1 Introduction

The surge in fossil fuel consumption and rapid economic expansion have exacerbated pollutant CO2 emissions. To combat this issue and preserve fossil fuels, renewable power sources (RPSs) offer a promising alternative. RPSs harness abundant and sustainable natural energy resources that do not deplete over time, providing a viable solution to reduce carbon emissions [1, 2]. As COP26 approaches, several countries have made new commitments, detailing their contributions to the global efforts towards achieving climate goals, particularly focusing on net zero emissions targets. As per this projection, the majority of the additional electricity production capacity by 2030 will be sourced from low-emission options. Energy from wind and solar is projected to be the main contributors, with a combined annual addition of almost 500 GW. As a result, coal utilization for power production is anticipated to decrease by 20% from its recent peak by the year 2030. With the successful implementation of all the announced pledges, global CO2 emissions attributed to energy are projected to decline by 40% by the year 2050 [3].

To ensure greater reliability, energy from wind and solar, which have a volatile nature, necessitates the integration of a unit for storing excess energy, such as a BS and/or a traditional power source, like a DE. Hybrid systems offer the flexibility to function either as grid-dependent or independent modes. In remote areas where the installation of electric utility becomes economically unviable due to escalating transmission line expenses, independent systems present a more favourable and optimal alternative [4]. One of the key difficulties faced in standalone hybrid power systems (SHPSs) is the task of obtaining the most efficient design. The major goal of optimal design is to reduce the expenses of producing electricity by SHPSs while ensuring a very reliable system and minimal pollutant emissions. Several assessment criteria are employed to determine the best size of SHPSs. Among the crucial indexes are reliability indexes such as loss of power supply probability (LPSP) and economic indicators like cost of energy (COE), along with environmental criteria such as CO2 emissions [5].

SHPSs often face challenges related to low load factors, which can lead to higher energy consumption from backup sources in order to satisfy overall demand, resulting in increased costs for the entire system. One of the solutions explored to address this issue is the implementation of suitable demand response strategies (DRSs). These strategies incentivize electricity consumers to decrease their consumption during system peak hours. This demand management approach helps utilize the available energy effectively without the need for additional generation [6]. DRSs can be classified into two primary categories based on the mechanism(s) behind changes in electrical load: incentive-based strategies (IBSs), which are system-led, and price-based strategies (PBS), which are market-led. Clients are offered “rewards” through IBSs when they reduce their energy consumption during peak times. Peak load management through PBSs is accomplished by implementing flexible electricity tariffs in order to smooth the load curve and relocate less essential loads from high-demand (peak) times to lower-demand (off-peak) times [7].

Lately, numerous optimization techniques have been utilized to address energy management challenges in SHPSs, aiming to achieve an optimal design. Several instances of these optimizers include the grey wolf optimizer [8], whale optimization algorithm [9], differential evolution [10], and harmony search algorithm [11]. Table 1 displays additional optimizers that have been employed to address the sizing issues of SHPSs integrating DRSs.

Table 1 Summary of optimizers for design SHPS
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The key contributions of this study are summarized as follows:

  • Different configurations of SHPS are presented and their performance is assessed using commonly employed economic, technical, and environmental criteria.

  • Analysing different incentive payments to identify the maximum acceptable amount that would make the integration of DRS economically viable.

  • Applying a novel optimizer named “MGO,” designed to effectively address the sizing problem.

To provide an overview of the paper's structure, Sect. 2 discusses the modelling of the proposed SHPS, encompassing its components and power management strategy. Section 3 delves into the optimization problems. Section 4 is dedicated to presenting the results and subsequent discussions. Lastly, Sect. 5 concludes the paper.

2 Modelling of proposed SHPS

According to Fig. 1, the suggested SHPS comprises a PVM, WT, BS, DE, AC loads, and a bidirectional converter. The majority of SHPS commonly rely on renewable systems such as PVM and WT that produce power intermittently. To manage the intermittent nature of their generated power, these systems incorporate the BS as the primary backup to supply energy during periods of energy deficit. Additionally, a DE system serves as the final backup, providing additional power if the BS is unable to meet the load requirements. Figure 2 illustrates the concept of utilizing the BS as the primary backup due to its rapid response time and its relatively lower operational expenses when operating at low power levels [21].

Fig. 1
figure 1

Typical SHPS schematic

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Fig. 2
figure 2

Comparing the expenses associated with using BS versus DE [21]

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2.1 PV modules

The electrical energy produced by solar modules can be affected in opposite ways by changes in ambient temperature and solar radiation. Higher ambient temperatures can decrease the output energy, while increased solar radiation can increase it. To calculate the amount of electrical energy that solar modules can generate (\({S}_{{\text{PVM}}}^{t}\)), the following formula can be used [22].

$$S_{{{\text{PVM}}}}^{t} = N_{{{\text{PVM}}}} *\eta _{{{\text{PVM}}}} *S_{{R\_{\text{PVM}}}} *\frac{{R^{t} }}{{R_{N} }}\left[ {1 - \begin{array}{*{20}c} \mu \\ \end{array} \left( {\left( {T_{{\text{a}}}^{t} + \begin{array}{*{20}c} {0.034} \\ \end{array} R^{t} } \right) - T_{N} } \right)} \right],$$
(1)

where \({N}_{{\text{PVM}}}\),\({\eta }_{{\text{PVM}}}\),\({S}_{R\_{\text{PVM}}}\),\({R}_{N}\),\({R}^{t}\),\({T}_{N}\),\({T}_{{\text{a}}}^{t}\), and \(\mu\) are the total number, efficiencies, capacity, radiation under standard conditions, radiation at time t, cell temperature at standard conditions, ambient temperature, and temperature coefficient of PVMs, respectively.

2.2 Wind turbine

The real output power (\({S}_{{\text{WT}}}^{t}\)) of a wind turbine can be determined by using the typical power curve characteristics of the turbine, as shown in the following calculation [23, 24].

$$S_{{{\text{WT}}}}^{t} = \left\{ {\begin{array}{*{20}l} {0,} \hfill & {V\left( t \right)\left\langle {V_{L} {\text{or}} V\left( t \right)} \right\rangle V_{H} } \hfill \\ {\left( {N_{{{\text{WT}}}} *\eta_{{{\text{WT}}}} *S_{{R\_{\text{WT}}}} } \right)*\frac{{V^{2} \left( t \right) - V_{L}^{2} }}{{V_{R}^{2} - V_{L}^{2} }},} \hfill & {V_{L} < V\left( t \right) < V_{R} } \hfill \\ {N_{{{\text{WT}}}} *\eta_{{{\text{WT}}}} *S_{{R\_{\text{WT}}}} ,} \hfill & {V_{R} < V\left( t \right) < V_{H} } \hfill \\ \end{array} } \right.,$$
(2)

where \({N}_{{\text{WT}}}\), \({\eta }_{{\text{WT}}}\), \({S}_{R\_{\text{WT}}}\), \({V}_{R}\), \({V}_{L}\) and \({V}_{H}\) denote the total number, efficiencies, rated power, rated speed, lowest and highest wind speed limitations of WT, respectively.

2.3 Diesel engine

A diesel engine is integrated into SHPS as a source of backup power to provide electricity when there is a shortage of power that cannot be met by the WTs, PVM, and BS. The fuel consumption rate of a DE (\({F}_{C\_{\text{DE}}}^{t}\)) in L/h can be determined on an hourly basis by using the following formula [25].

$${F}_{C\_{\text{DE}}}^{t}={\gamma }_{1}*{S}_{{\text{DE}}}^{t}+{\gamma }_{2}*{S}_{R\_{\text{DE}}},$$
(3)

where \({S}_{{\text{DE}}}^{t}\) and \({S}_{R\_{\text{DE}}}\) indicate hourly generated power and rated power of DE, respectively, \({\gamma }_{1}\) and \({\gamma }_{2}\) signify fuel consumption coefficients that are approximately equal to 0.246 and 0.08415, respectively.

2.4 Battery

The purpose of BS is to retain any extra energy produced by available sustainable sources so that it can be utilized when required. If the amount of electricity provided by renewable sources exceeds the demand, the BS can be charged and used as a first backup for the SHPS, as shown by Eq. (4). On the other hand, if the demand for power is greater than what is being generated by renewable sources, the BS can be discharged to meet the demand as presented by Eq. (5) [26, 27].

$${{\text{SOC}}}^{t}={{\text{SOC}}}^{t-1}\left(1-{\beta }_{{\text{BS}}}\right)+\left[\frac{{S}_{{\text{WT}}}^{t}-{S}_{L}^{t}}{{\eta }_{C}}+{S}_{{\text{PVM}}}^{t}\right]\cdot {\eta }_{{\text{Ch}}} \left(\mathrm{Charging process}\right)$$
(4)
$${{\text{SOC}}}^{t}={{\text{SOC}}}^{t-1}\left(1-{\beta }_{{\text{BS}}}\right)-\left[\frac{{S}_{L}^{t}-{S}_{{\text{WT}}}^{t}}{{\eta }_{C}}-{S}_{{\text{PVM}}}^{t}\right]\cdot {\eta }_{{\text{DCh}}} \left(\mathrm{Discharging process}\right),$$
(5)

where \({{\text{SOC}}}^{t}\), \({{\text{SOC}}}^{t-1}\), \({\beta }_{{\text{BS}}}\), and \({S}_{L}^{t}\) are BS's state of charge at a time \(t\), \(t-1\), self-discharge rate, and load demand, respectively, \({\eta }_{C}\), \({\eta }_{{\text{Ch}}}\) and \({\eta }_{{\text{DCh}}}\) denote converter, battery charging, and discharging efficiencies, respectively.

2.5 Bidirectional converter

A bidirectional converter has the ability to transfer power in both directions simultaneously. It can serve as a rectifier, allowing for the transfer of power from the AC bus to the DC bus while supplying DC power to the DC load and charging the BS. Alternatively, it can act as an inverter, providing an interface for power transfer from the DC bus to the AC load. Depending on the peak load requirement (\({S}_{L,P}\)), the capacity of the bidirectional converter (\({S}_{R\_C}\)) has been selected as follows [28]:

$${S}_{R\_C}={S}_{L,P}\cdot {\text{SF}},$$
(6)

where \({\text{SF}}\) is the safety factor, and it's advised to have a converter capacity that's roughly 25–30% greater than the peak load.

2.6 Demand response strategy

The challenge of enhancing reliability without enlarging SHPS and incurring additional costs can be addressed by implementing DRSs. In this work, I/C strategy is applied, which is a form of IBSs, to decrease energy usage during peak hours. In this strategy, clients who plan to participate have already consented to the predetermined level of energy reduction and corresponding reward. During peak times, the amount of new load demand (\({S}_{L,{\text{new}}}^{t}\)) resulting from the I/C strategy implementation can be determined by considering the load variation factor (\({\text{LVF}}\)) as follows:

$${S}_{L,{\text{new}}}^{t}={S}_{L}^{t}\cdot \left(1-{\text{LVF}}\right)$$
(7)

2.7 Power management strategy

During peak times, the load demand is adjusted to \({S}_{L,{\text{new}}}^{t}\) using Eq. (7) when DRS is implemented, while during all other periods, the load demand \({S}_{L}^{t}\) is met entirely. In this work, the primary source for supplying electricity to the load is by utilizing renewable systems (PVM and WT). As indicated by the flowchart in Fig. 3, if the available renewable systems are capable of fulfilling the load demand entirely, any surplus energy produced will be directed towards recharging the BS. Furthermore, any excess energy beyond the required charging level will be utilized in a dummy load. In the event that the renewable systems are unable to provide sufficient energy to meet the entire load demand, the BS will discharge power to meet the remaining load. When the combination of renewable systems and a BS cannot fully meet the electricity demand, a DE operation will be initiated to compensate for any energy deficit.

Fig. 3
figure 3

Flowchart of power management strategy

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3 Optimization problem

3.1 Cost of energy

The cost of energy (\({\text{COE}}\)) is a commonly used criterion for evaluating the economic feasibility of SHPSs. It is calculated using the following formula [29]:

$${\text{COE}}=\frac{{\text{ATE}}}{{\sum }_{t=1}^{8760}{S}_{L}^{t}}$$
(8)

The annual total expense (\({\text{ATE}}\)) can be computed as follows:

$${\text{ATE}}={\text{ACE}}+{\text{ARE}}+{\text{AOME}}+{\text{ADRSE}},$$
(9)

where \({\text{ACE}},\)\({\text{ARE}}\),\({\text{AOME}},\)and \({\text{ADRSE}}\) denote the expenses annually of capital, replacement, operation and maintenance, and implementing the DRS, respectively.

$$\mathrm{Net }\begin{array}{c}\mathrm{ present }\begin{array}{c}{\text{cost}}\end{array}\begin{array}{c}\begin{array}{c}\left({\text{NPC}}\right)\end{array}\end{array}\end{array}=\frac{{\text{ATE}}}{{\text{CRF}}}$$
(10)
$${\text{CRF}}=\frac{i{\left(1+i\right)}^{{L}_{{\text{S}}}}}{{\left(1+i\right)}^{{L}_{{\text{S}}}}-1},$$
(11)

where \({\text{CRF}}\), \({L}_{{\text{S}}},\)and \(i\) represent a factor affecting capital recovery, SHPS's lifespan, and interest rate, respectively.

The expense of implementing the DRS on an annual basis (\({\text{ADRSE}}\)) can be determined using the following formula [20]:

$${\text{ADRSE}}=\left[\left({\sum }_{t=1}^{8760}{S}_{L}^{t}-{\sum }_{t=1}^{8760}{S}_{L,{\text{new}}}^{t}\right)*p\right]/{\text{CRF}},$$
(12)

where \(p\) represents the incentive payment ($/kWh) made to clients for reducing their electricity consumption.

3.2 Loss of power supply probability

In simple terms, LPSP refers to the energy deficit in relation to the total amount of power required by the load during the entire operational time. LPSP values fall within the range of 0–1, where a value of zero indicates that the load demand has been completely supplied under all circumstances, while any nonzero value implies that the demand has not been entirely met. The LPSP is calculated by the relation as follows [30]:

$${\text{LPSP}}=\frac{{\sum }_{t=1}^{8760}{\begin{array}{c}{\text{energy}}\end{array}}_{\begin{array}{c}\begin{array}{c}{\text{deficit}}\end{array}\end{array}}\begin{array}{c}\begin{array}{c}\left(t\right)\end{array}\end{array}}{{\sum }_{t=1}^{8760}{S}_{L}^{t}}$$
(13)

3.3 Pollution (CO 2 ) emissions

One of the primary objectives of this research is to evaluate carbon emissions as an environmental criterion while designing SHPS. The amount of CO2 emitted by a DE (\({{\text{PE}}}_{{\text{DE}}}\)) is directly linked to its fuel consumption through the following relationship [31]:

$${{\text{PE}}}_{{\text{DE}}}={\sum }_{t=1}^{8760}{F}_{C\_{\text{DE}}}^{t}*{F}_{{\text{E}}\_{\text{DE}}}$$
(14)

, where \({F}_{{\text{E}}\_{\text{DE}}}\) denotes the emission factor of DE and has a value of 2.64 kg/L.

3.4 Objective function

The principal objective of the SHPS design, as stated in this research, is to diminish the \({\text{COE}}\), \({{\text{PE}}}_{{\text{DE}}},\) and \({\text{LPSP}}\), which can be established in the following manner:

$${\text{OF}}={\text{min}}\begin{array}{c}\left({\psi }_{1}\cdot {\text{COE}}+{\psi }_{2}\cdot {{\text{PE}}}_{{\text{DE}}}+{\psi }_{3}\cdot {\text{LPSP}}\right)\end{array}$$
(15)

3.5 Constraints

The SHPS components must adhere to specific constraints. First and foremost, as per Eq. (16), power balance must be maintained at all times. In this study, to avoid problems related to overcharging and undercharging, the BS's capabilities are restricted, as stated in Eq. (17). In this context, the maximum SOC (\({{\text{SOC}}}_{{\text{Max}}}\)) corresponds to the BS's complete capacity, while the minimum SOC (\({{\text{SOC}}}_{{\text{Min}}}\)) signifies the BS's inability to discharge completely. Another limitation presented in this research is the maximum allowable value of LPSP, which should not exceed 5%, as indicated in Eq. (18).

$${S}_{{\text{PVM}}}^{t}+{S}_{{\text{WT}}}^{t}+{S}_{{\text{DE}}}^{t}+{S}_{{\text{BS}}}^{t}={S}_{L}^{t}$$
(16)
$${{\text{SOC}}}_{{\text{Min}}}\le {{\text{SOC}}}^{t}\le {{\text{SOC}}}_{{\text{Max}}}$$
(17)
$${\text{LPSP}}\le 5\%$$
(18)

3.6 Mountain gazelle optimizer

The mountain gazelle optimizer is a recently developed meta-heuristic algorithm that takes its cues from the social interactions and hierarchical behaviour exhibited by wild mountain gazelles [32]. The MGO is mathematically formulated by incorporating the hierarchical and societal requirements exhibited by gazelles. This optimizer employs four major facets: bachelor male herds, maternity herds, solitary territorial males, and emigration, to explore and find food resources. Each gazelle (Xi) has the ability to join one of the three previously mentioned herds. The optimal global solution corresponds to the presence of a mature male gazelle within the territory of the herd. Figure 4 provides a depiction of the optimization process, illustrating the involvement of agents in the MGO. The algorithm introduced in this proposal includes exploitation and exploration stages, which involve the execution of four parallel processes. These processes are detailed below.

  1. (i)

    1st mechanism; territorial solitary males (\({M}_{{\text{TS}}}\))

Fig. 4
figure 4

MGO optimization procedure [32]

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Highly territorial, mature male gazelles establish solitary territories. They engage in battle for territory or dominance over females. The model for their territory can be described as follows:

$${M}_{{\text{TS}}}={M}_{g}-\left|\left({R}_{i,1}\cdot {H}_{Y}-{R}_{i,2}\cdot {X}^{t}\right)\cdot f\right|\cdot {C}_{R},$$
(19)

where \({M}_{g}\) represents the position vector of the best global solution, while \({R}_{i,1}\) and \({R}_{i,2}\) denote random integers either 1 or 2. The \({H}_{Y}\) vector represents the coefficient vector for the young male herd, calculated by Eq. (20). Additionally, the value of \(f\) is calculated utilizing Eq. (21), and \({C}_{R}\) is a coefficient vector that is randomly selected and updated following each iteration, calculated by Eq. (22).

$${H}_{Y}={X}_{{\text{Ra}}}\cdot {R}_{1}+{M}_{{\text{pr}}}\cdot {R}_{2}, {\text{Ra}}=\left\{\left[N/3,...,N\right]\right\},$$
(20)

where \({X}_{{\text{Ra}}}\) signifies a solution that is randomly selected from the range of \({\text{Ra}}\), \({M}_{{\text{pr}}}\) represents the average population, which is randomly generated (\(N/3\)). Here, \(N\) indicates population size. Moreover, \({R}_{1}\) and signify two random values that fall within the range of [0, 1].

$$f={N}_{1}^{D}\cdot {\text{exp}}\left(2-t\cdot \left(\frac{2}{T}\right)\right),$$
(21)

where \({N}_{1}^{D}\) represents a random number sampled from a standard distribution. \(T\) stands for the maximum number of iterations and \(t\) refers to the current iteration.

$$C_{R} = \left\{ {\begin{array}{*{20}l} {\left( {A + 1} \right) + R_{3} } \hfill \\ {A \cdot N_{2}^{D} } \hfill \\ {R_{4}^{D} } \hfill \\ {N_{3}^{D} \cdot N_{4}^{{D^{2} }} \cdot {\text{cos}}\left( {\left( {R_{4} \cdot 2} \right) \cdot N_{3}^{D} } \right)} \hfill \\ \end{array} } \right.$$
(22)
$$A=-1+t\cdot \left(\frac{-1}{T}\right)$$
(23)

In this context, \({R}_{3}\) and \({R}_{4}\) are random numbers chosen from the range [0, 1], while \({N}_{2}\), \({N}_{3},\)and \({N}_{4}\) represent random numbers generated from a normal distribution.

  1. (ii)

    2nd mechanism; maternity herds (\({H}_{{\text{M}}}\))

The presence of maternity herds is associated with the born of robust male gazelles. This behaviour can be represented and modelled as follows:

$${H}_{{\text{M}}}=\left({H}_{Y}+{C}_{2,R}\right)+\left({R}_{i,3}\cdot {M}_{g}-{R}_{i,4}\cdot {X}_{R}\right)\cdot {C}_{3,R},$$
(24)

where \({R}_{i,3}\) and \({R}_{i,4}\) denote random integers either 1 or 2, while \({X}_{R}\) signifies the position vector randomly picked from the population.

  1. (iii)

    3rd mechanism; bachelor male herds (\({H}_{{\text{BM}}}\))

During their maturation, male gazelles actively seek out territories and female gazelles. In this pursuit, young male gazelles engage in conflicts with other males to assert control over the territory and female gazelles. This action can be represented and modelled by:

$${H}_{{\text{BM}}}=\left({X}^{t}-D\right)+\left({R}_{i,5}\cdot {M}_{g}-{R}_{i,6}\cdot {H}_{Y}\right)\cdot {C}_{R}$$
(25)
$$D=\left(\left|{X}^{t}\right|+\left|{M}_{g}\right|\right)\cdot \left(2\cdot {R}_{6}-1\right)$$
(26)

In this context, \({R}_{i,5}\) and \({R}_{i,6}\) are random integers that can take the values 2 or 1, while \({R}_{6}\) represents a uniform random number chosen from the range [0, 1].

  1. (iv)

    4th mechanism; emigration to explore and find food (\({E}_{{\text{EF}}}\))

Mountain gazelles exhibit foraging behaviour, and they are capable of travelling vast distances during emigration to access food sources. Additionally, they possess remarkable running speed and excellent jumping power. This action can be represented and modelled as:

$${E}_{{\text{EF}}}=\left({\text{Ub}}-{\text{Lb}}\right)\cdot {R}_{7}+{\text{Lb}}$$
(27)

In this context, \({\text{Ub}}\) and \({\text{Lb}}\) represent the upper and lower limits of the problem, respectively. Additionally, \({R}_{7}\) is a random integer that can take the values 0 or 1.

Each of the four processes,\({ M}_{{\text{TS}}}\), \({H}_{M}\), \({H}_{{\text{BM}}}\), and \({E}_{{\text{EF}}}\), are utilized to create new generations of mountain gazelles. At the end of each era, all-mountain gazelles are arranged in a rising pattern based on their performance. The top-performing gazelles are retained in the population for the subsequent generation, while the remaining gazelles are eliminated due to their perceived weakness.

Fig. 5
figure 5

Flowchart of the MGO

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Figure 5 depicts the flowchart of the MGO algorithm.

4 Simulation results and discussions

4.1 Study region

Ras Sudr is a town in Egypt's South Sinai Governorate that is located on the Gulf of Suez, was chosen as an actual case study of a SHPS. In the context of the case study, Fig. 6a displays the monthly variations in irradiance, ambient temperature, and speed of wind at a height of 50 m over the course of one year. Figure 6b shows the average monthly load demand over the same period [33]. Some of the SHPS component specifications are also presented in Table 2. In this research, the simulation software "MATLAB" was employed to create a model and enhance the size of a SHPS. The “MGO” optimization method was selected to address sizing challenges with a set of specific parameters, including 100 maximum iterations and 20 search agents.

Fig. 6
figure 6

a Weather data of Ras Sudr (29°35.5′N, 32°42.3334′E), and b The average monthly load demand

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Table 2 Input parameters [34]
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4.2 An optimum design of scenario i

In this study's initial scenario, a combination system is created using renewable sources such as PVM and WT, along with backup units BS and DE, without considering DRS. By comparing the proposed scenarios listed in Table 3, it is clear that the system comprising 2000 PVMs, 20 WTs, 1980 batteries, and 100 kW DE has a COE of 0.2712 $/kWh, leading to an NPC of $7,942,540.6 and an LPSP of 0.012. Figure 7 demonstrates the convergence curves of various scenarios. At 406,923 kg, the highest annual carbon emissions are observed in this case. Figure 8 illustrates that sustainable sources account for 84% of the total energy supply, with PVMs contributing 39% and WTs providing 45%. The remaining 16% is covered by DE.

Table 3 An overview of various scenario’s simulation results with an incentive payment of 0.01 $/kWh
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Fig. 7
figure 7

The convergence performance of various scenarios

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Fig. 8
figure 8

Percentage of energy produced annually by PVM, WT, and DE in various scenarios

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4.3 An optimum design of scenario ii

In this scenario, the system construction remains identical to the initial case, but with the implementation of DRS. To begin with, when LVF is set to 10%, the SHPS is comprised of 1690 PVMs, 19 WTs, 4580 batteries, and 75 kW DE. On the other hand, when LVF is increased to 30%, the hybrid system is made up of 1600 PVMs, 17 WTs, 4204 batteries, and 70 kW DE. The results indicate that scenario ii is financially more favourable compared to the case without DRS implementation. The results unambiguously show that as the LVF is raised from 10 to 30% while providing a 0.01 ($/kWh) incentive payment, SHPS becomes more cost-effective. At LVF = 10%, the COE amounts to 0.2422 $/kWh, leading to NPC of 7,093,224 and LPSP of 0.003. While, at LVF = 30%, the COE decreases to 0.2342, resulting in NPC of 6,860,664.7 and LPSP of 0.0023.

In the first scenario, the annual carbon emissions were at their highest. However, with LVF set at 10%, there was a notable reduction of 20%, bringing the emissions down to 325,687 kg. The most significant decrease occurred at LVF = 30%, where the emissions were further reduced to 307,914 kg, representing a 24% reduction compared to the initial scenario. If the LVF is 10%, renewable sources make up 85% of the overall energy supply, where PVMs contribute 37%, and WTs provide 48%. The remaining 15% is supplied by conventional energy (DE). On the other hand, when the LVF increases to 30%, renewable sources account for 84% of the total energy supply, with PVMs contributing 38% and WTs providing 46%. The remaining 16% is covered by conventional energy.

Table 4 clearly shows that increasing the incentive paid to the participants in the strategy will result in a corresponding increase in the SHPS cost. Based on the results, at LVF = 10%, incentive payments ranging from 0.01 to 0.07 $/kWh are considered acceptable for making the implementation of DRS cost-effective compared to the SHPS without DRS. On the other side, at LVF = 30%, the implementation of DRS is considered cost-effective compared to the SHPS without DRS, only when incentive payments fall within the range of 0.01–0.03 $/kWh, as highlighted by the bold values.

Table 4 Outcomes of COE impacted by different incentive payments
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4.4 An optimum design of scenario iii

The final scenario in this work shares the same system configuration as the second one, except it does not include any conventional source (DE). The results indicate that if the LVF is set at 10%, the system will have 2850 PVMs, 21 WTs, and 6495 batteries, whereas if the LVF is raised from 10 to 30%, the hybrid power system will consist of 2850 PVMs, 18 WTs, and 6421 batteries. According to the results, scenario iii with LVF = 30% stands out as the most cost-effective among all cases, exhibiting the lowest COE at 0.2334 $/kWh, resulting in NPC of 6,836,445.5 $, and demonstrating LPSP of 0.0163. While, with LVF set at 10%, the COE amounts to 0.2418 $/kWh, leading to NPC of 7,082,116.6 $, and LPSP of 0.0184.

This scenario is environmentally friendly, as it does not include any traditional sources, resulting in zero carbon emissions. When the LVF is at 10%, the energy supply is divided, with 54% comes from PVMs and 46% from WTs. However, if the LVF is increased to 30%, the energy supply is divided differently, with PVMs contributing 59% and WTs providing the remaining 41%. According to the results, at LVF = 10%, the maximum acceptable incentive payment is 0.07 $/kWh, leading to a COE of 0.2705 $/kWh for making the implementation of DRS cost-effective. On the other hand, at LVF = 30%, the implementation of DRS is considered cost-effective only when the highest incentive payment allowed is 0.03 $/kWh, resulting in a COE of 0.2621 $/kWh, as highlighted by the bold values.

In this system configuration with LVF = 30%, Fig. 9 displays the hourly fluctuations of power produced for each component. The parameters include the energy supplied by PVMs (\({S}_{{\text{PVM}}}\)) and WTs (\({S}_{{\text{WT}}}\)), as well as the charging and discharging of energy in the BS (ECh and EDch). Lastly, it illustrates the SOC of the BS represented as a percentage of the battery bank's capacity (SOC %). Figure 10 depicts the results of the most cost-effective scenario (at LVF = 30%), specifically highlighting a particular day during the year (e.g., spanning from time 7656 to 7680). The daily load profile shows peak periods occurring between time 7670 and 7678. During these periods, a DRS is implemented, leading to a 30% reduction in the load. SDif represents the power gap between the energy needed for demand and the energy supplied by renewable sources. During the nighttime and early morning hours, no power is generated from PVMs. Consequently, the BS discharges to fulfil the power demand during these periods. When the sun comes up in the morning, the PVMs start generating more electricity, leading to the BS being charged by surplus energy.

Fig. 9
figure 9

Results of the simulation of the best solution identified in scenario iii with LVF = 30% for a year of operation (equal to 8760 h)

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Fig. 10
figure 10

Simulation results for a particular day of operation, spanning from 7656 to 7680 hour, under scenario iii with LVF of 30%

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5 Conclusion

This research paper focuses on the size optimization of different configurations under the influence of a DRS (I/C type). In a remote area of Egypt situated on the Gulf of Suez, SHPS comprising PVMs, WTs, BS, and conventional source of DE was utilized to provide power to the loads. The study employs the modern optimizer “MGO” to attain the technical, environmental, and economic goals of the SHPS. The results demonstrate that scenario iii (with LVF of 30%) is the most economically efficient one. It has the lowest COE of 0.2334 $/kWh and NPC of 6,836,445.5 $ among all the scenarios examined. This case leads to a 14% reduction in costs compared to the first scenario that was looked at. The last scenario is the most eco-friendly choice and avoids any carbon footprint (100% clean energy configuration). In this work, various incentive payment options are examined to determine the highest acceptable amount that would render the implementation of DRS economically viable. The results indicate that rewards between 0.01 and 0.07 $/kWh are deemed suitable for making the incorporation of DRS economically feasible compared to SHPS without DRS, when LVF is at 10%. However, when LVF is at 30%, DRS implementation is deemed cost-effective only if incentives fall within the range of 0.01–0.03 $/kWh. Future studies could incorporate various demand response strategies, along with an in-depth examination of their impact on hybrid system performance and a comprehensive analysis of their economic viability.