Electrical Engineering

https://doi.org/10.1007/s00202-025-03263-9

ORIGINAL PAPER

Incentive-based demand response policies for techno-economic

microgrid operation—a comparative analysis
Bishwajit Dey1 · Gulshan Sharma2 · Pitshou N. Bokoro2

Received: 14 May 2024 / Accepted: 1 July 2025

© The Author(s) 2025

Abstract
Power system optimisation academics have long been drawn to the idea of scheduling distributed energy resources (DERS)
optimally to decrease the generating cost of a low-voltage (LV) microgrid (MG) system. The present work implements a
correlational analysis between two different incentive-based demand response (IBDR) policies for load curtailment. The first
one involves a price elasticity matrix to emphasise paying incentives to the customers for curtailing load during peak hours
only. The second IBDR policy is an optimisation-based approach which involves customer willingness to deliver economic
benefit both to themselves and the DISCOM. The final restructured load demand is the base load demand minus the load
curtailed by the IBDR policies. Henceforth, generation cost minimisation is applied on the MG system for all three load
models. Three case studies are performed for an exhaustive techno-economic analysis of the subject MG system. The study
uses the recently created quick and easy circle search algorithm (CSA) as its optimisation tool. The generation cost was
decreased from $25,463 to $24,969 and $24,899 using IBDR1 and IBDR2 policies of load curtailment, respectively. During
IBDR1, 80kw load was curtailed, and the customers gained an incentive of $277, whereas using IBDR2 policy, 105 kW of
load was curtailed, and the DISCOM benefited $211. The consumers also benefited $500 in the process. Numerical results
also show that CSA outperformed various optimisation algorithms from the literature and ample algorithms implemented in
the work. Central tendency measurements further support the reliability and effectiveness of CSA.

Keywords Demand response · Microgrid energy management · Circle search algorithm · Load curtailment · Distributed
energy resources

Abbreviations EMS Energy management system

DSM Demand-side management
DER Distributed energy resources IDSM Integrated demand-side management
LV Low voltage GES Generalised energy storage
MG Microgrid VGWO Variegated GWO algorithm
IBDR Incentive-based demand response MOMFO Multi-objective moth flame optimization
CSA Circle search algorithm algorithm
DR Demand response GWO Grey wolf optimization
ELD Economic load dispatch GA Genetic algorithm
DEDP Dynamic economic dispatch problem TOU Time-of-use
DMCP Discrete-time mean consensus protocol DG Distributed generation
LLV Lower limit values
ULV Upper limit values
B Gulshan Sharma
gulshans@uj.ac.za WT Wind turbines
1 Department of Electrical Engineering, Manipal University
Jaipur, Jaipur, Rajasthan, India
2 Department of Electrical & Electronics Engineering
Technology, University of Johannesburg, Johannesburg,
South Africa

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1 Introduction problem for the IEEE 30 bus system, offering a range of tradi-
tional and cutting-edge metaheuristic optimisation methods
Generating and utilising electrical energy are essential for the for microgrid economic dispatch. Research in [11] focussed
functioning of modern society. Optimising economic load on microgrids powered by renewable energy sources such
dispatch (ELD) in the power system is crucial for minimis- as wind turbines, solar cells, and hydrogen storage devices.
ing power generation costs while meeting operational needs, Addressing the variability of renewable energy sources, a
especially with thermal power being the primary source cur- novel energy management approach has been developed util-
rently. When dealing with typical issues related to ELD, ising hydrogen storage. Considering load supply constraints,
the cost functions of generators are usually estimated using this approach aims to reduce operating costs of hydrogen
quadratic functions. When the load requirement is spread storage systems and batteries, along with expenses related to
across multiple generators, it impacts estimation, unit com- surplus and unsupplied energy. In their research, the authors
mitment, billing, and several other processes. [12] analysed the microgrid system holistically, considering
renewable power, energy storage, and load as integral com-
ponents. To efficiently manage the network source, storage
1.1 Brief literature review of the microgrid, and load, they proposed an optimisation
approach using a master–slave game. Minimising overall
The author of the paper [1] introduced an innovative opti- operational expenses is the goal of the master in this micro-
misation approach for renewable energy arrangements in grid game. In order to manage energy from several renewable
microgrids. An approach for multi-objective optimisation is sources, the authors of article [13] proposed a stochastic
developed for a diesel, wind, PV, and battery-based hybrid programming model based on an upgraded slime mould algo-
system. The primary goals are to reduce energy costs and rithm with multiple objectives. This method is expected to
power supply losses. The research in [2] compared and eval- improve the microgrid’s performance. In [14], using digi-
uated eight different metaheuristic approaches to optimise tal twins of wind and solar units, researchers examined how
the size of a hydrogen storage-equipped microgrid. The goal a utility-driven variable load shaping method affects non-
is to minimise the cost of the microgrid and maintain con- dispatchable energy sources in renewable microgrids. For
trol over the energy flow within the system. The author of network-coupled microgrids, they suggested a three-stage
the paper [3] developed a distributed optimisation algorithm stochastic energy management system (EMS) architecture
for a hybrid microgrid network to reduce the total genera- that would optimise day-ahead planning while minimising
tion cost in a dynamic economic dispatch problem (DEDP). operating cost.
The research paper [4] has delved into an optimisation strat- Using demand-side management (DSM) and a hybrid
egy of microgrid dispatching, taking into account the random intelligence approach, the authors of [15] reduced the total
fluctuations of renewable energy supplies and load demands. price of three microgrid structures. The unit commitment of
The author of the paper [5] introduced an innovative two- dispatchable fossil fuel generators is one of the practical diffi-
stage two-layer optimisation method to reduce the overall culties that they solve. A probabilistic energy modelling tech-
operation cost of a microgrid facing significant uncertainties nique for large-scale customers was created in the research
in load demand, generation, and scheduled outages. reported in [16]. This approach took into account a microtur-
The research work [6] focussed on optimising the energy bine, renewable energy sources, energy storage devices, and
production of a microgrid to meet demand, reduce CO2 emis- power exchange-based bilateral contracts. Big businesses
sions, and minimise operating costs. The researcher of [7] stood to gain the most from a reduction in the price of energy
discussed the increased operation cost of the generating units storage, demand-side management, and related technologies.
of distributed generation and electricity purchase cost in a The study in [17] concentrated on optimising multi-timescale
microgrid. They enhanced the discrete-time mean consensus CMES management at energy and power levels while taking
protocol (DMCP) by introducing the power offset elimina- into account source–load interaction. The researcher in [18]
tion term. A strategy for managing energy in multi-microgrid implemented a shifting strategy based on classifying loads
systems was proposed in a study [8]. This approach opti- into high priority and low priority, calculating the sizing of
mises the use of distributed resources, renewable energy, components for an autonomous rural mini-grid across four
and plug-in electric vehicles, resulting in favourable results load groups and load elasticity using particle swarm optimi-
for both the economy and the environment. Examining a sation. The paper [19] proposed an integrated demand-side
case study of a rural community in Nigeria, the study in management (IDSM) approach employing a non-cooperative
[9] explored ways to enhance the performance of an iso- game and multi-energy pricing methods for an energy sys-
lated solar/battery microgrid to meet the increasing load tem. According to the research paper [20], the researchers
requirements of a proposed solar/wind/diesel/battery micro- implemented the devices with adjusted loads on the system
grid. Researchers in [10] explore the optimal power flow

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side and the user side is integrated to construct a gener- two-layer optimisation model and the suggested approach,
alised energy storage (GES) model. The entire model giving according to the results of the simulations.
house to batteries, electric vehicles, flexible resources, cool- An optimal economic dispatch for a grid-connected micro-
ing and heating system was observed. Within the scope of the grid is presented in the article [40]. Wind, diesel, and solar
study presented in [21], researchers have implemented two photovoltaics are the power sources for the microgrid. A
changes, specifically opposition theory and sine cosine based demand response plan based on incentives is used to run
position update mechanism, with the intention of boosting the grid-connected microgrid. In order to address both the
the exploration and exploitation capabilities of the slime issue of low generation costs and the pollution produced
mould algorithm (SMA), which was recently established. by DERs in an LV grid-connected microgrid system, the
The study presents a cost-emissions operated dynamic eco- researcher in [41] suggested a DSM method that relies on
nomic dispatch (MOCEDED) algorithm that accounts for a hybrid intelligence technique. In order to reduce opera-
thermal, wind, and solar producing facilities [22]. tional costs, the article [42] employed bi-level optimisation.
The programme also accounts for the fact that solar and This study made use of a novel hybrid swarm intelligence
wind power curtailment is unpredictable. A coordinated algorithm that has proven useful for a number of optimi-
decision-making technique was used in the research [23], sation problems in the past; the technique was developed
which included making lower-level investment decisions for optimisation of power systems. In order to overcome the
with operational uncertainty using a two-objective stochastic limitations of the original weighted mean of vectors method-
programming formulation. Considering demand responses ology, such as being stuck in a local optimum, the researcher
and daily optimal operation, the proposed model is solved in [43] proposed a new method called LINFO to improve
on a three-bus grid that incorporates smart microgrids with the search capabilities. The research paper [44] discussed
distributed energy resources on each bus. In order to report MMG energy management by introducing and implementing
the ED issue in microgrids, the authors of the article [24] a modified capuchin search algorithm (MCapSA). As a multi-
proposed a data-driven NN approach. In order to better grasp objective function, the optimised function takes stability,
the spatio-temporal characteristics of renewable and con- voltage fluctuation, and cost into account. Optimal micro-
ventional electricity, together with intermittency difficulties, grid performance is evaluated in the research publication
a two-stage training approach is introduced. An improved [45] in relation to charging plug-in hybrid electric vehicles
method for creating an integrated power management sys- (PHEVs). In order to assess the behaviour of PHEVs, three
tem is described in the study article [25] by combining different charging patterns are considered: uncontrolled, reg-
particle swarm optimisation with simplex-based linear pro- ulated, and smart. By combining renewable power sources
gramming. Assuming a smart city’s consumption profile like wind and solar with electrical energy storage (EES)
allows for energy scheduling to be carried out. A demand devices, the article [46] outlined a two-tiered system for
response (DR) model for DSM in smart grid should be devel- regulating microgrids’ energy usage for the next day. The
oped, according to the researcher’s recommendation in the document [47] develops an innovative energy sharing method
article [26], using dynamic pricing (DP). The proposed DR for a centralised energy community. The proposal outlines a
model has the potential to change peak energy demand, which product differentiation strategy to enable the distribution of
would improve the dependability and constancy of the power green, local, and grey electricity among community mem-
system. An integrated demand response programme (DRP) bers, ensuring a centralised, preference-driven sharing and
for grid-connected MMGs was detailed in the article [27] promotion of sustainable practices, along with an inter-
together with the dynamic optimal power flow (DOPF) with nal pricing mechanism for the community market where
and without an energy source interruption. By factoring in members indirectly face grid and commodity expenses. The
the intuitive characteristics of different phases, the overall research [48] proposes a novel energy management sys-
cost throughout the whole duration is kept to a minimum. tem (EMS) that utilises weather and load predictions for
Theoretically, the authors of the paper [28] combine the great- the optimum scheduling and operation of PMG. This arti-
est advantages of the freshly developed grey wolf optimiser cle’s primary contribution is the development of a novel
(GWO), the sine cosine technique (SCA), and the crow search hybrid machine learning method that integrates the adaptive
algorithm (CSA) to produce a novel hybrid approach. In order neuro-fuzzy inference system (ANFIS), multilayer percep-
to solve the verified benchmark functions of the IEEE CEC- tron (MLP) artificial neural network (ANN), and radial basis
C06 2019 conference, this work introduces a novel hybrid function (RBF) ANN to accurately predict load and weather
variegated GWO algorithm (VGWO). Combining the crow data. In the research [49], a novel energy management sys-
search approach with the teaching and learning optimisation tem (EMS) has been introduced to alleviate variations of
algorithms, the research [29] suggested a teaching–learning renewable energy sources (RESs) using a two-tier corrective
crow search algorithm to solve the two-layer optimisation weather forecasting approach utilising multilayer percep-
model. Microgrids are operated economically by using the tron artificial neural networks (MLP-ANN). The study [50]

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introduces an innovative management system for facilitating 2.1 For DG units cost based fitness function
preference-driven energy sharing among diverse end-users
in a centralised renewable energy community. The suggested Fossil-fuelled generators often use a quadratic equation to
hierarchical mechanism entails each end-user conducting a illustrate their cost function. The complete equation of the
day-ahead self-scheduling according to internal electricity cost function is presented below [47]:
prices, followed by the community manager optimising intra-
⎡ ⎤
market exchanges concurrently and executing preference- 
24 n
based internal energy sharing to finalise the electricity billing CostDG  ⎣ (xi Pi, t + yi Pi, t + z i ) + Cgrid, t ∗ Pgrid, t ⎦
2

for the end-users. t1 i1

By column headings such as “optimisation algorithm”, (1)
“subject test system”, and “RES type”, Table 1 displays the
papers covered in the literature. C grid stands for the time-of-use (TOU) price of power,
where x, y, and z are the ith generator’s cost coefficients.
1.2 Novel contribution addressing the research gap The output power of the ith generator is represented by Pi ,
whereas the Pgrid is the power output of the grid. In an essen-
Researchers used various types of demand-side management tial limitation for fossil-fuelled generators, the valve-point
policies to shift and/or curtail load demand such that the effect requires adjusting valves to manage the flow of steam
distribution system is more cost-effective and efficient to and electricity; this is included in Eq. (2) of the economic
handle the surge in load demand. A valid correlative anal- dispatch issue [47].
ysis between different load shifting or curtail policies on the CostDG
same microgrid test system which could authenticate their 
24 
n  
cost-effective and efficient nature was not available to the  (xi Pi,2 t + yi Pi, t + z i + m i × sin(n i (Pi, min − Pi, t ))
t1 i1
best of author’s knowledge. The novel contribution of the
+ Cgrid, t ∗ Pgrid, t )
present work listed below bridges the research gap developed
by the extensive analysis of recently published literatures on (2)
optimal economic operation of microgrid systems:
Pi represents the electrical output power of the ith unit.
a. Two different types of incentive-based demand response While x i , yi , and zi are the ith generator’s cost coefficients,
policies, one which compensates the customer only and mi and ni are the valve-point effect coefficients. Because of
the other which compensates both the customer and DIS- this, where n is the number of DG units used, the total cost
COM, are employed for the economic operation of a is equal to Cost DG .
microgrid system
b. A comparative analysis between the IBDR policies was 2.2 Equality and inequality constraints
done to mark the efficient and economic approach.
c. A recently developed circle search algorithm was imple- All time indices must have their scheduled loads met, taking
mented as the optimization tool and the results were inequality constraints into account. The primary goal of the
compared with several other metaheuristic algorithms operation is to lessen the financial burden of meeting the
available in the literature concerning the microgrid sys- load demand from DGs, wind generation, and the grid. The
tem. equality constraints that do not take wind generation into
account are given by Eq. (3) while those that do so are given
by Eq. (4) [47].
Figure 1 summarises the above listed novel research con-
tribution of the paper.

n
Pit + Pgrid
t
 Pload
t
(3)
i1
2 Objective function formulation 
n
Pit + Pgrid
t t
+ PW  Pload
t
(4)
Meeting the electrical load demand efficiently under all limits i1
is the ultimate goal of ELD. Dynamic economic load dispatch
is required to meet the changing demand by allocating the Both the grid and distributed generation (DG) sources
appropriate load. The cost function is shown in Fig. 1 with need to keep their energy production within the specified
a continuous line and a dotted line, respectively, to indicate limitations if demand is to be met [47]. In order to meet
the influence of the valve points and their non-consideration. the demand for power, the grid and DGs must supply power

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Table 1 Exhaustive breakdown analysis of the literature survey

Objective Optimization tools used Method System description RES Year Ref

Reduce power loss Multi-objective moth Taguchi method and 10, 15, and 20 PV, WT 2023 [1]
and energy costs as flame optimization novel fuzzy decision residential houses
much as possible algorithm (MOMFO)
Energy storage Particle swarm A metaheuristic Electrolyser, fuel cell, PV, fuel cell 2023 [2]
system (ESS) optimization approach to photovoltaic (PV)
installation algorithm microgrid sizing system, battery
optimisation using capacity, and hydrogen
hydrogen storage tank capacity
Minimising Distributed optimization Distributed Hybrid microgrid PV, battery 2023 [3]
environmental algorithm optimization network
pollution and algorithm
generation cost
Reduce power loss SRSM modelling Microgrid Microgrid RES 2023 [4]
and energy costs as dispatching with
much as possible random renewable
energy and load
demand variations
Minimise MG 2-stage 2-layer Economic operation Three DGs, WT, and WT, BESS 2021 [5]
operating costs optimisation of MGs battery energy storage
device
Reduction on CO2 Multi-objective Multi-objective Microgrid PV, WT, BESS 2023 [6]
emissions and optimization optimisation,
operation cost of optimises CO2
microgrid emissions and
economic cost
Cost minimization Multi-agent Optimisation of DG 5 unit microgrid NA 2023 [7]
leader-following active power
consensus algorithm production and
(IMLCA) generating
operating cost of the
AC microgrid is
lessened
Better energy Hybrid grey wolf whale An incentive-based Five-microgrids test EV 2023 [8]
management (HGWW) enhanced demand system
optimization response
algorithm programme was
analysed
Cost minimization Particle swarm Solar and battery Village of Nigeria PV, WT, BESS 2023 [9]
optimization hybridised hybridised with wind,
microgrid solar, and
diesel/battery based
microgrid
Microgrid’s Ant-colony based Matpower IEEE 30 bus system NA 2023 [10]
economic issue algorithm
Cost of operation Developed grey wolf Grey wolf Renewable source PV, WT, FC 2022 [11]
optimization optimization uncertainty in MG
algorithm (GWO) algorithm
Cost of operation Master–slave game Master–slave game Source, storage, and PV, WT, BESS 2023 [12]
optimization load
Minimising Slime mould algorithm Multi-renewable Multi-renewable PV, WT, FC, 2023 [13]
generation cost sources-based sources-based
energy management Microgrid

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Table 1 (continued)

Objective Optimization tools used Method System description RES Year Ref

Cost of operation Black widow Using renewable Using real-time weather PV, WT 2023 [14]
optimization energy and data combination of
algorithm communication solar and wind
technologies,
microgrids (MG)
are self-sufficient
and use less fossil
fuel
Overall cost of Hybrid WOASCA Demand price Three microgrid systems NA 2022 [15]
microgrid elasticity with DSM
Reduction of cost Seagull algorithm Autoregressive Huge customers with PV, WT 2023 [16]
moving-average several energy sources
(ARMA)
Cost-effective RES Operation optimization Optimum Using real-time weather EV 2023 [17]
System multi-timescale data combination of
energy and power solar and wind
CMES management
considering
source–load
interaction
Overall cost of Particle swarm DSM in rural area Mini-grids in rural areas PV 2023 [18]
microgrid optimization
Reduce the cost Linear programming It depicts Regional integrated NA 2023 [19]
multi-energy market energy system
trade and energy
hub makeup
Cost-effective RES Genetic algorithm (GA) DSM along with RES DSM-based CCHP PV, solar 2023 [20]
System system System thermal
Better control of Slime mould algorithm Osma Multi-modal, uni-modal, NA 2023 [21]
DSM controller and multi-modal
functions
Reducing dynamic MOCEDED Dynamic economic Four units of PV, WT 2023 [22]
dispatch problem dispatch conventional plant
with PV and wind
Reduction of cost of Compromised Parameters of inde- 3-Bus grid with RES 2023 [23]
energy exchange programme planning pendence microgrid
technique performance index
Real-time economic Data-driven neural Neural network in Res incorporated PV, WT 2023 [24]
dispatch (ED) network microgrid microgrid
Reliability and Particle swarm Dependability of the Photovoltaic, PV, WT 2023 [25]
sustainability the optimisation energy management along with microturbine
microgrid system by
improving
microgrid producer
energy flow
scheduling
Power system stabil- Dynamic price Optimises the DP to A cluster of commercial PV 2022 [26]
ity and (DP)-based demand maximise its and residential loads in
reliability response (DR) utilities and reduce China
the load fluctuation

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Table 1 (continued)

Objective Optimization tools used Method System description RES Year Ref

Reduction of cost in Genetic algorithm To optimise power IEEE 33 and IEEE PV, WT, EV 2023 [27]
the entire day flow in 69-bus system
grid-connected
MMG integrated
demand response
programmes with
and without energy
source outages
Better management Variegated GWO Optimisation tool to CEC-C06 PV, WT, EV 2024 [28]
of energy algorithm (VGWO) handle three 2019 benchmark
developing and functions
complicated power
system optimisation
problems
Total system cost of Teaching–learning crow Demand response Grid connected and PV, WT, EV 2023 [29]
microgrid search algorithm optimization islanded microgrid
Better usage of Jellyfish optimization Exchange of energy Monte Carlo methods to PV, WT, EV 2023 [30]
energy trading among MGs evaluate load, plug-in
hybrid car charging,
and corresponding
RERs generating
intermittencies
Minimising Swarm optimization EPO and GSO Wind turbines, DG, ET, OV, ESS 2023 [31]
fluctuation of ideal PV capacity, and
frequency and ESS
voltage in MG
Low-carbon and the Multi-objective Economic advantages Community energy ESS 2021 [32]
economy operation optimization decrease carbon system
emissions and ease
energy supply strain
Continuity of power Robust Decreasing power IEEE 33 bus with BESS EV 2023 [33]
supply with less optimization method losses and serving
price (ROM) electricity markets
Decarbonizing the Mixed-integer linear Impact of ESS and Wind and solar plant PV, WT 2023 [34]
power industry programming (MILP) RES
Minimising energy Bi-level optimization Large multi-energy LMEC with HVAC EES, WT 2023 [35]
cost model consumer (LMEC)
with HVAC
Operation cost Flower pollination and Demand response 7 natural gas systems GT 2023 [36]
reduction grasshopper algorithm and 33-bus IEEE test
system
Balance between Interactive class topper Optimise microgrid Linked microgrid with ESS 2023 [37]
load and generation optimization (I-CTO) energy sources to battery storage and
reduce generation renewable energy
and emission costs
CO2 emission Adaptive particle swarm Reduce carbon Fuel cell in DG EV 2023 [38]
reduction optimization dioxide emissions
and use less
conventional energy
Optimal scheduling Sparrow search Microgrid energy 16 Cases with different PV, WT, FC, 2021 [39]
of management issue load BESS
microgrids
Minimising the cost Demand response Demand response Grid connected RES 2017 [40]
microgrid

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Table 1 (continued)

Objective Optimization tools used Method System description RES Year Ref

Minimising the cost CSAJAYA Five microgrid cases 5 Units with LV grid PV, WT 2023 [41]
with DERs analyse grid
participation tactics,
power market
pricing kinds, and
demand response
systems
Distribution system’s CSAJAYA By reorganising the Six units’ distribution WT 2023 [42]
operational costs load demand model system
and categorising
loads as elastic or
inelastic
Minimising the cost Circle search algorithm Incentive-based Low-voltage (LV) WT Our paper
with DERs (CSA) demand response microgrid (MG)
(IBDR) system

Fig. 1 Summary of the novel research contribution of the paper

within their limits, which can be shown below. Eq. (7).:

 β−1  β
β v v
P j, min ≤ P j ≤ P j, max (5) f v (v)  exp − , (v > 0) (7)
γ γ γ

where γ and β signify the scale and shape factor of Weibull

−Pgrid, min ≤ Pgrid ≤ Pgrid, max (6) PDF; and v represents the wind speed.
Equation (8) reflects the power production from individual
wind units, which is dependent on wind speed. The relation-
ship between power generation and wind speed is defined by
a linear model [59], expressed as:
2.3 Characterisation of wind generation
⎧  
v−vin
The Weibull PDF is employed to forecast the power output ⎪
⎨ PW vr −vin v ≤ vin ≤ v
generated by a wind turbine and the wind speed distribution. p PW v ≤ vin ≤ vot (8)
⎪
⎩
[48]. The function representing wind speed is expressed as 0 v < vin and v > vot

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where PW signifies rated wind power, p represents the moments, or concentrations expressed as m points for each
wind generation, ranging from 0 to PW , and vr , vin , and vot unknown parameter, the PEM focuses on statistical data. For
are rated, cut-in, cut-out wind speeds, respectively. each input random variable, including location and weight-
The Weibull PDF of power production from a wind turbine ing factor, which indicates the significance of the associated
(Eq. (9)) in the continuous interval (vin ≤ v ≤ vr ) is given by location in assessing the statistical moments of the output
[62]: random variable, the suggested Hong’s 2 m PEM generates
two probability concentrations. The definition of each input
⎡  ⎤(β−1) ⎡ ⎛  ⎞β ⎤
hp hp vector used in an appraisal is:
βhvin ⎣ 1 + 1 +
PW
⎦ ⎢ PW
⎠ ⎥
f p ( p)  × exp⎣−⎝ ⎦  
PW γ γ γ μ p1 , μ p1 , ....., pl, k , .....μpm (12)
(9)
Furthermore, pl,k may be computed using the formula
The probability of wind power production within the dis- below:
crete interval (p  0 or p  PW ) is expressed by Eqs. (10)
and (11): pl, k  μ pl + ζl, k θ pl (13)

P( p  0)  Pr (v < vin ) + Pr (v > vot ) where μ and θ are the mean and standard deviation of the
  input uncertain parameters, and ξ is the standard location.
vin β vot β (10) The weight coefficients (ω) and standard locations of the
1 − ex p − + exp −
γ γ unknown parameters are computed as follows.

P( p  PW )  Pr (v ≤ v ≤ vot ) 
 2
  λl, 3 λl, 3
vr β vot β (11) ζl, 1  + m+ (14)
= exp − + ex p − 2 2
γ γ 
 2
λl, 4 λl, 4
ζl, 2  + m+ (15)
2 2
2.4 Hong’s 2 m point estimation method (−1)3−k ζl, 2
for uncertainty modelling [49, 50] ωl, 1  × (16)
m ζl, 1 − ζl, 2
There are several significant uncertainties in the MGs operat- (−1)3−k ζl, 1
ing problem that need to be assessed, and the right approach ωl, 2  × (17)
m ζl, 1 − ζl, 2
for addressing uncertainties has to be used. The optimal
approach among the available options is determined by a The skewness and kurtosis in the aforementioned equa-
number of crucial elements, including the level of pre- tions are represented by λl,3 and λl,4 . Equation (18) calculates
cision needed and the body of knowledge regarding the the standard central moment of the unknown parameters
behaviours of unknown parameters. Assumption of this (λl,j ), and Eq. (19) displays the output variables’ PDF form.
paper: To address the problem’s uncertainty, a novel PEM Equations (20) and (21) yield, respectively, the anticipated
technique based on Hong’s 2 m PEM has been implemented. values and standard deviation of the output parameter as the
The main benefits of using the suggested PEM technique for ultimate result.
uncertainty modelling were its quick implementation time
M j ( pl)
while offering a suitable solution with high accuracy and its λl, j    j (18)
efficiency and effectiveness of the computational load for θ pl
large-scale power system challenges. The primary concept ∞
 j
underlying the PEM is to use the solution set of the deter- M j ( pl)  pl − μ pl f pl d pl (19)
ministic problem to calculate the statistical information of −∞
the output variables given a small number of estimated val-
   m 
k
ues of the input random variables. The wind power plant’s
μj  X Z j ∼
 ωl, k (Z (l, k)) j (20)
speed to power conversion is demonstrated using the Weibull
l1 k1
PDFs. 
    2
Hong’s 2 m PEM’s primary goal is to provide the best σj  X Z1 − X Z2 (21)
estimate of an unknown parameter by estimating the statis-
tical moments from the PDF of uncertain parameters based Hong’s PEM specific schemes consider one additional
on maximum likelihood [38]. To determine certain central evaluation of function F at the location composed of the

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means of the m input random variables (μp1 , μp2 ,…, μpl ,…, customers involved in the DR programme through the imple-
μpm ). As a result, there are k × m + 1 evaluations of F overall mentation of load curtailment/shift during that specific hour
for these systems. is I (t). The self-elasticity is characterised by E(t, t) while
The detailed process of the PEM approach described may the cross-elasticity is indicated by E(t, h). Elasticity is the
be summed up as follows in order to better understand the degree of responsiveness of load requirements to changes in
flowchart of Hong’s 2 m PEM implementation in the sug- the cost of electricity in the sector [51].
gested operational model in Fig. 2:
Cip ∂ L
E . (23)
L 0 ∂Csp
3 Economical techniques to lower microgrid Fluctuations in the price of electrical power will elicit
generating costs one of the following responses in demand. Certain loads,
like lighting loads, are not adjustable between periods and
3.1 Incentive-based demand response-1 (IBDR1): may only be activated or deactivated. Consequently, these
loads exhibit sensitivity only at a certain moment, known as
Those responsible for developing demand response strategies “self-elasticity”, which is negative consistently. Consump-
are either utility distribution authorities, electricity service tion may be moved from high-demand to low-demand times,
providers, or local power transporters. Consumers may get such as process loads. Multi-period sensitivity refers to this
load-reduction incentives either independently of their power phenomenon and is quantified by “cross elasticity”, which is
bill or along with the bill, which can be set according to consistently positive [48].
standard prices or may vary periodically. Load-reduction It is crucial to highlight that self-elasticities have a neg-
incentives may be delivered to consumers in any of these ative value, whereas cross-elasticities are positive. When
ways. When reliability is under threat or when prices are implementing a price-based demand response approach, it
too high, the grid operator will seek load reductions. Most is important to note that the initial electricity price Csp (t)
demand response systems have a mechanism to determine and the spot pricing Cip (t) may vary. A substantial variance
a customer’s baseline energy consumption, which allows between the initial and final electricity prices may lead to
observers to assess and verify the amount of a customer’s results like a DR programme with positive a benefit (Csp (t)
load response. Customers who enrol in demand response – Cip (t)). The burden is shifted from a more cost moment to
programmes but fail to contribute to events or meet their a minimum cost period. Nevertheless, our analysis focussed
prescribed requirements may be subject to penalties. on a demand response (DR) system where the beginning and
In order to construct the economic model of the load, the spot electricity prices are considered equal. Equation (24)
concept of price elasticity of demand is an essential com- demonstrates the decrease in load due to the execution of the
ponent. Here is a list of the adjusted loads included in the DR programme [48].
demand response programme. [51].
X (t)  ηL X (t) − L X (t)
L DR 0 DR
(24)
 
Csp (t) − Cip (t) + I (t)
L DR (t)  ηL 0
(t) 1 + E(t, t) + L DR
X (t) represents the reduction in power consumption
X X
Cip (t)
 24  at the“bs” which is the selected bus during t interval of time
Csp (h) − Cip (h) + I (h) as a result of the proposed demand response (DR) approach.
E(t, h)
Cip (h) During the specified time period, the entire required load at
h1.ht
(22) the bus “bs” can be expressed by L X and can be represented
as given in Eq. (25) [51].

Due to DR at time interval t, the load at bus X is L DRX (t), L X  (1 − η)L 0X (t) + L DR
X (t) (25)
where η is the load available for DR, represented as a per-
centage. At location of bus X and at the timing interval t,
L 0X (t) represents the initial demand value in (22). Csp (t) 3.2 Incentive-based demand response-2 (IBDR2)
signifies the spot electricity price, whereas Cip (t) indicates
the preliminary price of electricity correspondingly at tim- Assuming c( , m) represents the cost borne by a client who
ing intermission of t. Clients may adjust their own demands reduces electricity use by m MW. This study assumes that
according to the prevailing spot price of the power. If the per the mathematical function is provided as referenced in Ref.
hour spot price of the electricity is too high, the customer will [40]:
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 c( , m)  x1 m 2 + x2 m − x2 m (26)

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Fig. 2 Flowchart of Hong’s 2 m PEM implementation

x 1 and x 2 are the cost coefficient in this equation. repre- DISCOM benefit is expressed as [40]:
sents the customer type and is used to classify consumers
according to their willingness or preparedness to reduce the 
T 
J
! "
consumption of electric power. is standardised in the inter- max λ j, t m j, t − n j, t (27)
m, n
mission 0 ≤ ≤ 1, thus  1 for the most enthusiastic client t1 j1

and  0 for the minimum enthusiastic. We summarise all

the requirements that the cost function must meet:
3.2.1 Mandatory constraints [40]

• Presumed form c( , m)  x1 m 2 + x2 m − x2 m . T 
  
• x2 m term categories clients by means of . n j, t − x1 m 2j, t + x2 m j, t − x2 m j, t j
• As grows, slightly the cost drops. The client with the t 1
utmost willingness to pay (  1) has the lowest increment ≥ 0. for j  1, ......, J (28)
of cost and hence the highest marginal benefit, while the T 
  
clients with the lowest willingness to pay (  0) have n j, t − x1 m 2j, t + x2 m j, t − x2, t m j, t j
the highest increments in cost and therefore the lowest t1
marginal benefit. T 
  
∂c
• ∂m  2x1 m + x2 − x2 . ≥ n j−1, t − x1 m 2j−1, t + x2 m j−1, t − x2, j−1 m j−1, t j−1 ,
• Non-negative/positive change in cost. t1

• The marginal cost is inverse to cost function. for j  2, ....., j.

• Avoiding power waste: eliminating unnecessary energy (29)
expenses should cost (c( , 0)  0). 
T 
J
n j, t ≤ UB (30)
t1 j1
As practical constraints, we incorporate maximal power

T
targets and total budget into the model. The definitive m j, t ≤ CM j (31)
mathematical model which emphasises in maximising the t1

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to be at the centre point Xc. Below, we outline the primary

procedures of the CSA optimiser:
Initialisation: This is a crucial stage in the CSA,
since it ensures that all search agent dimensions are ran-
domly assigned. Many existing codes randomise dimensions
unevenly, leading to algorithms sometimes achieving optimal
solutions unexpectedly. Equation (32) states that the search
agents are first set up inside the search space’s upper limit
values (ULV) and lower limit values (LLV) as [52]:

X t  LLV + r × (ULV − LLV) (32)

where r represents a random vector within the range of 0 to

1.
Update search agent position: Location X t of the search
Fig. 3 Schematic workflow of IBDR2 agents is adjusted according to the most optimal position X c
outlined in Eq. (33) [52]:

UB represents the utility’s total budget and CMj is the X t  X c + (X c − X t ) × tan(θ ) (33)
daily limit of interruptible electricity for customerj. Con-
straint (28) [40] guarantees that the total daily reward a client The angle θ is crucial in the analysis and use of the CSA
receives is more than or equal to their day-to-day cost of and may be computed as follows (34) [52].:
disruption. Customer power is restricted that ensures by con- #
straint (29) [40], greater customer benefits are realised. The w × r and iter > (c × Maxiter)
incentive offered by the utility is not supposed to be more than θ (34)
w × p Otherwise
the budget of the utility and this ensures by constraint (30).
The overall daily power reduction of each customer not sup- w  w × r and - w (35)
posed to fall below their daily interruptible power limit and
 2
that ensures by constraint (31) [40]. The schematic workflow Iter
of IBDR2 is shown in Fig. 3. a − ∗ (36)
Maxiter
 0.5
Iter
p  1 − 0.9 × (37)
4 Proposed circle search algorithm Maxiter

the iteration counter is denoted by iter, consider a random

The circle search algorithm (CSA) [52] seeks the optimal
integer called rand, which falls within the range of 0–1,
solution by exploring random circles to expand the search
Maxiter is the highest possible count of iteration, and c is a
region. The primary reasons for choosing CSA as the opti-
constant that ranges from 0 to 1, indicating the proportion of
mization tool for the work in this paper are:
iterations maximum value. Equation (35) [52] demonstrates
that the fractional value w transitions ranged -π to 0 as the
• Recently developed, swift and popular. number of rounds increases. Another fractional point a tran-
• Only one governing equation; no complex stages and sitions from π to 0 as per Eq. (36) [52]. Now p is the variable
phases within the algorithm making it easy to code and transitions ranged 1 to 0 as per Eq. (37) [52]. Consequently,
execute. the angle θ ranged -π to 0.
• No tuning parameters. There are two potential scenarios for the CSA as outlined
below:
As seen in Fig. 4a, starting with the centre of the circle as a Case 1: Iter > (c.Maxiter): Angle θ  w × rand will be
point of reference, the angle between the tangent line’s con- constant, which can be utilised to improve the exploration
tacting point and the circle’s circumference gradually lowers process of the CSA and prevent local stagnation.
until it approaches the centre. The tangent line’s angle of Case 2: Iter < (c.Maxiter): The scenario consistently
contact with the point changes arbitrarily because this circle maintains angle θ  w × p, which may enhance the util-
could have been stuck in the local solution (Fig. 4b). The isation of the CSA.
CSA search agent is thought to be at the touching point Xt, Below mentioned Fig. 5 is the flowchart for working pro-
whereas the optimal location in the algorithm is expected cedure of CSA.

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Fig. 4 The processes of the CSA

algorithm

Fig. 5 Flowchart of CSA

5 Results and discussions with 60 population and 100 iterations. Table 2 lists the design
factors for the MG test system, which is a grid with six gener-
To address the load dispatch issue, an LV grid-connected ating units and a commitment of ± 50 kW. The time-of-usage
microgrid test system is taken into consideration in this work. (TOU) policy is followed by the dynamic grid price as dis-
Six traditional fossil fuel generators and six wind turbines played in Fig. 6 along with the hourly load demand of the
(WT) are included in the test system’s configuration. The cost subject MG system. The rated power, rated speed, cut-in
function, which must be minimised, is evaluated in a vari- speed, and cut-out speed of the mentioned wind farm are,
ety of scenarios using a variety of optimisation approaches, in that order, 30 kW, 15 m/s, 5 m/s, and 45 m/s. Figure 7
which are covered in detail in the sections that follow. The shows the wind speed to power conversion as mentioned in
optimisation tasks were executed on a desktop computer with Eq, (8). The wind speed data were gathered from [47]. Table
the following configuration: Processor 12th Gen Intel(R) 3 represents the price elasticity matrix necessary to evaluate
Core (TM) i5-12,500 3.00 GHz; Installed RAM: 8.00 GB IBDR1.
(7.70 GB usable). Thirty trials of the algorithms were run

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Table 2 DER Scalars [47]

Unit Gen1 Gen2 Gen3 Gen4 Gen5 Gen6 Grid

Max (kW) 80 50 35 30 40 200 50

Min (kW) 20 15 10 10 12 50 − 50
x ($/kW2 ) 0.0275 0.0625 0.00834 0.025 0.025 0.00975 TOU
y ($/kW) 1.75 1 3.25 3 3 2
z ($) 0 0 0 0 0 0
m ($) 16 14 12 13 13.5 18
n (rad/kW) 0.038 0.04 0.045 0.042 0.041 0.037

Fig. 6 Load demand and electricity market price

Fig. 8 Customers’ cost implications related to adjustments in incentive

values

5.1 Description of results obtained by evaluating

IBDR1: customer incentives for load curtailing
based on price elasticity matrix

Considering that 40 per cent of microgrid users participated

in the IBDR1 programme, 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 consid-
ered. The price elasticity matrix was gathered from [48]. The
total incentive costs associated with different incentive lev-
Fig. 7 Wind Speed and corresponding calculated wind power els are displayed in Fig. 8. It is evident that the expenses
for the DR participants consistently increased as the incen-
Table 3 Price elasticity matrix [51]
tive values were modified. Individually incentive price inside
Peak Off peak Valley the previously indicated ranging of $0.5 to $5 is then eval-
uated in relation to the cost of power generation and the
Off peak 0.016 − 0.1 0.01 total cost. The generating cost consists of the cost compo-
Valley 0.012 0.01 − 0.1 nents of the DERs as well as the purchasing and selling costs
Peak − 0.1 0.016 0.012 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

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Fig. 9 Variation in the MG system’s total cost and generating cost for Fig. 11 Impact of incentive values on the MG system’s load factor
various incentive values

21 when the original demand was at its peak. Due to the DR

CSA was used for optimization, Fig. 9 showcased the gener- programme’s involvement, the peak demand decreased by
ation cost and overall cost of producing active electricity. The 6.9 per cent, from 421 to 392 kW and an overall of 80 kW
graph indicates that the overall cost of the system declined load was curtailed at the end of the day. Figure 11 illustrates
until incentive values reached $2, at which point it began to how an increase in incentive value leads to an improvement in
increase. However, the cost of generating energy decreases load factor. The MG system without DR had an initial load
consistently as the value of incentives increases. Consider- factor of 0.7641, which progressively increased to 0.8123
ing the system’s complete cost had decreased to $24,969, it when the incentive value was $2.
is deemed that $2 is the model incentive price for additional
examination. $277.8352 must be given to customers as the 5.2 Description of results obtained by IBDR2:
incentive cost in order to achieve the highest incentive value. maximisation of DISCOM profit based
As a result, the MG system achieved an optimal reduction on customer willingness
in the cost of power production, calculated at $25,246 by
the DR algorithm. Figure 10a illustrates the system’s load In this level, CSA is employed to maximise DISCOM benefit,
requirement with and without demand response (DR), along as shown mathematically in Eq. (18). Table 4 shows three
with a $2 incentive value, whereas Fig. 10b clearly displays consumer kinds and their willingness to participate in the
that the load curtailment was performed during hours 17 to IBDR2 policy. Table 4 also shows that consumers 1, 2, and 3

Fig. 10 Load demand with and without IBDR1

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Table 5 Optimal parameters of

IBDR 2 Hourly load curtailing by customers Hourly incentives received by
(kW) customers ($)

Hours m1 m2 m3 n1 n2 n3

1 0.000 0.000 0.000 0.0000 25.9304 0.0007

2 0.000 0.000 0.000 0.0003 0.0012 0.0007
3 0.000 0.000 0.000 0.0003 0.0012 0.0007
4 0.000 0.000 0.627 0.0003 0.0012 0.0007
5 0.000 0.514 1.170 0.0003 0.0012 0.0007
6 0.000 0.709 1.310 0.0003 0.0012 0.0007
7 0.340 1.040 1.560 0.0003 0.0012 0.0007
8 0.726 1.340 1.780 0.0003 0.0012 0.0007
9 2.410 2.660 2.770 0.0003 0.0012 0.0007
10 1.740 2.130 2.370 26.6561 20.0210 0.0007
11 2.010 2.350 2.530 0.0003 0.0012 0.0007
12 2.560 2.780 2.850 0.0003 0.0012 0.0007
13 3.160 3.250 3.200 0.0003 0.0012 0.0007
14 3.780 3.730 3.570 27.2002 20.0210 0.0007
15 4.650 4.420 4.080 0.0003 20.0211 0.0007
16 2.910 3.050 3.060 20.8630 20.0210 19.1548
17 2.530 2.760 2.840 26.4027 20.0210 19.0002
18 1.910 2.270 2.480 14.3101 0.0012 19.0002
19 1.290 1.780 2.110 0.0014 0.0012 19.0002
20 0.000 0.221 0.947 0.0003 0.0012 27.2802
21 0.000 0.000 0.656 0.0003 20.0210 24.3912
22 0.000 0.000 0.081 0.0003 20.0211 19.0002
23 0.000 0.000 0.000 15.6034 0.0012 16.7395
24 0.000 0.000 0.000 1.4374 0.0012 37.8476
Total 30.016 35.004 39.9913 132.4794 166.0965 201.4241

Table 4 Customer cost function coefficients [40]

j 1 2 3

x1,j 1.079 1.378 1.847

x2,j 1.32 1.63 1.64
j 0 0.45 0.9
CMj (kWh) 30 35 40

can curtail power (PC) up to 30, 35, and 40 kWh, respectively.

Figure 12 depicts the hourly costs in $/kW fixed by utility for
customers on curtailing their load demand. Customers should
not spend more than $500 on incentives at the end of the day,
which is also the DISCOM (BL) budget. The utility gained a
maximum monetary advantage of $211.413. Table 5 shows
the ideal customer load curtailment values for each hour. It
can be seen that the overall load restricted by customers at the Fig. 12 Cost per hour of not providing power
end of the day aligns with their restrictions outlined in Table 4
and a total of 105 kW load was curtailed at the end of the day.

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Table 6 Minimised generation cost

Case 1 Case 2 Case 3

PSO [47] 25,468 25,532 280,014

TLBO [47] 25,475 25,542 28,013
SCA [47] 25,482 25,538 28,015
JAYA [47] 25,465 25,531 28,003
CSA [47] 25,465 25,531 28,002
CSAJAYA [47] 25,463 25,530 28,000
CIRCLE 25,463 25,530 28,000
CIRCLE + IBDR1 24,969 25,053 27,484
CIRCLE + IBDR2 24,899 24,988 27,435

influenced with IBDR1, and load demand influenced with

Fig. 13 Load Demand with and without IBDR2
IBDR2, respectively, as mentioned in Table 6. The hourly
load distribution between DERs in this scenario is displayed
Table 5 also shows that the total reward earned by consumers in Fig. 14d–f. It is evident that the grid has no negative values
at the end of the day matched the DISCOM’s maximum aim attached to it. Rather, the grid is only observed to supply
of $500. Figure 13 shows the hourly load demand before and electricity during the 1st to 6th hours and 23rd to 24th hours,
after the curtailment of loads by the consumers using IBDR2 when load demand is at its highest.
policy. Case 3: In this, the generating cost is decreased without
taking the RES into account. In this instance, the reduced gen-
eration cost was reduced to $28,000, $27,484, and $27,435
5.3 Generation cost minimization for various load for base load demand, load demand influenced with IBDR1,
demand profiles using CSA and load demand influenced with IBDR2, respectively, about
9% more than that of Case 1. This is a result of both the spike
In this stage, generation cost is minimised by proposed CSA in the fined emission costs and the increased fuel costs of the
for the base load demand and for the final load demands generators, which had to be used more frequently since the
obtained by subtracting the load curtailed by customers in RES was unavailable. Figures 14g–i shows the periodic out-
IBDR1 and IBDR2. Three cases are studied for all the three put of DERs for Case 3.
varieties of load demand models which are described below:
Case 1: This is the ideal case of microgrid operation. All of
the DERs in this instance are functioning within their permis- 5.4 Exhaustive techno-economic analysis
sible limits. The main factor contributing to the MG system’s
lowest generating cost compared to all other examples exam- Following grid behavioural analysis, the hourly power trans-
ined is the grid’s active participation in the purchasing and fer between the grid and the MG system was plotted and
selling of electricity. In this instance, the lowest generating displayed in Figs. 15a and b. As instance 2 (Fig. 15b) illus-
cost determined by CSA is $25,463, $24,969, and $24,899 trates, the grid’s minimum value is zero, indicating the grid’s
for base load demand, load demand influenced with IBDR1, passive involvement. For Case 1, the grid bought power from
and load demand influenced with IBDR2, respectively, as the MG system during the first 18 h when the load demand
mentioned in Table 6. When the lowest cost was achieved, was less and sold power during hours 1 through 7, 23rd, and
Fig. 14a–c displays the hourly load distribution between 24th as the load demand was high and electricity market price
DERs for Case 1. This case has been improvised in the other was low during these periods of time. For hours 12 through
two cases. 22, the electricity market price was high and hence power
Case 2: In this instance, the grid’s passive involvement is was bought back by the grid to curtail the cost of genera-
examined. This implies that the microgrid system may only tion the system. During case 2 as seen in Fig. 15b, the grid
purchase electricity from the grid when the DERs are unable remains passive delivering no power from 12th to 22nd h.
to provide the entire load demand for a certain period of time. Figure 16 shows the positive impact of IBDR implementa-
The grid is in inactive mode for the remainder of that duration. tion in reducing the generation cost of the system. 303 kW
In this instance, the generating cost was reduced to $25,530, of power was bought back by the grid when IBDR was not
$25,053, and $24,988 for base load demand, load demand considered. This increased to 326 kW and 398 kW for when

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Fig. 14 a Case 1 without IBDR, b Case 1 with IBDR1, c Case 1 with IBDR2, d Case 2 without IBDR, e Case 2 with IBDR1, f Case 2 with IBDR2,
g Case 3 without IBDR, h Case 3 with IBDR1, i Case 3 with IBDR2

IBDR1 and IBDR2 were considered, respectively. As men- 5.5 Nonparametric statistical analysis of proposed
tioned earlier, the minimum generation cost depends a lot CSA
on the active participation of grid especially in buying back
power from the MG system. In fact, from Fig. 16 we can see Eight other algorithms were studied along with proposed
more power was bought by the grid then being sold to the CSA to be implemented to minimise the generation cost of
MG system. Hence, the net power transacted between grid the MG system for all the cases. The algorithms are transient
and MG was negative at the end of the day. search optimiser (TSO) [53], slime mould algorithm (SMA)
CSA was also implemented to minimise the cost of gen- [54], seagull optimization algorithm (SOA) [55], salp swarm
eration of the given MG structure without considering grid algorithm (SSA) [56], reptile swarm algorithm (RSA) [57],
support. The minimal cost of the system as evaluated by CSA arithmetic optimization algorithm (AOA) [58], rat swarm
was $25,760. This increased to $28,360 when the RES sup- optimiser [59] and Aquila optimiser (AO) [60]. All of these
port was disregarded. These values match with those obtained algorithms were executed for 30 independent trials for all
by a CSAJAYA algorithm from [47]. the three cases and the generation costs were reported in
each case. The minimum, maximum, and mean generation
cost along with the standard deviation and elapsed time were

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Fig. 15 Grid transaction of power for a Case 1, b Case 2

Table 7 Measures of central

tendencies for different Optimization Cases Mean Standard Maximum Minimum Time
optimization algorithms Algorithms Deviation Lapse

CSA Case 1 25,463.1333 0.4342 25,465 25,463 2.7619

TSO (Active 25,559.8959 14.7048 25,589 25,530 2.8377
Grid)
SMA 25,463.4000 0.7240 25,465 25,463 10.7219
SOA 25,522.3326 6.1997 25,535 25,513 3.1139
SSA 25,628.1315 9.9784 25,646 25,606 6.0640
RSA 25,562.2293 14.6280 25,586 25,542 22.9588
AOA 25,475.2327 5.8703 25,493 25,467 2.6344
RSO 25,693.2554 24.4483 25,745 25,645 2.6332
AO 25,720.5318 8.9856 25,732 25,707 42.0483
CSA Case 2 25,530.3666 1.4016 25,536 25,530 35.5353
TSO (Passive 25,617.4830 4.4073 25,625 25,609 37.3998
Grid)
SMA 25,530.7999 2.5107 25,541 25,530 41.5350
SOA 25,558.4709 2.2730 25,562 25,555 37.0384
SSA 25,692.5842 5.1786 25,703 25,684 38.6100
RSA 25,677.2175 6.7798 25,688 25,665 57.7703
AOA 25,531.9996 4.5562 25,546 25,530 38.3087
RSO 25,742.3900 15.6177 25,753 25,698 35.7097
AO 25,754.40397 17.4200 25,788 25,728 45.2406
CSA Case 3 28,000.1333 0.3457 28,001 28,000 68.8594
TSO (With- 28,115.0323 7.6676 28,126 28,104 65.3931
out
SMA RES) 28,000.2333 0.4302 28,001 28,000 156.6906
SOA 28,060.3327 6.0191 28,070 28,053 46.3601
SSA 28,134.7146 6.6933 28,146 28,124 29.1264
RSA 28,121.7912 22.5884 28,157 28,089 388.4919
AOA 28,001.4000 0.4983 28,002 28,001 46.6883
RSO 28,258.6997 3.8965 28,265 28,252 32.7155
AO 28,271.2622 16.0944 28,302 28,244 74.8158

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generation cost in each scenario. Table 7 demonstrates the

low standard deviation and algorithm execution time, both
of which are strong indicators of the suggested CSA algo-
rithm’s resilience and effectiveness. Figure 18 shows the box
plot which is constructed with the help of measures of central
tendencies from Table 7.

6 Conclusion

This research article presents work that reduces the genera-

tion costs of a low-voltage microgrid system using two inte-
grated battery discharge rate techniques. The latter employs
Fig. 16 Total power transacted between grid and MG system an optimal approach to enhance DISCOM benefits by provid-
ing incentives to consumers for load curtailment depending
on their desire, while the former incorporates price elastic-
tabulated in Table 7. The features of the convergence curve ity to reduce load during peak hours and provide rewards to
are displayed in Fig. 17 after the CSA determined the lowest customers. This thereby reduces the generation costs of the

Fig. 17 Convergence curve characteristics of the algorithms for minimization of generation cost

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Fig. 18 Box plot representation of the algorithms for minimization of generation cost

MG system while conserving energy. The study’s findings taking into account the emission coefficients, and the pro-
lead to the following conclusion: posed optimization method might be evaluated to provide an
equitable solution for weighted economic emission dispatch.

• The IBDR2 policy resulted in a lower minimum genera-

tion cost than IBDR1 by requiring consumers to reduce Appendix
load demand by 105 kW, while IBDR1 only achieved a
reduction of 80 kW. The proposed IBDR2 strategy seeks Table A lists the symbols used in the equations. Table B
to optimise DISCOM advantages by taking into account enlists the abbreviations used in the text along with their full
client willingness, resulting in a low generation cost. The form. Table C mentions the value of tuning parameters used
only disadvantage of IBDR2 is the need for an optimization in different optimization algorithms.
technique, while IBDR1 may be readily assessed using the Table A: List of symbols
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 C grid Time-of-use (TOU)
price of power
enough to provide the best fitness function value for all
levels and instances examined.
x, y, and z Cost coefficients
i Index
Limitations influencing future research scope: The find- Pi Output power
ings of our research are very advantageous for microgrid Pgrid Output of grid
operators, particularly regarding cost efficiency and load mi and ni Valve point effect
management. By using our optimization strategies, oper- Cost DG Total cost
ators may substantially reduce operational expenses via d Ldu Variance of load
improved resource allocation and energy use. Enhanced demand
load management minimises the likelihood of interruptions Ldut Load demand under
and strengthens system stability by assuring more accu- uncertainty
rate fulfilment of energy demand. These upgrades result n1 Standard distribution
in significant cost savings, improved operational efficiency function
and more sustainable energy practices. Subsequent research Ld tf c Anticipated demand
should concentrate on many significant subjects. Incorporat- W dut Uncertainty of wind
ing battery energy storage systems (BESS) into optimization production
models is an effective method to reduce costs and enhance dWi Divergence of wind
output
energy reliability. Moreover, investigating the influence of
n2 Standard distribution
different load models on the environment may provide crit-
function
ical insights into their ecological effects and sustainability.
Analysing these components may provide microgrid solu-
tions that are more environmentally sustainable and efficient.
Similar research may be undertaken as a novel investigation,

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C grid Time-of-use (TOU) DER Distributed energy

price of power resources

W d tf c Projected wind IDSM Integrated

energy production demand-side
LD R management
X (t) The load at bus X
η Load available for GES Generalised energy
DR storage
L 0X (t) Initial demand value VGWO Variegated GWO
algorithm
Csp (t) Spot electricity price
MOMFO Multi-objective moth
Ci p (t) Preliminary price of flame optimization
electricity algorithm
E(t, t) Self-elasticity GWO Grey wolf
E(t, h) Cross-elasticity optimization
Csp (t) Spot pricing GA Genetic algorithm
Ci p (t) Initial electricity TOU Time-of-use
price DG Distributed generation
LD R
X (t) Reduction in power LLV Lower limit values
consumption at
the“bs” ULV Upper limit values
c( , m) Cost borne by a WT Wind turbines
client
CMj Daily limit of Table C: Specific tuning parameters of algorithms used
interruptible and their values
electricity
iter Iterations
γ ,β Scale and shape
factor of Weibull Algorithms Specific parameters
PDF with values
V in , vout vr Cut-in, cut-out, and
rated speed of wind TSO Constant k ∈ 2, z ∈
[0,2]
SMA vb and vc decreased
Table B: List of abbreviations from 2 to 0
SOA Control Parameter
(A) ∈ [2, 0]; fc ∈ 2
DER Distributed energy SSA c1 ∈ [01]; c2 ∈ [01];
resources RSA α ∈ 0.1, 0.5; β ∈ 0.1,
0.9
LV Low voltage AOA α  5; μ  0.5
MG Microgrid RSO R ∈ [1, 5]; C ∈ [0, 2]
IBDR Incentive-based AO α ∈ 0.1, 0.5; δ ∈ 0.1,
demand response 0.9
CSA Circle search
algorithm
DR Demand response Acknowledgements N/A
ELD Economic load
dispatch Author contributions Author one and two are responsible for simu-
lation, results, analysis and for writing and preparing the draft of the
DEDP Dynamic economic manuscript. Author three is responsible for reading and for providing
dispatch problem critical review of the manuscript.
DMCP Discrete-time mean
consensus protocol Funding Open access funding provided by University of Johannes-
burg. This research received no specific grant from any funding agency
EMS Energy management
in the public, commercial, or not-for-profit sectors.
system
DSM Demand-side Data availability No datasets were generated or analysed during the
management current study.

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Electrical Engineering

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permitted by statutory regulation or exceeds the permitted use, you will 16. Bodong S, Wiseong J, Chengmeng Li, Khakichi A (2023) Eco-
need to obtain permission directly from the copyright holder. To view a nomic management and planning based on a probabilistic model in
copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. a multi-energy market in the presence of renewable energy sources
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