# Optimal Coordination of Aggregated Hydro-Storage with Residential Demand Response in Highly Renewable Generation Power System: The Case Study of Finland

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## Abstract

**:**

## 1. Introduction

## 2. Modeling Methodology

#### 2.1. Base-Load Generation Modeling

#### 2.2. Hydro-Generation Modeling

#### 2.3. Renewable Generation Modeling

#### 2.4. Two-Capacity Building Model for HVAC Loads

^{m}, whereas the other is distributed to the indoor air, C

^{a}. While C

^{a}is much smaller than C

^{m}, it plays an inevitable role in assessing the indoor air dynamics. This model has two unknown temperature variables, namely, the indoor temperature, θ

^{a}, and the building mass temperature, θ

^{m}. Figure 2 illustrates this model.

^{x}. The generated air is of convective type and is allocated to the indoor air node. For heat flows, the ground temperature, θ

^{g}, must be considered. The windows installed in the building have a small thermal mass compared to the building envelope. The different node points and the HVAC unit are connected through heat conductance, or whenever there is heat flow, they are connected by heat capacity. The building mass node is located at a vague depth inside the building and hence represents the average temperature of the building mass. It is assumed that the internal heat transfer by electric appliances and occupants is negligible.

^{a}. The parameters were determined by minimizing the difference between the response from IDA and two-capacity model.

#### 2.5. Electric Vehicle

## 3. Mathematical Formulation

_{1m}is the time step when EV m leaves the home and t

_{2m}is the time interval when it arrives home in each day over the study period. Equation (15) enables the EV storage to mutate between specified levels only, while Equation (16) bounds the EV charging power. The hydro storage management is modeled in Equations (17) and (18). The constraint Equation (19) specifies that hydro generation is always committed between minimum and maximum levels. Constraints Equations (20)–(22) preserve the total demand of each flexible load for each household over the study period i.e., yearly individual flexible demand for each household remains constant. Equations (23)–(25) determine the total DR of different flexible loads in each time slot.

## 4. Case Study

#### 4.1. Input Data

- Case I
- The hydro storage was optimized to accommodate for RESs variability without activating DR through residential flexible loads of detached houses. The charging of EV was also uncontrolled.
- Case II
- The hydro storage was optimized while coordinating with DR through direct control of HVAC, EWH, and EV charging loads. DR enrollment was assumed 100%.

#### 4.2. Simulation Results

#### 4.3. Sensitivity Analyses

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Indices and sets | |

t, T | Index and set of time slot |

t_{1m}, t_{2m} | Time step when EV m leaves and arrives home respectively on daily basis |

$\Delta t$ | Difference between two time slots |

n, N | Index and set of household |

m, M | Index and set of Electric Vehicle |

Parameters | |

${{\displaystyle c}}_{w}$ | Specific heat capacity of water (J/kg/K) |

${{\displaystyle C}}^{a}$ | Indoor air heat capacity (J/°C) |

${{\displaystyle C}}^{m}$ | Building fabric capacity (J/°C) |

${{\displaystyle d}}_{t,m}$ | Distance travelled by EV m at time t (mile) |

${{\displaystyle D}}_{t}^{Critical}$ | Total critical demand in the system at time t (Wh) |

${{\displaystyle H}}^{e}$ | Heat conductance between external air and indoor air node points (W/°C) |

${{\displaystyle H}}^{g}$ | Heat conductance between indoor air and ground node points (W/°C) |

${{\displaystyle H}}^{m}$ | Heat conductance between indoor air and building mass node points (W/°C) |

${{\displaystyle H}}^{y}$ | Heat conductance between external air and building mass node points (W/°C) |

${{\displaystyle H}}^{x}$ | Heat conductance between HVAC air and indoor air node points (W/°C) |

${{\displaystyle Inflow}}_{t}^{hydro}$ | Hydro-inflows at time t (Wh) |

${{\displaystyle P}}_{t}^{Nuclear}$ | Nuclear power production at time t (W) |

${{\displaystyle P}}_{t}^{CHP-city}$ | CHP-city power production at time t (W) |

${{\displaystyle P}}_{t}^{CHP-ind}$ | CHP-industry power production at time t (W) |

${{\displaystyle P}}_{t}^{REN}$ | RES production at time t (W) |

${{\displaystyle P}}_{\mathrm{max}}^{hydro},{{\displaystyle P}}_{\mathrm{min}}^{hydro}$ | Maximum and minimum limits for hydro-power generation (W) |

${{\displaystyle P}}_{\mathrm{max},m}^{EV}$ | Rated maximum charging power of EV m (W) |

${{\displaystyle P}}_{\mathrm{max},n}^{ewh}$ | Rated maximum power of EWH of household n (W) |

${{\displaystyle P}}_{\mathrm{max},n}^{TSch}$ | Rated maximum charging power of thermal storage of household n (W) |

${{\displaystyle Q}}_{\mathrm{max},n}^{hvac}$ | Rated maximum power of HVAC unit of household n (W) |

${{\displaystyle SOC}}_{\mathrm{max}}^{hydro},\text{\hspace{0.17em}}{{\displaystyle SOC}}_{\mathrm{min}}^{hydro}$ | Maximum and minimum limits for SOC of aggregated hydro storage (Wh) |

${{\displaystyle SOC}}_{\mathrm{max},n}^{TS},{{\displaystyle SOC}}_{\mathrm{min},n}^{TS}$ | Maximum and minimum limits for SOC of thermal storage of household n(Wh) |

${{\displaystyle SOC}}_{\mathrm{max},m}^{EV},{{\displaystyle SOC}}_{\mathrm{min},m}^{EV}$ | Maximum and minimum limits for SOC of EV m (Wh) |

${{\displaystyle \theta}}_{\mathrm{max},n}^{a}\text{\hspace{0.17em}},{{\displaystyle \theta}}_{\mathrm{min},n}^{a}$ | Maximum and minimum limits for ambient temperature of household n (°C) |

${{\displaystyle \theta}}_{t}^{e}$ | External temperature at time t (°C) |

${{\displaystyle \theta}}_{t,n}^{x}$ | Temperature of the ventilation air of household n at time t(°C) |

${{\displaystyle \theta}}^{in}$ | Temperature of inlet cold water in the hot water tank (°C) |

${{\displaystyle \theta}}_{t,n}^{g}$ | Ground node temperature of household n at time t (°C) |

${{\displaystyle \theta}}_{\mathrm{max},n}^{dhw},\text{\hspace{0.17em}}{{\displaystyle \theta}}_{\mathrm{min},n}^{dhw}$ | Maximum and minimum limits for DHW temperature of household n (°C) |

${{\displaystyle V}}_{n}^{\mathrm{tan}k}$ | Volume of hot water tank of household n (L) |

${{\displaystyle V}}_{t,n}^{use}$ | Volume of hot water used by household n at time t (L) |

${\eta}_{c}\text{\hspace{0.17em}}$ | Charging efficiency of EV storage |

${{\displaystyle \eta}}_{ev}$ | Travel efficiency of EV (Wh/mile) |

${{\displaystyle \Psi}}_{n}$ | Total thermal charging demand of household n over the period T (Wh) |

${{\displaystyle \varphi}}_{n}$ | Total EWH demand of household n over the scheduling period T (Wh) |

${{\displaystyle \beta}}_{m}$ | Total EV charging demand of EV m over the scheduling period T (Wh) |

Variables | |

${{\displaystyle D}}_{t}^{Flex}$ | Total flexible demand at time t (W) |

${{\displaystyle D}}_{t}^{HVAC}$ | Total HVAC demand at time t (W) |

${{\displaystyle D}}_{t}^{EWH}$ | Total EWH demand at time t (W) |

${{\displaystyle D}}_{t}^{EV}$ | Total EV charging demand at time t (W) |

${{\displaystyle P}}_{t}^{hydro}$ | Hydro power production at time t (W) |

${{\displaystyle P}}_{t,n}^{ewh}$ | EWH power of household n at time t (W) |

${{\displaystyle P}}_{t,n}^{TSch}$ | Thermal storage charging power of household n at time t (W) |

${{\displaystyle P}}_{t,m}^{EV}$ | Charging power of EV m at time t (W) |

${{\displaystyle Q}}_{t,n}^{hvac}$ | HVAC power consumption of household n at time t (W) |

${{\displaystyle SOC}}_{t,m}^{EV}$ | SOC of EV m at time t (Wh) |

${{\displaystyle SOC}}_{t}^{hydro}$ | SOC of aggregated hydro-storage at time t (Wh) |

${{\displaystyle SOC}}_{t,n}^{TS}$ | SOC of thermal storage of household n at time t (Wh) |

${{\displaystyle \theta}}_{t,n}^{a}$ | Ambient temperature of household n at time t (°C) |

${{\displaystyle \theta}}_{t,n}^{dhw}$ | DHW temperature of household n at time t (°C) |

${{\displaystyle \theta}}_{t,n}^{m}$ | Building mass temperature of household n at time t (°C) |

${{\displaystyle \mu}}_{t,n}^{}$ | Thermal storage loss coefficient of household n at time t (Wh) |

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**Figure 11.**CHP–city replaced with surplus RESs (70% penetration) for Case II: (

**a**) CHP production; (

**b**) RESs curtailments.

Case Study | Load Curtailment (TWh) | RES Curtailment (TWh) |
---|---|---|

Case I | 4.13 | 5.84 |

Case II | 0.98 | 1.65 |

Case Study | Curtailment | Mean Value (TWh) | Standard Deviation (TWh) | Lower 95% Confidence Bound (TWh) | Upper 95% Confidence Bound (TWh) |
---|---|---|---|---|---|

Case I | Load | 3.748 | 0.267 | 3.695 | 3.8 |

Generation | 5.168 | 0.277 | 5.113 | 5.222 | |

Case II | Load | 0.653 | 0.19 | 0.6078 | 0.698 |

Generation | 1.112 | 0.274 | 1.047 | 1.177 |

RES Penetration (%) | Aggregated Generation as % of Total Demand | Case I | Case II | ||
---|---|---|---|---|---|

Load Curtailment (TWh) | RES Curtailment (TWh) | Load Curtailment (TWh) | RES Curtailment (TWh) | ||

35 | 102.1 | 4.130 | 5.84 | 0.982 | 1.65 |

40 | 107.23 | 3.215 | 9.339 | 0.484 | 4.921 |

45 | 112.41 | 2.586 | 13.128 | 0.320 | 8.456 |

50 | 117.6 | 2.248 | 17.207 | 0.227 | 12.538 |

55 | 122.8 | 1.974 | 21.351 | 0.176 | 16.790 |

60 | 127.98 | 1.752 | 25.546 | 0.143 | 21.082 |

65 | 133.15 | 1.566 | 29.777 | 0.117 | 25.419 |

70 | 138.34 | 1.409 | 34.038 | 0.095 | 29.781 |

RES Penetration (%) | RES Curtailment (TWh) | Reduction in Curtailment (%) | CHP-city Electricity Production (TWh) | CHP-city Heating Production (TWh) | CHP-city Total Production (TWh) |
---|---|---|---|---|---|

35 | 0.174 | 89.45 | 11.628 | 37.51 | 49.14 |

40 | 0.67 | 86.38 | 10.970 | 35.39 | 46.36 |

45 | 1.424 | 83.16 | 10.313 | 33.27 | 43.58 |

50 | 2.510 | 79.98 | 9.603 | 30.98 | 40.58 |

55 | 3.885 | 76.86 | 8.923 | 28.785 | 37.71 |

60 | 5.617 | 73.35 | 8.318 | 26.832 | 35.15 |

65 | 7.445 | 70.71 | 7.724 | 24.916 | 32.64 |

70 | 9.644 | 67.62 | 7.212 | 23.265 | 30.48 |

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**MDPI and ACS Style**

Bashir, A.A.; Lehtonen, M.
Optimal Coordination of Aggregated Hydro-Storage with Residential Demand Response in Highly Renewable Generation Power System: The Case Study of Finland. *Energies* **2019**, *12*, 1037.
https://doi.org/10.3390/en12061037

**AMA Style**

Bashir AA, Lehtonen M.
Optimal Coordination of Aggregated Hydro-Storage with Residential Demand Response in Highly Renewable Generation Power System: The Case Study of Finland. *Energies*. 2019; 12(6):1037.
https://doi.org/10.3390/en12061037

**Chicago/Turabian Style**

Bashir, Arslan Ahmad, and Matti Lehtonen.
2019. "Optimal Coordination of Aggregated Hydro-Storage with Residential Demand Response in Highly Renewable Generation Power System: The Case Study of Finland" *Energies* 12, no. 6: 1037.
https://doi.org/10.3390/en12061037