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Issue
Sci. Tech. Energ. Transition
Volume 80, 2025
Article Number 7
Number of page(s) 13
DOI https://doi.org/10.2516/stet/2024105
Published online 06 January 2025

© The Author(s), published by EDP Sciences, 2025

Licence Creative CommonsThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1 Introduction

1.1 Aims

The smart electrical grid represents a significant advancement in the way electricity is generated, distributed, and consumed, fundamentally transforming the landscape of energy management [1]. This sophisticated system integrates state-of-the-art technologies, such as smart meters, sensors, and advanced communication tools, to create a more efficient and responsive power network [2]. At its core, the intelligent grid utilizes real-time data analytics to monitor and manage electricity flow, allowing for a more dynamic interaction between energy producers and consumers [3]. This capability enables utilities to better predict demand patterns, optimize energy distribution, and reduce waste [4–6]. By leveraging renewable energy sources, such as solar and wind, the intelligent grid can facilitate a more sustainable energy ecosystem, decreasing reliance on fossil fuels and minimizing environmental impact [6–9]. Moreover, the intelligent grid enhances the reliability and resilience of the power supply. With the ability to detect and respond to outages or fluctuations in demand almost instantaneously, utilities can implement corrective measures swiftly, ensuring a more stable electricity supply [10]. This responsiveness is particularly crucial in the face of increasing energy demands and the growing prevalence of extreme weather events that can disrupt traditional power systems [11]. Consumers also benefit from the intelligent grid through improved Demand Response Programs (DRPs). Smart appliances and home energy management systems allow individuals to monitor their energy usage in real-time, enabling them to make informed decisions about their consumption patterns [12, 13]. This not only empowers consumers to reduce their energy bills but also encourages more sustainable practices, as users can shift their usage to off-peak times when energy is cheaper and more abundant [14]. Furthermore, the intelligent electrical grid fosters greater collaboration between various stakeholders in the energy sector, including utilities, regulators, and consumers. By facilitating the exchange of information and resources, this system promotes innovative solutions and encourages the development of new business models, such as demand response programs and peer-to-peer energy trading [15–17]. In summary, the intelligent electrical grid is a transformative development that enhances the efficiency, reliability, and sustainability of electricity generation, distribution, and consumption. By harnessing advanced technologies and fostering greater collaboration among stakeholders, it paves the way for a more resilient and responsive energy future, ultimately benefiting both consumers and the environment [18–20].

1.2 Related studies and contributions

Some related studies by the researchers on optimal operation of the energy system are provided. Authors in [21] the issue of managing energy in a microgrid to reduce operational expenses and increase reliability has been addressed. In [22] power flow analysis in electrical networks is done considering optimal sizing of resources and operation of energy storage systems via economical dispatching modeling. In [23], the modeling analytical theory has been utilized to decrease the total generating and operating expenses in electrical networks without considering DRP. Authors in [24] used power demand shifting of DRP in electrical system reduction of the losses and electricity bill of consumers in peak times. In [25] interval optimization approach is implemented for reduce the operational cost and management of uncertainty of the electricity prices in electrical networks. The mathematical program with complementarity constraints solved a multi-level stochastic formulation in order to decrease operational cost as discussed in reference [26]. A multi-objective framework for distribution network has been introduced in [27] to reduce operating costs, and enhance voltage profiles by energy storage. In reference [28], optimal power flow regulation was introduced for the electrical microgrid system to achieve cost-effective operation. In [29], an energy optimization approach was explained using non-linear modeling to decrease power losses and improve voltage bus in grid-connected network. In reference [30], the epsilon method was employed to reduce costs and voltage fluctuations in a microgrid that is linked to the utility grid. In [31], a multi-objective framework was employed for the management of energy within a microgrid. This approach aims to minimize the costs associated with unsupplied power, and operation. A day-ahead energy management with DRP that focus on load shifting to lower operational expenses and enhance the reliability of a microgrid. This approach takes into account the electrical energy storage system, as discussed in reference [32].

This study focuses on the efficient operation of the smart electrical network through the integration of energy management and DRP. The approach employs a multi-stage and multi-objective function modeling technique to achieve optimal performance. In the initial stage, the DRP is modeled to enhance consumption management on the demand side, ensuring that energy usage is both efficient and responsive to varying demands. The second stage of the process involves optimizing several key factors, including operating costs, emissions, power losses, and voltage profiles, all framed as multi-objective functions. This optimization is conducted with focus on effective consumption management on the demand side. The Elephant Herding Optimization (EHO) method is utilized to solve the optimal operation of the electrical network. Ultimately, the implementation of the DRP results in significant reductions in costs, emissions, and losses, while simultaneously enhancing the voltage profile of the electrical network. Hence, novelties and contributions of this paper can be summarized as follow:

  • (A)

    An efficient operation of the electrical network through the integration of energy management and DRP are proposed.

  • (B)

    A multi-stage and multi-objective function modeling technique are used to achieve optimal performance.

  • (C)

    Modeling DRP is proposed to optimal power flow in first stage energy optimization.

  • (D)

    The optimization of operating costs, emissions, power losses, and voltage profiles, all framed as multi-objective functions in second stage.

2 Overview and modeling framework of smart electrical network

In Figure 1, overview of smart electrical network as 33-bus test system is shown. The network including two Diesel Generators (DGs), two PhotoVoltaic (PV) systems, Wind Turbine (WT) system and consumers. The consumers (C1–C5) are participated in DRP approach. The test system is connected to main grid and resources for meet demand.

thumbnail Fig. 1

Overview of smart electrical network.

2.1 Modeling framework

The framework of mathematical modeling for smart electrical network is as follow:

2.1.1 DRP model

Modeling DRP is implemented considering Consumer’s discomfort in the first stage as follow [33]: ψ j h = e β j ( PNS j h P j h ) - 1 . $$ {\psi }_j^h={e}^{{\beta }_j\left(\frac{{\mathrm{PNS}}_j^h}{{P}_j^h}\right)}-1. $$(1)

Where:

ψ j h $ {\psi }_j^h$ = Discomfort of jth consumer in time h.

βj = Ability of jth consumers for demand reduction.

PNS j h $ {\mathrm{PNS}}_j^h$ = Power curtailed of jth consumers in time h.

P j h $ {P}_j^h$ = Power of load demand in time h.

Also, implementation of the DRP can be enhanced profits for main grid. Therefore, profits for main grid are as follow: C = ∑ j = 1 J ( a PNS j h - γ h PNS j h ) . $$ C=\sum_{\mathrm{j}=1}^{\mathrm{J}}\left(a{\mathrm{PNS}}_j^h-{\mathrm{\gamma }}^{\mathrm{h}}{\mathrm{PNS}}_j^h\right). $$(2)

Where:

a = Electricity prices.

γh = Incentive rates for demand curtailed.

The participation of consumers in the DRP is influenced by the incentives offered and the degree of discomfort they encounter, which is quantified as the consumer’s benefit in equation (3). Consequently, consumers will engage in the demand response program only when their benefits are favorable. CB j = γ h PNS j h - ψ j h . $$ {\mathrm{CB}}_j={\gamma }^h{\mathrm{PNS}}_j^h-{\psi }_j^h. $$(3)

Finally, modeling DRP considering maximization of profits for main grid can be modeled as follow [34]: DRP = ∑ h = 1 H ∑ j = 1 J (   a   × PNS j h - γ h × PNS j h ) . $$ \mathrm{DRP}=\sum_{h=1}^H\sum_{j=1}^J\left(\enspace a\enspace \times {\mathrm{PNS}}_j^h-{\mathrm{\gamma }}^{\mathrm{h}}\times {\mathrm{PNS}}_j^h\right). $$(4)

The constraints in first stage are as follow: PNS j min , h ≤ PNS j h ≤ PNS j max , h . $$ {\mathrm{PNS}}_j^{\mathrm{min},h}\le {\mathrm{PNS}}_j^h\le {\mathrm{PNS}}_j^{\mathrm{max},h}. $$(5)

The maximum and minimum rates of the Power curtailed and incentive are modeled by (5) and respectively. The upper and lower boundaries of this range are determined by the main grid energy price, as indicated in (7) and (8), where: η = [0, 1]. γ min ≤   γ h   ≤ γ max $$ {\gamma }^{\mathrm{min}}\le \enspace {\gamma }^h\enspace \le {\gamma }^{\mathrm{max}} $$(6) γ max = min ( a ) $$ {\gamma }^{\mathrm{max}}=\mathrm{min}(a) $$(7) γ min = η min ( a ) . $$ {\gamma }^{\mathrm{min}}=\eta \mathrm{min}(a). $$(8)

Each consumer will be offered an incentive to alleviate the discomfort linked to reduced power availability. Consequently, consumers will engage in the DRP only when the benefits they receive are positively valued, as indicated by equation (9). γ h PNS j h - ψ j h > 0 . $$ {\gamma }^h{\mathrm{PNS}}_j^h-{\psi }_j^h>0. $$(9)

2.1.2 Multi objective function model

The multi-objective functions are modeled in second stage as follow:

A) Power losses

The reduction of power losses is first objective in second stage [35]: f 1   = Min   [ ∑ i = 1 N ∑ j = 1 N α ij ( P i P j + Q i Q j ) + β ij ( Q i P j - P i Q j ) ] $$ {f}_1\enspace =\mathrm{Min}\enspace \left[\sum_{i=1}^N\sum_{j=1}^N{\alpha }_{{ij}}\left({P}_i{P}_j+{Q}_i{Q}_j\right)+{\beta }_{{ij}}\left({Q}_i{P}_j-{P}_i{Q}_j\right)\right] $$(10) α ij = r ij V i V j cos ( δ i - δ j ) $$ {\alpha }_{{ij}}=\frac{{r}_{{ij}}}{{V}_i{V}_j}\mathrm{cos}\left({\delta }_i-{\delta }_j\right) $$(11) β ij = r ij V i V j sin ( δ i - δ j ) . $$ {\beta }_{{ij}}=\frac{{r}_{{ij}}}{{V}_i{V}_j}\mathrm{sin}({\delta }_i-{\delta }_j). $$(12)

Where:

Pi and Pj = Active power flow in ith and jth, respectively.

Qi and Qj = Reactive power flow in ith and jth, respectively.

rij and xij = Element of ijth line resistance and reactance, respectively.

N = Number of buses.

B) Voltage deviation

The second objective in second stage is voltage improvement [36]: f 2 = Min [ ∑ i = 1 N ( V i - 1 ) 2 ] . $$ {f}_2=\mathrm{Min}\left[\sum_{i=1}^N{\left({V}_i-1\right)}^2\right]. $$(13)

C) Voltage stability index

The maximizing voltage stability index is third objective in second stage [37]: f 3 = Max [ min ( VSI ij ) ] . $$ {f}_3=\mathrm{Max}\left[\mathrm{min}\left({\mathrm{VSI}}_{{ij}}\right)\right]. $$(14)

Where: VSI ij = V j 4 - 4 ( P i r ij + Q i x ij )   V j 2 - 4 ( P i x ij - Q i r ij ) 2 . $$ {\mathrm{VSI}}_{{ij}}={V}_j^4-4\left({P}_i{r}_{{ij}}+{Q}_i{x}_{{ij}}\right)\enspace {V}_j^2-4{\left({P}_i{x}_{{ij}}-{Q}_i{r}_{{ij}}\right)}^2. $$(15)

D) Operation costs

In fourth objective, operation costs are minimalized [38–41]: f 4 = Min [ ( aP Grid h + ∑ j ∈ N G a j P G 2 + b j P G + C j ) ] . $$ {f}_4=\mathrm{Min}\left[\left({{aP}}_{\mathrm{Grid}}^h+{\sum }_{j\in {N}_G}^{}{a}_j{P}_G^2+{b}_j{P}_G+{C}_j\right)\right]. $$(16)

Where:

P Grid h $ {P}_{\mathrm{Grid}}^h$ = Power of main grid.

P G j $ {P}_{{G}_j}$ = Active power of the distributed generator j.

aj, bj, cj = Cost function coefficients for DGj.

E) Emission pollution

The last objective in second stage is minimizing emission [42, 43]: f 5 = Min [ ∑ m = 1 M ∑ k = 1 K R K K ENV P M ] . $$ {f}_5=\mathrm{Min}\left[\sum_{m=1}^M\sum_{k=1}^K{R}_{\mathrm{K}}{K}_{\mathrm{ENV}}{P}_{\mathrm{M}}\right]. $$(17)

Where:

RK = Type of Emission pollution for DGs.

KENV = Amount of Emission pollution of DGs.

PDG = Power of DGs.

2.1.3 Constraints

The constraints in second stage are as follow:

A) Power balance

The power balance is modeled considering meet demand by resources energy at each time as follow [44]: P Grid h + ∑ j = 1 N s P Solar h + ∑ j = 1 N DG P M h + ∑ j = 1 N W P Wind h = ∑ j = 1 N c P j h - ∑ j = 1 J PNS j h + P Loss h . $$ {P}_{\mathrm{Grid}}^h+\sum_{j=1}^{{N}_{\mathrm{s}}}{P}_{\mathrm{Solar}}^h+\sum_{j=1}^{{N}_{\mathrm{DG}}}{P}_{\mathrm{M}}^h+\sum_{j=1}^{{N}_{\mathrm{W}}}{P}_{\mathrm{Wind}}^h=\sum_{j=1}^{{N}_{\mathrm{c}}}{P}_j^h-\sum_{j=1}^J{\mathrm{PNS}}_j^h+{P}_{\mathrm{Loss}}^h. $$(18)

Where:

NS = Number of PV.

NDG = Number of DG.

NW = Number of WT.

P Solar h $ {P}_{\mathrm{Solar}}^h$ = Power of PV at time h.

P Wind h $ {P}_{\mathrm{Wind}}^h$ = Power WT at time h.

P Loss h $ {P}_{\mathrm{Loss}}^h$ = Power losses at time h.

B) Generation limit

The power generation of the DGs has minimum and maximum rates as follow [45, 46]: P M min ≤ P M h ≤ P M max . $$ {P}_{\mathrm{M}}^{\mathrm{min}}\le {P}_{\mathrm{M}}^h\le {P}_{\mathrm{M}}^{\mathrm{max}}. $$(19)

C) Voltage limit

The voltage of buses in network is limited as follow [47]: V min ≤ V i h ≤ V max . $$ {V}^{\mathrm{min}}\le {V}_i^h\le {\mathrm{V}}^{\mathrm{max}}. $$(20)

3 Methodology

In this section, methodology for solving problem is proposed. The methodology is as follow:

A) Normalization of objectives

In this section, normalization of objective by TOPSIS method is done as follow [48]: Optimize [ f 1 ( x ) , f 2 ( x ) , … … … f n 2 ( x ) ] . $$ \mathrm{Optimize}\left[{f}_1(x),{f}_2(x),\dots \dots \dots {f}_{{n}_2}(x)\right]. $$(21)

The essential steps in the TOPSIS process are detailed below:

1) To find m solutions, identify the objective function n and organize the solutions in matrix format as specified in (22), where fij represents the value of the ith alternative for the jth objective.

2) A normalized matrix is formulated to normalize the solution’s attributes using equation (23). F = [ f 11 f i 2 … … … f 1 n f 21 f 22 … … … f 2 n . . . . . . . . f m 1 f m 2 … … … f mn ] $$ F=\left[\begin{array}{cccc}{f}_{11}& {f}_{\mathrm{i}2}& \dots \dots \dots & {f}_{1\mathrm{n}}\\ {f}_{21}& {f}_{22}& \dots \dots \dots & {f}_{2\mathrm{n}}\\.&.&.&.\\.&.&.&.\\ {f}_{\mathrm{m}1}& {f}_{\mathrm{m}2}& \dots \dots \dots & {f}_{\mathrm{mn}}\end{array}\right] $$(22) r ij = f ij ∑ i = 1 m f ij 2 . $$ {r}_{{ij}}=\frac{{f}_{{ij}}}{\sqrt{{\sum }_{i=1}^m{{f}_{{ij}}}^2}}. $$(23)

3) A weighted decision-making matrix is developed to incorporate various weights into the objective function, as demonstrated in equation (24). v ij = w j r ij . $$ {v}_{{ij}}={w}_j{r}_{{ij}}. $$(24)

4) Identify the Positive Ideal Solution (PIS) and the Negative Ideal Solution (NIS), which represent the optimal and least favorable outcomes for each individual objective, respectively, as outlined in equations (25) and (26). PIS = { v 1 + , v 2 + , v 3 + , … … … … . , v n + } $$ \mathrm{PIS}=\left\{{v}_1^{+},{v}_2^{+},{v}_3^{+},\dots \dots \dots \dots.,{v}_n^{+}\right\} $$(25) NIS = { v 1 - , v 2 - , v 3 - , … … … … . , v n - } . $$ \mathrm{NIS}=\left\{{v}_1^{-},{v}_2^{-},{v}_3^{-},\dots \dots \dots \dots.,{v}_n^{-}\right\}. $$(26)

The members of PIS and NIS are chosen based on equations (27) and (28), respectively. v j + = { max ( v ij ) for   objective   j   maximization min ( v ij ) for   objective   j   minimization   $$ {v}_j^{+}=\left\{\begin{array}{cc}\mathrm{max}\left({v}_{{ij}}\right)& \mathrm{for}\enspace \mathrm{objective}\enspace {j}\enspace \mathrm{maximization}\\ \mathrm{min}\left({v}_{{ij}}\right)& \mathrm{for}\enspace \mathrm{objective}\enspace {j}\enspace \mathrm{minimization}\end{array}\enspace \right. $$(27) v j - = { max ( v ij ) for   objective   j   minimization min ( v ij ) for   objective   j   maximization   . $$ {v}_j^{-}=\left\{\begin{array}{cc}\mathrm{max}\left({v}_{{ij}}\right)& \mathrm{for}\enspace \mathrm{objective}\enspace j\enspace \mathrm{minimization}\\ \mathrm{min}\left({v}_{{ij}}\right)& \mathrm{for}\enspace \mathrm{objective}\enspace j\enspace \mathrm{maximization}\end{array}\enspace \right.. $$(28)

5) For every solution, the Euclidean distances d i + $ {d}_i^{+}$ and d i - $ {d}_i^{-}$ are calculated from the positive and optimal solutions, utilizing equations (29) and (30) respectively. d i + = ∑ j = 1 n ( v ij - v j + ) 2 $$ {d}_i^{+}=\sqrt{{\sum }_{j=1}^n{\left({v}_{{ij}}-{v}_j^{+}\right)}^2} $$(29) d i - = ∑ j = 1 n ( v ij - v j - ) 2 . $$ {d}_i^{-}=\sqrt{{\sum }_{j=1}^n{\left({v}_{{ij}}-{v}_j^{-}\right)}^2}. $$(30)

6) The relative closeness index for each solution is calculated as outlined in equation (31). The optimal solution is identified by having the highest rate. C i + = d i + d i + + d i - . $$ {C}_i^{+}=\frac{{d}_i^{+}}{{d}_i^{+}+{d}_i^{-}}. $$(31)

B) Optimization method

The EHO algorithm is used as optimization method for obtained optimal values of decision variables. The EHO technique is represented mathematically through the below steps [49]:

1) All elephants in the clan, with the exception of the matriarch, are informed of their relative positions regarding the optimal and least favorable options as outlined in equation (32). Z new , cj , i = Z cj , i + α ( Z best , cj , i - Z cj , i ) r . $$ {Z}_{\mathrm{new},{cj},i}={Z}_{{cj},i}+\alpha ({Z}_{\mathrm{best},{cj},i}-{Z}_{{cj},i}){r}. $$(32)

Where:

Zcj,i = Old position of ith elephant Cj,th clan.

Znew,cj,i = New position of ith elephant Cj,th clan.

α = Scaling factor situated between [0, 1].

Zbest,cj,i = The best position of the ith elephant in the Cj,th.

r = Random number between [0 1].

2) The position of the optimal solution signifies the clan’s matriarch. This position is refreshed based on the clan’s center (Zcenter,cj) as outlined in equation (33). The clan’s center is determined based on the positions of all members, as outlined in equation (34). Z new , cj , i = ρ Z center , cj $$ {Z}_{\mathrm{new},{cj},i}=\rho {Z}_{\mathrm{center},{cj}} $$(33) Z center , cj = ∑ i = 1 n Z cj , i / n z . $$ {Z}_{\mathrm{center},{cj}}=\sum_{i=1}^n{Z}_{{cj},i}/{n}_{\mathrm{z}}. $$(34)

Where:

Ρ = scale factor in the interval [0, 1].

nz = Number of elephants in each group.

3) The most problematic elephants are isolated from their family units. To maintain the clan’s population, the separated males are replaced with new elephant calves. The placement of these calves is determined by equation (35). Where: Zworst,cj,i is the new babies’ position in the cjth clan. Zmax, Zmin are the maximum and minimum boundaries for each clan or group. Z worst , cj , i = Z min + r ( Z max - Z min + 1 ) . $$ {Z}_{\mathrm{worst},{cj},i}={Z}_{\mathrm{min}}+r\left({Z}_{\mathrm{max}}-{Z}_{\mathrm{min}}+1\right). $$(35)

Where:

Zworst,cj,i = New babies’ position in the cjth clan.

Zmax, Zmin = Maximum and minimum boundaries for each clan or group.

Elephant calves, as indicated by equation (35), will choose a location at random. However, it is observed that the adult elephants tend to position their young close to more dominant females to protect them from potential predators. The newly created elephants are expected to be situated close to a more dominant female, as indicated by equations (36) and (37). Z worst , cj , i = Z fitness cj $$ {Z}_{\mathrm{worst},{cj},i}={Z}_{{\mathrm{fitness}}_{{cj}}} $$(36) Z fitness cj = μ Z local , cj . $$ {Z}_{{\mathrm{fitness}}_{{cj}}}=\mu {Z}_{\mathrm{local},{cj}}. $$(37)

Where:

μ = Random proximity factor between [0.9–1.1].

Zlocal,cj = Local best position of the elephant of the cjth clan.

4) Continue to iterate through steps 1–4 until the convergence or stopping criteria are met.

3.1 Combined methodology

In this section, EHO algorithm and TOPSIS method for solving proposed optimization is combined. The intricacy of the situation results in a variety of potential solutions, highlighting the need for an effective strategy to pinpoint the best option among the competing alternatives. In Figure 2, combined methodology for solving problem is shown. The following steps are considering for solving problem:

  • 1

    Assign a random number of m populations of elephants.

  • 2

    Determine the values for the n objective functions referenced in a matrix in equation (38).

thumbnail Fig. 2

Combined methodology for solving problem.

D = [ f 11   f 12   f 13 ⋯ f 1 n ⋮ ⋱ ⋮ f m 1   f m 2   f m 3 ⋯ f mn ] $$ D=\left[\begin{array}{ccc}{f}_{11}{\enspace {f}}_{12}\enspace {f}_{13}& \cdots & {f}_{1n}\\ \vdots & \ddots & \vdots \\ {f}_{m1}\enspace {f}_{m2}\enspace {f}_{m3}& \cdots & {f}_{{mn}}\end{array}\right] $$(38)

  • 3

    Utilize the TOPSIS method on matrix D to identify the optimal solution along with its associated energy generation and the reduced power for consumers, based on the established DRP values.

  • 4

    Revise the elephant locations for each clan, excluding the highest and lowest ones.

  • 5

    Revise the top and bottom elephant locations within each group.

  • 6

    Repeat steps 1–5 till reach the maximum number of iterations.

4 Numerical simulation and results analysis

In this section, results analysis of the numerical simulation is carried out considering implementation of the DRP and proposed methodology.

4.1 Impact of DRP in first stage

The information and input data of energy resources such as DGs, PV, WT and main grid are extracted from references [50–53]. As well, data like load demand, emission factors, energy prices and 33-bus test system are taken from references [54–56]. The MATLAB software is used for simulation of optimization problem. As mentioned before, consumers C1-C5 are participated in DRP in test system. In Figure 3, participation of the consumers in DRP via demand reduction method is shown. In this figure, Consumer 4 has maximum rate of load reduction in DRP. The total reduced load by DRP and consumers is equal to 6217.38 kW. In Figure 4 values of profit and incentives for consumers by DRP is depicted. As shown, Consumer 4 has highest rate of incentive. Also, profit of system has maximum rate at hours 7:00–22:00. In Table 1 total values of profit, incentive and demand reduction is listed. The values of incentives for consumers 1–5 are equal to 15.03$, 27.49$, 10.04$, 105.85$ and 42.50$, respectively. The profit values are 30.46$, 56.48$, 20.91$, 214.54$ and 87.26$, respectively.

thumbnail Fig. 3

Participation of the consumers in DRP via demand reduction method.
thumbnail Fig. 4

Values of profit and incentives for consumers by DRP.
Table 1

Total values of profit, incentive and demand reduction.

4.2 Impact of DRP on second stage

The analyses and impact of DRP on multi-objective functions in second stage for operation of smart electrical network is proposed in this section.

4.2.1 Analysis of objectives without considering DRP

In this section, we delve into optimizing multi-objective functions, specifically excluding the influence of the DRP. The optimization process employs a synergistic approach that integrates the EHO method with the TOPSIS method. This combined methodology is designed to effectively navigate the complexities of multi-objective optimization, allowing for a more comprehensive evaluation of various competing objectives. To better understand the power generation landscape, Figure 5 illustrates the contributions from various sources, including the main grid, DGs, PVs, and WT. This visual representation highlights the diverse energy mix utilized in the system, showcasing how each component plays a role in meeting the overall energy demand. Furthermore, Figure 6 presents the voltage levels across the 33-bus test system, offering insights into the electrical performance and stability of the network. The voltage levels are critical for ensuring the reliability and efficiency of power delivery, particularly in a multi-source generation environment. The optimization results yield specific values for the multi-objective functions, which include power losses, voltage deviation, voltage stability, operational costs, and emissions. These values are recorded as follows: power losses at 1.088 MW, voltage deviation at 0.02801 p.u, voltage stability at 0.8231 p.u, operational costs amounting to 6801.33$, and emissions measured at 98.34 g/MW. These results indicate that the current optimization strategy does not achieve the optimal values necessary for effectively meeting load demand, particularly during peak periods. The inability to meet load demand optimally during peak times underscores the need for further refinement of the optimization approach, potentially incorporating additional factors such as demand response strategies or enhanced forecasting techniques to better align generation with consumption patterns.

thumbnail Fig. 5

Power generation of resources without DRP.
thumbnail Fig. 6

Voltage of buses without DRP.

4.2.2 Analysis of objectives with considering DRP

This section delves into the significant impact of DRP on various objective functions related to power generation and distribution. The analysis begins with Figure 7, which visually represents the power generation from different energy resources when DRP is implemented. Figure 7 highlights how DRP can effectively manage and optimize the output from these resources, leading to more efficient energy production. In Figure 8, a comparative analysis of power losses is presented, showcasing the differences in losses experienced with and without the implementation of DRP. The data indicates a notable decrease in overall power losses, which can be attributed to a reduction in load demand and a more efficient power flow within the test system. This reduction is crucial for enhancing the overall efficiency of the power network. Further insights are provided in Figure 9, which illustrates voltage deviation across the system. A lower voltage deviation is indicative of a more stable and reliable power supply, which is essential for maintaining the integrity of the electrical grid. Figure 10 complements this analysis by depicting the power exchange dynamics between various resources and the main grid, emphasizing the role of DRP in facilitating smoother interactions and energy transfers. Figure 11 presents the voltage profile across the buses in the system, offering a detailed view of how voltage levels are maintained throughout the network. This profile is critical for understanding the operational health of the grid and the effectiveness of DRP in stabilizing voltage levels. The quantitative results from the second stage of the analysis reveal the values of key objective functions: power losses are recorded at 0.803 MW, voltage deviation at 0.0189 p.u, voltage stability at 0.8472 p.u, operational costs at 4138.25$, and emissions at 88.56 g/MW. These figures underscore the tangible benefits of implementing DRP. The implementation of DRP leads to substantial reductions across several metrics: operational costs decrease by 39.15%, emissions are reduced by 9.94%, power losses diminish by 33.35%, and voltage deviation is lowered by 30.73%. Additionally, voltage stability sees an improvement of 3.66% when compared to scenarios that do not utilize DRP. These findings clearly illustrate that DRP play a pivotal role in enhancing the performance of objective functions within the power system. By facilitating peak shaving of demand, DRP not only optimizes the generation of energy resources but also contributes to a more sustainable and efficient energy landscape.

thumbnail Fig. 7

Power generation of resources without DRP.
thumbnail Fig. 8

Power losses with and without DRP.
thumbnail Fig. 9

Voltage deviation with and without DRP.
thumbnail Fig. 10

Power exchange with main grid.
thumbnail Fig. 11

Voltage of buses with DRP.

5 Conclusions

This paper delves into the optimal operation of the electrical network, emphasizing the importance of energy management and the implementation of a DRP. The concept of optimal operation is approached through the lens of multi-stage and multi-objective function modeling, which allows for a comprehensive analysis of various operational parameters. In the initial stage of the modeling process, the focus is placed on the demand side, specifically on optimizing consumption management through the DRP. This involves strategies that encourage consumers to adjust their energy usage during peak demand periods, thereby alleviating stress on the grid and promoting a more balanced energy consumption pattern. By incentivizing users to shift their energy usage, the DRP not only enhances the overall efficiency of the electrical network but also contributes to a more sustainable energy future. The second stage of the modeling process expands the scope to include a multi-objective function model that seeks to optimize several critical factors simultaneously. These factors include operating costs, greenhouse gas emissions, power losses, and voltage profiles. By addressing these objectives concurrently, the model aims to create a holistic approach to energy management that prioritizes effective consumption management while also ensuring the reliability and stability of the electrical network. To solve the optimal operation of the electrical network, the paper employs an innovative approach known as EHO. This optimization technique is inspired by the social behavior of elephants and is particularly effective in navigating complex, multi-dimensional problems. The results of implementing the DRP within this intelligent electrical grid framework are promising. The demand response program not only leads to lower operational costs but also significantly reduces emissions associated with electricity generation. Additionally, the optimization process minimizes power losses and enhances the voltage profile across the network, contributing to a more stable and efficient electrical system.

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All Tables

Table 1

Total values of profit, incentive and demand reduction.

In the text

All Figures

thumbnail Fig. 1

Overview of smart electrical network.
In the text
thumbnail Fig. 2

Combined methodology for solving problem.
In the text
thumbnail Fig. 3

Participation of the consumers in DRP via demand reduction method.
In the text
thumbnail Fig. 4

Values of profit and incentives for consumers by DRP.
In the text
thumbnail Fig. 5

Power generation of resources without DRP.
In the text
thumbnail Fig. 6

Voltage of buses without DRP.
In the text
thumbnail Fig. 7

Power generation of resources without DRP.
In the text
thumbnail Fig. 8

Power losses with and without DRP.
In the text
thumbnail Fig. 9

Voltage deviation with and without DRP.
In the text
thumbnail Fig. 10

Power exchange with main grid.
In the text
thumbnail Fig. 11

Voltage of buses with DRP.
In the text

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