Optimal Scheduling of a Multi-Energy Hub with Integrated Demand Response Programs

Abstract

This paper presents an optimal scheduling framework for a multi-energy hub (EH) that integrates electricity, natural gas, wind energy, energy storage systems, and demand response (DR) programs. The EH incorporates key system components including transformers, converters, boilers, combined heat and power (CHP) units, and both thermal and electrical energy storage. A novel aspect of this work is the joint coordination of multi-carrier energy flows with DR flexibility, enabling consumers to actively shift or reduce loads in response to pricing signals while leveraging storage and renewable resources. The optimisation problem is formulated as a mixed-integer linear programming (MILP) model and solved using the CPLEX solver in GAMS. To evaluate system performance, five case studies are investigated under varying natural gas price conditions and hub configurations, including scenarios with and without DR and CHP. Results demonstrate that DR participation significantly reduces total operating costs (up to 6%), enhances renewable utilisation, and decreases peak demand (by around 6%), leading to a flatter demand curve and improved system reliability. The findings highlight the potential of integrated EHs with DR as a cost-effective and flexible solution for future low-carbon energy systems. Furthermore, the study provides insights into practical deployment challenges, including storage efficiency, communication infrastructure, and real-time scheduling requirements, paving the way for hardware-in-the-loop and pilot-scale validations.

1. Introduction

The growing penetration of renewable energy resources and the rapid increase in multi-energy demand have created significant challenges for the secure and economic operation of energy systems [1]. Conventional electricity, natural gas, and thermal networks are often planned and operated independently, which limits opportunities for efficiency improvement, system flexibility, and resilience. The energy hub (EH) concept has therefore emerged as a promising paradigm for coordinating multiple energy carriers and conversion technologies within an integrated optimisation framework [2]. In particular, coupling electricity, natural gas, and thermal energy flows within a single hub allows operators to exploit cross-vector flexibility. For example, a combined heat and power (CHP) unit can simultaneously balance heat and electricity demand, while thermal and electrical energy storage systems (ESS) provide temporal flexibility. Such integration enables better utilisation of distributed generation resources, particularly in rural or remote areas, and reduces reliance on costly network reinforcements [3]. With the increasing variability of renewable energy such as wind, additional flexibility measures are required. Demand response (DR) programs provide an effective solution by encouraging consumers to shift or reduce loads in response to time-varying prices or incentives. Integrating DR into multi-energy hubs enhances system flexibility by enabling consumers to alter not only the timing but also the form of energy consumed, thereby improving reliability, reducing operating costs, and facilitating renewable integration [4]. Despite significant progress, several open questions remain. Most existing works have investigated either single-carrier systems (e.g., electricity-only with DR) or limited multi-carrier hubs without full integration of renewables, storage, and demand response. Furthermore, operational security aspects—both physical (energy balance, storage feasibility) and informatic (coordination and control underprice signals) are often simplified, limiting real-world applicability [5,6]. This study addresses these gaps by proposing a comprehensive optimal scheduling model for a multi-energy hub that integrates electricity, natural gas, wind energy, energy storage systems, and demand response. The model is formulated as a mixed-integer linear programming (MILP) problem to ensure tractability and scalability. Unlike prior works, the proposed framework evaluates hub performance across five operational case studies under varying fuel price scenarios and component configurations, providing new insights into the combined roles of DR, storage, and CHP in reducing costs and peak demand.

Related Literature Reviews

An energy hub (EH) is a relatively recent idea in energy system integration, and it offers a viable way to carry out future energy systems, especially in rural areas. Numerous techniques, each with its own set of objectives and limitations, have been used in recent research on the best way to operate an EH while taking the demand response program into account [7]. The demand response program problem for a residential energy hub with vehicle-to-grid (V2G) and renewable energy sources (RES) is formulated in ref. [8], demonstrating how the type of demand response program used severely impacts the customer’s annual cost. To help the unit take part in demand response (DR) programs and bid in the day-ahead electricity market, the authors in [9] created an operational optimisation scheduling model, like MILP or stochastic programming. The findings demonstrated that optimal DR program participation resulted in load shifting to hours with low energy prices, which lowers unit costs and boosts network resilience. A dynamic pricing-based model of the active DR program for industrial users is presented [10]. An agent-based method has been presented for simulating customer behaviour to engage in DR programs and select the optimal behavioural pattern considering different industrial processes for the three cement plants. The findings show that active DR deployment reduces peak demand in industrial units and smooths the load curve throughout the system in comparison to passive DR.

More recent works have extended EH formulations to incorporate uncertainty. Maghsoodi et al. [6] developed a probabilistic scheduling model considering correlations between uncertain variables in EHs with renewable sources. Miao et al. [8] proposed a multi-energy inertia-based support strategy with gas network constraints, demonstrating new opportunities for resilience. Other studies, such as Germscheid et al. [9], examined industrial DR under uncertain short-term prices, while Song et al. [10] considered bi-level dispatch in integrated gas–electric systems.

While these studies provide valuable insights, three key limitations remain:

• Many models are confined to single-carrier systems or limited EH structures, without fully capturing the synergies between electricity, gas, heat, renewables, storage, and DR.
• The majority of existing DR studies emphasise cost minimisation, but neglect cross-carrier substitution effects that arise in integrated hubs.
• Few works critically examine practical constraints such as storage charging/discharging logic, efficiency losses across converters, and operational feasibility under varying market conditions.

This paper builds on and extends these studies by presenting a comprehensive EH scheduling framework that incorporates multi-carrier energy flows, wind generation, dual storage systems, and demand response, validated across five operational scenarios. Compared with recent works such as [11], which emphasise single-carrier DR optimisation, the proposed study advances the state of the art by explicitly modelling cross-vector flexibility and assessing its implications for system cost, reliability, and demand flattening.

The following is a summary of the paper’s main contributions:

• Development of an MILP-based optimisation framework for a decentralised multi-energy hub that simultaneously integrates multiple carriers (electricity, heat, natural gas), wind generation, storage, and DR.
• Critical analysis of the interactions between storage systems, renewable resources, and DR under different market and technical conditions, highlighting their combined impact on operational cost and demand profile.
• Introduction of case studies that demonstrate how DR participation under both high and low gas prices can reshape hub operations, reduce peak demand, and improve renewable utilisation.
• Identification of research and practical implications for the real-world deployment of multi-energy hubs, including operational security and informatics challenges.
• Investigation of the effects of low-cost gas for both DRS and non-DRS scenarios.
• Assessment of DRS in the absence of CHP.

The remaining sections of the paper are structured as follows. Section 2 introduces the suggested mode’s system description. Section 3 outlines the problem formulation of the proposed model, including the objective function. Section 4 case studies and simulation results analysis. Section 5 discusses the conclusion and future research direction.

2. Proposed Smart Energy Hub Model Description

This paper employs a comprehensive energy hub model. The model incorporates inputs, converters, and energy storage to meet different demands. It is applied to assess the effects of demand response programs in a decentralised smart energy hub. The structure of the proposed smart energy hub is shown in Figure 1. It is powered by wind, natural gas, and electricity networks. Energy carriers are converted through gas boilers, combining heat and power (CHP) units, transformers, and converters. The hub also incorporates energy storage systems for both heat and electricity. This paper considers the demand for natural gas, electricity, and heat. In addition, the proposed model includes demand response capabilities for electricity demand.

3. Problem Formulation

3.1. Objective Function

The objective function of the proposed model in this paper focuses on the price of energy purchased from different networks, the money that is earned from selling power to the network, the cost of charging and discharging heat storage devices and batteries, and lastly, the cost of the demand response (DR). Thus, the goal of this study is to minimise operating costs within a 24 h period while considering various constraints. Equation (1) represents the objective function of the best management of the suggested decentralised smart energy hub:

$$\begin{array}{ll}Min TOC=& {\displaystyle \sum _{t=1}^{24}}\left[{\rho }_t^{{elec}_{price}}{P}_t^{{elec}_{input}}\right]+\left[{\rho }_t^{{WT}_{price}}{P}_t^{{WT}_{input}}\right]\left[{\rho }_t^{{gas}_{price}}{P}_t^{{gas}_{input}}\right]\\ & \hspace{1em}\hspace{1em}+\left[{\rho }_t^{{BESS}_{price}^{unit}}\left(P_t^{{BESS}_{ch}}+P_t^{{BESS}_{dch}}\right)\right]\\ & \hspace{1em}\hspace{1em}+\left[{\rho }_t^{{HSS}_{price}^{unit}}\left(P_t^{{HSS}_{ch}}+P_t^{{HSS}_{dch}}\right)\right]\\ & \hspace{1em}\hspace{1em}+\left[{\rho }_t^{{DR}_{price}^{elec}}\left(P_t^{{DR}_{shup}}+P_t^{{DR}_{shdo}}\right)\right]-\left[{\rho }_t^{{elec}_{net}^{price}}{P}_t^{{elec}_{output}}\right]\end{array}$$

(1)

where ${\rho }_t^{{elec}_{price}}$ is the price of electricity purchased from the network at time t, $P_t^{{elec}_{input}}$ is purchased electric power from the network at time t, $P_t^{{WT}_{input}}$ is generated wind power at hour t, ${\rho }_t^{{WT}_{price}}$ is the price of wind power at time t, ${\rho }_t^{{gas}_{price}}$ is the price of natural gas purchased from the network at time t, $P_t^{{gas}_{input}}$ is natural gas purchased from the network at time t, ${\rho }_t^{{BESS}_{price}^{unit}}$ is the unit cost of battery storage, $P_t^{{BESS}_{ch}}/P_t^{{BESS}_{dch}}$ is the charged/discharged power of the battery storage system, ${\rho }_t^{{HSS}_{price}^{unit}}$ is the unit cost of heat storage systems, $P_t^{{HSS}_{ch}}/P_t^{{HSS}_{dch}}$ is the charged/discharged power of the heat storage system, ${\rho }_t^{{DR}_{price}^{elec}}$ is the cost of shifting electricity demand at hour t, $P_t^{{DR}_{shup}}/P_t^{{DR}_{shdo}}$ is the shift up/down of electricity demand by DR, and ${\rho }_t^{{elec}_{net}^{price}}$ is the price of selling electricity to the network at time t.

3.2. Constraints of Wind Power

The WT-rated power and wind speed determine the amount of electricity power generated by WT ($P_t^{{WT}_{input}})$. When WT obtains a minimum wind speed ($w_{ci})$, it begins to generate power and keeps going until it reaches the rated wind speed ($w_r)$. The WT generates power at the rated power of the WT upon receiving the rated wind speed. The WT will shut off if the wind speed is more than the maximum amount ($w_{co})$, or less than the minimum amount ($w_{ci})$. Z, x, and y are connected to the WT attributes.

$$P_t^{{WT}_{input}}=\left\{\begin{array}{c}0 w<w_{ci}\\ P_{Cap}^{WT}\left(z-{yw}_t+{xw}_t^2\right) \\ 0 { w}_r\le w<w_{co}\end{array}\right. w_{ci}\le w<w_r$$

(2)

3.3. Operation Constraints

The smart energy hub’s optimal performance necessitates considering a few restrictions, satisfying which will result in the system operating at its best. These limitations are listed one at a time below.

3.3.1. Demand Constraints

The following formulation can be used to express the power equilibrium restrictions for meeting needs for heat, gas, and power.

3.3.2. The Smart Energy Hub Electricity Demand Constraint

The electricity requirement for the smart energy hub, as indicated by Equation (3), can be generated by the electrical network, CHP, WT, BESS, and DR. The electricity demand is shown by $P_t^{{Elec}_{dem}}$. The variables $P_t^{{elec}_{input}}$; $P_t^{{chp}_{input}^{elec}}$, and $P_t^{{WT}_{input}}$ denote the purchased electricity, gas for CHP, and wind power, respectively, from the network. The BESS charged and discharged power are represented by $P_t^{{BESS}_{dch}}$ and $P_t^{{BESS}_{ch}}$. $P_t^{{DR}_{shup}}$ and $P_t^{{DR}_{shdo}}$ indicate shifted downward and upward electricity demands, respectively. The electricity efficiency of transformers, the gas-to-electricity efficiency of CHP, and the electricity efficiency of converters are denoted by the values ${\eta }_{elec}^{Trnsf},$ ${\eta }_{{gas}_{elec}}^{chp}$, and ${\eta }_{elec}^{WT}$, respectively.

$$\begin{array}{ll}{P}_t^{{Elec}_{dem}}=& {\eta }_{elec}^{Trnsf}\left(1-{\alpha }^{line}\right)P_t^{{elec}_{input}}+{\eta }_{{gas}_{elec}}^{chp}{P}_t^{{chp}_{input}^{elec}}+{\eta }_{elec}^{WT}{P}_t^{{WT}_{input}}\\ & \hspace{1em}\hspace{1em}+{\eta }_{dch}^{BESS}{P}_t^{{BESS}_{dch}}-{\displaystyle \frac{1}{{\eta }_{ch}^{BESS}}}{P}_t^{{BESS}_{ch}}+P_t^{{DR}_{shdo}}-P_t^{{DR}_{shup}}\\ & \hspace{1em}\hspace{1em}-P_t^{{elec}_{output}}\end{array}$$

(3)

where: ${\alpha }^{line}\in \left[\mathrm{0,1}\right):$ per-unit line loss factor between PCC and EH bus.

${\eta }_{elec}^{Trnsf}$: transformer efficiency.

${\eta }_{{gas}_{elec}}^{chp}$: CHP gas-to-electricity efficiency (net AC).

${\eta }_{elec}^{WT}$: generator (converter/inverter) efficiencies in the wind conversion chain.

$P_t^{{WT}_{input}}$: Available wind power from the turbine power curve at time ttt.

${\eta }_{ch}^{BESS}, {\eta }_{dch}^{BESS}$: battery charge/discharge efficiencies on the AC side.

3.3.3. The Smart Energy Hub Heat Demand Constraint

Equation (4) illustrates the hub heat requirement, which can be met by HSS, boiler, and CHP. The hub heat demand is shown by $P_t^{{Heat}_{Dem}}$. For CHP and boiler, the purchased gas power from the network is indicated by $P_t^{{chp}_{input}^{heat}}$ and $P_t^{{boiler}_{input}^{heat}}$. HSS is represented by the discharged and charged energies $P_t^{{HSS}_{dch}}$ and $P_t^{{HSS}_{ch}}$. The gas to heat efficiencies of CHP and boiler are denoted by ${\eta }_{{gas}_{heat}}^{chp}$ and ${\eta }_{{gas}_{heat}}^{boiler}$, respectively.

$$P_t^{{Heat}_{Dem}}=\left[{\eta }_{{gas}_{heat}}^{chp}{P}_t^{{chp}_{input}^{heat}}+{\eta }_{{gas}_{heat}}^{boiler}{P}_t^{{boiler}_{input}^{heat}}+P_t^{{HSS}_{dch}}-P_t^{{HSS}_{ch}}\right]$$

(4)

3.3.4. The Smart Energy Hub Gas Demand Constraint

Less than the gas needed for the boiler and CHP, purchased network gas can meet the gas requirement for the smart energy hub, as indicated by Equation (5). The gas demand for the smart energy hub is $P_t^{{gas}_{Dem}}$. $P_t^{{gas}_{input}}$ represents the gas power that was purchased from the network.

$$P_t^{{gas}_{Dem}}=\left[P_t^{{gas}_{input}}-P_t^{{chp}_{input}^{heat}}+P_t^{{boiler}_{input}^{heat}}\right]$$

(5)

3.4. Network Constraints

The network’s capacity in the equations limits the amounts of bought power and gas from the networks and sold heat power to the networks, according to Equations (6) and (7). The maximum capacities of the electricity, gas, and heat networks are denoted by $P_t^{{elec}_{input}^{Max}}$ and $P_t^{{gas}_{input}^{Max}}$, respectively.

$$0\le P_t^{{elec}_{input}}\le P_t^{{elec}_{input}^{Max}}$$

(6)

$$0\le P_t^{{gas}_{input}}\le P_t^{{gas}_{input}^{Max}}$$

(7)

3.4.1. Converters Constraints

According to Equation (8) through (10), the installed optimised capabilities of the Transformer ($P_{Cap}^{Trnsf}$), CHP ($P_{Cap}^{chp}$), and boiler ($P_{Cap}^{boiler}$) should be the limit on the purchased network power and network gas for CHP and boiler.

$${\eta }_{elec}^{Trnsf}{P}_t^{{elec}_{input}}\le P_{Cap}^{Trnsf}$$

(8)

$${\eta }_{{gas}_{elec}}^{chp}{P}_t^{{chp}_{input}^{heat}}\le P_{Cap}^{chp}$$

(9)

$${\eta }_{{gas}_{heat}}^{boiler}{P}_t^{{boiler}_{input}^{heat}}\le P_{Cap}^{boiler}$$

(10)

3.4.2. The Smart Energy Hub Components Constraints

$P_{Cap}^{Trnsf}$; $P_{Cap}^{chp}$; $P_{Cap}^{boiler}$; $P_{Cap}^{WT}$; $P_t^{{BESS}_{Cap}}$, and $P_t^{{HSS}_{Cap}}$ for transformer, CHP, boiler, WT, BESS, and HSS, respectively, represent the necessary and optimal capacities of the hub components. The maximum quantities that can be installed in the smart energy hub should set a limit on the optimised capacities of the hub’s component parts. In Equations (11)–(16), the allowed maximum amounts for each hub component are as follows: $P_{Cap}^{{Trnsf}_{Max}}$; $P_{Cap}^{{chp}_{Max}}$; $P_{Cap}^{{boiler}_{Max}}$; $P_{Cap}^{{WT}_{Max}}$; $P_t^{{BESS}_{Cap}^{Max}}$, and $P_t^{{HSS}_{Cap}^{Max}}$.

$$P_{Cap}^{Trnsf}\le P_{Cap}^{{Trnsf}_{Max}}$$

(11)

$$P_{Cap}^{chp}\le P_{Cap}^{{chp}_{Max}}$$

(12)

$$P_{Cap}^{boiler}\le P_{Cap}^{{boiler}_{Max}}$$

(13)

$$P_{Cap}^{WT}\le P_{Cap}^{{WT}_{Max}}$$

(14)

$$P_t^{{BESS}_{Cap}}\le P_t^{{BESS}_{Cap}^{Max}}$$

(15)

$$P_t^{{HSS}_{Cap}}\le P_t^{{HSS}_{Cap}^{Max}}$$

(16)

3.5. Energy Storages Constraints

The model optimises the overall performance of the energy network by combining the restrictions of electricity and thermal energy storage to guarantee that the energy storage system runs safely, effectively, and within its specified capabilities.

3.5.1. Electrical Battery Storage Constraints

To store excess electricity created and release it when needed, BESS is used [12]. Based on the available power over the previous hour, the current amount of power that has been charged and discharged, and the amount of power loss of BESS in Equation (17), the available power in BESS ($P_t^{BESS})$ is estimated. In Equation (18), power loss ($P_t^{{BESS}_{loss}}$) is expressed. The BESS’s available power should be restricted to the lowest and highest accessible power levels as stated in Equation (19). The variables ${\alpha }_{loss}^{{BESS}_{Min}}$ and ${\alpha }_{loss}^{{BESS}_{Max}}$ represent the minimum and maximum power amounts of the BESS. Equations (20) and (21) should additionally limit the power quantity of the BESS that is charged ($P_t^{{BESS}_{ch}}$) and discharged ($P_t^{{BESS}_{dch}}$). In Equation (22), binary variables of the BESS’s charge ($I_{elec}^{{BESS}_{ch}}$) and discharge ($I_{elec}^{{BESS}_{dch}}$) prevent BESS from being charged and discharged simultaneously. The charge and discharge efficiencies of the BESS are represented by ${\eta }_{elec}^{{BESS}_{ch}}$ and ${\eta }_{elec}^{{BESS}_{dch}}$ respectively.

$$P_t^{BESS}=P_{t-1}^{BESS}+P_t^{{BESS}_{ch}}-P_t^{{BESS}_{dch}}-P_t^{{BESS}_{loss}}$$

(17)

$$P_t^{{BESS}_{loss}}={\alpha }_{loss}^{BESS}{P}_t^{BESS}$$

(18)

$${\alpha }_{loss}^{{BESS}_{Min}}{P}_t^{BESS}\le P_t^{BESS}\le {\alpha }_{loss}^{{BESS}_{Max}}{P}_t^{BESS}$$

(19)

$${\alpha }_{loss}^{{BESS}_{Min}}{\eta }_{elec}^{{BESS}_{ch}}{I}_{elec}^{{BESS}_{ch}}\le P_t^{{BESS}_{ch}}\le {\alpha }_{loss}^{{BESS}_{Max}}{\eta }_{elec}^{{BESS}_{ch}}{I}_{elec}^{{BESS}_{ch}}$$

(20)

$${\alpha }_{loss}^{{BESS}_{Min}}{\eta }_{elec}^{{BESS}_{dch}}{I}_{elec}^{{BESS}_{dch}}\le P_t^{{BESS}_{dch}}\le {\alpha }_{loss}^{{BESS}_{Max}}{\eta }_{elec}^{{BESS}_{dch}}{I}_{elec}^{{BESS}_{dch}}$$

(21)

$$0\le I_{elec}^{{BESS}_{ch}}+I_{elec}^{{BESS}_{dch}}\le 1$$

(22)

To account for minimum self discharge, the BESS includes a minimum drain constraint which prevent unrealistic idle states as show in Equation (23) below:

$$P_t^{BESS}\ge {\alpha }_{Min}^{{BESS}_{loss}}$$

(23)

3.5.2. Thermal Storage Constraints

The accessible energy of HSS ($P_t^{HSS})$ found in Equation (24) is calculated by considering the energy loss of HSS, the energy that was available an hour ago, as well as the energy that is now charged and discharged. Calculating heat energy loss ($P_t^{{HSS}_{loss}}$) is done using Equation (25). The least and maximum amounts of TS that can be accessed should be used to limit the available heat energy of HSS in Equation (26). The min/max factors of the min/max heat energy amount of HSS are represented by ${\alpha }_{loss}^{{HSS}_{Min}}$ and ${\alpha }_{loss}^{{HSS}_{Max}}$. Equations (27) and (28) limit the amounts of charged ($P_t^{{HSS}_{ch}}$) and discharged ($P_t^{{HSS}_{dch}}$) heat energy of HSS. ($I_{heat}^{{HSS}_{ch}}$) and ($I_{heat}^{{HSS}_{dch}}$) are binary variables of HSS that inhibit the charging and discharging performances in the interim in Equation (29). The charge and discharge efficiencies of HSS are shown by ${\eta }_{heat}^{{HSS}_{ch}}$ and ${\eta }_{heat}^{{HSS}_{dch}}$, respectively.

$$P_t^{HSS}=P_{t-1}^{HSS}+P_t^{{HSS}_{ch}}-P_t^{{HSS}_{dch}}-P_t^{{HSS}_{loss}}$$

(24)

$$P_t^{{HSS}_{loss}}={\alpha }_{loss}^{HSS}{P}_t^{HSS}$$

(25)

$${\alpha }_{loss}^{{HSS}_{Min}}{P}_t^{HSS}\le P_t^{HSS}\le {\alpha }_{loss}^{{HSS}_{Max}}{P}_t^{HSS}$$

(26)

$${\alpha }_{loss}^{{HSS}_{Min}}{\eta }_{heat}^{{HSS}_{ch}}{I}_{heat}^{{HSS}_{ch}}\le P_t^{{HSS}_{ch}}\le {\alpha }_{loss}^{{HSS}_{Max}}{\eta }_{heat}^{{HSS}_{ch}}{I}_{heat}^{{HSS}_{ch}}$$

(27)

$${\alpha }_{loss}^{{HSS}_{Min}}{\eta }_{heat}^{{HSS}_{dch}}{I}_{heat}^{{HSS}_{dch}}\le P_t^{{HSS}_{dch}}\le {\alpha }_{loss}^{{HSS}_{Max}}{\eta }_{heat}^{{HSS}_{dch}}{I}_{heat}^{{HSS}_{dch}}$$

(28)

$$0\le I_{heat}^{{HSS}_{ch}}+I_{heat}^{{HSS}_{dch}}\le 1$$

(29)

3.6. Demand Response Constraints

A portion of the electricity demand can be consumed during periods of low electricity demand and lowered during periods of high electricity demand. In Equation (30), the total decreased demand must match the entire increased demand. $P_t^{{DR}_{shdo}}$ and $P_t^{{DR}_{shup}}$ present shifted down and shifted up electricity demands respectively. The electricity load participation factors for shifting down and shifting up in that order are ${LPF}_{elec}^{{DR}_{Shdo}}$ and ${LPF}_{elec}^{{DR}_{Shup}}$. Equations (31) and (32) provide for the up and down shifting of the demand for electricity, respectively. The binary variables in Equation (33) that represent shifting up ($I_t^{{DR}_{shup}}$) and shifting down ($I_t^{{DR}_{shdo}}$) prevent simultaneous shifting of performances.

$$\sum _{t=1}^{24}{P}_t^{{DR}_{shup}}=\sum _{t=1}^{24}+P_t^{{DR}_{shdo}}$$

(30)

$$0\le P_t^{{DR}_{shup}}\le {LPF}_{elec}^{{DR}_{Shup}}{P}_t^{{DR}_{dem}^{elec}}{I}_t^{{DR}_{shup}}$$

(31)

$$0\le P_t^{{DR}_{shdo}}\le {LPF}_{elec}^{{DR}_{Shdo}}{P}_t^{{DR}_{dem}^{elec}}{I}_t^{{DR}_{shdo}}$$

(32)

$$0\le I_t^{{DR}_{shup}}+I_t^{{DR}_{shdo}}\le 1$$

(33)

4. Case Studies and Simulation Results Analysis

The hourly wind speed is shown in Figure 2. The demand response program has been taken into consideration for optimising the energy hub depicted in Figure 3 to minimise operating expenses. The energy hub operation was analysed using five case studies considering the availability of a demand response program. This study looks at the results of five different DR programs. The descriptions of a handful of case studies used in this investigation are used in this study. In the first and second scenarios, the impact of the energy hub’s inclusion in the DR program is assessed assuming a moderately high price for natural gas. Both the third and fourth scenarios provide an adequate operation schedule for the energy hub with and without participation in the DR project, presuming low natural gas prices. The final scenario involves the removal of CHP from the energy hub and an evaluation of the effects of carrier interactions for the duration of the DR program. The centre of energy in Figure 3 shows different hourly load demands for heat, electricity, and natural gas. The hourly electricity cost are also shown in Figure 4. The MILP model of the problem of optimising the energy hub while taking the DR program into consideration has been solved using the CPLEX 22.1.0 solution method in the GAMS 37.2.0. software. The numerical results for the various occurrences are independently analysed in the following sections.

4.1. An Energy Hub Case Study with Five Different Operational Scenarios

Five scenarios of a single energy hub were utilised to evaluate the suggested paradigm, as listed below.

• Scenario Number 1: Optimisation of the smart energy hub while taking the high cost of natural gas into consideration, but without addressing DR.
• Scenario Number 2: Optimising the smart energy hub while considering the concurrent DR program and high natural gas prices.
• Scenario Number 3: Optimising the smart energy hub while ignoring DR and taking into consideration the cheap price of natural gas.
• Scenario Number 4: Optimisation of the smart energy hub considering the simultaneous low natural gas price and DR program.
• Scenario Number 5: Optimisation of the smart energy hub without considering the implementation of CHP.

4.2. Simulation and Results Analysis

• Scenario 1:

Given the perceived higher cost of natural gas in this scenario, the suggested energy hub should be billed at USD 0.055 for each kilowatt of gas it consumes from the network. Additionally, in this instance, the power and gas boiler network acts as a backup system if the CHP is not built, with the CHP functioning as the main source of heat and electricity at the proposed energy hub. The numerical results for this situation are shown in Figure 5. Figure 5 displays the optimal operating schedule for the energy hub’s performance over the course of a day.

In this scenario, the energy hub is made up of two different power-producing technologies: wind turbines and CHP. The CHP component of the system allows for the sale of any excess electricity to the network. The negative figures in the above table for the power exchanged with the network represent the sale of this power to the network. Due to the high cost of natural gas, the energy centre occasionally purchases electricity from the grid to make up for power shortages instead of using CHP.

The energy hub will make it possible to sell additional energy to the network, and the wind turbine in the SEH will allow production of local power from RES. Due to the CHP’s limited capacity in the absence of a turbine, selling electricity to the grid is only practical early in the day when demand is low. Nevertheless, it is possible to sell energy all day, even in the afternoon when the market price of electricity is higher than it is in the morning, by adding a wind turbine. As a result, energy sales rise, increasing prices and SEH revenues.

A BESS has been designed in conjunction with the wind turbine to reduce the intermittent effects of this source on the hub energy’s performance and to better match the power production with the consumption pattern. A sizable amount of the hourly electricity demand is satisfied by the BESS, which also charges during off-peak hours and discharges during the hour when market electricity costs are at their greatest (18:00 hrs). Peak hours are when wind turbines and CHP generate the most electricity, and this is also when BESS discharges are at their maximum. When the network is at its busiest, the energy hub can fulfil all its demand and even sell excess energy to it at the greatest price, thanks to the confluence of these factors.

The boiler fills in the gaps to provide heat when the CHP cannot meet demand during specific hours. Furthermore, excess energy is stored in the storage during periods of low heat demand, and during peak hours, the storage discharges some of its stored energy to offset part of the demand, hence reducing the SEH’s operating expenses. The total running costs of the SEH in this case are USD 15,576.73 M/USD as seen in

Table 1. Comparison of the total operation cost between Scenarios 1 and 2 and Scenarios 3 and 4, respectively.

Scenarios	Total Operation Cost (M/USD)
Scenario 1	15,576.73
Scenario 2	15,270.20
Scenario 3	65,094.20
Scenario 4	61,395.50

. The following case in point looks at the ramifications of providing the SEH with DR capabilities.

• Scenario 2:

What sets this scenario apart from the previous one is the SEH’s ability to participate in the DR program. The graphical findings for Scenario 2 are shown in Figure 6.

Because it can move the load, the SEH in this scenario changes some of its demand from peak to off-peak hours. The demand for SEH thus decreases during peak hours and rises during off-peak hours. Consequently, the SEH uses its own energy-producing resources to produce more energy than it consumes during peak hours, and in certain situations, it is even able to sell the excess energy it generates back to the network. On the other hand, because of the load shift, CHP will be used more during off-peak hours, when it can help meet part of the additional demand. More people will purchase petrol from the network because of this. As shown in Figure 5 and Figure 6, the quantity of gas obtained from the network has grown from 30,521.1 kW in instance 1 to 30,911.2 kW in Scenario 2. As for Figure 7 and Figure 8. A graphical representation of the stated notions is presented in Figure 7 and Figure 8. The amount of electricity generated by the CHP and the amount exchanged with the grid are displayed graphically in these results.

As can be seen, when demand shifted to off-peak hours, the amount of CHP produced increased during hours 1, 2, 4, and 24. This load shift has an effect on the power traded with the network curve in a way that raises purchases from the network at hours 2, 3, 21, and 22, and decreases sales to the network at hours 6 and 7. The selling of electricity to the network at hour 17, increased network sales at hour 18, and decreased network purchases at hour 19 were the outcomes of fluctuations and decreases in peak-hour demand. Running expenses for the SEH are 15,270.2 M/USD as seen in Table 1; because of these factors being combined, this is less than in the first instance.

• Scenario 3:

In Scenario 3, natural gas is consistently more affordable than electricity. Furthermore, as the energy hub cannot participate in DR initiatives, all demand must be met in line with the intended pattern. The graphical findings for Scenario 3 are shown in Figure 9.

The use of CHP has increased noticeably in this scenario compared to Scenario 1 since natural gas is less expensive than electricity. In this case, the energy hub that could use many energy carriers decides to use less expensive energy carriers to meet a specific need. According to the chart, the amount of power produced by CHP in this instance is 7823.7 kW, which is 1516.1 kW more than in Scenario 1. This increase in CHP use results in approximately 2799 kW more fuel purchases from the network than in the first scenario. In Figure 10, this increase is seen. The graph indicates that more petrol has been purchased from the network over most of the day.

Another problem is the decline in boiler manufacturing. The increased production of CHP reduces the need for auxiliary sources and the use of boilers. Additionally, as the amount of thermal energy generated by CHP rises, so does the requirement for thermal storage. This is because CHP production is linked with the thermal demand pattern. In this case, when the CHP production exceeds the heat requirement, the heat storage is replenished periodically during the day, and when it is released, it not only meets a significant amount of the thermal demand but also eliminates the need for boilers. Figure 5 and Figure 9 illustrate that the heat storage has a charge and discharge power that is more than twice that of Scenario 1. Reliance on the electrical grid and the quantity of electricity network purchases will decrease with the adoption of natural gas as an energy source and its continuous use. For a more precise comparison, see Figure 11. Figure 11 shows how to exchange electrical power with the network in Scenarios 1 and 3.

The graph clearly shows a decrease in purchases from the electrical grid, especially in the morning and evening. This is seen in Scenario 1; purchasing electricity from the grid was more cost-effective at the time than producing power using natural gas. In contrast, CHP meets the need for these hours in Scenario 3, and because natural gas prices have decreased, some of this demand is fulfilled by purchases made from the network. Thanks to improved CHP power generation, it is now viable to sell electricity to the grid even during the middle of the day. The energy hub’s operating costs have dropped significantly, to 65,094.2 M/USD as seen in Table 1, because of increased use of more cost-effective energy carriers, less reliance on the power grid, and enhanced ESS performance in this scenario. The following example, in which natural gas is a cheap energy source, looks at the effects of DR participation.

• Scenario 4:

In this instance, the DR capacity is only utilised to produce electricity, even at a fair price for natural gas. The Scenario 3 results are shown graphically in Figure 12.

In this instance, like in Scenario 2, some electricity consumption is shifted from network peak hours to off-peak hours. The effects of demand variations on the demand curve for electrical energy in Scenarios 2 and 4 are shown in Figure 13.

Demand variations lead to larger network sales during certain periods and lower network purchases during peak times. Figure 14 shows the electric power exchange curve for the network. This graph shows that the energy hub will be able to increase its capacity to sell excess electricity to the network and make money while simultaneously reducing its reliance on the network during peak hours. The energy hub will be able to depend less on the network during peak hours thanks to distributed power sources like wind turbines and combined heat pumps. By doing this, the network’s stability will increase, and its peak demand will be reduced. The system’s operational expenses are decreased because of the shifting demand, which is satisfied during off-peak hours. With a sum of 61,395.5 M/USD, as seen in Table 1, Scenario 4 has the smallest sum of all the examples studied thus far.

• Scenario 5:

Here, we will assume that the energy hub under investigation does not have CHP and instead gets its power from the grid and wind turbines. Thermal energy will be produced by the boiler. In this scenario, the integration of several networks through multiple energy carriers is lost, making the direct acquisition of power-generating units from the relevant network necessary to satisfy fluctuating demands. We then contrast this scenario with two previous ones that had two high and two low natural gas prices. Figure 15 shows how to exchange electricity with the network in Scenario 5, as opposed to Scenarios 1 and 2. In Scenario 5, if the DR program is not carried out, the largest electricity purchase is scheduled to correspond with the energy’s peak price (i.e., the network’s peak demand), which elevates the network’s peak demand and rises operational costs for customers.

However, as DR capabilities increase and demand shifts to off-peak hours, the amount of electricity purchased from the network during peak hours decreases. During expensive periods, the system must pay a high price to meet demand because it still depends on the network’s purchasing power. The system’s capacity to transition between different energy carriers and the installation of CHP reduce energy purchases from the network significantly. The energy hub sells electricity at the full price and does not buy power from the network even during peak hours.

In this instance, the energy hub’s participation in the DR program will result in higher sales of electricity to the grid at peak times and higher purchases made during off-peak hours, which will reduce operating expenses.

Utilising CHP reduces reliance on the electrical grid, as seen in Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15 and Figure 16, which results in a higher gas buy volume from the gas network. The graph shows how the network’s gas purchases grow significantly with the inclusion of CHP. When purchasing gas from the network first thing in the morning, when the cost of electricity and natural gas is almost equal, adding CHP has little effect. However, when the cost of electricity increases throughout the day, the energy hub is more eager to meet its needs from a less costly carrier, which causes it to produce more power through CHP and, as a result, buy more gas from the network.

If the electricity exchange curve for the low fuel price mode is taken into consideration, as shown in Figure 17, it can be demonstrated that the power purchase from the grid in the scenario of utilising CHP is cheaper than the scenario of eliminating CHP at all times of the day. It can be argued that the utilisation of natural gas for electricity production and the load shifting to low-cost times often cause the consumption curve in this scenario to flatten. Furthermore, even while petrol consumption rises during peak electricity hours and less electricity is bought from the grid during these periods, the cost of the consumers’ energy bills decreases. From a financial perspective, the electrical grid’s daily expenses decrease due to the flattening of the curve and reduced production and transmission costs, while the profit margin of the gas firm increases with increased sales of natural gas.

Thus, it can be said that the incorporation of DR programs into the architecture of smart energy hubs lowers utility profits, flattens the demand curve, and reduces peak demand while maintaining customer comfort.

5. Conclusions

This study developed and analysed an optimal scheduling model for a multi-energy hub (EH) integrating electricity, natural gas, wind energy, energy storage systems, and demand response (DR) programs. The problem was formulated as a mixed-integer linear programming (MILP) model and solved using CPLEX 22.1.0 in GAMS. 37.2.0. The model was tested under five operational scenarios with varying gas price conditions and component configurations, including cases with and without DR participation and CHP units. The results demonstrate that integrating DR into EH operations significantly improves operational efficiency. Specifically, DR enables demand shifting that reduces total operating costs by up to 6%, increases renewable energy utilisation, and lowers peak demand by approximately 6%, thereby flattening the demand curve. The coordinated operation of CHP, storage, and DR also enhances system flexibility by allowing substitution between electricity, gas, and heat carriers. This study’s findings highlight several practical implications. First, while simulation results show substantial benefits, real-world deployment requires careful consideration of hardware constraints (e.g., response times of storage, minimum discharge levels), communication infrastructure, and cybersecurity of DR signals. Second, although MILP ensures tractable optimisation, implementation in real-time systems may demand heuristic or AI-based methods for faster scheduling under uncertainty. Finally, the demonstrated cost and reliability improvements suggest that EHs with DR could play an important role in future low-carbon energy systems, particularly in regions with high renewable penetration and volatile gas prices. In summary, the proposed model shows how multi-carrier coupling, storage integration, and DR flexibility can jointly reduce costs, enhance reliability, and improve renewable integration in smart energy hubs. Future research should focus on validating the framework in hardware-in-the-loop or pilot-scale demonstrations and exploring real-time control strategies using artificial intelligence or reinforcement learning to address dynamic market and network conditions.