An optimal schedule model of multi-energy hubs network integrating solar energy

Received Feb 29, 2020 Revised Mar 25, 2021 Accepted May 4, 2021 Recently, multi-energy systems based on energy hub are introduced because of significant benefits in reducing energy and emission cost. This paper proposed an optimal schedule model of multi-energy hubs networks consisting of energy hubs, renewable sources, and energy storage which are connected by electrical and natural gas distribution networks. In the proposed mixedinteger nonlinear programming model, the objective is to minimize the operation, energy, and emission costs of energy hubs with both renewable sources and storage and energy distribution networks. The proposed schedule framework allows simultaneously selections of optimal operation structure of EHs together with the optimal operation parameters of energy distribution networks and therefore this model can maximize the profit of the entire largescale multi-energy hubs network. Besides, the operation parameters and energy loss of both electrical and natural gas distribution networks are considered in conjunction with optimal operation of energy hubs and thus guarantee the operation and optimization of the network in all operational scenarios. The IEEE 5-bus test system is utilized to demonstrate the applicability of the proposed model. The simulation results show the feasibility of the proposed model, and demonstrate that the energy hubs, renewable sources, and energy storage in the proposed structure significantly enhance the efficiency of the multi-energy hubs network by reducing not only energy and operation costs but also emission.. Keyword:


INTRODUCTION
Energy Hub (EH) has been introduced and applied in multi-energy systems in combination with renewable resources because of its significant benefits in reducing energy and emission cost [1]- [3]. Within EHs, multiple energy types can be converted, conditioned, and stored to optimize the use of energy resources, enhance efficiency, reduce emissions and costs, and increase the reliability of energy systems. Although efficiency is improved, the integration of EHs and distribution networks still brings a lot of challenges to system operation. Therefore, the operation and planning of systems containing different energy carriers have been studied and presented in many publications.
The principles to construct simulation models of components in an integrated multi-energy system based on the energy hub concept have been introduced in [4]. A multi-energy system should be structurally divided into several functional blocks concerning different channels of energy types. The input and output parameters of the blocks are consistent and interconnected. The concept of energy hubs, the research gaps remaining in the areas of modelling, optimization, and energy hub application are present in this research [5]. This research presents several assessment studies regarding the scheduling scheme of energy hubs. Controlling technologies were introduced but there is a lack of research on modelling, optimization, and energy hub application. Similarly, the characteristics of energy system models and existing modelling tools together with challenges in the field of modelling and optimization of the energy systems are also introduced in the studies [6] [7]. There stage is to schedule for the exchange power between the distribution network and the EHs with the constrained condition of each EH obtained in the first stage. In these studies, the energy storage devices, which have a significant influence on the effectiveness of the EH integrated renewable sources, were not considered.
The loss cost of networks and renewable sources is simultaneously considered in an optimal problem which finds the minimum of energy and emission costs [23]. The game theory was used to solve the optimal scheduling of a multi-energy hub system in this study. The results showed the optimal scheduling of multienergy hub systems using game theory has economic value and certain practical engineering value. A mathematical model for the optimal energy management of an urban energy network with energy hubs has also been presented in [24]. The objective function which seeks to minimize the total operational and maintenance costs of the network of energy hubs is integrated into MILP and solved in the General Algebraic Modeling Software (GAMS). The authors in the study [25] developed the model and optimization of a complex network of energy hubs while considering the integration of both electrical and natural gas systems. The optimal model includes an objective function to minimize both cost terms and terms related to emissions and constraints. The function is applied to compute two cases using actual data. Results showed the creation of a network of energy hubs is an effective strategy for reducing system total costs and emissions. Moreover, using a complex network of energy hubs has qualitative benefits of increasing reliability and reducing electrical grid congestion. The change of loads and output power of sources is analysed under typical curves of the day. However, the energy loss is only determined under loss factors of electricity and natural gas flow into the EHs, feeders, and pipelines whereas they ignored the operation parameters of energy networks such as node voltages and optimal power flow of the electrical network, pressures of pipelines in natural gas network.
A novel technique for optimum operation and configuration of multiple energy hubs is also proposed with different types of energy sources, generation, and multi-type energy storage devices to feed electrical, heating, and gas demands [26]. The optimal framework is a multi-objective optimization problem formulated to maximize social welfare and minimize emissions. The uncertainties of renewable energy sources were considered in the proposed model and the genetic algorithm is used to solve the overall optimization problem. The Newton-Raphson method was used to solve the problem of heat and gas flow to determine the state variables and check the constraints of the system. The different configurations of the EH are assumed and then they are comparatively analysed by the objective function which maximizes social welfare and minimizes emissions. The results proved that increasing the system size improved the performance parameters and EH stability. However, only five assumed structures are used to test the effects of equipment in EH of energy systems, and therefore optimizing the structure of the EH in the optimal problems of multi-energy hub system networks is not completed.
In general, the above studies have shown the effectiveness of the optimal operation methods for each EH individually as well as multiple EHs connected to large-scale networks. However, in proposed optimal operation models for large-scale multi-energy hubs networks, most of them only individually optimize the EHs or distribution networks in two-stage models without optimizing the cost of the entire system. Moreover, the operation parameters of energy networks are not considered thus the operation cannot be guaranteed in practice. In this study, the structure and optimal schedule model of a multi-energy hubs network consisting of EHs, renewable sources, energy storages, and both electrical and natural gas networks are proposed. The main contributions of the research are as follows: • Optimizing the energy and operation costs of all networks including EHs. Renewable sources and storage and energy distribution networks consisting of electric and natural gas distribution networks are simultaneously determined in a mixed-integer nonlinear programming problem. • The optimal operation structure of the EHs is selected with the optimal operation parameters of energy distribution networks and therefore this model can maximize the profit of the entire large-scale multienergy hubs network. • The operation parameters and energy loss of both electrical and natural gas distribution networks are simultaneously considered with EHs and thus guarantee the operation and optimization of the network in all operational scenarios. The remainder of this paper is organized as follows. In Section 2, the network and energy hub modelling formulation is presented and the mathematical formulation of this optimal schedule problem is established in Section 3. Section 4 presents a case study with numerical results. Finally, the conclusions are presented in Section 5.

NETWORK AND ENERGY HUB MODELING FORMULATION
In general, the structure of an energy hub network often includes the different EHs which are connected through different transmission networks such as electrical distribution network (EDN) and gas To effectively improve the EHs, the different multi-energy forms are incorporated within the residential, commercial, agricultural, and industrial sectors. A typical EH, as shown in figure 2, widely has been applied in recent researches [9] [28]. In this structure, the input energy forms include the electricity and nature gas together with solar energy source are converted and conditioned by combined heat and power (CHP), gas boiler (GB), Electrical Chiller (EC), Absorption Chiller (AC), a solar heat exchanger (SHE), transformer (TR) and stored/generated by BESS to supply for loads consisting of electricity, heating, and cooling. 11 12 1 1 1 Based on the structure of EH in figure 2 and the coupling matrix in equation (1), the energy balance constraints of EH i are proposed as the following expression: e  g  ge  pv  be  be  be  be  ,  , ).
The BESS can charge when the high output power of PV or low loads and electrical price. On the contrary, when the peak loads with high electrical price, or low output power of PV, the BESS discharge to reduce the cost of the system. The charge/discharge decision of BESS is expressed through two binary variables ( .. , ch h dis h ) and the balance between charge and discharge energy in the calculation cycle represented in equations (5) and (6) . , max.
The stored energy level of BESS is limited by the SOC value which is increased in the charge time and decreased in the discharge time as represented in the equation (7) [30]. Besides, to ensure the lifetime of BESS, the stored energy has the following lower and upper bounds as equation (8)

Solar energy resource modeling
The solar irradiance is uncertain and always varies with an hour in day and season in the year. While the output power of PV depends on solar irradiance and the operating ambient temperature and thus it also varies with an hour in day and season in the year. Therefore, the output power of PV in each hour ( pv h P ) is analysed as expression (9)  Similarly, the thermal power generated by SHE also varies with the solar irradiance [24] as well as operating temperature because the collector efficiency is a linear function of operation temperature [20]. Therefore, the output power of SHE can be described by functions of time as equation (10)

Modeling of distribution network among energy hubs
The EH network composes of interconnected multi-energy hubs by the electrical and gas distribution networks. In each node, the EH is connected with both electrical and gas distribution networks. The input power of EHs receives from the EDN is the electrical power ( , e ih P ) and GDN is the gas power , () g ih P . Hence, , e ih P and , g ih P become loads of EDN and GDN, respectively.

Modeling of electricity network
The AC nonlinear power flow model of EDN with N nodes is presented in equation (11) [34]. In which, , . .cos( ) To ensure the devices of EDN are not overloaded by thermal limit, the operation power flow in feeders ; , Additionally, the voltage profile at buses must be guaranteed in a limit allowing the ordinary operation of the EDN as presented in equation (13). The voltage at the substation bus connected to utility grid is assumed to constant while the voltage at load buses often varies under the change of load. Therefore, these voltages are limited between minimum voltage profile min U and maximum voltage profile max U . ,

Modeling of natural gas network
A typical GDN consists of gas producers, compressor stations, pipelines, and customers or loads. The gas flow in the pipelines to connected nodes can be expressed as equation (14)  Due to decreased gas pressure during transmission, the compressor can be utilized to ensure sufficient gas pressure. Hence, the compressor demand can be approximated as equation (15)  and maximum power of the gas flow in pipeline ij.

MATHEMATICAL MODEL
Due to different energy carriers available at the inputs as well as outputs and the possibility of internal power conversion of the EHs, the energy hub network has high flexibility and thus the power flows in the network can be controlled within a certain degree of freedom to optimize the operation cost as well as technic parameters of the system. Hence, the problem of optimal operation of the EHs and energy networks is modelled as a MINLP problem in this section.

Objective function
The objective function to be minimized takes into account cost terms of energy and operation, and terms related to emissions in a computed cycle ( The electrical price is often the Time-Of-Use (TOU) and is the simplest form of the dynamic price while natural gas prices are constant [24][25] [34].

Constraints
According to the network and EHs modelling explained in Section 2, the electrical and thermal balance constraints as well as the operational constraints for each EH are presented in equations (3)- (8). Similarly, the EDN constraints include equations (11)-(13) and the GDN constraints consist of equations (14)- (16).
Additionally, the supply capacity of the systems is limited by the capacity and energy stored as expression (21) with the maximum allowable power in node i of electricity ( max.i e S ) and natural gas ( max.i g P ). , Similarly, the power limit of the CHP and GB is presented in constraints (22) with the maximum power of the CHP ( max .i chp P ) and GB ( max .i gb P . ; . (1 ) .( . . . ) . + (1-). . + . , The optimal operation problem of the EHs is based on the ability to control the power flow of conversion devices. Therefore, the conversion limits of the devices at each hour are expressed as:

Solution method
The proposed model is formulated with a nonlinear model mixed to integer variables to optimize the operation of each EH including energy conversion technologies as well as the energy hub network. The proposed model is formulated with a nonlinear model mixed to integer variables to optimize the operation of each EH including energy conversion technologies as well as the energy hub network. To solve the MINLP problem, a lot of solvers are presented in the existing literature [35]. In which, BONMIN is the best solver for solving the MINLP non-convex problems of GAMS environment that is a high-level modelling system for mathematical programming and optimization [36] [37]. BONMIN implements three different algorithms to solve MINLPs consisting of simple branch-and-bound algorithms, outer-approximation-based decomposition algorithm, and outer-approximation-based branch-and-cut algorithm. It is not an exact solver only for convex problems but taking into consideration the values of the heuristic solutions to solve the problem efficiently for convergence compared to the other mention solvers or meta-heuristic algorithms. Additionally, the problems are successfully solved with the least computational burden [38]. For the above reasons, this research is directed towards the use of BONMIN solver to find out an optimal solution to the proposed problem.

RESULTS AND DISCUSSION 4.1 Test structure and assumptions of case study
To investigate the feasibility and efficiency of the proposed model, the IEEE 5-bus network structure is utilized in this research shown in figure 3 [39] [40]. The parameters are changed and the GDN also is added to match the problem. In each node of the energy distribution network, an EH with a typical structure introduced in figure 2 is connected to receive the energy from a distribution network. The total electricity and natural gas of the energy hub network are purchased from the utility electrical grid and gas producer through electrical and gas substation, respectively. The input parameters of EHs are shown in Table 1 [23]- [25]. In which, the total conversion efficiency of CHP is 0.85 with 40% converted to electricity and 45% converted to heat. The efficiency of EC and AC depends on the coefficient of performance (COP) of them and equal about 60%. Similarly, the capacity limits of the equipment as well as the supply substations to ensure the proper operation of the EHs. Input parameters of the distribution networks are assumed in figure 3, the normal voltage of the EDN is 22kV connected to the utility grid through substation at node 1. Similarly, the gas substation at node 1 supplies for EHs through the pipelines of the GDN with a loss factor of about 5% [23] [25].
The energy demand of the EHs is assumed the difference and daily variation as shown in figure 4 with a power factor about 0.9. Similarly, the typical one-day variation of the PV, and SHE power is displayed in figure 5 and the daily energy price is presented in figure 6. The natural gas prices are constant while the electrical prices are TOU prices with reactive power prices depending on average compensation for reactive power support which is calculated based on a support factor of about 10% of the active power prices [41] [42].

Sensitivity analysis on the change of electrical price
The sensitivity of the total cost, as well as the electricity and natural gas purchased from the market of the proposed energy hub network with respect to the electrical price, is analysed. It is assumed that the electrical price varies from 0 to 150% of the base price in different analysed scenarios. The change of total cost together with the electricity and natural gas received from the supply substation of the energy hub network is expressed in figure 15. It can be seen that at first when the price is low (0 -50%), all electricity demand should be purchased from the market and supplied by the PV. The operating power of CHP is zero and thus the all heat demand is supplied by the GB and SHE with the maximum power. The total cost of the network fast increases depending on the electrical price. When the electrical price increases (50% -110%), the CHP is selected to supply both electricity and heat for loads. This means the natural gas received from the substation increases while the electricity received reduces. In this scenario, the total purchased energy increases due to the low efficiency of the CHP. However, the total cost increases more slowly due to electricity supplied from CHP with constant gas prices. When the price is from 110% and above, the CHP and GB should be operated with maximum power because the electrical price produced by CHP is cheaper than the purchase price from the market. This means the natural gas and electricity received from the substation in this scenario are constant.

CONCLUSION
The purpose of this paper is to optimize the operating schedule for the multi-energy system within the context of interaction in a network of multi-energy hubs. Hence, an optimal scheduling problem for a network of multienergy hubs considering the availability of solar and the utility energy distribution network is formulated. The problem was formulated with the objective function that minimizes the energy and operation cost of the network, the constraints of electricity, heat and cooling demand, and the constraints of the distribution network operation. The proposed model is examined in a case study of the IEEE 5-bus network structure. The numerical simulation showed significant efficiency of the conversion between energies in EHs by CHP, EC, and AC lead to reducing not only the energy cost of EHs but also the loss of distribution networks. Besides, technical parameters of both the EDN and the GDN are always guaranteed in all cases and they are improved in cases where CHP, PV, SHE, and BESS are utilized. The price sensitivity analysis also shows that CHP starts to be operated when the price is about 50% of the base price and the operation power is at the maximum level when the price is larger than 110% of the base price. Additionally, the interconnection of multi-energy hubs with conversion devices in a network still has the potential for reducing emissions. However, the uncertainty of output power of PV resource and real-time electricity price should be handled. Hence, future research work must focus on investigating the influence of different levels of variability parameters to improve the practicality of the optimal scheduling model.