RT: The DA optimization is solved with the heating load flexibility and the operation is updated by solving the RT optimization. The aggregator is also able to control the loads.

#### 4.2. Results

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

## Indices and sets

i | Index of heating load model |

k | Time step index |

l | Index of averaging block |

s | Scenario index |

θ | Set of building model parameters |

## Parameters and Constants

A1–A4 | Building model parameters |

B1–B3 | Building model parameters |

β^{+}, β^{−} | Weighting factors of imbalance power trade |

ΔT | Allowed temperature band for control |

ΔT^{L} | Allowed temperature deviation from set-point |

d | Fixed electricity consumption |

$\overline{E}$ | Maximum heating power |

E^{F} | Heating load forecast |

H^{↑}, H^{↓} | Indicates direction of regulation |

K | Length of optimization period |

K^{b} | Length of averaging period |

λ | DA market price, spot price |

λ^{↑}, λ^{↓} | Up/downregulating prices |

λ^{S+}, λ^{S−} | Prices of positive/negative imbalance power |

m | Margin in consumer tariff |

ρ | Probability of a scenario |

S | Number of scenarios |

T^{a,F} | Forecast of indoor temperature evolution set-point |

T^{set} | Indoor temperature |

## Variables (non-negative)

ΔE^{+} | Increase in heating power |

E | Heating power |

E^{A} | Heating power after adjustments |

E^{R} | Real-time heating power |

P^{DA} | Day-ahead procurement |

P^{↑}, P^{↓} | Up/downregulating power, regulating power bids |

P^{A+}, P^{A−} | Positive/negative heating load adjustment |

P^{R}: | Real-time electricity consumption |

P^{S+}, P^{S−} | Positive/negative imbalance power |

T^{a}, T^{m} | Indoor and building mass temperatures |

u | Generic control signal |

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**Figure 1.**Flowchart of the control strategy. The notation correspond to the notation of day-ahead (DA) and real-time (RT) optimization problems.

**Figure 2.**(

**a**) Generated scenarios for the fixed load; and (

**b**) Generated scenarios for regulating prices.

**Figure 3.**Average time series illustrating the operation. (

**a**) DA forecast, DA procurement, actual simulated consumption, and fixed load; (

**b**) Activated regulation and adjustments; (

**c**) Locally optimized indoor temperature and the temperature after control.

**Figure 4.**Daily values. (

**a**) Stacked bar graph presenting the components of aggregator’s profit. Negative values are cost and positive income. The values above the bars are the daily profits; (

**b**) Grouped bar graph presenting the amount of up/downregulation (up is negative value), positive/negative imbalance powers, and energy trading.

© 2016 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/).

## Share and Cite

**MDPI and ACS Style**

Alahäivälä, A.; Lehtonen, M.
Increasing the Benefit from Cost-Minimizing Loads via Centralized Adjustments. *Energies* **2016**, *9*, 983.
https://doi.org/10.3390/en9120983

**AMA Style**

Alahäivälä A, Lehtonen M.
Increasing the Benefit from Cost-Minimizing Loads via Centralized Adjustments. *Energies*. 2016; 9(12):983.
https://doi.org/10.3390/en9120983

**Chicago/Turabian Style**

Alahäivälä, Antti, and Matti Lehtonen.
2016. "Increasing the Benefit from Cost-Minimizing Loads via Centralized Adjustments" *Energies* 9, no. 12: 983.
https://doi.org/10.3390/en9120983