Numéro
Sci. Tech. Energ. Transition
Volume 79, 2024
Decarbonizing Energy Systems: Smart Grid and Renewable Technologies
Numéro d'article 88
Nombre de pages 10
DOI https://doi.org/10.2516/stet/2024089
Publié en ligne 30 octobre 2024

© The Author(s), published by EDP Sciences, 2024

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.

Nomenclature

Indices

tT : Time

nN : EG

mM : Consumers

i, J, Λ: Bus

Parameters

A, B, C : Fuel cost factors of EGs

CSU, CSD: Cost sharing up and down for EGs

UP, DP : Ramp up and ramp down for EGs

UT, DT : Up and down time for EGs

Δ: Level of participation IN shifting demand

ξpr: Prices offered for demand reduction

D, QD : Active and reactive demand of consumers

Vref: Voltage references

Decision variables

C N : EG’s cost

CDR: Demand reduction’s cost

P n : EG’s power

VΛ: Voltage index

λ : Status of the demand reduction (Binary variable)

kDR, wDR: Status of the starting and ending times for demand reduction (Binary variable)

α Off, α On : Status of the EG’s in off and on modes (Binary variable)

1 Introduction

1.1 Motivations and background

Smart grid management involves utilizing cutting-edge technologies and data analysis to enhance the efficiency of electricity distribution and usage [1]. This involves real-time monitoring of electricity demand patterns, integrating renewable energy sources, and employing predictive algorithms to forecast demand fluctuations [2, 3]. By leveraging artificial intelligence, grid operators can make informed decisions to balance supply and demand, reduce outages, and enhance the overall reliability of the electricity grid [4, 5]. This proactive strategy does not just enhance effectiveness but also promotes the shift towards a more sustainable energy system. Smart grid solutions encompass a range of technologies and systems designed to improve the efficiency of electricity consumption [68]. These options consist of smart meters, demand response initiatives, and automated energy management systems that give consumers the ability to oversee and regulate their energy consumption instantly. By providing users with detailed insights into their consumption patterns, smart grid technologies encourage energy conservation and enable dynamic pricing models that incentivize off-peak usage. Additionally, these solutions facilitate better integration of energy resources in the grid [9, 10]. The Demand Side Management (DSM) involves sophisticated strategies and tools to optimize electricity usage across the grid. This involves the utilization of demand response, enabling consumers to modify their energy usage in peak times for monetary rewards. Smart grids utilize real-time data analytics to identify peak demand times and communicate with consumers and businesses to reduce load [1114]. Furthermore, DSM can incorporate automated systems that adjust energy usage based on grid conditions, ensuring a more balanced and efficient energy distribution while minimizing the need for additional generation capacity [15, 16]. Smart grid technology plays a crucial role in controlling electricity demand by enabling real-time communication between utilities and consumers. Through the use of smart meters and advanced metering infrastructure, utilities can monitor consumption patterns and implement demand response strategies effectively [17, 18]. This technology allows for the dynamic adjustment of electricity prices based on demand, encouraging consumers to shift their usage to off-peak times [1922]. Additionally, smart grid systems can automatically manage loads by temporarily reducing power to non-essential devices during peak demand periods, thereby preventing grid overload and enhancing overall system stability [2328].

In Figure 1, the proposed electrical grid in off-mode is shown, in which electrical generators (EGs), operators and consumers are cooperated based on exchange data for optimal energy dispatch in the system.

thumbnail Fig. 1

Proposed electrical grid in off-mode.

1.2 Previous researches and contributions

Some previous studies are examined in this section. Authors in [29] presented resources to design and sit in an electrical system by long-term planning for minimising costs in the system. In [30] modeling control system is proposed for voltage regulation in off-grid systems via an oscillations damping mechanism. In [31] installing storage systems in off-grid systems is proposed for voltage control and load-shedding management via optimal generation in peak demand. The power dispatch in electrical systems by electric vehicles in parking lots is proposed in [32] to improve reliability and reduce costs. The author in [33] power management of electrical systems considers economic and environmental issues studied via optimal siting and load dispatch strategy. In [34] energy management is implemented for efficiency improvement and cost reduction in the off-smart grid in homes via optimal operation of the generation side. The local power generation in the off-grid system by renewable energy resources is presented in [35] via optimal sizing and siting. The multiple modelling of energy systems by design approaches of resources with consideration of environmental, reliability and economic indices is done in [36]. The configuration modelling of electrical grids is proposed in [37] for improving reliability and reducing power losses. The uncertainty modelling of electrical systems considering load demand and power production by renewable energies is implemented in [38]. In [39] planning of multiple energy systems for improving the performance of electrical systems through optimal cooperation is proposed. In [40] scheduling model of electrical systems by HOMER software for optimal siting and design of resources is proposed. In [41] hydrogen storage systems and parking lots of electrical cars are proposed for the optimal operation of electrical systems in the critical status of system.

This paper presents a day-ahead power scheduling strategy specifically designed for off-grid electrical systems, emphasizing the critical role of consumer participation in the energy management process. The study recognizes that active involvement from consumers can lead to more efficient energy usage and improved system performance. To facilitate this engagement, the research proposes innovative bi-DSM techniques, which include strategic conversion and demand shifting. These techniques are aimed at encouraging consumers to adjust their energy consumption patterns, thereby enhancing their participation. To systematically address the challenges associated with power scheduling, a multi-objective optimization model is developed. This model focuses on two primary objectives: improving voltage profiles within the electrical system and minimizing operational energy costs. By optimizing these two aspects, the research aims to create a more reliable and cost-effective energy supply for off-grid systems. To solve the optimization problem, the enhanced epsilon-constraint method is employed. This method is particularly effective in generating non-dominated solutions, allowing for the simultaneous consideration of both voltage profile improvements and operational energy cost reductions. By utilizing this approach, the research ensures that trade-offs between the two objectives are effectively managed, leading to a more balanced and efficient power scheduling strategy. The General Algebraic Modeling System (GAMS) software is recommended as a powerful tool for addressing the optimization challenges presented in this research. GAMS provides a robust platform for formulating and solving complex mathematical models, making it an ideal choice for the proposed multi-objective optimization framework. In addition to the optimization techniques, the research incorporates a blend of decision-making approaches, including weight sum and fuzzy methods. These approaches are utilized to identify the optimal non-dominated solutions from the set of potential outcomes generated by the optimization process. By integrating these decision-making strategies, the research enhances the robustness of the solution selection process, ensuring that the chosen solutions align with the preferences and priorities of stakeholders. To validate the effectiveness of the proposed approach, numerical simulations are conducted on various case studies, specifically focusing on the electrical system. These simulations provide empirical evidence of the impact of demand-side participation on optimizing power dispatch. The results demonstrate that consumer engagement significantly contributes to achieving multiple objectives, such as improved voltage stability and reduced operational costs. Overall, this research underscores the importance of consumer participation in off-grid electrical systems and presents a well-structured framework for day-ahead power scheduling. By leveraging advanced optimization techniques and decision-making methods, the study offers valuable insights into how DSM can enhance the efficiency and reliability of off-grid energy systems.

2 Bi-DSM approaches modelling

The Bi-DSM approaches modelling as load-shifting and load reduction methods are formulated as follows [4245]:

The load-shifting method is formulated by equations (1)(2) as follows: D ( t ) = t ' m = 1 M D ( t ' , t ) - i m = 1 M D ( t , t ' ) m , t $$ \begin{array}{cc}D(t)=\sum_{{t}^{\prime}^{}\sum_{m=1}^MD({t}^{\prime},t)-\sum_i^{}\sum_{m=1}^MD(t,{t}^{\prime})& \forall m,t\end{array} $$(1) 0 t ' m = 1 M D ( t , t ' ) Δ × m = 1 M D ( t ) m , t . $$ \begin{array}{cc}0\le \sum_{{t}^{\prime}^{}\sum_{m=1}^MD(t,{t}^{\prime})\le \Delta \times \sum_{m=1}^MD(t)& \forall m,t\end{array}. $$(2)

And load-reduction method is formulated by equations (3)(5) as follows: C DR = m = 1 M t = 1 T ξ pr × D ( t ) × λ ( t ) m $$ \begin{array}{cc}{C}_{\mathrm{DR}}=\sum_{m=1}^M\sum_{t=1}^T{\xi }_{\mathrm{pr}}\times D(t)\times \lambda (t)& \forall m\end{array} $$(3) k DR ( t ) - w DR ( t ) = λ ( t ) - λ ( t - 1 ) m , t $$ \begin{array}{cc}{k}_{\mathrm{DR}}(t)-{w}_{\mathrm{DR}}(t)=\lambda (t)-\lambda (t-1)& \forall m\end{array},t $$(4) k DR ( t ) + w DR ( t ) 1 m , t . $$ \begin{array}{cc}{k}_{\mathrm{DR}}(t)+{w}_{\mathrm{DR}}(t)\le 1& \forall m\end{array},{t}. $$(5)

3 Multiple objectives model

The multiple objectives are modelled considering minimizing operation costs and voltage profile improvement as follows:

3.1 Operation cost objective

The operation cost modelling is computed considering costs of demand reduction and EG units as follows: min f EO = t = 1 T [ n = 1 N C N ( t , N ) + C DR ( t ) ] $$ \mathrm{min}{f}_{\mathrm{EO}}=\sum_{t=1}^T\left[\sum_{n=1}^N{C}_N\left(t,N\right)+{C}_{\mathrm{DR}}(t)\right] $$(6)

where, C N ( N , d ) = { AP n 2 ( t , N ) + BP n ( t , N ) + C } + { C SU × α on ( t ,   N ) } + { C SD × α off ( t ,   N ) } . $$ {C}_N\left(N,d\right)=\left\{{{AP}}_n^2\left(t,N\right)+{{BP}}_n\left(t,N\right)+C\right\}+\left\{{C}_{\mathrm{SU}}\times {\alpha }^{\mathrm{on}}\left(t,\enspace N\right)\right\}+\left\{{C}_{\mathrm{SD}}\times {\alpha }^{\mathrm{off}}\left(t,\enspace N\right)\right\}. $$(7)

3.2 Voltage profile model

The voltage profile improvement is computed as follows: min f TO = t = 1 T | i , j Λ N V Λ ( t , Λ ) - V ref | . $$ \mathrm{min}{f}_{\mathrm{TO}}=\sum_{t=1}^T\left|\sum_{i,j\in \mathrm{\Lambda }}^N{V}_{\mathrm{\Lambda }}\left(t,\mathrm{\Lambda }\right)-{V}_{\mathrm{ref}}\right|. $$(8)

4 Constraints model

4.1 Power balance constraint

The power balance constraint is modelled for active and reactive powers as follows: n = 1 N P n ( t , N ) - D ( t , M ) = i , j Λ V i ( t , i ) × V j ( t , j ) × Y i , j × cos [ θ i , j + δ j ( t , j ) - δ i ( t , i ) ] t , Λ $$ \begin{array}{cc}\sum_{n=1}^N{P}_n\left(t,N\right)-D(t,M)=\sum_{i,j\in \mathrm{\Lambda }}^{}{V}_i\left(t,i\right)\times {V}_j\left(t,j\right)\times {Y}_{i,j}\times \mathrm{cos}\left[{\theta }_{i,j}+{\delta }_j\left(t,j\right)-{\delta }_i(t,i)\right]& \forall t,\mathrm{\Lambda }\end{array} $$(9) n = 1 N Q n ( t , N ) - QD ( t , M ) = i , j Λ V i ( s , t , i ) × V j ( s , t , j ) × Y i , j × sin [ θ i , j + δ j ( s , t , j ) - δ i ( s , t , i ) ] s , t , Λ . $$ \begin{array}{cc}\sum_{n=1}^N{Q}_n\left(t,N\right)-{QD}(t,M)=\sum_{i,j\in \mathrm{\Lambda }}^{}{V}_i\left(s,t,i\right)\times {V}_j\left(s,t,j\right)\times {Y}_{i,j}\times \mathrm{sin}\left[{\theta }_{i,j}+{\delta }_j\left(s,t,j\right)-{\delta }_i(s,t,i)\right]& \forall s,t,\mathrm{\Lambda }\end{array}. $$(10)

4.2 Voltage constraint

The constraint of the voltage profile is modelled by (11): V Λ min V Λ ( s , t , Λ ) V Λ max s , t , Λ . $$ \begin{array}{cc}{V}_{\mathrm{\Lambda }}^{\mathrm{min}}\le {V}_{\mathrm{\Lambda }}(s,t,\mathrm{\Lambda })\le {V}_{\mathrm{\Lambda }}^{\mathrm{max}}& \forall s,t,\mathrm{\Lambda }\end{array}. $$(11)

4.3 EG constraints

The EGs have various technical constraints, including power generation limits, ramp-up and down rates, and minimum up and down times. These constraints are as follows: P N min P N ( t , N ) P N max t , Λ $$ \begin{array}{cc}{P}_N^{\mathrm{min}}\le {P}_N(t,N)\le {P}_N^{\mathrm{max}}& \forall t,\mathrm{\Lambda }\end{array} $$(12) P N ( t , N ) - P N ( t - 1 , N ) UP t , N $$ \begin{array}{cc}{P}_N\left(t,N\right)-{P}_N(t-1,N)\le {UP}& \forall t,N\end{array} $$(13) P N ( t - 1 , N ) - P N ( t , N ) DP t , N $$ \begin{array}{cc}{P}_N\left(t-1,N\right)-{P}_N(t,N)\le {DP}& \forall t,N\end{array} $$(14) α On ( t , N ) + τ = T + 1 min ( T , t - 1 + UT ) α Off ( τ , N ) 1 t , N $$ \begin{array}{cc}{\alpha }^{\mathrm{On}}\left(t,N\right)+\sum_{\tau =T+1}^{\mathrm{min}(T,t-1+{UT})}{\alpha }^{\mathrm{Off}}(\tau,N)\le 1& \forall t,N\end{array} $$(15) α Off ( t , N ) + τ = T + 1 min ( T , t - 1 + DT ) α On ( τ , N ) 1 t , N . $$ \begin{array}{cc}{\alpha }^{\mathrm{Off}}\left(t,N\right)+\sum_{\tau =T+1}^{\mathrm{min}(T,t-1+{DT})}{\alpha }^{\mathrm{On}}(\tau,N)\le 1& \forall t,N\end{array}. $$(16)

5 Solution method

The solution method for handling and solving multiple objective problems is done by enhanced epsilon-constraint technique with the mathematical formulation as follows [46]: min [   f 1 ( x ) - δ n = 1 N s n r n   ] 10 - 6 δ 10 - 3 . $$ \begin{array}{cc}\mathrm{min}\left[\enspace {f}_1(x)-\delta \sum_{n=1}^N\frac{{s}_n}{{r}_n}\enspace \right]& {10}^{-6}\le \delta {\le 10}^{-3}\end{array}. $$(17)

Subject to: f n ( x ) + s n + ε n z n = 2,3 , ,   N ; s n R + . $$ \begin{array}{cc}{f}_n(x)+{s}_n+{\epsilon }_n^z& n=\mathrm{2,3},\dots,\enspace N;{s}_n\in {R}^{+}\end{array}. $$

And: ε n z = f n max - [ f n max - f n min q n - 1 ] × z z = 0,1 , ,   q n . $$ \begin{array}{cc}{\epsilon }_n^z={f}_n^{\mathrm{max}}-\left[\frac{{f}_n^{\mathrm{max}}-{f}_n^{\mathrm{min}}}{{q}_n-1}\right]\times z& z=\mathrm{0,1},\dots,\enspace {q}_n\end{array}. $$(18)

Where:

n = nth objective function.

δ = Slack variable.

x = Decision variable.

q n  = Equal range.

ε n z $ {\epsilon }_n^z$ = zth interval of nth objective.

r n = Objectives range.

5.1 Decision-making modeling

In this section, the optimal solution of the voltage and operation cost in multiple objectives is obtained by weight sum and fuzzy methods as a decision-making approach. The generated non-dominated solutions of voltage and operation cost are normalized by the fuzzy method in equation (19). Then, the optimal solution is achieved by the weight sum method in equation (20) [47]: ϑ n m = { 1 f n m f n min f n max - f n m 1 f n min f n m f n max 0 f n m f n max $$ {\vartheta }_n^m=\left\{\begin{array}{cc}1& {f}_n^m\le {f}_n^{\mathrm{min}}\\ \frac{{f}_n^{\mathrm{max}}-{f}_n^{\mathrm{m}}}{1}& {f}_n^{\mathrm{min}}\le {f}_n^m\le {f}_n^{\mathrm{max}}\\ 0& {f}_n^m\ge {f}_n^{\mathrm{max}}\end{array}\right. $$(19) ϑ n m = n = 1 N ω n ϑ n m m = 1 M i = 1 I ω n ϑ n m n = 1 N ω n = 1 ω n 0 . $$ \begin{array}{ccc}{\vartheta }_n^m=\frac{\sum_{n=1}^N{\omega }_n{\vartheta }_n^m}{\sum_{m=1}^M\sum_{i=1}^I{\omega }_n{\vartheta }_n^m}& \sum_{n=1}^N{\omega }_n=1& {\omega }_n\ge 0\end{array}. $$(20)

Where:

f n m $ {f}_n^m$ = Membership function of objectives.

ϑ n m $ {\vartheta }_n^m$ = Quantity of objectives.

6 Case studies

The proposed multiple objective optimisations are confirmed in this section via case studies considering the implementation and non-implemention of DSM in an electrical grid in off-grid mode. The case studies are expressed in Table 1.

Table 1

Cases in this paper.

Figure 2, shows an electrical grid in off-grid mode as a 33-bus system. The DICOPT solver and mixed integer non-linear program (MINLP) are used for solving proposed optimisation in GAMS software.

thumbnail Fig. 2

Electrical grid in off-grid mode.

In Figure 3, the contract between the operator and consumers for the load-reduction method is shown. The information on systems like EGs, load demand and level of participation in load shifting are extracted from references [4851]. The voltage reference is 1 pu and all consumers participate in DSM.

thumbnail Fig. 3

Contract among operators and consumers for load-reduction method.

6.1 Results

The results of optimisation considering case studies are analyzed in this section. The proposed day-ahead power scheduling without and with considering DSM in cases 1 and 2 are examined, respectively.

In Figure 4, results and solutions of multiple objectives in case 1 for voltage and operation cost are shown. The solutions are generated by enhanced epsilon-constraint and by using weight sum and fuzzy methods; the optimal solution is determined in red colour in Figure 4. The voltage profile and operation cost are 8.8 pu and $3233.3 in the optimal solution, respectively.

thumbnail Fig. 4

Determined optimal solution in Case 1.

Also, the value of the voltage of buses in the 33-bus system is depicted in Figure 5. The voltage index at bus 18 is experiencing a significant drop, attributed to peak consumption levels and the extended length of the power lines required to meet demand.

thumbnail Fig 5

Voltage of buses in electrical grid in Case 1.

Figure 6 illustrates the power produced by the EGs. It is evident that EG 1 generates less power than other EGs, primarily because of the high cost of fuel.

thumbnail Fig 6

EGs’ power generated in Case 1.

On the other side, DSM is implemented in case 2. In Figure 7, the implementation of DSM with load shifting and load reduction is shown. By using DSM, load demand with DSM in some hours is more than the original demand. This reaction is due to the implementation of load-shifting method. The solutions of multiple objectives in case 2 for voltage and operation cost are shown in Figure 8. The voltage profile and operation cost are equal to 7.6 pu and $2965.3 in the optimal solution, respectively.

thumbnail Fig 7

Implememtion of DSM in Case 2.

thumbnail Fig 8

Determined optimal solution in Case 2.

By using DSM, operation cost is reduced by 21.58% and voltage index is improved by 13.36% than case 1, respectively.

Figure 9 shows the voltage of buses for Case 2. Optimal consumption by DSM during peak hours enhances the improvement of voltage buses’ deviation from the reference voltage. Figure 10 shows how DSM helps optimize the production of EGs during peak demand, resulting in decreased costs for power flow and EGs.

thumbnail Fig. 9

Voltage of buses in electrical grid in Case 2.

thumbnail Fig. 10

EGs’ power generated in Case 2.

7 Conclusions

This research presented scheduling power for electrical systems in off-grid mode a day in advance, with a focus on engaging consumers. Strategic conversion and demand shifting are suggested for consumer engagement in DSM strategies. A model with multiple goals is created to enhance the voltage profile and lower the operational energy expenses. Enhanced epsilon-constraint technique generates non-dominated solutions for voltage profile and operation energy cost simultaneously. The GAMS software is suggested for resolving optimization issues. Weight sum and fuzzy procedures are used together to discover the best non-dominated solutions through decision-making techniques. The results demonstrate the significant impact of demand-side involvement in enhancing power scheduling and achieving the best possible outcome for several goals.

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All Tables

Table 1

Cases in this paper.

All Figures

thumbnail Fig. 1

Proposed electrical grid in off-mode.

In the text
thumbnail Fig. 2

Electrical grid in off-grid mode.

In the text
thumbnail Fig. 3

Contract among operators and consumers for load-reduction method.

In the text
thumbnail Fig. 4

Determined optimal solution in Case 1.

In the text
thumbnail Fig 5

Voltage of buses in electrical grid in Case 1.

In the text
thumbnail Fig 6

EGs’ power generated in Case 1.

In the text
thumbnail Fig 7

Implememtion of DSM in Case 2.

In the text
thumbnail Fig 8

Determined optimal solution in Case 2.

In the text
thumbnail Fig. 9

Voltage of buses in electrical grid in Case 2.

In the text
thumbnail Fig. 10

EGs’ power generated in Case 2.

In the text

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