# Advantages of Minimizing Energy Exchange Instead of Energy Cost in Prosumer Microgrids

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Microgrid under Study

#### 2.2. Optimization Process for the Battery Scheduling

**,**t = 1, 2, …, 24 h, respectively. In cooperative mode these vectors collect the sum of both prosumers. A 24-element vector ${P}_{B}^{i}\left(t\right)$, t = 1, 2, …, 24 h, is composed of the dispatched active power schedule of prosumer’s battery i. In cooperative mode all batteries within the community are considered. The adopted sign convention is positive for charging and negative for discharging. Elements ${P}_{B}^{i}\left(t\right)$ (hourly dispatched active power scheduled for every battery) are the values to be scheduled according to the optimization process; therefore, they will be the result of the GA technique. Original demand D (t) is then modified to ${D}_{mod}\left(t\right)$, according to the battery contribution, as shown in Equation (1).

^{®}to minimize the objective function subjected to a set of constraints, as explained below.

- State of charge (SoC) range: Battery manufacturers recommend keeping the SoC (percentage of charge related to the rated capacity) within a safe operational range [SoC
_{min}, SoC_{max}]. Dynamic equation for SoC calculation is shown in Equation (4), under the assumption of unity charging/discharging efficiency. A discretization of Equation (4) is done in this constraint, which is shown in Equation (5), and minimum and maximum limits are assumed to be 20% and 100% respectively, taking [25] as reference:$${\mathrm{SoC}}^{i}\left(t\right)={\mathrm{SoC}}^{i}\left(0\right)+\frac{1}{{C}_{nom}^{i}}{\displaystyle \underset{0}{\overset{t}{\int}}{P}_{B}^{i}(t)dt},$$$${\mathrm{SoC}}_{min}^{i}\le {\mathrm{SoC}}_{init}^{i}+\frac{{\displaystyle \sum _{t=1}^{24}{P}_{B}^{i}(t)\Delta t}}{{C}_{nom}^{i}}\le {\mathrm{SoC}}_{max}^{i}.$$

- Charge/discharge power: The charging/discharging power is bounded by the battery specifications and by the battery’s power electronics converter rated power. Equation (6) describes this constraint, in which ${P}_{\mathrm{max},dis}^{i}$ and ${P}_{\mathrm{max},ch}^{i}$ are the maximum allowed power for discharging and charging (−2000 W and 2000 W have been respectively assumed).$${P}_{\mathrm{max},dis}^{i}\le {P}_{B}^{i}(t)\le {P}_{\mathrm{max},ch}^{i}.$$
- Power gradient limitation: It is desirable that batteries’ SoC presents a smooth variation along the day. Abrupt changes in SoC along with frequent alternating between charge and discharge modes negatively affect the battery lifetime [26,27]. Therefore, an additional constraint has been included to avoid large power oscillations between two consecutive hours. A maximum power gradient ΔP
_{B}is considered with that purpose, as presented in Equation (7). A value of 300 W has been selected for ΔP_{B}, obtained from the maximum difference observed between consecutive hours in a daily profile averaged for a year in a real house.$$\left|{P}_{B}^{i}(t)-{P}_{B}^{i}(t+1)\right|\le \Delta {P}_{B}.$$

_{B}, depending on whether individual or coordinated scheduling is being performed. The final solution will consist in the set of hourly battery charging/discharging power values which minimizes the objective function subject to defined constraints.

## 3. Results

_{grid}, obtained from the nodal (in individual operation) or the whole system (coordinated operation) power balance, computed by Equation (10), and the accumulated energy import E

_{imp}and export E

_{exp}during the whole day, computed by Equations (11) and (12) respectively. One must note that P

_{grid}should not be higher than the line capacity (4.6 kW for each dwelling or 9.2 kW for the common supply line):

_{bnt}denotes the energy cost before network tariffs in €/day, and is calculated by Equation (13):

_{grid}sign, the cost is positive when the energy is imported.

_{grid}.

_{ant}by means of Equation (14):

#### 3.1. Individual Schedule of Batteries

_{grid}, according to Equation (10). It can be observed that line capacity of each dwelling is not exceeded in any cases.

_{imp}and exported E

_{exp}(according to Equations (11) and (12) respectively), are reported in Table 2.

_{bnt}is obviously lower when COF is used, this approach leads to higher energy interchange with the grid, which adds costs in terms of network tariffs both when importing and exporting energy (although with different unitary cost). In the case of MOF, CP is reduced as well as imported and exported energy, leading to considerably lower network tariffs. As a consequence, this is the approach with the lowest Cost

_{ant}for prosumer 1 and produces similar revenues for prosumer 2.

#### 3.2. Coordinated Schedule of Batteries

_{grid}is always far from the capacity of the common supply line (9.2 kW). In the case of COF, energy import is reduced in comparison to the case without ESS, but energy export is increased, since only economic factors are considered to reach the optimal solution.

_{grid}and the evolution of the SoC of batteries are also shown in Figure 11 and Figure 12 respectively.

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

CET: | Consumer Energy Tariff |

C^{i}_{nom}: | Nominal capacity of battery i |

COF: | Cost objective function |

Cost_{ant}: | Cost after network tariffs |

Cost_{bnt}: | Cost before network tariffs |

CP: | Contracted Power |

CP_{i}: | Contracted Power of prosumer i |

CP_{MG}: | Contracted Power of the whole microgrid |

CPT: | Consumer Power Tariff |

D (t): | Demanded power at hour t |

DER: | Distributed Energy Resource |

D_{mod} (t): | Modified demand at hour t |

DSR: | Demand-Side Response |

E_{exp}: | Exported energy along the whole day |

E_{imp}: | Imported energy along the whole day |

ESS: | Energy Storage System |

f_{cost}: | Fitness function to be minimized according to COF |

FIT: | Feed-in Tariffs |

f_{mismatch}: | Fitness function to be minimized according to MOF |

G (t): | Generated power at hour t |

GA: | Genetic Algorithm |

MOF: | Mismatch objective function |

O&M: | Operation and Maintenance |

P2P: | Peer-to-Peer |

P_{B}^{i} (t): | Battery power of battery i at hour t |

PET: | Producer Energy Tariff |

P_{grid}: | Power in the interconnection with the main grid |

P^{i}_{max,ch}: | Maximum charge power for battery i |

P^{i}_{max,dis}: | Maximum discharge power for battery i |

Pr (t): | Energy market price at hour t |

PV: | Photovoltaic |

SC: | Self-Consumption rate |

SoC: | State of Charge |

SoC^{i}_{init}: | State of Charge of battery i at the beginning of the day |

SoC^{i}_{max}: | Maximum allowed State of Charge of battery i |

SoC^{i}_{min}: | Minimum allowed State of Charge of battery i |

SS: | Self-Sufficiency rate |

ΔP_{B}: | Maximum power gradient between consecutive hours |

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**Figure 4.**Generation, demand and modified demand hourly power curves during scheduled 24 h: (

**a**) Prosumer 1, COF; (

**b**) Prosumer 1, MOF; (

**c**) Prosumer 2, COF; (

**d**) Prosumer 2, MOF.

**Figure 5.**P

_{grid}during scheduled 24 h (positive values for import energy flow and negative for export): (

**a**) Prosumer 1, without ESS; (

**b**) Prosumer 1, COF; (

**c**) Prosumer 1, MOF; (

**d**) Prosumer 2, without ESS; (

**e**) Prosumer 2, COF; (

**f**) Prosumer 2, MOF.

**Figure 6.**SoC of batteries during scheduled 24 h: (

**a**) Prosumer 1, COF; (

**b**) Prosumer 1, MOF; (

**c**) Prosumer 2, COF; (

**d**) Prosumer 2, MOF.

**Figure 7.**Generation, demand and modified demand hourly power curves of the whole microgrid, during scheduled 24 h: (

**a**) COF; (

**b**) MOF.

**Figure 8.**P

_{grid}of the whole microgrid during scheduled 24 h (positive values for export energy flow and negative for import): (

**a**) Without ESS; (

**b**) COF; (

**c**) MOF.

**Figure 10.**Generation, demand and modified demand hourly power curves of the whole microgrid, during scheduled 24 h, in the new case study: (

**a**) COF; (

**b**) MOF.

**Figure 11.**P

_{grid}during scheduled 24 h (positive values for export energy flow and negative for import), in the new case study: (

**a**) Without ESS; (

**b**) COF; (

**c**) MOF.

Prosumer | Indicator | Without ESS | COF | MOF |
---|---|---|---|---|

Prosumer 1 | SC | 0.6327 | 0.4611 | 0.7568 |

SS | 0.3306 | 0.2410 | 0.3955 | |

Prosumer 2 | SC | 0.1384 | −0.0177 ^{1} | 0.3427 |

SS | 0.5083 | −0.0651 ^{1} | 1.2582 ^{2} |

^{1}SS < 0 is due to negative values of D

_{mod}(t) in Equation (9).

^{2}SS > 1 means that imported energy is higher than household daily demand.

Prosumer | Indicator | Without ESS | COF | MOF |
---|---|---|---|---|

Prosumer 1 | |E_{imp}| (kWh) | 27.203 | 27.047 | 20.495 |

|E_{exp}| (kWh) | 7.801 | 11.445 | 4.893 | |

Prosumer 2 | |E_{imp}| (kWh) | 2.844 | 4.361 | 0.014 |

|E_{exp}| (kWh) | 18.297 | 21.614 | 13.952 |

Prosumer | Indicator | Without ESS | COF | MOF |
---|---|---|---|---|

Prosumer 1 | CP (kW) | 4.2 | 4.4 | 3.9 |

Cost_{bnt} (€/day) | 1.2959 | 1.0258 | 1.0610 | |

Cost_{ant} (€/day) | 2.9351 | 2.6809 | 2.3723 | |

Prosumer 2 | CP (kW) | 2.7 | 2.6 | 2.1 |

Cost_{bnt} (€/day) | −1.0278 | −1.1826 | −0.9135 | |

Cost_{ant} (€/day) | −0.6120 | −0.7088 | −0.6871 |

Indicator | Without ESS | COF | MOF |

SC | 0.4168 | 0.3112 | 0.5950 |

SS | 0.3814 | 0.2847 | 0.5444 |

Indicator | Without ESS | COF | MOF |
---|---|---|---|

|E_{imp}| (kWh) | 28.720 | 27.606 | 15.553 |

|E_{exp}| (kWh) | 24.771 | 29.257 | 17.204 |

**Table 6.**Economic indicators for the whole microgrid, and individual CP and sum of both prosumers costs with individual schedule.

Type of Schedule | Indicator | Without ESS | COF | MOF |
---|---|---|---|---|

Coordinated (whole microgrid) | CP_{MG}(kW) | 4.2 | 4.8 | 3.3 |

Cost_{bnt} (€/day) | 0.2680 | −0.1604 | −0.0756 | |

Cost_{ant} (€/day) | 1.9826 | 1.5700 | 0.9617 | |

Individual (sum of both prosumers) | CP_{1}/CP_{2} (kW) | 4.2/2.7 | 4.4/2.6 | 3.9/2.1 |

Cost_{bnt} (€/day) | 0.2681 | −0.1568 | 0.1475 | |

Cost_{ant} (€/day) | 2.3231 | 1.9721 | 1.6852 |

**Table 7.**SC and SS rates, energy import and export and economic indicators for the whole coordinated microgrid, in the new case study.

Indicators | Without ESS | COF | MOF |
---|---|---|---|

SC | 0.4783 | 0.4456 | 0.7004 |

SS | 0.4555 | 0.4244 | 0.6671 |

|E_{imp}| (kWh) | 24.285 | 20.071 | 9.248 |

|E_{exp}| (kWh) | 22.161 | 23.547 | 12.724 |

CP (kW) | 3.6 | 4.2 | 1.9 |

Cost_{bnt} (€/day) | 0.1059 | −0.3326 | −0.2308 |

Cost_{ant} (€/day) | 1.5614 | 1.0006 | 0.3807 |

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## Share and Cite

**MDPI and ACS Style**

González-Romera, E.; Ruiz-Cortés, M.; Milanés-Montero, M.-I.; Barrero-González, F.; Romero-Cadaval, E.; Lopes, R.A.; Martins, J.
Advantages of Minimizing Energy Exchange Instead of Energy Cost in Prosumer Microgrids. *Energies* **2019**, *12*, 719.
https://doi.org/10.3390/en12040719

**AMA Style**

González-Romera E, Ruiz-Cortés M, Milanés-Montero M-I, Barrero-González F, Romero-Cadaval E, Lopes RA, Martins J.
Advantages of Minimizing Energy Exchange Instead of Energy Cost in Prosumer Microgrids. *Energies*. 2019; 12(4):719.
https://doi.org/10.3390/en12040719

**Chicago/Turabian Style**

González-Romera, Eva, Mercedes Ruiz-Cortés, María-Isabel Milanés-Montero, Fermín Barrero-González, Enrique Romero-Cadaval, Rui Amaral Lopes, and João Martins.
2019. "Advantages of Minimizing Energy Exchange Instead of Energy Cost in Prosumer Microgrids" *Energies* 12, no. 4: 719.
https://doi.org/10.3390/en12040719