# Demand Side Management Based Power-to-Heat and Power-to-Gas Optimization Strategies for PV and Wind Self-Consumption in a Residential Building Cluster

^{1}

^{2}

^{*}

## Abstract

**:**

^{−1}.

## 1. Introduction

- Single building: Optimization of PV self-consumption.
- Cluster: Optimization of PV self-consumption.
- Cluster: Optimization of PV and small wind turbine self-consumption.
- Cluster: Autarky and increased carbon dioxide emission saving with the application of a hydrogen system.

#### 1.1. State of the Art

#### 1.1.1. Building Demand Prediction

#### 1.1.2. Metaheuristic Optimization in the Field of HVAC Systems

#### 1.1.3. Seasonal Hydrogen Storage

## 2. Methodology

#### 2.1. Pilot Site

#### 2.2. Modelling Approach

#### 2.2.1. Building Model

#### 2.2.2. Decentral Energy Supply System

#### 2.2.3. Central Hydrogen System for Seasonal Energy Storage

- PEM Electrolyzer.
- Multi-stage (isothermal) hydrogen compressor.
- Hydrogen storage tank.
- PEM Fuel Cell.

#### Electrolyzer

^{2}, 300 cm

^{2}or 1250 cm

^{2}). Finally the number of needed cells can be calculated with the rated power, the active cell area and the assumed cell voltage at the maximal operating current density.

#### Compressor

#### Storage Cylinder

^{−1}and the targeted storage pressure, the needed cylinder volume is determined.

#### Fuel Cell

^{2}or 400 cm

^{2}), the number of cells from the cell voltage (0.63 V) and the maximal current density ( $0.4$ $\mathrm{A}$ $\mathrm{c}$$\mathrm{m}$

^{−2}) with data from Bai et al. [24].

#### 2.2.4. Small Wind Turbines

#### 2.3. Household Electricity Demand

#### 2.4. Domestic Hot Water Demand

#### 2.5. Building Model Calibration

- Preprocessing of monitoring and weather data (filling of measurement gaps, unification of time steps).
- Application of a (genetic) optimization algorithm to the building parameters such as operating limit temperature, air exchange rate, room set point temperature, hysteresis of the buffer storage (heating and DHW) as well as the room heating hysteresis.
- The calibration takes place as INSEL-Python co-simulation using the DEAP (Distributed Evolutionary Algorithms in Python [27]) toolbox. The simulation is performed in one minute time steps, but the results and measured values are averaged to 60 min, otherwise a calibration is sometimes not possible due to the high fluctuation of the heat pump operation.
- As last step an assessment of the calibration results is carried out for a validation period that differs from the calibration period with a with a different data set.

#### 2.6. Optimization of Scheduled Heat Pump Operation

**Mode -1:**Normal operation.**Mode 0:**No heat pump operation. The optimization algorithm cannot select this mode directly, as this would cause the heat pump to go out of operation at every possibility, e.g., in a cost optimization scenario. This mode is used to realize possible blocking times by a sub script.**Mode 1:**Forced heat pump operation to load the space heating thermal buffer storage.**Mode 2:**Forced heat pump operation to load the DHW thermal buffer storage.**Mode 3:**Forced heating of the buildings thermal mass. Thereby the heat pump can operate reguarly and load the thermal buffer storages according to demand.

#### 2.6.1. PV Self-Consumption

#### 2.6.2. PV and Wind Self-Consumption

#### 2.7. Calculation of Carbon Dioxide Emission Savings and Prevention Costs

^{−1}], the amount of recovered waste heat ${E}_{HeatToNetwork}$ [kWh] and the emission factor for district heating ${e}_{heat}$ [ $\mathrm{k}\mathrm{g}$$\mathrm{kWh}$

^{−1}].

#### 2.8. Weather Data

## 3. Results

#### 3.1. Building Model Calibration Outcome

#### 3.2. Impact of Weather Prediction Inaccuracy

#### 3.2.1. Building Heat Demand

#### 3.2.2. PV Power Generation

#### 3.3. Best Parameters for Schedule Optimization

#### 3.4. Single Building Operation

#### Optimized Self-Consumption

#### 3.5. Building Cluster Operation

#### 3.5.1. Optimized PV Self-Consumption

#### 3.5.2. Optimized PV and Wind Self-Consumption

#### 3.6. Adding of Hydrogen Systems with and without Small Wind Turbines

- Base Scenario: Decentral PV and Heat Pumps.
- Optimization: Optimized Heat Pump operation to increase PV self-consumption based on weather forecast data.
- Optimization + Hydrogen System: Seasonal hydrogen storage system with electricity-driven fuel cell to operate the heat pumps with surplus PV power stored from the summer months. Heat recovery from the electrolyzer and the fuel cell and heat injection into a district heating network are considered.
- Optimization + Hydrogen System + Small Wind Turbines (SWT): Additional small wind turbines to increase the power production throughout the year.

## 4. Discussion

#### 4.1. Modelling

#### 4.2. Optimization Case Studies

#### 4.3. Hydrogen System Potential

^{−1}). If the heat produced by the electrolyzer and the fuel cell is recovered and fed into a district heating network, the CO${}_{2}$ prevention costs could be reduced by 30%. In our investigated scenario, the hydrogen system would depend on external hydrogen deliveries to maintain its operation in the winter months. The adding of small wind turbines to increase the power output of the cluster on the other hand leads to an annual surplus hydrogen production of the system, which could be sold. Nevertheless, the adding of small wind turbines results in even higher CO${}_{2}$ prevention costs ( $2.23$ €$\mathrm{k}\mathrm{g}$

^{−1}). The next steps aim at finding an optimum for the dimensioning of the hydrogen system based on the achievable CO${}_{2}$ prevention costs.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

$\alpha $ | Roughness exponent [-] |

$ACO$ | Ant colony optimization |

$ANN$ | Artificial neural network |

$BFGS$ | Broyden-Fletcher-Goldfarb-Shanno |

C | Cost [€] |

c | Cost factor [-] |

$CAPEX$ | Capital expenditures |

$CIS$ | Copper indium gallium selenide solar cell |

$DEAP$ | Distributed evolutionary algorithms in python |

$DHW$ | Domestic hot water |

e | CO${}_{2}$ emission factor [kg/kWh] |

E | Energy [kWh] |

$EA$ | Evolutionary algorithm |

$EV$ | Electric vehicle |

$FC$ | Fuel cell |

$GA$ | Genetic algorithm |

h | Height [m] |

$HVAC$ | Heating, ventilation, and air conditioning |

I | Current [A] |

$kNN$ | k-nearest neighbors |

$LEM$ | Local energy management system |

$\dot{m}$ | Mass flow [kg/s] |

m | Mass [kg] |

$MAPE$ | Mean absolute percentage error |

$MPC$ | Model predictive control |

$MPP$ | Maximum power point tracking |

$NRMSE$ | Normalized root mean square error |

P | Power [kW] |

${p}_{c}$ | Crossover probability [-] |

${p}_{m}$ | Mutation probability [-] |

$PEM$ | Polymer electrolyte membrane |

$PSO$ | Particle swarm optimization |

$PV$ | Photovoltaic |

$RC$ | Resistor–capacitor |

$RES$ | Renewable energy sources |

$RLF$ | Residential load factor |

$SVM$ | Support vector machine |

$SWT$ | Small Wind Turbine |

${t}_{life}$ | Lifecycle [a] |

v | Speed [m/s] |

$\widehat{y}$ | Predicted value [kW] |

y | Measured value [kW] |

## Appendix A. Calibration Results

## Appendix B. Prediction Error Due to Weather Forecast Inaccuracy

**Figure A4.**Impact of weather prediction inaccuracy on cumulative electrical heat pump energy demand.

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**Figure 2.**Building model node interconnections. Own representation based on [22].

**Figure 3.**Parameter variation genetic algorithm without constrains. (

**a**): Dependency on mutation and crossover probabilities for all population sizes and number of generations; (

**b**): Dependency on population size and number of generations for all mutation and crossover probabilities.

**Figure 4.**Parameter variation genetic algorithm with constrains. (

**a**): Number of generations and population size set to 50; (

**b**): Crossover probability set to ${p}_{c}$ = 0.9 and mutation probability set to ${p}_{m}$ = 0.3.

**Figure 10.**Daily optimization improvement for a building cluster with normal storage size for the month April.

**Figure 11.**Daily optimization improvement (PV and wind) for a building cluster with normal storage size for the month February.

**Table 1.**Comparison of different building demand prediction methods. Own representation based on [6].

Method | Required | Typical | User- | Computational | Model |
---|---|---|---|---|---|

Input Data | Applications | Friendliness | Demand | Accuracy | |

White Box (Detailed) | Detailed physical information | DOE-2, EnergyPlus, TRYSYS, ESP-r INSEL | Low | High | High |

White Box (Simplified) | Physical information | Heating degree day method, temperature frequency method, RLF (Residential Load Factor) | Average | Average | Relativly high |

Grey Box | Physical information and historical data | RC Network | Low, average | Low, average | Relatively high |

Black Box | Historical data | ANN, SVM, Regression- analysis, Clustering | Low | Low, average | High except regression |

Wind Speed [m/s] | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Power [kW] | 0 | 0.05 | 0.2 | 0.4 | 0.6 | 0.8 | 1.3 | 2.0 | 3.0 | 3.9 | 4.5 | 5.0 | 5.2 | 5.3 |

Source | Emission Factor | Source |
---|---|---|

Power From Grid | $0.408$$\mathrm{k}\mathrm{g}$$\mathrm{kWh}$ | [32] |

District Heating | $0.243$$\mathrm{k}\mathrm{g}$$\mathrm{kWh}$ | [33] |

Component | Specific Costs | Unit | Source |
---|---|---|---|

PEM Electrolyzer | $2000+1000\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{P}_{EL}$ | €$\mathrm{k}$$\mathrm{W}$^{−1} | [19] |

Compressor | $2545\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{P}_{comp}$ | €$\mathrm{k}$$\mathrm{W}$^{−1} | [23] |

Hydrogen Storage | $15\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{m}_{{H}_{2}}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}LH{V}_{{H}_{2}}$ | €$\mathrm{kWh}$^{−1} | [19] |

PEM Fuel Cell | $2000+1000\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{P}_{EL}$ | €$\mathrm{k}$$\mathrm{W}$^{−1} | [19] |

Battery | $500\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{E}_{bat}$ | €$\mathrm{kWh}$^{−1} | [34] |

Small Wind Turbine (5 kW) | 24,000 | € | own assumption |

Hydrogen Delivery | 9 | €$\mathrm{k}\mathrm{g}$^{−1} | own assumption |

Building ID | Indoor | Hyst Space | Hyst DHW | Hyst Room | Heating Stop | Air Ex |
---|---|---|---|---|---|---|

Temp [°C] | [°C] | [°C] | [°C] | Temp [°C] | Rate [1/h] | |

Initial Param. | 20.0 | 5.0 | 5.0 | 2.0 | 10.0 | 0.30 |

Param. Range | 15.0–25.0 | 0.01–10.0 | 0.01–10.0 | 0.01–3.0 | 8.0–18.0 | 0.00–0.60 |

Building ID | NRMSE | NRMSE | E, Measured | E, Predicted |
---|---|---|---|---|

Original | Calibrated | [kWh] | [kWh] | |

01 | 30.8% | 18.4% | 105.1 | 100.0 |

02 | 40.6% | 26.1% | 81.1 | 72.4 |

09 | 49.8% | 47.6% | 92.4 | 92.6 |

10 | 68.3% | 32.9% | 62.8 | 62.0 |

12 | 32.2% | 29.7% | 138.1 | 133.4 |

19 | 41.7% | 32.7% | 117.1 | 103.1 |

20 | 19.0% | 19.0% | 83.6 | 83.0 |

22 | 45.4% | 23.8% | 53.2 | 46.8 |

24 | 45.8% | 28.3% | 68.7 | 56.1 |

25 | 36.5% | 20.8% | 61.7 | 57.2 |

Building ID | Indoor | Hyst Space | Hyst DHW | Hyst Room | Heating Stop | Air Ex |
---|---|---|---|---|---|---|

Temp [°C] | [°C] | [°C] | [°C] | Temp [°C] | Rate [1/h] | |

01 | 16.7 | 2.3 | 0.01 | 0.7 | 17.0 | 0.20 |

02 | 16.7 | 1.7 | 0.1 | 0.01 | 14.0 | 0.04 |

09 | 20.3 | 7.0 | 7.3 | 2.2 | 11.0 | 0.02 |

10 | 15.7 | 0.3 | 0.3 | 0.3 | 14.0 | 0.00 |

12 | 19.3 | 7.7 | 8.3 | 0.7 | 13.0 | 0.32 |

19 | 20.0 | 4.0 | 4.7 | 0.4 | 9.0 | 0.10 |

20 | 20.3 | 0.7 | 4.7 | 0.4 | 15.0 | 0.60 |

22 | 16.7 | 5.0 | 0.3 | 0.8 | 17.0 | 0.12 |

24 | 16.0 | 1.3 | 0.3 | 0.3 | 14.0 | 0.04 |

25 | 17.3 | 0.1 | 0.1 | 0.4 | 15.0 | 0.00 |

**Table 8.**Comparison of heating electricity demand prediction error according to weather data forecasting duration.

Measured Weather Data | 24 h Forecast | 48 h Forecast | |
---|---|---|---|

NRMSE | 14.2% | 16.7% | 20.6% |

**Table 9.**Comparison of PV generation prediction error according to weather data forecasting duration.

24 h Forecast | 48 h Forecast | 72 h Forecast | |
---|---|---|---|

NRMSE | 9.7% | 9.6% | 10.6% |

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Opt | 3.8% | 7.0% | 10.4% | 10.6% | 14.9% | 15.4% | 16.6% | 12.5% | 10.8% | 6.7% | 4.5% | 3.9% |

Meas Opt | 0.9% | 4.6% | 4.0% | 6.6% | 5.0% | 1.6% | 0.6% | 3.1% | 3.3% | 3.9% | 1.4% | 1.1% |

Ad Hoc | 1.2% | 5.2% | 4.8% | 8.0% | 8.1% | 5.0% | 5.9% | 6.8% | 5.8% | 4.7% | 1.7% | 1.5% |

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Opt | 4.7% | 9.8% | 12.5% | 15.0% | 20.9% | 18.4% | 19.5% | 17.0% | 15.9% | 10.0% | 5.6% | 4.4% |

Meas Opt | 1.1% | 5.8% | 3.0% | 4.9% | 2.2% | 7.0% | 2.6% | 5.9% | 5.4% | 2.9% | 2.1% | 1.7% |

Ad Hoc | 1.8% | 6.0% | 4.1% | 6.9% | 5.7% | 9.4% | 8.5% | 8.8% | 7.0% | 4.9% | 2.7% | 2.1% |

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Opt | 1.6% | 3.3% | 3.5% | 5.0% | 6.2% | 6.6% | 4.3% | 4.5% | 5.0% | 4.3% | 2.4% | 1.5% |

Meas Opt | 0.0% | −0.1% | 0.1% | −0.2% | 0.2% | 0.4% | −0.4% | 0.8% | 0.3% | 0.0% | −0.4% | −0.1% |

Ad Hoc | 0.3% | 0.5% | 0.9% | 0.6% | 1.1% | 1.4% | 0.6% | 1.2% | 1.2% | 1.1% | 0.5% | 0.3% |

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Opt | 1.9% | 4.1% | 4.5% | 5.3% | 7.7% | 5.4% | 4.2% | 5.4% | 3.9% | 4.5% | 3.2% | 1.8% |

Meas Opt | −0.2% | 1.6% | 0.7% | 1.3% | 1.0% | 1.0% | 0.5% | 1.1% | 0.4% | 0.1% | 0.5% | 0.1% |

Ad Hoc | 0.3% | 1.9% | 1.5% | 1.5% | 2.0% | 1.7% | 0.9% | 1.7% | 0.8% | 1.0% | 0.7% | 0.4% |

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Opt | 3.6% | 7.4% | 5.6% | 7.8% | 6.8% | 6.6% | 6.5% | 5.3% | 7.3% | 6.0% | 5.3% | 0.0% |

Meas Opt | −0.2% | 2.2% | −0.6% | 0.5% | −0.3% | −0.4% | −0.1% | −0.2% | 1.1% | −0.3% | −1.9% | 0.1% |

Ad Hoc | 0.4% | 2.8% | 0.9% | 1.3% | 1.4% | 1.3% | 0.8% | 1.3% | 1.6% | 0.9% | 0.9% | 0.4% |

Parameter | Hydrogen System | SWT and Hydrogen System |
---|---|---|

Electrolyzer Power | 78 kW | 107 kW |

Electrolyzer Cells | 45 | 62 |

ELectrolyzer Cell Area | 300 cm^{2} | 300 cm^{2} |

Max. Hydrogen prod. Rate | $1.51$$\mathrm{k}\mathrm{g}$$\mathrm{h}$^{−1} | $2.08$$\mathrm{k}\mathrm{g}$$\mathrm{h}$^{−1} |

Storage Volume | $29.5$${\mathrm{m}}^{3}$ | $37.43$${\mathrm{m}}^{3}$ |

Initial Storage Tank Filling | 35$\mathrm{M}$$\mathrm{Pa}$ | 15$\mathrm{M}$$\mathrm{Pa}$ |

FC Power | 37.5 kW | 37.4 kW |

FC Cells | 345 | 344 |

FC Area | 400 cm^{2} | 400 cm^{2} |

Compressor Power | 17.75 kW | 24.5 kW |

Parameter | w/o SWT | With SWT |
---|---|---|

${E}_{grid}$ w/o ${H}_{2}$ | 48,385 kWh | 36,974 kWh |

${E}_{grid}$ w/ ${H}_{2}$ | 59 kWh | 70 kWh |

Parameter | Hydrogen System | SWT and Hydrogen System |
---|---|---|

Estimated System CAPEX | $597.852$€ | $930.342$€ |

Annual Hydrogen Refill Costs | $4.724$€ | $-2.452$€ |

${c}_{C{O}_{2},saving}$ | $1.76$€$\mathrm{k}\mathrm{g}$^{−1} | $2.23$€$\mathrm{k}\mathrm{g}$^{−1} |

${c}_{C{O}_{2},saving}$ (Heat Recovery) | $1.23$€$\mathrm{k}\mathrm{g}$^{−1} | $1.55$€$\mathrm{k}\mathrm{g}$^{−1} |

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**MDPI and ACS Style**

Brennenstuhl, M.; Lust, D.; Pietruschka, D.; Schneider, D.
Demand Side Management Based Power-to-Heat and Power-to-Gas Optimization Strategies for PV and Wind Self-Consumption in a Residential Building Cluster. *Energies* **2021**, *14*, 6712.
https://doi.org/10.3390/en14206712

**AMA Style**

Brennenstuhl M, Lust D, Pietruschka D, Schneider D.
Demand Side Management Based Power-to-Heat and Power-to-Gas Optimization Strategies for PV and Wind Self-Consumption in a Residential Building Cluster. *Energies*. 2021; 14(20):6712.
https://doi.org/10.3390/en14206712

**Chicago/Turabian Style**

Brennenstuhl, Marcus, Daniel Lust, Dirk Pietruschka, and Dietrich Schneider.
2021. "Demand Side Management Based Power-to-Heat and Power-to-Gas Optimization Strategies for PV and Wind Self-Consumption in a Residential Building Cluster" *Energies* 14, no. 20: 6712.
https://doi.org/10.3390/en14206712