# Energy hub modeling to minimize residential energy costs considering solar energy and BESS

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## Abstract

This paper aims to optimize total energy costs in an operational model of a novel energy hub (EH) in a residential area. The optimization problem is set up based on daily load demand (such as electricity, heat, and cooling) and time-of-use (TOU) energy prices. The extended EH model considers the involvement of solar photovoltaic (PV) generation, solar heat exchanger (SHE), and a battery energy storage system (BESS). A mathematical model is constructed with the objective of optimizing total energy cost during the day, including some constraints such as input-output energy balance of the EH, electricity price, capacity limitation of the system, and charge/discharge power of BESS. Four operational cases based on different EH structures are compared to assess the effect of solar energy applications and BESS on the operational efficiency. The results show that the proposed model predicts significant changes to the characteristics of electricity and gas power bought from utilities, leading to reduced total energy cost compared to other cases. They also indicate that the model is appropriate for the characteristics of residential loads.

## Keywords

Natural gas price Electricity price Energy Hub Optimal operation General algebraic modeling system (GAMS) Solar Battery energy storage system (BESS)## 1 Introduction

In recent years, the formation and development of the Energy Internet (EI) through energy hubs (EH) [1] have shown a new direction towards achieving global energy security. Heat energy and electrical energy are two types of primary energy that account for a significant proportion of the total current demand. The combination of heat and power is a big step towards the higher performance of the system by considering different energy types simultaneously rather than focusing on one type of energy (i.e., electrical energy) as discussed in the previous research [2, 3, 4, 5].

Rapidly increasing urbanization leads to suddenly growing residential energy use to meet various demands. Typical EH models of residential energy use include electricity, heat, and cool. The establishment and operation of residential EH attract lots of attention from scientists: an EH optimization model for a household was designed with the objective of minimizing energy cost in [6, 7]; EH modeling of domestic appliances in residential areas in Canada was conducted in [8], solving problems of peak load, minimal carbon dioxide emission, and energy usage costs; and a model suitable for the residential loads was set up in [9, 10] considering real time pricing for optimal operation of EH.

Along with the development of the EI, renewable energy and energy storage technology are the two solutions being rapidly developed under the pressure of rising energy demand in modern society. In recent years, solar photovoltaic (PV) generation and solar heat exchanger (SHE) have been widely adopted through shortened construction time due to their modular structure and fewer restrictions on installation space [11, 12, 13]. These clean energy sources will be well adapted to loads in residential areas. However, before the concept of an EH appeared at the Swiss Federal Institute of Technology in Zurich [14, 15], no research exploited the use of solar energy in a coordinated way, including heat and electricity, rather than individually. Therefore, EH modeling and optimal operation need to consider these two types of energy to fully improve the efficiency of solar energy. Recently, a study [9] constructed an EH operational model to minimize energy cost and emission cost for a typical house in the UK in which solar energy (electricity and heat supply via PV and SHE) was used to replace proportions of electricity and gas bought from utilities. However, the EH structure did not fit with the characteristics of residential loads because the output only considered the use of electricity and heat power; in addition, the need for cooling is also very high in some climates.

Battery energy storage systems (BESS) are a fundamental solution to improve power supply reliability and economic efficiency of PV. For example, [16] coordinated BESS with PV in planning problems to reduce investment costs, operating and environmental pollution; [17] obtained improved economic efficiency by adjusting the load curve to reduce purchasing power costs of the system. Besides, the BESS can be used to adjust the load curve by storing electricity in off-peak hours and generating back to the grid during peak hours [18, 19]. Hence, a BESS is an efficient energy storage method which is mentioned in some studies about the distribution grid, and there are many EH models taking into account energy storage devices to improve the operational efficiency of the system [6, 8, 9, 20, 21, 22, 23]. But so far, there is no research about the involvement of BESS as an integrated part of an EH model.

Generally speaking, PV and SHE have transformed energy usage in residential areas, while BESS are becoming important. It is very important to model an EH which includes PV, SHE and BESS to improve the operational efficiency of multiple forms of energy consumption. Therefore, this study aims to present an extended EH model to optimize total energy use costs for loads in residential areas. This extended model considering the involves solar energy (provided by PV and SHE) combined with BESS. The proposed structure uses both air-conditioners (AC) and absorption chillers (ACh) simultaneously to meet the cooling demands of loads in residential areas and to enhance the flexibility of converting between different types of energy.

Nowadays, optimization has been widely applied in scientific research to solve practical problems. Some outstanding fields using optimizing method are meteorology and natural calamities [24], irrigation [25], and environmental factors [26]. The use of optimizing methods is an increasing tendency in the energy field. Recent research about the optimal operation of an EH has used different approaches, different objective functions and constraints, and diverse tools including high-level programming languages such as Matlab, Fortran, Delphi, C++ [27]. A high-level programming language widely used in the optimization of EH, the general algebraic modeling system (GAMS) [6, 10, 21, 28, 29], uses built-in algorithms (solvers) [30]. Therefore, this study uses language GAMS in order to solve the optimal operational problem of EH, based on the energy cost to supply residential area loads. The objective is to minimize the total energy cost of the system. The resulting program will be more flexible than other available application programs, along with fulfilling consumer demands.

The remainder of the paper is structured as follows: Section 2 presents the basic structure of an EH; the complete EH model is proposed considering solar energy and BESS. The role of BESS technology in managing solar energy through SHE and PV is proposed in Section 3. Section 4 introduces the objective function and other mathematical constraints of the optimization model. Simulation results for four cases with different structures are compared in Section 5 to assess the impact of solar energy (PV, SHE) and BESS on the operational efficiency of EH, especially the maximum capacity use of BESS. Finally, conclusion and future work are provided in Section 6.

## 2 EH model for residential areas load

### 2.1 Description

*E*

_{e}and

*E*

_{g}respectively, and output power, such as electricity and heat, which are named

*L*

_{e}and

*L*

_{h}respectively. In addition, this EH also allows the participation of distributed generation (DG) with input

*E*

_{DG}and output

*L*

_{DG}. The features of storage (S

_{1}, S

_{2}) and conversion (c

_{1}, c

_{2}) of electricity and heat energy are also included. The EH model is mathematically described using the following equation [31]:

*c*

_{ ij }is the connecting factor that indicates the relationship between the

*i*th input power and the

*j*th output power;

*E*

_{ i },

*i*= 1, 2…,

*m*, is the power input;

*L*

_{ j },

*j*= 1, 2…,

*n*is the converted power output.

### 2.2 EH modeling for residential areas load

*L*

_{e}is supplied through the distribution grid, the MT, and solar PV. Cooling energy

*L*

_{c}is provided by the AC and the ACh; heat energy

*L*

_{h}is supplied by the MT, a gas boiler (GB) and partly from SHE. Therefore, through this model, the demands for heat, electricity, and cooling energy can be transferred flexibly between devices, along with fully exploiting the use of solar energy.

As the energy price for residential areas is assumed to comprise a time of use (TOU) electricity price and a constant gas price, this research does not include a thermal storage system in order to reduce the investment cost and the complexity of EH.

## 3 Solar and BESS technologies

### 3.1 Solar

The output power of PV generation and SHE depends on the intensity of solar radiation. Solar radiation varies both in time and space; but for solar panels and SHE that are installed in a fixed location, the influence of space can be ignored. Therefore, the output power of PV generation and SHE can be described by functions of time.

### 3.2 BESS technology

BESS has been the leading energy storage technologies, with advantages in energy density and high efficiency, which can work over both short and long periods due to low direct energy use or self-discharge. Therefore, BESS has been widely applied in distributed grids [32]. BESS consists of different storage technologies referred to as ‘batteries’. Examples of such battery technologies include [33, 34] lead acid batteries, sodium sulphur batteries, lithium-ion batteries, and nickel batteries, each of which has specific characteristics and economic effectiveness.

The chemical technology most widely used today is a lead-acid battery, which has low investment and maintenance costs and small self-discharge coefficient, but suffers from low life expectancy and pollutes the environment [35, 36]. The sodium-sulphur battery is an interesting research topic for new applications because it has high energy density, low investment and operational costs, long life cycle, deep discharge ability, and high pulse power capacity, although this technology works at high temperature [36]. Similarly, the flow battery, such as vanadium redox battery (VRB) and zinc bromine battery (ZnBr), can be manufactured with high energy capacity, but their low energy density and very high investment costs have limited their application [37].

Lithium-ion (Li-ion) and nickel-cadmium (Ni-Cd) battery technologies have attracted much concern from different researchers. Factors such as high energy density or high efficiency contribute to the attractiveness of such technologies. They have got significant access to the field of consuming electronics and hybrid transport [35].

The output power of PV generation depends on the intensity of solar radiation which varies daily; TOU energy prices also change with a daily profile. Therefore, this paper concentrates on the problem of the optimal use of BESS: storing electricity in off-peak hours and supplying the load during peak hours.

The optimal operation problem of an EH is presented in Section 4. So as to minimize the cost of residential energy use, we need to optimize the input electricity and heat, within the constraints of the rated charging and discharging power of the BESS when it is used from time to time during the day. The cost objective function is minimized within the constraints on conversion efficiency, capacity limitations of devices in the system, energy balance, conversion limitations, and the charging and discharging rate of the BESS.

## 4 Mathematical model

### 4.1 Objective function

*E*

_{e}(

*t*) and

*E*

_{g}(

*t*) are the received electricity and natural gas, respectively, at the EH input at hour

*t;*and

*c*

_{e}(

*t*) and

*c*

_{g}(

*t*) are the electricity and natural gas prices at hour

*t*, respectively.

### 4.2 Constraints

#### 4.2.1 Energy balance

- 1)
Energy balance constraints of the EH

*L*

_{e}(

*t*),

*L*

_{h}(

*t*) and

*L*

_{c}(

*t*), and energy purchased from system

*E*

_{e}(

*t*) and

*E*

_{g}(

*t*) at time

*t*is expressed by:

*t*, respectively;

*E*

_{PV}(

*t*) is the electric power output of the PV panels at hour

*t*; \(\nu_{\text{AC}} (t)\), \(\nu_{\text{MT}} (t)\), \(\nu_{\text{ACh}} (t)\) are the dispatch ratios of electricity, natural gas, and heat conversion at hour

*t*, respectively, as indicated in Fig. 3; \(\eta_{\text{ge}}^{\text{MT}}\), \(\eta_{\text{gh}}^{\text{MT}}\) are the gas-to-electricity and heat conversion efficiency of the MT; \(\eta_{\text{T}}\), \(\eta_{\text{GB}}\), \(\eta_{\text{h}}^{\text{ACh}}\), \(\eta_{\text{e}}^{\text{AC}}\) are efficiency of transformers, GB, ACh, and AC, respectively; \(L_{\text{h}}^{\text{SHE}} (t)\) is the heat power output of the SHE at hour

*t*.

- 2)
Energy balance constraints of the BESS

*H*

_{1}and

*H*

_{2}are the total charging time and discharging time of the BESS per day, respectively.

#### 4.2.2 Charging and discharging time of BESS

#### 4.2.3 Power limitation

#### 4.2.4 Conversion limitations

*t*include \(\nu_{\text{AC}} (t)\), \(\nu_{\text{MT}} (t)\) and \(\nu_{\text{ACh}} (t)\), which are state variables that show what proportion of input power is directed through the corresponding devices from time to time. Constraints of these state variables are expressed in equations as:

#### 4.2.5 Energy prices

For a residential area, the energy prices are based on the TOU principle [38, 39]. A TOU price is the simplest form of dynamic price. The primary objective of the pricing program is to encourage less energy consumption during the peak hours.

Thus, the requirement in this part is to solve the optimization problem to find solution sets \(X = \left\{ {E_{\text{g}} (t), \, E_{\text{e}} (t), \, \nu_{\text{ACh}} (t), \, \nu_{\text{MT}} (t), \, E_{\text{BESS}}^{\text{dis}} (t), \, E_{\text{BESS}}^{\text{ch}} (t)} \right\}\) satisfying the objective function (2) within constraints (3–14).

## 5 Simulation result

- 1)
Fully exploiting solar energy in the forms of electricity and heat through PV generation and SHE.

- 2)
Considering the presence of the BESS which has been used very effectively in the distribution grid to provide efficient energy storage and timely response to changes in system conditions.

- 3)
Separating the cooling demand of loads, by proposing a structure using both AC and ACh devices to increase the ability to convert from electricity and heat to cooling.

Proposed hub components in 4 simulated cases

Case | Base EH | Solar | BESS |
---|---|---|---|

1 | √ | ||

2 | √ | √ | |

3 | √ | √ | |

4 | √ | √ | √ |

### 5.1 Database

Data applied to the 4 cases, as shown in Table 1, include electricity, heating, and cooling demand on a typical day; electricity price; natural gas price; devices’ parameters and capacity limits of the system; and parameters of PV generation, SHE and BESS, which are explained in detail as follows.

#### 5.1.1 Electricity, heat, and cooling demands

#### 5.1.2 Energy prices

#### 5.1.3 Device parameters and power limitations of the system

Efficiency data

\(\eta_{\text{e}}^{\text{AC}}\) | \(\eta_{\text{ge}}^{\text{MT}}\) | \(\eta_{\text{GB}}\) | \(\eta^{\text{T}}\) | \(\eta_{\text{gh}}^{\text{MT}}\) | \(\eta_{\text{h}}^{\text{ACh}}\) |
---|---|---|---|---|---|

0.85 | 0.4 | 0.88 | 0.95 | 0.5 | 0.9 |

Capacity constraint data

\(E_{\text{e}}^{ \hbox{max} }\)(MW) | \(E_{\text{g}}^{ \hbox{max} }\)(MW) |
---|---|

5 | 3 |

#### 5.1.4 Parameters of PV, SHE and BESS

Based on the assumption that the BESS uses a NaS battery with 10 years life cycle and having high efficiency of 0.9, the BESS has a power of 450 kW and a capacity of 4200 kWh.

### 5.2 Optimization results

The results for optimal operation of an EH in the 4 cases in Table 1 are detailed as follows.

#### 5.2.1 Case 1

#### 5.2.2 Case 2

Total energy costs of 4 cases

Case | 1 | 2 | 3 | 4 |
---|---|---|---|---|

Total energy costs ($/day) | 5760 | 5050 | 5648 | 4893 |

#### 5.2.3 Case 3

#### 5.2.4 Case 4

Case 4 assesses the impact of solar energy and a BESS simultaneously on the optimal operation of an EH. The results show that the energy bought from utilities is reduced significantly compared to other cases (Fig.10), especially during the peak hours. The highest electricity input reached 2.12 MW during the off-peak period (10 PM). The optimized charge/discharge profile for the BESS is shown in Fig. 11. Due to the additional supply of PV energy and heat power of SHE, the operation of BESS is changed significantly, specifically during the time from 1 AM to 5 AM and 9 PM to 12 AM. The addition of solar PV input means that the energy capacity of the BESS is more effectively used, and the BESS continues to supply load throughout the peak hours with high electricity price (10 AM to 7 PM). The total cost of energy bought from utilities, in this case, is also the lowest as shown in Table 4. Therefore the EH including PV generation, SHE and a BESS brings greater efficiency than the remaining 3 cases.

#### 5.2.5 Discussion

- 1)
The proposed extended EH model is suitable for the diverse demands of residential load; simulation results show that the optimization model can respond quickly to the changing load and electricity price, allowing the model to consider the change of PV generation and SHE energy over time and season.

- 2)
The comparative results of 4 cases with different structures clarify the role and influence of BESS and solar energy on the operational effectiveness of EH by minimizing the total cost of input energy (Table 4); reducing peak load demand leads to reduce sources and investment costs for power system upgrades.

Although the investment costs of the PV generation, SHE, and BESS equipment are quite high, the economic efficiency of EH operation shows that these costs would be partially offset by saved energy costs of the system. The result shows that the extended EH model is a useful contribution to the current trend of energy system development and renewable energy applications.

## 6 Conclusion

- 1)
The first is a new structure for the EH model that fits with the characteristics of loads in residential areas. The proposed extended EH model exploits two types of solar energy through PV generation and SHE, while taking into account the use of electrical energy storage by using a BESS that has been previously used effectively in the distribution grid.

- 2)
The second is an optimized operational model of EH with the objective to minimize total energy costs bought from utilities. Four cases with different structures have been set up to assess specifically the influence of solar energy and a BESS on the effectiveness of the EH operation. The optimization results show that the EH involving PV generation, SHE and a BESS could reduce total cost of energy bought from utilities by 15% while fully meeting the demand. This is a reliable basis for research and development of energy hubs using renewable energy.

It is shown that the structure of the EH greatly affects the operational efficiency. Therefore, further research on constructing optimal operational strategies for EH with different structures should be undertaken in order to provide specific assessments of the influence of each device in the model on the system’s operation. Moreover, when considering the results of the EH model in this paper, although a survey has been conducted on the output power characteristics of PV generation and the average daily load profile, the load constantly changes with time due to features of residential demand. The generation characteristics of distributed generators depend heavily on primary and secondary energy sources, these generating characteristics need to be properly understood. Therefore, further research must be conducted to improve the EH model to include the uncertainty of both distributed generation and load.

## Notes

### Acknowledgements

This work was supported by National Natural Science Foundation of China (No. 51377060).

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