To maximize energy profit with the participation of electricity, natural gas, and district heating networks in the day-ahead market, stochastic scheduling of energy hubs taking into account the uncertainty of photovoltaic and wind resources, has been carried out. This has been done using a new meta-heuristic algorithm, improved artificial rabbits optimization (IARO). In this study, the uncertainty of solar and wind energy sources is modeled using Hang’s two-point estimating method (TPEM). The IARO algorithm is applied to calculate the best capacity of hub energy equipment, such as solar and wind renewable energy sources, combined heat and power (CHP) systems, steam boilers, energy storage, and electric cars in the day-ahead market. The standard ARO algorithm is developed to mimic the foraging behavior of rabbits, and in this work, the algorithm’s effectiveness in avoiding premature convergence is improved by using the dystudynamic inertia weight technique. The proposed IARO-based scheduling framework’s performance is evaluated against that of traditional ARO, particle swarm optimization (PSO), and salp swarm algorithm (SSA). The findings show that, in comparison to previous approaches, the suggested meta-heuristic scheduling framework based on the IARO has increased energy profit in day-ahead electricity, gas, and heating markets by satisfying the operational and energy hub limitations. Additionally, the results show that TPEM approach dependability consideration decreased hub energy’s profit by 8.995% as compared to deterministic planning.

Consumers in the commercial, industrial, and residential sectors are all linked to energy networks [

Several investigations on the concept of an energy center have been carried out. In [

A fresh paradigm for the efficient administration of energy hubs is described in reference [

The review of previous studies has shown that the planning of energy hubs requires a stochastic approach that is implemented in terms of implementation and has a low computational cost. In addition, this presented a stochastic approach based on the market model for energy hubs should be able to maximize their revenue in day-ahead electricity, gas and heating markets. According to the literature evaluation, most of the stochastic programming is presented by the Monte Carlo simulation method. This method depends on the probability distribution function of the inputs and has a very high computational cost. On the other hand, efficient and coordinated planning of hub energy equipment in cooperation with all types of electricity, gas and heating networks requires a strong solver due to the non-linear and multi-dimensional nature of the problem. In addition, methods for one-dimensional and multi-dimensional approximations for the linearization of non-convex functions of natural gas transmission, generator cost and compressor performance are presented in the literature, these linearizations are not required when using meta-heuristic algorithms. Therefore, the review of the literature shows that there is a need for a stochastic energy hub planning framework with easy implementation and low computational cost in cooperation with day-ahead electricity, gas and heating markets for energy economic analysis with the aim of maximizing energy profit. This paper uses the two-point estimation method along with a meta-heuristic algorithm that has high computational power and optimization, and can provide the conditions to achieve maximum profit from an energy hub in the conditions of uncertainty of energy resources production.

In this article, the stochastic scheduling of the energy hub using an approach called Hang’s two-point estimation method (TPEM) is presented. The goal of the paper is to achieve the maximum possible profit from the production of energy in the future market. Participants include networks for the distribution of electricity, natural gas, and district heating. According to NFL theory [

The major contributions of this paper are listed below:

Providing a stochastic scheduling framework including photovoltaic and wind energy sources, CHP, boiler, and energy storage based on Hang’s two-point estimation method.

Maximization of energy profit due to participation in electricity, natural gas, and heating markets based on optimal scheduling framework of an energy hub.

Evaluation of changes in load levels and the forced output rate of renewable energy resources and CHP equipment in solving the problem of hub scheduling and energy profit.

A new meta-heuristic algorithm called the improved ARO algorithm based on dynamic inertia weight for solving energy hub schedules.

Comparing the performance of the optimal energy hub scheduling framework based on IARO with the traditional methods of ARO, PSO, and SSA.

The paper is organized in such a way that in

The day-ahead market, with the aim function of maximizing energy profit, and with the restrictions of network operation and hubs are all taken into consideration in this section’s stochastic scheduling presentation for participation in the electricity, natural gas, and district heating networks. The energy hub model and analytical approach are discussed in the paragraphs that follow.

In this research, to maximize profits, hub energy stochastic scheduling utilizing Hang’s two-point estimate method (TPEM) is given in the market confronting electricity, natural gas, and district heating. The sale of active and reactive power in the electricity market, as well as the revenue of the hub energy in the day-ahead natural gas and district heating markets, are all included in the goal function of profit maximization of the energy hub. This objective function is described as follows:

The power flow constraints in electricity, natural gas, and district heating networks are presented below [

The active and reactive power balance in different buses

Active and reactive power flow of lines

Voltage angle in the base bus

The voltage angle in the base buses are set at zero, i.e., _{e}_{,t }= 0, ∀

Balance of gas power and flow

The balance of gas power in different buses and gas flow through the pipeline at hour t are as follows:

The heating power balance in buses

Heat power flow

Heat power flow through a pipeline at time t is as follows:

^{p}^{q}^{S}^{S}

The operating restrictions in the networks for electricity, natural gas, and district heating are discussed in this section.

Voltage range of buses

Allowed capacity of lines and stations

Bus pressure limit

The capacity of gas pipes and station

The thermal limit of buses

The capacity of the station and heating pipeline

The hub energy in this research consists of solar and wind renewable energy sources, storage, electric parking, CHP, and a boiler, and it is linked to the regional heating network to deliver and receive energy.

Based on

Also, the boiler power balance equation and capacity constraints are defined based on

Hong’s two-point estimate method (TPEM), an approximation approach for calculating the uncertainty of solar and wind energy sources, is utilized in this article. Using the TPEM approach, certain representative points (s points for each variable) have been identified under the heading of concentrations based on the data supplied by the center of moments. Using the answers found for the representative points, these points were utilized to solve the model and the statistical data of the random output variable [

Consider that _{l}_{l,s}_{l,s}_{l}_{l}_{l,s}_{l}_{l}

The power of solar and wind renewable resources, in addition to loads, has been represented arbitrarily in the energy management issue. For each emphasis, the key element of energy management, the energy hub, must be used. The following is thought of as the problem’s solution:

The flowchart of the proposed stochastic methodology based on PEM and IARO is depicted in

Step 1) Setting the first and second moments of random output variables to 0:

Step 2) In this step, the random input variable _{l}

Step 3)

Step 4) In this step, two estimated positions

Step 5) The hub energy management problem is solved for each focus.

Step 6) In this step, the raw moments of the output variables are updated.

Step 7) Steps 2 to 6 are repeated until all concentrations of input random variables are considered. If all concentrations and variables are considered, go to Step 8, and otherwise go to Step 2.

Step 8) Stop the algorithm and save the random output variables.

In this study, an improved artificial rabbits optimization (IARO) is applied for optimal programming of the energy hub to maximize the energy profit in partnership with electricity, natural gas and district heating networks in the day-ahead market considering the uncertainty of photovoltaic and wind resource production. The role of the presented optimization algorithm is as a solver to determine the optimal capacity of hub energy equipment including photovoltaic and wind renewable energy sources, combined heat and power (CHP) system, boiler, energy storage and electric vehicles in the day-ahead market, as the profit of the system is maximized (

The ARO algorithm is based on rabbits’ natural habitat survival techniques [

In other words, they are not happy with the grass in their region and seek far afield, which is termed detour foraging. Rabbits tend to explore for food in far-off locations, therefore they have little interest in searching for food in their immediate surroundings. Within its territory, the ARO algorithm assigns each rabbit a certain number (d) of hiding spots. When searching for food, rabbits may sometimes take into account the location of other rabbits. In this technique, rabbits may receive enough food to eat while they are hunting for more food by congregating around a food source. Therefore, “detour foraging” refers to the practice of each searcher attempting to improve their position relative to the other searchers by introducing a disruption. The following is an explanation of how the detour foraging model is presented [_{1} to _{3} denotes three random numbers in the range (1, 0).

A rabbit creates many hiding sites (

A variety of hiding spots are created around a rabbit throughout each dimension

Rabbits are not interested in selecting one of the hiding locations at random in order to hide from the hunter and avoid being pursued. According to this definition of random concealing behavior [_{4} and _{5} stand for integers between 0 and 1, again at random. The _{4} and _{5} represent numbers between 0 and 1, randomly. According to the above equations, the

The position of the

In the ARO algorithm, rabbits often engage in detour foraging, but as iterations go on, they also engage in random hiding. As a result, the rabbit loses energy over time. The energy component is thus given as follows [

As a result, the ARO creates a population of rabbits at random to serve as candidate answers in the search space. The rabbit changes its location to a randomly selected rabbit from the population or a randomly selected rabbit drawn from the hides with each iteration. Factor A undergoes a declining process as the repetitions rise, forcing every rabbit in the population to carry out the transfer procedure. To get the best response from the algorithm, it has been modified until it meets the convergence condition.

The non-linear dynamic weight inertia [

This section uses the HTPEM and IARO to demonstrate the results of stochastic hub energy scheduling and management in various networks that are exposed to electricity, gas, and district heating networks in day-ahead markets. In order to maximize hub profits, the hub energy scheduling issue is treated as an optimization problem. In this work, the optimization issue is solved using the IARO algorithm, and the performance of the algorithm is evaluated against that of the traditional ARO, PSO, and SSA approaches. Each algorithm’s population, maximum iteration, and a number of independent executions are chosen as 100, 200, and 25 accordingly. Each algorithm is executed 25 times and the best solution among all executions is selected as the final solution. Also, the performance of the algorithms are evaluated using a statistical analysis including the Best, Mean and Worst, std indices. The proposed method is implemented in Matlab software on a personal computer with Intel Core i7-4510U, up to 3.1 GHz, 8 GB RAM, and Windows 10, 64-bit.

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

ARO [ |
– | – |

PSO [ |
C1, C2 (personal and social constants) | 2 |

Wmax and Wmin (maximum and minimum inertia weight) | 0.9, 0.2 | |

SSA [ |
c2, c3 (random numbers) | [0, 1] |

The system under study consists of a 12-line electrical network with 9 buses, a gas network with 4 buses and 5 pipes, and an urban heating network with 9 buses and 9 pipelines (

Electrical network | Natural gas network | District heating network | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Line | R | X | F^{e,max} |
Pipeline | sign | F^{g,max} |
Pipeline | F^{h,max} |
||

1-2 | 0.02 | 0.06 | 0.90 | 1-2 | 3 | 1 | 1.1 | 1-2 | 15 | 1.00 |

1-5 | 0.05 | 0.12 | 0.50 | 1-3 | 3.5 | 1 | 3.0 | 1-3 | 18.5 | 1.30 |

2-3 | 0.05 | 0.12 | 0.65 | 1-4 | 4 | 1 | 1.2 | 2-3 | 17.5 | 0.20 |

2-4 | 0.06 | 0.08 | 0.75 | 2-3 | 4.5 | −1 | 0.6 | 2-7 | 18.5 | 0.50 |

2-5 | 0.06 | 0.11 | 0.80 | 3-4 | 4.5 | 1 | 0.8 | 3-4 | 19.5 | 0.65 |

3-4 | 0.07 | 0.11 | 1.20 | 3-6 | 19 | 0.20 | ||||

4-5 | 0.01 | 0.04 | 0.65 | 4-5 | 15 | 0.35 | ||||

4-7 | 0.01 | 0.03 | 0.90 | 5-6 | 19 | 0.10 | ||||

5-6 | 0.02 | 0.05 | 1.10 | 6-7 | 19.5 | 0.20 | ||||

6-9 | 0.10 | 0.09 | 0.30 | |||||||

7-8 | 0.02 | 0.07 | 1.30 | |||||||

8-9 | 0.08 | 0.12 | 0.35 |

Electrical network | Natural gas network | District heating network | ||||
---|---|---|---|---|---|---|

Bus | L^{P} |
L^{q} |
Node | L^{h} |
Node | L^{g} |

1 | 0 | 0 | 1 | 0 | 1 | 0 |

2 | 0 | 0 | 2 | 0.8 | 2 | 0 |

3 | 0 | 0 | 3 | 0.7 | 3 | 0 |

4 | 0.9 | 0.3 | 4 | 0.9 | 4 | 0 |

5 | 0.7 | 0.5 | 5 | 0.6 | ||

6 | 1 | 0.2 | 6 | 0.5 | ||

7 | 0 | 0 | 7 | 0.7 | ||

8 | 0.5 | 0.5 | ||||

9 | 0.3 | 0.3 |

System | Location | RES | Storage | EVs | CHP | Boiler | Load (p.u) | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

E | G | h | HD^{P} |
HD^{q} |
HD^{h} |
HD^{g} |
||||||

Hub 1 | 2 | - | - | ✓ | ✓ | ✓ | 0.8 | 0.4 | 0 | 0 | ||

Hub 2 | 3 | - | - | ✓ | ✓ | ✓ | 0.5 | 0.3 | 0 | 0 | ||

Hub 3 | 7 | - | - | ✓ | ✓ | ✓ | 0.6 | 0.4 | 0 | 0 | ||

Hub 4 | 5 | 4 | 7 | ✓ | ✓ | 0.2 | 0.1 | 0.3 | 0 | |||

Hub 5 | 8 | - | - | ✓ | ✓ | ✓ | 0.4 | 0.2 | 0 | 0 | ||

Hub 6 | 6 | 3 | 6 | ✓ | ✓ | ✓ | ✓ | ✓ | 0.4 | 0.2 | 0.2 | 0 |

Hub 7 | 9 | 2 | 5 | ✓ | ✓ | ✓ | ✓ | ✓ | 0.4 | 0.2 | 0.2 | 0 |

The implementation of a new meta-heuristic algorithm called IARO allows for the optimal and deterministic scheduling of energy hubs without taking into account the unpredictability of renewable energy sources with the goal of maximizing profits in the day-ahead markets in various electricity, natural gas, and urban heating networks. The standard ARO, PSO, and SSA algorithms and the IARO algorithm have also been compared for their effectiveness in handling the energy hub scheduling issue.

Algorithm/Item | Convergence iteration | Profit ($) | Solution time (s) | Algorithm status |
---|---|---|---|---|

IARO | 12 | 509.40 | 152 | Globally optimal |

ARO | 48 | 502.11 | 169 | Locally optimal |

PSO | 47 | 504.74 | 158 | Locally optimal |

SSA | 32 | 503.21 | 164 | Locally optimal |

Algorithm/Index | Best ($) | Worst ($) | Mean ($) | Std ($) |
---|---|---|---|---|

IARO | 509.40 | 502.28 | 507.65 | 55.04 |

ARO | 502.11 | 488.92 | 495.44 | 87.35 |

PSO | 504.74 | 498.36 | 500.07 | 58.73 |

SSA | 503.21 | 492.50 | 497.26 | 80.54 |

Using the HTPEM approach outlined in

Algorithm/Item | Convergence iteration | Profit ($) | Solution time (s) | Algorithm status |
---|---|---|---|---|

IARO | 33 | 463.59 | 174 | Globally optimal |

ARO | 35 | 455.06 | 198 | Locally optimal |

PSO | 33 | 461.95 | 181 | Locally optimal |

SSA | 48 | 458.32 | 192 | Locally optimal |

Algorithm/Index | Best ($) | Worst ($) | Mean ($) | Std ($) |
---|---|---|---|---|

IARO | 463.59 | 502.28 | 507.65 | 55.04 |

ARO | 455.06 | 488.92 | 495.44 | 87.35 |

PSO | 461.95 | 498.36 | 500.07 | 58.73 |

SSA | 458.32 | 492.50 | 497.26 | 80.54 |

In this section,

Algorithm/Item | Profit ($) |
---|---|

IARO (Deterministic) | 509.40 |

IARO (Stochastic) | 463.59 |

[ |
504.74 |

[ |
461.95 |

In this section, the performance of the IARO in solving the problem is compared with the well-known GA [

Algorithm/Item | Convergence iteration | Solution time (s) | Profit ($) |
---|---|---|---|

IARO | 33 | 174 | 463.59 |

GA | 48 | 186 | 449.16 |

GWO | 39 | 182 | 457.20 |

CSA | 30 | 177 | 460.88 |

The daily power and profit curves for various energies in deterministic and stochastic scheduling modes are shown in

The proposed method has optimal performance under changes in working conditions as well as changes in load demand. The purpose of evaluating the uncertainty of photovoltaic and wind renewable energy sources power as well as the load demand of the energy hub is the ability of the system in these conditions and to be robustness to the existing uncertainties. Hub energy system has maintained its performance level in achieving maximum energy profit in the conditions of uncertainty of renewable power generation and load demand. The proposed hub energy planning scheme has high scalability because it can be expanded to multiple and wider energy hubs. The proposed plan is practical and can provide the planners of energy hub systems in the energy industry with full knowledge of the economic evaluation of these types of systems and also the maximum revenue generation from them. Because in the proposed plan, a real approach to hub energy planning is included, taking into account the economic aspect of monetization as well as the technical aspect of generation and load demand uncertainties.

To maximize the energy profit, this article uses stochastic scheduling of energy hubs to participate in the future energy market using electricity, natural gas, and urban heating networks while taking into account the unpredictability of solar and wind generation. IARO’s new algorithm was introduced. In order to maximize the profit from the hub energy while fulfilling operational and hub restrictions, the optimum energy scheduling of the hub equipment was established, and the scheduling issue was put into practice. The study’s conclusions are as follows:

The results revealed that in the day-ahead market based on deterministic planning, the IARO, ARO, PSO, and SSA methods achieved energy profits of $509.40, $502.11, $504.74, and $503.21, respectively. This demonstrates the superior performance of the proposed framework based on IARO, which is the market leader in achieving the highest energy profits.

Considering the uncertainty has decreased the system’s profit by 8.99 percent based on the IARO method, according to the results of the stochastic scheduling of hub energy using the IARO, ARO, PSO, and SSA methods. Energy profit of 463.59 dollars, 455.06 dollars, 461.95 dollars, and 458.32 dollars was obtained in the future market.

The findings demonstrated that the participation level of solar and wind power has dropped in stochastic planning as a consequence of the unpredictability of these sources, which has impacted system profit.

The findings showed that the price of electricity, natural gas, and heating energy has a substantial impact on the system’s profitability. The results also demonstrated that the next day’s gas market profits are higher due to the reception of gas energy by CHP and steam boilers. The gas is fully negative the next day.

Access to accurate data of renewable energy sources and their uncertainty is one of the major limitations of the research. Robust hub energy planning based on the combined method of information gap decision theory and meta-heuristic algorithm is proposed for future work.

The authors extend their appreciation to the Deputyship for Research and Innovation, the Ministry of Education in Saudi Arabia for funding this research work through the Project Number (IFP-2022-35).

This research is supported by the Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia under Project Number (IFP-2022-35).

Conceptualization, M.A., A.A., Y.Q., A.S.A., M.Z., A.B.A. and M.G.B.A.; methodology, M.A. and A.A.; software, M.A. and A.S.A.; validation, M.A., Y.Q. and A.A.; formal analysis, M.A., A.KA., Y.Q., A.S.A., M.Z., A.B.A. and M.G.B.A.; investigation, M.A., A.A., Y.Q., A.S.A., M.Z., A.B.A. and M.G.B.A.; resources, M.A., A.A., Y.Q., A.S.A., M.Z., A.B.A. and M.G.B.A.; data curation, M.A., A.A., Y.Q., A.S.A., M.Z., A.B.A. and M.G.B.A.; writing—original draft preparation, A.S.A., and A.A.; writing—review and editing, M.A., A.A., Y.Q., A.S.A., M.Z., A.B.A. and M.G.B.A.; visualization, M.A., A.A., Y.Q., A.S.A., M.Z., A.B.A. and M.G.B.A.; supervision, A.A., Y.Q., A.S.A., M.Z., A.B.A. and M.G.B.A.; project administration, M.A., A.A., Y.Q., A.S.A., E.S., M.Z., A.B.A. and M.G.B.A. All authors have read and agreed to the published version of the manuscript.

The authors declare that they have no conflicts of interest to report regarding the present study.