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

1 Introduction

Generating and utilising electrical energy are essential for the functioning of modern society. Optimising Economic Load Dispatch (ELD) in the power system is crucial for minimising power generation costs while meeting operational needs, especially with thermal power being the primary source currently. When dealing with typical issues related to ELD, the cost functions of generators are usually estimated using quadratic functions. When the load requirement is spread across multiple generators and several other processes. The author of the paper [1] introduced an innovative optimisation approach for renewable energy arrangements in microgrids. An approach for multi-objective optimisation is developed for a diesel, wind, PV, and battery-based hybrid system. The primary goals are to reduce energy costs and power supply losses. The research in [2] compared and evaluated eight different metaheuristic approaches to optimise the size of a hydrogen storage-equipped microgrid. The goal is to minimise the cost of microgrids and maintain control over the energy flow within the system. The author of the paper [3] developed a distributed optimisation algorithm to reduce the total cost in a Dynamic Economic Dispatch Problem (DEDP). The research paper [4] has delved into an optimisation strategy of microgrid dispatching, taking into account the random fluctuations of renewable energy supplies and load demands. The author of the paper [5] introduced an innovative two-stage two-layer optimisation method to reduce the overall operation cost of a Microgrid facing significant uncertainties in load demand, generation and scheduled outages. The research work [6] focused on optimising the energy production of a microgrid to meet demand, reduce CO₂ emissions, and minimise operating costs. The researcher [7] discussed the increased operation cost of the generating units and electricity purchase cost in microgrids. A strategy for managing energy in Multi-MicroGrid (MMG) systems was proposed in a study [8]. This approach optimises the use of distributed resources, renewable energy, and plug-in electric vehicles, resulting in favourable results for both the economy and the environment. Examining a case study of a rural community in Nigeria, the study in [9] explored ways to enhance the performance of an isolated solar/battery microgrid to meet the increasing load requirements of a proposed solar/wind/diesel/battery microgrid. Researchers in [10] explore the optimal power flow problem, offering a range of traditional and cutting-edge metaheuristic optimisation methods for microgrid economic dispatch. Research in [11] focused on microgrids powered by renewable energy sources such as wind turbines, solar cells, and hydrogen storage devices. Addressing the variability of renewable energy sources, a novel energy management approach has been developed utilising hydrogen storage. Considering load supply constraints, this approach aims to reduce the operating costs of hydrogen storage systems and batteries, along with expenses related to surplus and unsupplied energy. In their research, the authors [12] analysed the microgrid system holistically, considering renewable power, energy storage, and load as integral components. To efficiently manage the network source, storage of the microgrid and load, they proposed an optimisation approach using a master-slave game. Minimising overall operational expenses is the goal of the master in this microgrid game. In order to manage energy from several renewable sources, the authors of article [13] proposed a stochastic programming model based on an upgraded slime mould algorithm with multiple objectives. This method is expected to improve the microgrid’s performance. In [14], using digital twins of wind and solar units, researchers examined how a utility-driven variable load shaping method affects non-dispatchable energy sources in renewable microgrids. For network-coupled microgrids, they suggested a three-stage stochastic architecture that would optimise day-ahead planning while minimising operating costs. Using Demand Side Management (DSM) and a hybrid intelligence approach, the authors of [15] reduced the total price of three microgrid structures. The unit commitment of dispatchable fossil fuel generators is one of the practical difficulties that they solve. A probabilistic energy modelling technique for large-scale customers was created in the research reported in [16]. This approach took into account microturbine, renewable energy sources, energy storage devices, and power exchange-based bilateral contracts. Big businesses stood to gain the most from a reduction in the price of energy storage, demand-side management, and related technologies. The study in [17] concentrated on optimising multi-timescale Control Mechanism for Energy System (CMES) management at energy and power levels while taking into account source-load interaction. The researcher in [18] implemented a shifting strategy based on classifying loads into high priority and low priority. Calculating the sizing of components for an autonomous rural mini-grid across four load groups and load elasticity using particle swarm optimisation. Within the scope of the study presented in [19–21], researchers have implemented two changes, specifically opposition theory and sine cosine-based position update mechanism, to boost the exploration and exploitation capabilities of the Slime Mould Algorithm (SMA), which was recently established. The study presents a cost-emissions operated dynamic economic dispatch (MOCEDED) algorithm that accounts for thermal, wind and solar-producing facilities [22]. The programme also accounts for the fact that solar and wind power curtailment is unpredictable. A coordinated decision-making technique was used in the research [23], which included making lower-level investment decisions with operational uncertainty using a two-objective stochastic programming formulation. Considering demand responses and daily optimal operation, the proposed model is solved on a three-bus grid that incorporates smart microgrids with Distributed Energy Resources (DERs) on each bus. To report the ED issue in microgrids, the authors of the article [24] proposed a data-driven NN approach. To better grasp the spatio-temporal characteristics of renewable and conventional electricity, together with intermittency difficulties, a two-stage training approach is introduced. An improved method for creating an integrated power management system is described in the study article [25] by combining particle swarm optimisation with simplex-based linear programming. Assuming a smart city’s consumption profile allows for energy scheduling to be carried out. A Demand Response (DR) model for DSM in a smart grid should be developed, according to the researcher’s recommendation in the article [26], using Dynamic Pricing (DP). The proposed DR model has the potential to change peak energy demand, which would improve the dependability and constancy of the power system. An integrated Demand Response Programme (DRP) for grid-connected MMGs was detailed in the article [27] together with the Dynamic Optimal Power Flow (DOPF) with and without an energy source interruption. By factoring in the intuitive characteristics of different phases, the overall cost throughout the whole duration is kept to a minimum. Theoretically, the authors of the paper [28] combine the greatest advantages of the freshly developed Grey Wolf Optimizer (GWO), the Sine Cosine technique (SCA), and the Crow Search Algorithm (CSA) to produce a novel hybrid approach. In order to solve the verified benchmark functions of the IEEE CEC-C06 2019 conference, this work introduces a novel hybrid Variegated GWO Algorithm (VGWO). Combining the crow search approach with the teaching and learning optimisation algorithms, the research [29] suggested a teaching-learning crow search algorithm to solve the two-layer optimisation model. Microgrids are operated economically by using the two-layer optimisation model and the suggested approach, according to the results of the simulations. The article [30] further into how MGs may make the most of energy trading on both the internal and external markets, including utility grid exchanges. In their efforts to provide a new paradigm for microgrids, the researchers of the study [31] made an effort. By merging Emperor Penguin Optimizer (EPO) with Glowworm Swarm Optimisation (GSO), a new method called Hybrid Emperor Penguin Glowworm Swarm Optimisation (HEPGSO) is developed here. Costs associated with energy supply, Diesel Generators (DGs), power loss, and voltage variations may all be decreased using the techno-economical method. A Demand-Side Management (DSM) strategy for Automatic Control of Energy System (ICES) is laid out in the article [32]. The first step in determining the efficiency of energy conversion in response to variations in load rate is to build a dynamic ER model. A pricing strategy that takes into account both renewable energy output and load demand in real time is proposed for DR in the context of renewable energy production. For the best possible size and placement of electric vehicle charging stations, the research paper [33] offered an uncertainty-based optimisation methodology that is based on robust optimisation and a scenario approach. By reducing power losses and offering energy market services, the proposed method hopes to reap the benefits of Electrical Vehicles Control System’s (EVCS) adaptability. In [34], the author examined how a grid-connected microgrid handles Energy Storage Systems (ESS) and variations in renewable power generation in relation to reducing greenhouse gas emissions. The research study [33] presented a bilevel optimisation paradigm that helps a big Load Management for Energy Center (LMEC) that uses its own energy resources to satisfy its power, heating, and cooling needs while also optimising the price of electricity on the market. The article [35] detailed how demand-side management came to be to save operational costs and dispatch power optimally. To compensate for renewable energy’s unreliability, the microgrid is coupled to the national gas grid. A study paper [36] introduced a microgrid energy management scheme based on Interactive Class Topping Optimisation (I-CTO) that considers several parameters, including renewable energy sources, demand side management, battery storage systems, and interconnections. To limit generation and emission costs, the proposed technique aims to efficiently organise varied energy sources in the microgrid. Finding the best spot for Fault Control Systems (FCS) by using the East Delta Network (EDN) was outlined practically in the paper [37]. Changes to the electrical distribution network’s infrastructure may be necessary when transportation is powered by electricity. Within the framework of price-based DRP, the study article [38] put up a novel problem for MG energy management. Improving operating costs for DG units and utility power exchange prices are studied in relation to variable pricing elasticity. An optimal economic dispatch for a grid-connected microgrid is presented in the article [39]. Wind, diesel, and solar photovoltaics are the power sources for the microgrid. A demand response plan based on incentives is used to run the grid-connected microgrid. To address both the issue of low generation costs and the pollution produced by DERs in an LV grid-connected microgrid system, the researcher in [40] suggested a DSM method that relies on a hybrid intelligence technique. To reduce operational costs, the article [41] employed bi-level optimisation. This study made use of a novel hybrid swarm intelligence algorithm that has proven useful for several optimisation problems in the past; the technique was developed for the optimisation of power systems. To overcome the limitations of the original weighted mean of vectors methodology, such as being stuck in a local optimum, the researcher in [42] proposed a new method called LINFO to improve the search capabilities. The research paper [43] discussed MMG energy management by introducing and implementing a modified Capuchin Search Algorithm (MCapSA). As a multi-objective function, the optimised function takes stability, voltage fluctuation, and cost into account. Optimal microgrid performance is evaluated in the research publication [44] about charging Plug-in Hybrid Electric Vehicles (PHEVs). To assess the behaviour of PHEVs, three different charging patterns are considered: uncontrolled, regulated, and smart. By combining renewable power sources like wind and solar with Electrical Energy Storage (EES) devices, the article [45] outlined a two-tiered system for regulating microgrids’ energy usage for the next day. The novel contribution of the present work listed below bridges the research gap developed by the extensive analysis of recently published literature on the optimal economic operation of microgrid systems:

• (a)

  Two different types of Incentive-Based Demand Response (IBDR) policies, one which compensates the customer only and the other which compensates both the customer and DIStribution COmpany (DISCO), are employed for the economic operation of a microgrid system

• (b)

  A comparative analysis between the IBDR policies was done to mark the efficient & economic approach.

• (c)

  A recently developed Circle Search Algorithm (CSA) was implemented as the optimization tool and the results were compared with several other metaheuristic algorithms available in the literature concerning the microgrid system.

2 Objective function formulation

The aim of this study is formulated is as follows:

2.1 For DG units cost based fitness function

Fossil-fuelled generators often use a quadratic equation to illustrate their cost function. The complete equation of the cost function is presented below:$$\mathrm{Cos}{\mathrm{t}}_{\mathrm{DG}}=\sum _{t=1}^{24}\left[\sum _{i=1}^n{(x}_i{P}_{i,t}^2+y_i{P}_{i,t}+z_i)+C_{\mathrm{grind},t},P_{\mathrm{grind},\mathrm{t}}\right].$$(1)

C_grid stands for the Time-Of-Use (TOU) price of power, where x, y, and z are the ith generator’s cost factors. The output power of the ith generator is represented by P_i , whereas the P_grid is the power generated by the grid. An essential limitation for fossil-fueled generators, the valve-point effect requires adjusting valves to manage the flow of electricity; this is included in (2) of the dispatch issue.$$\mathrm{Cos}{\mathrm{t}}_{\mathrm{DG}}=\sum _{t=1}^{24}\sum _{i=1}^n{(x}_i{P}_{i,t}^2+y_i{P}_{i,t}+z_i +|m_i\times \sin \left(n_i\right(P_{i,\min }-P_{i,t})|\left)\right).$$(2)

P_i is the power of the ith unit. While x_i , y_i , and z_i are the ith generator’s cost coefficients, m_i and n_i are the valve point effect coefficients.

2.2 Constraints

All time indices must have their scheduled loads met, taking inequality constraints into account. The primary goal of the operation is to lessen the financial burden of meeting the load demand from DGs, wind generation, and the grid. The equality constraints that do not take wind generation into account are given by equation (3) while those that do so are given by equation (4) [46].$$\sum _{i=1}^n{P}_i^t+P_G^t=P_{\mathrm{load}}^t$$(3) $$\sum _{i=1}^n{P}_i^t+P_G^t+P_W^t=P_{\mathrm{load}}^t$$(4)

To satisfy the power demand, both the grid and DGs need to deliver electricity within their specified capacities, as illustrated below:$$P_{j,\min }\le P_j\le P_{j,\max }$$(5) $$-P_{G,\min }\le P_G\le P_{G,\max }.$$(6)

2.3 Wind turbine model

Equation (7) mentions the mathematical model of a linear wind profile as follows:$$P_{\mathrm{jj},t}^w=\{\begin{array}{cc}{P}_{\mathrm{jj}}^r\times \left(\frac{v_t^w-v_{\mathrm{jj}}^{\mathrm{in}}}{v_t^r-v_{\mathrm{jj}}^{\mathrm{in}}}\right)& v_{\mathrm{jj}}^{\mathrm{in}}\le v_t^w\le v_{\mathrm{jj}}^r\\ P_{\mathrm{jj}}^r& v_{\mathrm{jj}}^r\le v_t^w\le v_{\mathrm{jj}}^{\mathrm{out}}\\ 0& \mathrm{otherwise}\end{array}$$(7)

2.4 Wind uncertainty modelling

When dealing with wind, uncertainty modelling is essential to account for its stochastic behaviour. Here are the expressions used in the uncertainty modelling of the study’s expected load demand and wind output:$$L{d}_u^t=\mathrm{dL}{d}_u{n}_1+L{d}_{\mathrm{fc}}^t$$(8) $$\mathrm{dL}{d}_u=0.6\sqrt{L{d}_{\mathrm{fc}}^t}$$(9)dLd_u represents the variance of load demand, whereas ${\mathrm{Ld}}_u^t$ represents the load demand under uncertainty. n₁ represents the standard distribution function with an anticipated demand of $L{d}_{\mathrm{fc}}^t$ $$W{i}_u^t=\mathrm{dW}{i}_u{n}_2+{\mathrm{Wi}}_{\mathrm{fc}}^t$$(10) $${\mathrm{dWi}}_w=0.8\sqrt{{\mathrm{Wi}}_{\mathrm{fc}}^t}.$$(11)

The uncertainty of wind production is characterized by $W{d}_u^t$, while the divergence of wind output is represented by dWi, n₂ represents the standard distribution function. ${\mathrm{Wd}}_{\mathrm{fc}}^t$ represents the projected wind energy production at time t.

3 Economical techniques to lower microgrid generating costs

3.1 Incentive-Based Demand Response-1 (IBDR1)

Those responsible for developing demand response strategies are either utility distribution authorities, electricity service providers, or local power transporters. Consumers may get load-reduction incentives either independently of their power bill or along with the bill, which can be set according to standard prices or may vary periodically. Load-reduction incentives may be delivered to consumers in any of these ways. When reliability is under threat or when prices are too high, the grid operator will seek load reductions. Most demand response systems have a mechanism to determine a customer’s baseline energy consumption, which allows observers to assess and verify the amount of a customer’s load response. Customers who enrol in demand response programs but fail to contribute to events or meet their prescribed requirements may be subject to penalties.

To construct the economic model of the load, the concept of price elasticity of demand is an essential component. Here is a list of the adjusted loads included in the Demand Response programme [47].$$\begin{array}{c}{L}_{X\left(t\right)}^{\mathrm{DR}}=\eta L_X^0\left(t\right)\left[1+E\left(t,t\right)\left(\frac{C_{\mathrm{sp}}\left(t\right)-C_{\mathrm{ip}}\left(t\right)+I\left(T\right)}{C_{\mathrm{ip}}\left(t\right)}\right)\right]\\ +\sum _{h\ne 1, h\ne t}^{24}E\left(t,h\right)\left(\frac{C_{\mathrm{sp}}\left(h\right)-C_{\mathrm{ip}}\left(h\right)+I\left(h\right)}{C_{\mathrm{ip}}\left(h\right)}\right)\end{array}$$(12)

Due to DR at time interval t, the load at bus X is $L_X^{\mathrm{DR}}\left(t\right)$, where η is the load available for DR, represented as a percentage. At the location of bus X and the timing interval t, $L_X^0\left(t\right)$ represents the initial demand value in (12). C_sp (h) signifies the spot electricity price, whereas C_ip (t) indicates the preliminary price of electricity correspondingly at the timing intermission of t. Clients may adjust their own demands according to the prevailing spot price of the power. If the per-hour spot price of the electricity is too high, the customer will adjust the electrical load to a period with a lower spot energy price. The value of the incentive price for hour t is provided to customers involved in the DR programme through the implementation of load curtailment/shift during that specific hour is I(t). The self-elasticity is characterized by E(t, t) while the cross-elasticity is indicated by E(t, h). Elasticity is the degree of responsiveness of load requirements to changes in the cost of electricity in the sector [47].$$E=\frac{C_{\mathrm{ip}}}{L_0}·\frac{\partial L}{{\partial C}_{\mathrm{sp}}}$$(13)

Fluctuations in the price of electrical power will elicit one of the following responses in demand. Certain loads, like lighting loads, are not adjustable between periods and may only be activated or deactivated. Consequently, these loads exhibit sensitivity only at a certain moment, known as “self-elasticity”, which is negative consistently. Consumption may be moved from high-demand to low-demand times, such as process loads. Multi-period sensitivity refers to this phenomenon and is quantified by “cross elasticity”, which is consistently positive [47].

It is crucial to highlight that self-elasticities have a negative value, whereas cross-elasticities are positive. When implementing a price-based demand response approach, it is important to note that the initial electricity price C_sp (t) and the spot pricing C_ip (t) may vary. A substantial variance between the initial and final electricity prices may lead to results similar to a DR programme with positive a benefit (C_sp (t) – C_ip (t)). The burden is shifted from a more cost moment to a minimum cost period. Nevertheless, our analysis focused on a Demand Response (DR) system where the beginning and spot electricity prices are considered equal. Equation (14) demonstrates the decrease in load due to the execution of the DR programme.$$\Delta L_X^{\mathrm{DR}}\left(t\right)=\eta L_X^0\left(t\right)-L_X^{\mathrm{DR}}\left(t\right)$$(14)

$\Delta L_X^{\mathrm{DR}}\left(t\right)$ represents the reduction in power consumption at the “bs” which is the selected bus during t interval of time period as a result of the proposed Demand Response (DR) approach. During the specified time period, the entire required load at the bus “bs” can be expressed by L_X and can be represented as given in below equation:$$L_X=\left(1-\eta \right)L_X^0\left(t\right)+L_X^{\mathrm{DR}}\left(t\right).$$(15)

3.2 Incentive-Based Demand Response-2 (IBDR2)

Assuming c(Δ, m) represents the cost borne by a client who reduces electricity use by m MW. This study assumes that the mathematical function is provided as follows:$$c\left(\Delta , m\right)=x_1,m^2+x_2,m-x_2,m\Delta$$(16)x₁ and x₂ are the cost co-efficient in this equation. Δ represents the customer type and is used to classify consumers according to their willingness or preparedness to reduce the consumption of electric power. Δ is standardized in the intermission 0 ≤ Δ ≤ 1, thus Δ = 1 for the most enthusiastic client and Δ = 0 for the minimum enthusiastic. We summarise all the requirements that the cost function must meet:

• Presumed form c(Δ, m) = x₁m ² + x₂m – x₂mΔ.

• x₂, mΔ term categories clients by means of Δ.

• As Δ grows, slightly the cost drops. The client with the utmost willingness to pay (Δ = 1) has the lowest increment of cost and hence the highest marginal benefit, while the clients with the lowest willingness to pay (Δ = 0) have the highest increments in cost and therefore the lowest marginal benefit.

• $\frac{\partial c}{\partial m}=2x_{1}m+x_2-x_2\Delta$.

• Non-negative/positive change in cost.

• The marginal cost is inverse to cost function.

• Avoiding power waste: eliminating unnecessary energy expenses should cost (c(Δ, 0) = 0).

As practical constraints, we incorporate maximal power targets and total budget into the model. The definitive mathematical model which emphasizes maximizing the DISCO benefit is expressed as [39]:$${\max }_{m,n}\sum _{t=1}^T\sum _{j=1}^J[{\lambda }_{j,t}{m}_{j,t}-n_{j,t}].$$(17)

3.2.1 Mandatory constraints

$$\begin{array}{cc}\sum _{t=1}^T[n_{j,t}-\left(x_1{m}_{j,t}^2+x_2{m}_{j,t}-x_2{m}_{j,t}{\Delta }_j\right)]\ge 0,& \mathrm{for} j=1,\dots ,J\end{array}$$(18) $$\begin{array}{cc}\sum _{t=1}^T[n_{j,t}-\left(x_1{m}_{j,t}^2+x_2{m}_{j,t}-x_2{m}_{j,t}{\Delta }_j\right)]& \\ \ge \sum _{t=1}^T[n_{j-1,t}-\left(x_1{m}_{j-1,t}^2+x_2{m}_{j-1,t}-x_2{m}_{j-1,t}{\Delta }_{j-1}\right)]& \mathrm{for} j=2,\dots ,J\end{array}$$(19) $$\sum _{t=1}^T\sum _{j=1}^J{n}_{j,t}\le \mathrm{UB}$$(20) $$\sum _{t=1}^T{m}_{j,t}\le {\mathrm{CM}}_j$$(21)

UB represents the utility’s total budget and CM_j is the daily limit of interruptible electricity for customer j. Constraint (18) guarantees that the total daily reward a client receives is more than or equal to their day-to-day cost of disruption. Customer power is restricted and ensured by constraint (19), and greater customer benefits are realised. The incentive offered by the utility is not supposed to be more than the budget of the utility and is ensured by constraint (20). The overall daily power reduction of each customer is not supposed to fall below their daily interruptible power limit and that ensured by constraint (21).

4 Proposed circle search algorithm

The CSA aims to find the best solution by investigating random circles to broaden the search area. The main motivations for selecting CSA as the optimization method for this study are [48]:

• Recently developed, swift and popular.

• Only one governing equation; No complex stages and phases within the algorithm making it easy to code and execute.

• No tuning parameters.

Using the centre of the circle as a reference point, the angle formed between the tangent line at its contact point and the circumference of the circle decreases progressively as it nears the center. The angle at which the tangent line meets the point can vary unpredictably since the circle may have been positioned within the local solution. The CSA search agent is considered to be at the contact point X_t , while the algorithm’s optimal position is anticipated to be at the centre point X_c . Below, we detail the key steps of the CSA optimizer.

4.1 Initialization

This phase in the CSA is vital, as it guarantees that every dimension of the search agent is assigned randomly. Many existing codes randomise dimensions unevenly, leading to algorithms sometimes achieving optimal solutions unexpectedly. Equation (22) states that the search agents are first set up inside the search space’s upper limit values (ULV) and lower limit values (LLV) as:$$X_t=\mathrm{LLV}+\mathrm{r}\times \left(\mathrm{ULV}-\mathrm{LLV}\right).$$(22)

4.2 Update position

The placement of the search agents is modified to align with the most advantageous position specified in equation (23):$$X_t=X_c+\left(X_c-X_t\right)\times \tan \left(\theta \right).$$(23)where θ can be computed as follows:$$\theta =\{\begin{array}{cc}w\times \mathrm{rand}& \mathrm{iter}>(c\times \mathrm{Maxiter})\\ w\times p& \mathrm{Otherwise}\end{array}$$(23) $$w=w\times \mathrm{rand}-w$$(24) $$a=\mathrm{\Pi }-\mathrm{\Pi }\times {\left(\frac{\mathrm{Iter}}{\mathrm{Maxiter}}\right)}^2$$(25) $$P=1-0.9\times {\left(\frac{\mathrm{Iter}}{\mathrm{Maxiter}}\right)}^{0.5}$$(26)the iteration counter is denoted by iter, consider a random integer called rand, which falls within the range of 0 to 1, Maxiter is the highest possible count of iteration, and c is a constant that ranges from 0 to 1, indicating the proportion of iterations maximum value. Equation (24) demonstrates that the fractional value w transitions ranged from −π to 0 as the number of rounds increases. Another fractional point is a transition from π to 0 as per equation (25). Now p is the variable transitions ranged from 1 to 0 as per equation (26). Consequently, the angle θ ranged from −π to 0.

5 Results and discussions

To address the load dispatch issue, an LV grid-connected microgrid test system is taken into consideration in this work. Six traditional fossil fuel generators and six Wind Turbines (WT) are included in the test system’s configuration. The cost function, which must be minimised, is evaluated in a variety of scenarios using a variety of optimisation approaches, which are covered in detail in the sections that follow. Table 1 lists the design factors for the first test system, which is a grid with six generating units and a commitment of ±50 kW. The Time Of Usage (TOU) policy is followed by the dynamic grid price as displayed in Figure 1 along with the hourly load demand of the subject MG system. To address both the wind energy and the power dispatch issue, a dynamic wind speed is taken into consideration. In addition, an analysis is conducted wind speed profile to determine the maximum penetration of wind power as shown in Figure 2.

Fig. 1 Load demand and electricity market price.

Fig. 2 Wind speed and corresponding calculated wind power.

5.1 Description of results obtained by evaluating IBDR1: Customer incentives for load curtailing based on price elasticity matrix

Considering that 40% of microgrid users participated in the IBDR1 program, an evaluation was conducted on the remaining three cases. During the initial evaluation of the incentive cost for consumers in the DR programme, a variety of incentive values ranging from $0.5 to $5 were considered. The price elasticity matrix was gathered from [47]. The total incentive costs associated with different incentive levels are displayed in Figure 3. It is evident that the expenses for the DR participants consistently increased as the incentive values were modified. Individually incentive price inside the previously indicated range of $0.5 to $5 is then evaluated in relation to the cost of power generation and the total cost. The generating cost consists of the cost components of the DERs as well as the purchasing and selling costs incurred by the grid. The total cost is the summation of the minimum generation cost and the incentive cost that will be provided to the customer as a benefit. Once the recommended CSA was used for optimization, Figure 4 showcased the generation cost and overall cost of producing active electricity. The graph indicates that the overall cost of the system declined until incentive values reached $2, at which point it began to increase. However, the cost of generating energy decreases consistently as the value of incentives increases. Considering the system’s complete cost had decreased to $24969, it is deemed that $2 is the model incentive price for additional examination. $277.8352 must be given to customers as the incentive cost in order to achieve the highest incentive value. As a result, the MG system achieved an optimal reduction in the cost of power production, calculated at $25246 by the DR algorithm. Figure 5a illustrates the system’s load requirement with and without demand response (DR), along with a $2 incentive value whereas Figure 5b displays that the load curtailment was performed during hours 17–21 when the original demand was at its peak. Due to the DR program’s involvement, the peak demand decreased by 6.9%, from 421 kW to 392 kW and an overall of 80 kW load was curtailed at the end of the day. Figure 6–8 illustrates how an increase in incentive value leads to an improvement in load factor. The MG system without DR had an initial load factor of 0.7641, which progressively increased to 0.8123 when the incentive value was $2. Also, optimal parameter in IBDR 2 is listed.

Fig. 3 Customers’ cost implications related to adjustments in incentive values.

Fig. 4 Variation in the MG system’s total cost and generating cost for various incentive values.

Fig. 5 Load demand with and Without IBDR1.

Fig. 6 Impact of incentive values on the MG system’s Load factor.

Fig. 7 Cost per hour of not providing power.

Fig. 8 Load demand with and without IBDR.

5.2 Generation cost minimization for various load demand profiles using CSA

In this stage generation cost is minimized by the proposed CSA for the base load demand and for the final load demands obtained by subtracting the load curtailed by customers in IBDR1 and IBDR2. Three cases are studied for all three varieties of load demand models which are described below:

Case 1: All of the DERs in this instance are functioning within their permissible limits. The main factor contributing to the MG system’s lowest generating cost compared to all other examples examined is the grid’s active participation in the purchasing and selling of electricity. In this instance, the lowest generating cost determined by CSA is $25463, $24969 and $24899 for base load demand, load demand influenced with IBDR1 and load demand influenced with IBDR2 respectively as mentioned in Table 2.

Case 2: In this instance, the grid’s passive involvement is examined. This implies that the microgrid system may only purchase electricity from the grid when the DERs are unable to provide the entire load demand for a certain period. The grid is in inactive mode for the remainder of that duration. In this instance, the generating cost was reduced to $25530, $25053 and $24988 for base load demand, load demand influenced by IBDR1 and load demand influenced by IBDR2 respectively as mentioned in Table 3.

6 Conclusion

This minimizes the generating costs of an LV MG system using two IBDR approaches. This helps to lower the generating cost of the MG system at a later stage while also saving energy. The findings from the study lead to the following conclusions:

• IBDR2 policy yielded a minimum generation cost compared to IBDR1 by insisting the customers to curtail 105 kW of load demand whereas only 80 kW of load demand was curtailed by the former IBDR1. The proposed IBDR2 policy aimed to maximize the DISCO benefit considering customer willingness yielded a minimal generation cost. The only demerit of IBDR2 is that it needs an optimization approach whereas IBDR1 can be evaluated easily given the price elasticity matrix.

• Case studies confirm that RES and the grid play an active and vital role in reducing the cost of generating.

• The suggested CSA was quick, reliable, and effective enough to provide the best fitness function value for all levels and instances examined.

Future research might examine how adding energy storage systems (ESS) to the MG system, such as batteries and electric cars affects the system’s generating cost. This will also evaluate the efficiency and resilience of the proposed CSA in managing the many restrictions related to EVs and batteries.

Funding

Zhejiang Provincial Department of Education “Exploration of EMS Talent Base Based on the Integration of Industry and Education” (202107175) Ministry of Education “Construction of Electronic Technology Practice Teaching Base” (202101232027).

References

All Tables

All Figures

	Fig. 1 Load demand and electricity market price.
In the text

	Fig. 2 Wind speed and corresponding calculated wind power.
In the text

	Fig. 3 Customers’ cost implications related to adjustments in incentive values.
In the text

	Fig. 4 Variation in the MG system’s total cost and generating cost for various incentive values.
In the text

	Fig. 5 Load demand with and Without IBDR1.
In the text

	Fig. 6 Impact of incentive values on the MG system’s Load factor.
In the text

	Fig. 7 Cost per hour of not providing power.
In the text

	Fig. 8 Load demand with and without IBDR.
In the text