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Energy Engineering
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DOI: 10.32604/ee.2024.043294

ARTICLE

Optimal Bidding Strategies of Microgrid with Demand Side Management for Economic Emission Dispatch Incorporating Uncertainty and Outage of Renewable Energy Sources

Mousumi Basu1, Chitralekha Jena2, Baseem Khan3,4,* and Ahmed Ali4

1Department of Power Engineering, Jadavpur University, Jadavpur, India
2School of Electrical Engineering, KIIT University, Bhubaneswar, India
3Department of Electrical and Computer Engineering, Hawassa University, Hawassa, Ethiopia
4Department of Electrical and Electronic Engineering Technology, Faculty of Engineering and the Built Environment,University of Johannesburg, Johannesburg, South Africa
*Corresponding Author: Baseem Khan. Email: baseemkh@hu.edu.et
Received: 06 June 2023; Accepted: 28 November 2023; Published: 26 March 2024

Abstract: In the restructured electricity market, microgrid (MG), with the incorporation of smart grid technologies, distributed energy resources (DERs), a pumped-storage-hydraulic (PSH) unit, and a demand response program (DRP), is a smarter and more reliable electricity provider. DER consists of gas turbines and renewable energy sources such as photovoltaic systems and wind turbines. Better bidding strategies, prepared by MG operators, decrease the electricity cost and emissions from upstream grid and conventional and renewable energy sources (RES). But it is inefficient due to the very high sporadic characteristics of RES and the very high outage rate. To solve these issues, this study suggests non-dominated sorting genetic algorithm II (NSGA-II) for an optimal bidding strategy considering pumped hydroelectric energy storage and DRP based on outage conditions and uncertainties of renewable energy sources. The uncertainty related to solar and wind units is modeled using lognormal and Weibull probability distributions. TOU-based DRP is used, especially considering the time of outages along with the time of peak loads and prices, to enhance the reliability of MG and reduce costs and emissions.

Keywords: Micro-grid; distributed energy resources; demand response program; uncertainty; outage

Nomenclature

PSP | Pumped storage plant
FC | Cost function
FE | Emission function
aGi,bGi,cGi | Cost coefficients of ith gas turbine
αGi,βGi,γGi | Emission coefficients of ith gas turbine
URi, DRi | Upper and lower ramp limits of ith gas turbine
PGit | Output of ith gas turbine
PGimin, PGimax | Minm and Maxm limit of generation for ith gas turbine
Pgrid,t | Power procured from upstream grid at time t
Pgridmax | Maximum power exchange between MG and upstream grid
cgridt | Grid electricity price at time t
egridt | Emission of grid power at time t
Pwjt | Wind power available of jth wind turbine at time t
Pwjmin, Pwjmax | Minm and Maxm generation limits for jth wind turbine
Pwrj | Wind power rated of jth wind turbine
dwj | Direct cost coefficient for the jth wind turbine
vin | Cut- in velocity of wind
vout | Cut-out velocity of wind
vr | Velocity of rated wind
vwt | Forecasted velocity of wind
α,β | Scale and shape factors for Weibull PDFs
μLog,σLog | Lognormal PDF’s standard deviation and mean
μNorm,σNorm | Standard deviation of the mean and variance
PPVkt | Power output from kth PV plant
Psrk | Equivalent rated power output of the PV plant
G | Forecast of radiation of solar
Gstd | Radiation from the sun in a normal environment
Rc | Specific level of radiation
dPVk | Direct cost co-efficient for the kth solar PV plant
uwj, owj | Penalty and reserve cost for the jth wind turbine
uPVk, oPVk | Penalty and reserve cost for the kth PV plant
Pghlt | Generated power of lth PSP at time t
Pphlt | Pumping power of lth PSP
Pghlmin, Pghlmax | Minm and maxm generation power limits of lth PSP
Pphlmin, Pphlmax | Minm and maxm pumping power limits of lth PSP
Qghlt(Pghlt) | Discharge rate of lth PSP
Qphlt(Pphlt) | Pumping rate of lth PSP
Qspent,TOT,l | Total amount of water spent for generation of lth PSP
Qpump,TOT,l | Total amount of water pumped of lth PSP
Qnet,spent,l | Net amount of water spent by lth pumped storage hydraulic unit during operation cycle
Vres,lt | Volume of water in upper reservoir of lth PSP
Vres,lmin, Vres,lmax | Minm and maxm limits of upper reservoir storage of lth PSP
Vres,lstart, Vres,lend | Specified volume of water at starting and final in upper reservoir of lth PSP
Incmax | Maxm increased load at any hour (MW)
LBase,t | Forecasted base load
DRt | Percentage of forecasted based load participated in DRP
DRmax | Limit on how much of the base load can participate in DRP
Inct | Amount of increased load
Lst | Shiftable load
F | Failure rate (failure times/year)
FPV,Fw | Wind and solar power system’s maximum failure rate (failure times/hour)
MTTR | Mean time to repair
MDTi,MUTi | Mean down and up time of ith gas turbine
ρ | Rate of forced outage
ρRepair,ρAging,ρWeather | Forced outage rate due to repairable, aging, and weather dependent failure
ρwjt,ρPVkt | At time t, forced outage rate of jth wind turbine and kth solar power plant
λ | Probability of failure
Swjt | ‘1’ if jth wind power unit is scheduled on at time t and otherwise ‘0’
SPVkt | ‘1’ if k th Solar PV plant is scheduled at time t and otherwise ‘0’
SGjt | ‘1’ if ith gas turbine is scheduled on at time t and otherwise ‘0’
Ton,i,(t−1),Toff,i,(t−1) | On and off condition of ith gas turbine before (t−1)th time
t, T | Time index and scheduling period
Tgen | Set containing time intervals where PSP operate in generation mode
Tpump | Set containing time intervals where PSP operate in pumping mode
N G | No. of thermal generating units
N w | No. of wind turbine
N PV | No. of solar PV plant
N Pump | No. of PSP

1  Introduction

When it comes to a smart grid, the most important component is the microgrid (MG), which provides an efficient energy system with better power quality, reliability, and economics to grid-independent end-user locations. As smart grid technology advances, MGs must continue to function with a very well-pumped-storage-hydraulic (PSH) unit and increase customer engagement through demand-side management [1,2]. Thus, MG can purchase power from upstream grid-connected, distributed energy sources with the advantage of time-varying electricity prices to meet its demand. When it comes to renewable energy, though, there are several issues that make it difficult for MG operators to purchase power from day-ahead markets at variable prices so that costs and pollution may be reduced concurrently. Hence, to bid for electricity in the day-ahead market, MG should plan an optimal bidding strategy to buy power from the upstream grid with a demand response program (DRP), taking into consideration the uncertainty and outages of the sources of renewable energy.

The best bidding strategy has been studied in the below mentioned references in order to reduce energy prices in the deregulated electricity market and to improve the dependability of the power system. Optimal Control of a Microgrid with Distributed Renewable Generation and Battery Energy Storage is presented in reference [3]. Stochastic programming and two-stage stochastic programming [4] have been used to design a bidding strategy for MG that maximizes both power scheduling and profit maximization [5]. A bi-level programming-based energy bidding strategy for MG has been proffered in reference [6], in which a stochastic model of uncertain renewable energy sources and loads is considered. A integrated demand response in multi-energy microgrids using deep reinforcement learning is presented in reference [7]. In reference [8], a day-ahead bidding strategy for grid-tied residential MG has been proposed. A robust optimization-based day-ahead bidding approach has been employed in reference [9] for maximizing the profit from the joint energy and spinning reserve markets. In reference [10], DRP is introduced in the bidding operation of MG to facilitate customers with active participation with the MG aggregator and system operator. Small-scale MGs are involved in a DRP-assisted real-time balancing bidding process in a hierarchical market model [11]. Another DRP-aided short-term bidding framework for MG has been represented in reference [12] as a robust optimization-based best-cost model.

The gas turbine discharges many pollutants, like SOx, NOx, and CO2, into the atmosphere for electric utilities. The ambiance of reducing greenhouse gases is one of the important concerns. The Clean Air Act of 1990 was intended to reduce greenhouse gases and acid rain. So for that, the gas turbine must decrease its sulfur oxide (SOx) and NOx levels of emission [13]. Today’s society is looking for a secure and reliable source of energy that is both cost-effective and environmentally friendly.

1.1 Literature Review

A variety of tactics are suggested to decrease ambient greenhouse gases [14]. Dispatching, considering emissions, is preferable among these.

On the basis of historical data and a list, concerns about renewable energy resources (RER) are simulated. Bidding tactics in references [10–12] include demand response programs (DRPs) to relieve load only during times of high demand or high cost. DRP integration, on the other hand, may significantly improve the MG’s dependability and operating costs during DER outages.

Based on economic environmental dispatch (EED) with DRP, this study proposes an efficient bid for MG based on the outages of intermittent renewable energy sources [15,16]. Wind turbine (WT) units use the Weibull PDF (WPDF), whereas solar photovoltaic (PV) units use the well-established Lognormal PDF (LPDF). These PDFs are widely used to estimate renewable energy sources’ uncertainty probabilities. Within the anticipated upper and lower limits [17], all of the potential scenarios are mapped with repetition. To encourage MG to make precise decisions on power generation dispatch during bidding, penalty costs for underestimates and reserve costs for overestimations of RER outputs are included in the primary costs [16]. Forced outages are more likely to occur due to RER facilities’ remoteness and difficult operating conditions. RER unit outage probability also follows certain mathematical formulations or PDFs based on distinct types of failures, such as repairable, aging, and weather-related [18–25]. References [26,27] discussed the economic dispatch problem using different computationally intelligent techniques. Considering the uncertainty and outage modeling of RERs, the MG operator performs the EED to settle the optimal power dispatch schedules of generators and pumped-storage-hydraulic (PSH) units and electricity purchasing in the day-ahead market to facilitate its bidding optimization. Here, NSGA-II is suggested to solve the EED problem. The techno-economic evaluation of combined power-to-hydrogen technology and hydrogen storage in an optimal bidding approach for microgrids with high penetration rates of renewable energy units was proposed by the authors in reference [28]. A grid-connected multi-microgrid system’s ideal heat and power energy management, taking demand response and bidding strategy into account, was suggested by authors in reference [29] as an economic-environmental risk-averse approach. The coordinated optimal bidding techniques of aggregated microgrids were devised by the authors in reference [30]. In order to do this, demand-side management based on game theory is applied in an environment where electricity is sold. A clever predict-and-optimize framework for the bidding strategy of microgrids in a day-ahead electricity market was proposed by the authors in reference [31]. The effect of the ideal pump storage unit size on microgrid operational costs and energy market bidding was examined by the authors in reference [32]. The effect of the ideal pump storage unit size on microgrid running costs and energy market bidding was examined by authors in reference [33].

1.2 Research Gaps

Based on the review performed in the previous section, it is concluded that the previous researchers did not incorporate the emission constraints into the economic dispatch problem. Moreover, most of the researchers did not consider the demand-side management response. At last, various researchers did not consider the uncertainty and outages of renewable energy sources.

1.3 Contribution

To address the research gaps discussed in the previous subsection, the authors have made the following contributions to this manuscript:

1.    Optimal bidding strategies for microgrids with demand-side management are presented.

2.    Economic dispatch is proposed by incorporating uncertainty and outages from renewable energy sources.

3.    Emission constraints are incorporated into the economic dispatch.

4.    The non-dominated sorting genetic algorithm II (NSGA-II) is utilized for economic emission dispatch.

1.4 Organization of the Manuscript

The organization of the manuscript is as follows: Section two presents the problem formulation. Section three presents the proposed methodology. Section four presents the results and discusses them, followed by the conclusion.

2  Problem Formulation

The proposed MG is considered to be grid-connected and consists of gas turbines (GTs), a solar PV plant, wind power generation units, a pumped-storage-hydraulic (PSH) unit, and loads. Day-ahead weather data and electricity prices are assumed to be known from historical data and other factors. The MG operator must determine the degree of energy purchase from the upstream grid and GTs, solar PV plant, wind turbine, and PSH production in order to minimize overall cost and emissions simultaneously while taking into account associated constraints. For the sake of problem formulation, the following objective functions with constraints were used.

2.1 Modelling of the System

2.1.1 Arrangement of Probability of Solar Power Plant and Wind Turbine

Because of its unpredictability and intermittent nature, integrating solar power and wind turbines into an MG is difficult. MG’s steady state security is imbalanced if demand spikes because of an underestimation of renewable power and an overestimation of its reserve capacity buffers, which wastes extra energy. MG’s overall production and operating costs in energy bid planning are impacted by each of these factors. The use of probability distribution functions (PDFs), such as lognormal and Weibull, to assess penalty costs for underestimates and reserve costs for underestimates has led to a wide range of uncertainty models, such as beta, gumbel, and lognormal. The results of Eqs. (1) and (2) are well-followed by lognormal or Weibull PDFs [16].

fG(G)=1G×σLog×2×Π×e−{−(ln⁡G−μLog)22×μLog2} for G>0(1)

fv(v)=(βα)×(vα)(β−1)×e−(bα)β for 0<v<∞(2)

2.1.2 Model of Wind Power

At time t, the output power [18] of the jth wind turbine for a particular velocity of wind is given as

Pwjt=0, for vwt<vin and Pwjt=Pwrj×(vwt−vinvr−vin)

Pwjt=Pwrj×(vwt−vinvr−vin), for vi≤vwt≤vr(3)

Pwjt=Pwrj, for vr≤vwt≤vout

2.1.3 Model of Solar Power

At time t, the output power [19] from the kth PV solar plant is given as

PPVkt=Psrk×(G2GstdRc), for 0<G<Rc(4)

PPVkt=Psrk(GGstd),forG≥Rc

2.1.4 PV Power Probabilities

The PV power probability is the same as the related solar power irradiation probability, in terms of Eq. (5).

fPV(PPV)=fG(G)(5)

2.1.5 Wind Turbine Power Probabilities

Wind power probabilities for discrete zones, i.e., for the first and third cases of (3), may be estimated using Eqs. (6) and (7) [15].

fw(Pw)|PW=0=1−e−(vinα)β+e−(voutα)β(6)

fw(Pw)|PW=PWr=−e−(vinα)β−e−(voutα)β(7)

As in the second situation in Eq. (3), the probability of WT power in the uninterrupted zone may be calculated in Eq. (8).

fw(Pw)=β×(vr−vin)αβ+Pwr×[vin+PwPwr×(vr−vin)](β−1)×e−(vin+PwPwr×(vr−vin)α)β(8)

2.2 Modelling Outage of Wind Turbine and Solar Power Plant

As a result of harsh climatic conditions, renewable energy sources are often driven out of service owing to the deterioration of their components and the inability to repair them. For any power system, the repairable forced outage rate is given as Eq. (9) [16].

ρRepair=F×MTTR8760(9)

The component aging failure model typically follows the normal PDF throughout the service duration. The aging rate of failure is determined by Eq. (10).

ρAging=1σNorm×2×Π×e−(T−μNorm)22×σNorm2(10)

For a time period of Δt, by exponential distribution as Eq. (11), the weather-dependent failure model is modeled as follows:

ρWeather=1−e−λ×Δt(11)

As a result, a multi-factor independent outage occurs, and the outage rate may be estimated using the union set idea. For any renewable unit, the forced outage rate can be given by Eq. (12).

ρ=ρRepair∪ρAging∪ρWeather=ρRepair+ρAging+ρWeather−ρRepair×ρAging−ρAging×ρWeather−ρweather×ρRepair−ρRepair×ρAging×ρWeather(12)

2.3 Objective with Constraints

For optimal bidding, simultaneously total cost and emission are optimized considering every operational constraint. Total cost is the sum of the energy costs purchased from the grid, the fuel and operation costs of gas turbines, and the operation costs of solar PV plants and wind turbines during the entire time scale. Total emissions are the sum of emissions corresponding to the purchase of grid power and emissions from gas turbines.

2.3.1 Cost

As fuel costs rise, gas turbine output power increases quadratically. Solar PV and wind turbine operations include reserve expenses for overestimation of direct costs and penalties for underestimating dispatchable solar electricity and wind power, respectively. The total cost is the sum of the fuel cost of GT power, the cost of power purchased from the grid, and the operational cost of the PV solar plant and wind turbine [28–31].

FC=∑t=1T[∑i=1NG{(aGi+bGi×PGit+cGi×PGit2)×SGit}+(cgridt×Pgrid,t)+∑j=1Nw{dwj×Pwjt+Owjt(Pwjt)+Uwjt(Pwjt)}×Swjt+∑k=1NPV{dPVk×PPVkt+OPVkt(PPVkt)+UPVkt(PPVkt)}×SPVkt](13)

where Swjt={1,ρwjt<Fw0,otherwise and SPVkt={1,ρPVkt<FPV0,otherwise

On dispatchable wind power, the overestimation reserve cost and the underestimation penalty cost are modeled, respectively, in Eqs. (14) and (15).

Owjt(Pwjt)=owj×∫PwjtminPwjt(Pwjt−y)×fw(y)dy(14)

Uwjt(Pwjt)=uwj×∫PwjtPwjtmax(y−Pwjt)×fw(y)dy(15)

Reserve costs and penalties for underestimated dispatchable solar power costs are modeled in Eqs. (16) and (17), respectively.

OPVkt(PPVkt)=oPVk×∫PPVktminPPVkt(PPVkt−x)×fPV(x)dx(16)

UPVkt(PPVkt)=uPVk×∫PPVktPPVktmax(x−PPVkt)×fPV(x)dx(17)

2.3.2 Emission

The ambient greenhouse gases, such as SOx, NOx, and CO2, produced by gas turbines are modeled separately. But, for evaluation purposes, the total emission of greenhouse gases is given as the sum of a quadratic function, while the total emission is the sum of emissions from gas turbines and emissions of power taken from the upstream grid.

FE=∑t=1T[∑i=1N G{(αGi+βGi×PGit+γGi×PGit2)×SGit}+(egridt×Pgrid,t)](18)

2.3.3 Power Balance Constraint

The limit of power balance is depicted in Eqs. (19) and (20), which state that the power procured from the grid, GTs, WTs, PVs, and PSH units will be scheduled according to the load considering DRP. Assuming that, when load is curtailed due to DRP, at that time LSt = 0, and when load is shifted to base load demand, at that time no load is curtailed.

Pgrid,t+∑i=1N G(PGit×SGit)+∑j=1N w(Pwjt×Swjt)+∑k=1N PV(PPVkt×SPVkt)+∑l=1NpumpPghlt=(1−DRt)×LBase,t+Lst t∈Tgen(19)

Pgrid,t+∑i=1N G(PGit×SGit)+∑j=1N w(Pwjt×Swjt)+∑k=1N PV(PPVkt×SPVkt)−∑l=1N pumpPphlt=(1−DRt)×LBase,t+Lstt∈Tpump(20)

The transfer capacity of the line that connects the MG to the main grid limits the amount of power that can be procured from the upstream grid (Eq. (21)).

0≤Pgrid,t≤Pgridmax(21)

2.3.4 Pumped-Storage-Hydraulic (PSH) Unit Constraints

Vres,l(t+1)=Vres,lt+Qphlt(Pphlt), l∈N pump, t∈Tpump(22)

Vres,l(t+1)=Vres,lt−Qghlt(Pghlt), l∈N pump,  t∈Tgen(23)

Pghlmin≤Pghlt≤Pghlmax l∈N pump, t∈Tgen(24)

Pphlmin≤Pphlt≤Pphlmax l∈N pump, t∈Tpump(25)

Vres,lmin≤Vres,lt≤Vres,lmax l∈N pump, t∈T(26)

At the beginning and end, the volume of water in the top reservoir of the PSH unit is taken, and the net amount used by the PSH unit is equal to zero.

Vres,l0=Vres,lT=Vres,lstart=Vres,lend(27)

Qnet,spent,l=Qspent,TOT,l−Qpump,TOT,l=∑t∈TgenQghlt(Pghlt)−∑t∈TpumpQphlt(Pphlt)=0(28)

2.3.5 Generation Limits of Gas Turbine

PGimin≤PGit≤PGimax i∈N G, t∈T(29)

2.3.6 Ramp Rate Limits of Gas Turbine

PGit−PGi(t−1)≤URi,i∈N G, t∈TPGi(t−1)−PGit≤DRi, i∈N G, t∈T(30)

{(Ton,i,(t−1)−MUTi)×(SGi(t−1)−SGit)≥0,i∈N G,t∈T(TOff,i,(t−1)−MDTi)×(SGit−SGi(t−1))≥0,i∈N G,t∈T(31)

3  Demand Side Management

Demand-side management (DSM) programs have numerous advantages, such as improving the power system’s security, reducing costs, and so on. Strategic conservation, demand response, and so on are some of the types of programs. The DSM is modeled using time-of-use (TOU) software [21], which fixes the net load demand. Off-peak or less expensive times are used to shift some demand away from peak times. Consequently, the load curve flattens, and the probable operating costs fall. Using Eq. (32) as a starting point, the TOU program numerical model is restricted by Eqs. (33)–(36).

Lt=(1−DRt)×LBase+Lst(32)

∑t=1TLst=∑t=1TDRt×LBase,t(33)

LInct=Inct×LBase,t(34)

DRt≤DRmax, t∈T(35)

Inct≤Incmax, t∈T(36)

4  Non-Dominated Sorting Genetic Algorithm-II

The non-dominated sorting genetic algorithm (NSGA) was developed by Deb et al. [23] to cope with multi-objective optimization algorithms. Non-domination is used to grade solutions, while fitness distribution is used to control diversity. Srinivas et al. [24] pioneered the non-dominated sorting genetic algorithm II, which gives a more effective solution in terms of fitness distribution parameters than its predecessor. Because of space restrictions, NSGA-complete II’s description is not provided here. The flow chart of NSGA-II is demonstrated in Fig. 1.

Figure 1: Flowchart of NSGA-II

5  Simulation Results

The proposed NSGA-II-based day-ahead optimal bidding strategy for MG based on economic environmental dispatch (EED) with DRP considering outages of intermittent renewable energy sources is performed using numerical simulation. Simulation outcomes of the test system are used to match the efficacy of the suggested NSGA-II with strength pareto evolutionary algorithm 2 (SPEA 2) [25]. Tables A1–A3in Appendix A present the data for the grid-connected MG model’s three gas turbines, one solar PV unit, one wind turbine, and one PSH unit. Table A4 shows the predicted loads and prices of power for the next 24 h, a day in advance. As a result of DSM, 15% of the load of the 16th and 17th h and 20% of the 19th h load were moved. The emission of grid electricity is assumed to be 50 kg per MWh. The following features describe the PSH plant: Generating mode: Qght is positive when generating, Pght is positive and 0 ≤ Pght ≤ 6 MW, Qght(Pght) = 4 + 2Pght acre-ft/hr.

Pumping mode: Qpht is negative when pumping; Ppht is negative and −6 < Ppht ≤ 0 MW, Qpht (Ppht) = −12 acre-ft/h with Ppht = −6 MW.

Operating limitations: During pumping, the pumped hydro plant will be allowed to operate at a maximum power level of around 6 megawatts. During the first 24 h, the reservoir must be 160 acre-feet deep. Without taking spillage into account, the water inflow rate is ignored.

Figs. 2i and 2iishow the upper and lower projected limits for solar irradiation and wind velocity, respectively. Fig. 2 shows a rapid variation in the velocity of the wind at 16 o’clock (Fig. 2ii). High winds cause turbulent weather, which in turn causes renewable energy units to fail. As shown in Fig. 2, weather-dependent historical data may be used to estimate the failure rates of PV and WT units. Fig. 2iv depicts the comparable forced outage rates for those units. There are large failure rates for PV systems in the 16th and 17th h, as can be shown in Fig. 2iv. The WT unit has high failure rates in the 16th to 18th h. For PV and WT unit repairmen, the 17th or 18th h is necessary.

Figure 2: (i) Forecast limits of solar irradiation. (ii) Upper and lower forecast limits of wind speed. (iii) Failure probabilities (λ) for PV and WT. (iv) Forced outage rates of PV and WT units

The two opposing criteria are the total cost and the total amount of emissions. Each goal function, such as total cost and total emission, is reduced using a real-coded evolutionary algorithm in order to explain the relationships between the objective functions (RCGA). Using these parameters, the population size, the maximum number of iterations, the crossover, and the mutation probabilities are all set to 100, 200, 0.9, and 0.02.

NSGA-II has been used to simultaneously optimize both the total cost and the total emission goals. SPEA 2 has helped as a reference point in resolving this issue.

SPEA 2 and NSGA-II have a population size of 20, 30, 0.9, and 0.2, respectively, for crossover and mutation probabilities.

Electricity generated from gas turbines, wind, solar, and pumped storage, as well as power obtained from the upstream grid, is summarized in Table 1. In addition, Table 2 presents the hourly generation (MW) schedule acquired from emission dispatch. Data on the generation of gas turbine, wind, solar, and pumped storage, as well as electricity obtained from the upstream grid through economic emission dispatch, are presented in Tables 3 and 4accordingly. Economic dispatch, emission dispatch, and economic emission dispatch all contribute to the overall cost and total emissions in Table 5. Figs. 3i and 3iishow the convergence characteristics of costs and emissions. Fig. 3iii shows, for instance, the distribution of the 20 non-dominated solutions obtained by NSGA-II and SPEA2 in their most recent iteration, which was derived by occurring as the result of cost and emission objectives.

Figure 3: (i) Cost convergence characteristic. (ii) Emission convergence characteristic. (iii) Pareto-optimal front acquired from the last iteration

After analyzing the results and comparing the performances of NSGA-II with SPEA 2, it was found that the proposed NSGA-II method provides a better result in terms of cost and emissions compared to SPEA 2.

6  Conclusion

An NSGA-II-based day-ahead optimal bidding strategy for MG based on economic environmental dispatch is proposed with consideration of DRP under outage conditions and uncertainties about renewable energy sources. The uncertainty related to solar and wind units is modeled using lognormal and Weibull probability distributions. TOU-based DRP is used, especially considering the time of outages along with the time of peak loads and prices, to enhance the reliability of MG and reduce costs and emissions. The cost obtained by using NSGA-II was 130407 US dollars, whereas for SPEA 2, it was 131451 US dollars. The emission obtained using NSGA-II was 16098 kg, whereas for SPEA 2, it was 16286 kg.

Acknowledgement: All authors acknowledge the support and cooperation of their respective institutions.

Funding Statement: The authors received no specific funding for this study.

Author Contributions: The authors confirm contribution to the paper as follows: study conception and design: Mousumi Basu, Chitralekha Jena, Baseem Khan, Ahmed Ali; data collection: Mousumi Basu, Chitralekha Jena, Baseem Khan, Ahmed Ali; analysis and interpretation of results: Mousumi Basu, Chitralekha Jena, Baseem Khan, Ahmed Ali; draft manuscript preparation: Mousumi Basu, Chitralekha Jena, Baseem Khan, Ahmed Ali. All authors reviewed the results and approved the final version of the manuscript.

Availability of Data and Materials: All data are presented in the paper.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.

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Appendix A

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