# A Comprehensive Evaluation Model on Optimal Operational Schedules for Battery Energy Storage System by Maximizing Self-Consumption Strategy and Genetic Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Configuration of the Battery Energy System

#### 2.2. Mathematical Modeling on the Energy Storage Component

#### 2.2.1. PV Array

_{pv}and V

_{pv}are considered as the panel current (A) and voltage (V), respectively, γ is the PV curve-fitting parameter, R

_{s}is the module series resistance (Ω), I

_{L}is the photocurrent (A) and I

_{o}is the diode reverse saturation current. All parameters should be determined from experiments or real operation. The power extracted from the panel is the product of the output current and the voltage. To obtain the maximum power via the MPPT maximum power extraction method, the output current is given as Equation (2):

#### 2.2.2. Battery Bank

_{b}denotes the rated battery capacity during an entire roundtrip (kWh), t is time iteration (h), P

_{b,ch}is the battery charging power (kW), P

_{b,dis}is the discharge power (kW), η

_{ch}is the battery charging efficiency (96%), η

_{dis}is the discharge efficiency (96%), Δt is time step for calculation (Δt = 1 h for this study), Φ is the binary number, 1 represents battery charge and 0 represents battery discharge.

#### 2.3. Performance Indicators for System Evaluation

#### 2.3.1. Technical Indicators

_{p,d}is the total PV direct-used generation supplied to the users (kWh), E

_{p,b}is the PV production used to charge the battery bank (kWh) and E

_{pv}is the total PV generation (kWh).

_{de}is the total load demand (kWh), while the load cover ratio (LCR) is defined as the ratio of energy supplied by the battery energy storage system to the load demand, which is expressed as:

_{b,d}is the total energy covered by batteries to the load (kWh).

#### 2.3.2. Economic Indicators

_{pv}(t) is the cost for the operation of the PV system at the t-th time step, which could be calculated as:

_{pv}(t) is the PV generation at the t-th time step (kWh), c

_{pv}represents the average cost of PV generation ($/kWh), which in this study was taken as 0.06886 $/kWh [6].

_{b}(t) denotes the maintenance cost due to battery degradation at the t-th time step:

_{total}(t) is the battery aging at the t-th time step. c

_{b}is the unit capacity cost of the battery ($/kWh) including the initial investment and maintenance cost [6], as given by Equation (12).

_{i}is the initial investment per unit capacity of the battery ($/kWh) and c

_{m}is the maintenance cost per unit capacity of the battery ($/kWh). For ease, it was taken as 20% of the initial investment.

#### 2.4. Rule-Based MSC Strategy

_{b}(t) is the battery charging or discharging power (kW). The parameters are subject to the following constraints:

- (1)
- Battery charge/discharge rate limit:

- (2)
- The state of charge (SOC) limit:

_{min}and SOC

_{max}are the lower and upper limits for SOC of the battery, respectively.

#### 2.5. Building Energy Demand Prediction

#### 2.5.1. Individual Needs and Preferences

#### 2.5.2. Establishment of Building Energy Demand Model

- (1)
- External envelope

_{envelope}is the heat transfer coefficient (W/m

^{2}/K), and F

_{envelope}denotes the overall heating exchange area of the building envelope. $\xi $ is the time lag, t

_{τ−ξ}is the time during which the temperature propagation wave acts on the external wall of the building envelope, Δ is the temperature modification for the corresponding location of the building, and T

_{n}is indoor temperature setting. It should be noted that owing to the transient heat exchange of the external building envelope, the load does not occur immediately but lags for a period. To determine the time lag, the heat transfer of the building envelope could be considered as one-dimensional ideal heat conduction:

_{0}denotes daily temperature variation periodicity.

- (2)
- Load from people indoor

_{people}is the number of people allowed determined by per capita floor area. Usually, the sensible heat dissipation q

_{r}of an adult man per hour could be approximated to 70 W. The load factor of the sensible heat dissipation of humans depends on occupancy duration at the building, which could vary from 0.1 to 0.8.

- (3)
- Lighting and household electric appliances load

_{i}is number of the the i-th type of appliances category, W

_{i}represents single power of the i-th device, X

_{τ}is the simultaneous use coefficient or load factor which could vary in the range of 0.5~0.9 depending on different continuous working hours.

#### 2.5.3. Machine Learning Approach for Building Energy Demand

## 3. Results

#### 3.1. Data Collection and Analysis for Battery Storage System

#### 3.1.1. Number of People Using Energy

^{2}[28]. By converting the value in square feet, we obtained an average floor area per capita of 700 ft

^{2}ranging from 646 ft

^{2}to 753 ft

^{2}. For a typical house size of 1600 ft

^{2}(about 148 m

^{2}), after dividing it by the average floor area per capita, there would be a capacity of 2 to 3 people per house, with mostly 2 people per house.

#### 3.1.2. Appliances That Need Energy

#### 3.1.3. Time Intervals When People at Home Use Energy

#### 3.2. Operation Schedules of the Battery Storage System for a Typical House

^{2}house. Specifications of the solar panel are listed in Table 5, which could be adjusted in accordance with the solar radiation condition during the day time in the USA and the rated power generation capacity. Hourly power generation at day time is given in Figure 9. We found that at noon from 10:00 to 16:00, the PV panel reached its peak generation when the solar radiation was strongest. Given the instant PV power supply of the system, the optimal schedule of battery operation state could be robustly determined using the genetic algorithm on the basis of the MSC strategy, Figure 10 and Figure 11 present the weekly and daily operation round trip of three different battery types. In general, a very subtle difference exists between them as they all feature schedules of cyclic charging at noon and discharging at night.

^{5}$, 0.76/2.44$, and 0.715/1.18 × 10

^{5}$ for Discover AES, Electriq PowerPod2 and Tesla Powerwall+, respectively. Discover AES was in best health state, while Tesla Powerwall+ had the minimum cost. In general, the total cost of Discover AES was medium with the best SOH, making it the ideal option for the long-term operation of a battery energy storage system.

#### 3.3. Operation Schedules of the Battery Storage System with Energy Demand Prediction

^{2}/person and 20 W/m

^{2}for summer (75 W/m

^{2}for winter), respectively. Annual weather data of the typical meteorological year in the USA was extracted to represent the typical monthly outdoor environment during the whole year for building energy calculation as presented in Figure 18. Specifics of daily outdoor temperature are given in Table 9. Additionally, we selected a new case with relatively weak solar radiation for PV system power generation as depicted in Figure 19. The corresponding instant PV power during the day is presented in Figure 20.

## 4. Discussion

- (1)
- Generic applicability: Building energy demand acts as the optimization objective for the energy storage strategy but it has many techno-economic indicators. This model was enhanced from previous studies, which typically focused on only one or two evaluation indicators. It could comprehensively evaluate the integrated objective, and is thus more applicable to complex scenarios.
- (2)
- Convenient implementation: As shown in the flow chart for simulation in Figure 3, this model could easily be applied in a real project. It performs simplified modeling on the core components of the battery system and commonly used techno-economic indicators. Moreover, it is based on the GA approach for global optimization, and makes a clear distinction between the charging and discharging phase considering the classical MSC strategy. Therefore, the optimization could be conveniently implemented for a real control strategy
- (3)
- Good scalability: The model shows great potential in terms of its scalability. This paper investigated a simple battery energy system configuration, and more energy storage components could be easily incorporated and integrated with the original system. Moreover, this model also provides a test bed for new techno-economic indicators applicable to the optimization and evaluation of the system.

## 5. Conclusions

- (1)
- This comprehensive evaluation model for the operational schedule of a battery storage system could account for both technological and economic indicators, and the optimal solution based on MSC strategy genetic algorithm could be found.
- (2)
- The three types of batteries including Discover AES, Electriq PowerPod2 and Tesla Powerwall+ could be considered as options for energy storage. For short term operation, there exists subtle differences in the technical performance among them but Tesla Powerwall+ was the most cost-effective option.
- (3)
- According to long-term simulation, Discover AES had a relatively higher total operation cost, but it resulted in the lowest level of battery aging. Therefore, Discover AES has the advantage of using PV generation in a timely manner to suit the load demand.
- (4)
- The machine learning approach provides a feasible option for us to adapt our optimization model based on the MSC strategy and GA method for arbitrary battery storage scenarios with different energy demand features.

^{2}house with an approximate envelope of 1280 ft

^{2}, the solar energy stored could total up to 21.78 kWh, which amounts to almost two Tesla Powerwall+ batteries’ usable capacity but with a nearly zero cost of operation.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A2.**State of charge for Discover AES batteries during the operation. (

**a**) batteries 1~4; (

**b**) batteries 5~8; (

**c**) batteries 9~12; (

**d**) batteries 13~16.

**Figure A4.**State of charge for Electriq PowerPod2 batteries during the operation. (

**a**) batteries 1~4; (

**b**) batteries 5~8; (

**c**) batteries 9~12.

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**Figure 2.**Flowchart of the optimal operation strategy for a battery energy storage system with solar energy resource.

**Figure 4.**Optimal operation schedules for individual battery energy storage system with building energy demand prediction.

**Figure 6.**Energy consumption ratio of a typical house in USA. (

**a**) Three parts of electric power in the typical house; (

**b**) Three parts of daily energy consumption in the typical house.

**Figure 14.**Performance evaluation of the battery storage system: SCR, SSR, LCR and power supply imbalance ratio. (

**a**) SCR; (

**b**) SSR; (

**c**) LCR.

**Figure 17.**State of charge for Tesla Powerwall+ batteries during the operation. (

**a**) batteries 1~4; (

**b**) batteries 5~9.

**Figure 19.**Sun radiation of the new scenario in study: Solar_radiation_1 is the case studied in Section 5 and Solar_radiation_2 is the case studied in this section for generalization evaluation.

**Figure 20.**PV power generation according to the sun radiation of the new scenario studied in this section for generalization evaluation.

Parameter | Range of Value |
---|---|

Occupancy interval (h) | 0.5~10 |

Building floor area (ft^{2}) | 600~2600 |

Thermal conductivity (W/m/K) | 0.1~0.5 |

Outdoor temperature (°C) | −4~30 |

Indoor temperature (°C) | 24~26 |

Solar radiation intensity (W/m^{2}) | 50~850 |

Number of people per house | 1~4 |

Number of electric appliances per house | 15~45 |

Average electric power of appliances (kW) | 0.5~5 |

Number | Electrical Appliance | Average Power Consumption and Daily Work Hours | Number | Electrical Appliance | Average Power Consumption and Daily Work Hours |
---|---|---|---|---|---|

1 | Stove | 2.00 kW/0.67 h | 16 | Computer and laptop | 0.350 kW/9.0 h |

2 | Microwave | 1.150 kW/0.33 h | 17 | Cellphone | 0.005 kW/9.0 h |

3 | Ice Cream Maker | 1.800 kW/0.1 h | 18 | Lawn Mower | 1.200 kW/0.2 h |

4 | Dishwasher | 1.350 kW/1.0 h | 19 | Vacuum Cleaner | 0.675 kW/0.3 h |

5 | Rice Cooker | 0.500 kW/0.5 h | 20 | Electric vehicle | 10.00 kW/3.0 h |

6 | Food Processor | 0.350 kW/0.1 h | 21 | Heat pump | 15.00 kW/3.67 h |

7 | Blender | 0.350 kW/0.1 h | 22 | Air Conditioner | 2.500 kW/9.0 h |

8 | Electric Kettle | 2.100 kW/0.3 h | 23 | Space Heater | 3.500 kW/12.0 h |

9 | Clothes Dryer | 2.500 kW/0.67 h | 24 | Radiator | 0.500 kW/0.3 h |

10 | Sewing Machine | 0.075 kW/0.5 h | 25 | Humidifier | 0.038 kW/2.0 h |

11 | Washing Machine | 0.500 kW/0.67 h | 26 | Water Heater | 7.700 kW/3.67 h |

12 | Iron | 1.000 kW/0.3 h | 27 | Evaporative Cooler | 2.600 kW/3.0 h |

13 | Hairdryer | 2.150 kW/0.27 h | 28 | Freezer | 0.050 kW/6.67 h |

14 | TV (49 Inch) | 0.085 kW/6.0 h | 29 | Fan (Desk) | 0.018 kW/0.4 h |

15 | Lighting | 1.200 kW/9.0 h | 30 | Ceiling Fan | 0.065 kW/1.5 h |

Battery | Cost(USD) | Battery Type | Weight(lbs.) | Dimension(L × W × D in inches) |

Deka solar 8GCC2 6V 198 | $368 | SGLA | 68 | 10.25 × 7.1 × 10.9 |

Trojan L-16-SPRE 6V 415 | $492 | FLA | 118 | 11.7 × 6.9 × 17.6 |

Discover AES 7.4 kWh | $6478 | LFP | 192 | 18.5 × 13.3 × 14.7 |

Electriq PowerPod2 | $13,000 | LFP | 346 | 27.5 × 50 × 9 |

Tesla Powerwall+ | $8500 | NMC | 343.9 | 62.8 × 29.7 × 6.3 |

Continuous Power Rating(kW) | Instaneous Power Rating (kW) | Round-Trip Efficiency(%) | Usable Capacity(kWh) | |

0.049 kW (for 20 h)−0.017 kW (for 100 h) | Not Available | 80~85% | 1.18 kWh | |

0.19 kW (for 10 h)−0.023 kW (for 100 h) | Not Available | 80~85% | 2.5 kWh | |

6.65 kW | 14.4 kW (for 3 s) | >95% | 7.4 kWh | |

7.6 kW | 9 kW (for 60 s) | 96.60% | 10 kWh | |

7 kW | 10 kW (for 10 s) | 90.00% | 13.5 kWh |

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

Life cycle number | 4000 |

SOC_{min} | 0.05 |

SOC_{max} | 1 |

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

PV curve-fitting parameter γ | 0.004576 °C/V |

Module series resistance | 10 Ω |

Regression coefficient of photocurrent | 0.075 A m^{2}/W |

Regression coefficient of module temperature | 0.03125 °C m^{2}/W |

Referrence diode reverse saturation current | 90 A |

PV voltage adjustment range by MPPT controller | 200~600 V |

Indicators | Discover AES | Electriq PowerPod2 | Tesla Powerwall+ |
---|---|---|---|

SOH | 0.999 | 0.999 | 0.999 |

Total cost ($) | 3.36 × 10^{4} | 4.87 × 10^{4} | 2.36 × 10^{4} |

SCR during the day | 1.0 | 1.0 | 1.0 |

SSR (max) | 6.1 | 6.1 | 6.1 |

SSR (min) | 0.8 | 0.8 | 0.8 |

LCR (max) | 5.9 | 5.4 | 4.3 |

LCR (min) | 0.43 | 0.47 | 0.59 |

Power supply imbalance ratio (max) | 4.94 | 4.44 | 3.3 |

Power supply imbalance ratio (min) | −0.57 | −0.52 | −0.41 |

Operation Time | Indicators | Discover AES | Electriq PowerPod2 | Tesla Powerwall+ |
---|---|---|---|---|

One year | SOH | 0.967 | 0.952 | 0.943 |

Total cost ($) | 3.36 × 10^{4} | 4.87 × 10^{4} | 2.36 × 10^{4} | |

Two years | SOH | 0.934 | 0.904 | 0.886 |

Total cost ($) | 6.72 × 10^{4} | 9.74 × 10^{4} | 4.72 × 10^{4} | |

Three years | SOH | 0.901 | 0.856 | 0.829 |

Total cost ($) | 1.08 × 10^{5} | 1.46 × 10^{5} | 7.08 × 10^{4} | |

Four years | SOH | 0.868 | 0.808 | 0.772 |

Total cost ($) | 1.34 × 10^{5} | 1.95 × 10^{5} | 9.44× 10^{4} | |

Five years | SOH | 0.835 | 0.76 | 0.715 |

Total cost ($) | 1.68 × 10^{5} | 2.44 × 10^{5} | 1.18 × 10^{5} |

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

Building floor area (ft^{2}) | 2000 |

Number of people per area (/ft^{2}) | 4 |

Occupancy interval (h) | 7 |

Thermel resistance (m^{2}‧ K/W) | 1.35 |

Thermal conductivity (W/m/K) | 0.17 |

Specific thermal capacity (J/kg/K) | 800 |

Thermal diffusion coefficient (m^{2}/s) | 4.98 × 10^{−5} |

Wall thickness (mm) | 230 |

Delay of the temperature wave | 0.1963 |

Month | Daily Temperature Distribution | Month | Daily Temperature Distribution |
---|---|---|---|

January | ${T}_{air}\left(t\right)=1+5\mathrm{sin}\left(\frac{\pi}{12}\left(t-6\right)\right)$ | July | ${T}_{air}\left(t\right)=24.5+6.5\mathrm{sin}\left(\frac{\pi}{12}\left(t-6\right)\right)$ |

February | ${T}_{air}\left(t\right)=3.5+5.5\mathrm{sin}\left(\frac{\pi}{12}\left(t-6\right)\right)$ | August | ${T}_{air}\left(t\right)=24+6\mathrm{sin}\left(\frac{\pi}{12}\left(t-6\right)\right)$ |

March | ${T}_{air}\left(t\right)=7.5+5.5\mathrm{sin}\left(\frac{\pi}{12}\left(t-6\right)\right)$ | September | ${T}_{air}\left(t\right)=20+6\mathrm{sin}\left(\frac{\pi}{12}\left(t-6\right)\right)$ |

April | ${T}_{air}\left(t\right)=13+6\mathrm{sin}\left(\frac{\pi}{12}\left(t-6\right)\right)$ | October | ${T}_{air}\left(t\right)=14+6\mathrm{sin}\left(\frac{\pi}{12}\left(t-6\right)\right)$ |

May | ${T}_{air}\left(t\right)=17.5+6.5\mathrm{sin}\left(\frac{\pi}{12}\left(t-6\right)\right)$ | November | ${T}_{air}\left(t\right)=8.5+5.5\mathrm{sin}\left(\frac{\pi}{12}\left(t-6\right)\right)$ |

June | ${T}_{air}\left(t\right)=22+6\mathrm{sin}\left(\frac{\pi}{12}\left(t-6\right)\right)$ | December | ${T}_{air}\left(t\right)=3+5\mathrm{sin}\left(\frac{\pi}{12}\left(t-6\right)\right)$ |

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

Total power generation of PV (kWh) | 193.16 |

Total building demand during the day (kWh) | 30.48 |

Total building demand during the night (kWh) | 23.92 |

Energy demand gap (kWh) | 138.75 |

Energy imbalance ratio | 71.83% |

Number of batteries needed for Discover AES | 4 |

Number of batteries needed for Electriq PowerPod2 | 3 |

Number of batteries needed for Tesla Powerwall+ | 2 |

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

Total power generation of PV (kWh) | 193.16 |

Total building demand during the day (kWh) | 122.9 |

Total building demand during the night (kWh) | 146.07 |

Energy demand gap (kWh) | −75.8 |

Energy imbalance ratio | 39.24% |

Number of batteries needed for Discover AES | 17 |

Number of batteries needed for Electriq PowerPod2 | 13 |

Number of batteries needed for Tesla Powerwall+ | 10 |

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## Share and Cite

**MDPI and ACS Style**

Zhao, Y.; Qin, X.; Shi, X.
A Comprehensive Evaluation Model on Optimal Operational Schedules for Battery Energy Storage System by Maximizing Self-Consumption Strategy and Genetic Algorithm. *Sustainability* **2022**, *14*, 8821.
https://doi.org/10.3390/su14148821

**AMA Style**

Zhao Y, Qin X, Shi X.
A Comprehensive Evaluation Model on Optimal Operational Schedules for Battery Energy Storage System by Maximizing Self-Consumption Strategy and Genetic Algorithm. *Sustainability*. 2022; 14(14):8821.
https://doi.org/10.3390/su14148821

**Chicago/Turabian Style**

Zhao, Yazhou, Xiangxi Qin, and Xiangyu Shi.
2022. "A Comprehensive Evaluation Model on Optimal Operational Schedules for Battery Energy Storage System by Maximizing Self-Consumption Strategy and Genetic Algorithm" *Sustainability* 14, no. 14: 8821.
https://doi.org/10.3390/su14148821