Introduction

The transition of the current global power system to the smart grid model has led to various attempts to integrate green renewable energy and energy storage equipment into distribution networks [1, 2]. With the huge integration of decentralized energy resources and changing energy demands, new energy production and consumption models have been introduced into traditional energy system architectures [3, 4]. New technologies for power generation and storage are being developed and sold, including solar power devices, wind turbines, microturbines, fuel cells, thermal unit, gas turbines, superconducting magnetic energy storage (SMES), super-capacitors, and battery storage systems. However, in this article, the most developed and widely used technologies namely wind, solar, battery, and thermal unit are discussed [5].

The microgrid concept assumes that the load and energy clusters operate as a centralized or decentralized hierarchical control system. Furthermore, unlike transmission systems, MG is essentially a distributed network. This creates a variety of issues related to the functioning of grid performance and grid balance. An attractive method is a microgrid. It can adapt to different types of grid and market environments. In addition to the ability to switch between islanded and grid-connected mode of operation to improve power supply demand, it is an attractive option for the associated partners and it enhances system efficiency, including a reduction in congestion, voltage control, and reducing losses [6, 7]. Optimal resource allocation task in the microgrid, such as unit commitment (UC), also requires special attention when adding different resources of energy like battery storage system [8].

Due to the different types of complications in the microgrid, many algorithms have recently been proposed to inspect this area [9]. More or less, all works for conventional UC problems have been enhanced and relatively transformed into settings of the grid applications [10].

Considering the high performance and adaptability of the optimization technique of mixed-integer linear programming (MILP) and the accessibility of solvers, MILP has been used in many recent studies to solve UC problems and it has the capability to find a global optimal solution. In [11], a mixed-integer linear programming method for a centralized energy management system (EMS) has been developed for the unit commitment scheduling and economic dispatch of microgrid units. Generation scheduling to minimize the cost for both operator and consumer with storage technology is investigated in [12]. A network constrained dispatch of renewable energy is discussed in [13]. Integrated energy supply planning to minimize operating costs under uncertainty is proposed in [14]. Based on MILP, high-precision processes have been developed to optimize microgrids such as thermal generators, fuel cells, microturbines, and battery energy storage systems (BESS) [15]. Much effort has been made to develop optimization algorithms to optimize microgrid operations, but few have taken into consideration different aspects of power system operations with the same problem. Till now, from the authors’ knowledge, no contribution has been made considering the renewable sources and demand response flexibility as mentioned in Table 1. This paper proposes a cost-based unit commitment model that integrates renewable energy and BESS into MG.

Table 1 Review of unit commitment studies in renewable energy-based electrical system
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The block diagram of AC microgrid under consideration is shown in Fig. 1 and the simulation approach is given in Fig. 2.

Fig. 1
figure 1

Block diagram of AC microgrid under test

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Fig. 2
figure 2

Simulation approach

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The main contributions of the study are given as follows:

  1. 1.

    Explaining the role of wind, solar, and BESS technologies and demand response flexibility, in improving MG power dispatch, and reducing total operating costs, fuel costs, start-up, and shutdown costs.

  2. 2.

    To investigate different situations to emphasize the accuracy of the given architecture and analyze the simulation results under different scenarios.

  3. 3.

    General Algebraic Modeling System (GAMS) optimization software is used to obtain the decision variables in the unit commitment problem.

The remaining paper is organized as follows: Unit commitment problem is expressed by modeling the integrated energy system in section II, and detailed information about datasets is provided. Different simulation results and the case studies are explained in Section III. Lastly, the conclusion is made up based on the simulation result in section IV.

Problem Formulation

There are three major components of the cost function in every problem of unit commitment: thermal unit fuel cost, start-up cost, and shutdown cost. The objective function is to minimize the total operating cost of local generating units. This will also include the wind curtailment cost in case of wind technology is considered. In this paper, optimization modeling for wind generation, solar photovoltaic generation, conventional thermal generator, and battery system is developed. Further, the developed system is solved considering demand flexibility, and the simulation model is discussed. The optimization model with different constraints is expressed in the following section. The optimization model with different constraints is expressed in the following section.

Objective Function

The objective function (OF) for cost minimization is given by

$$OF=\sum_{i,t}\{F{C}_{i,t}+{STC}_{i,t}+\mathrm{S}D{C}_{i,t}\}+{\sum }_{t}{F}^{wc}$$
(1)

where FCi,t is the fuel cost for thermal generators, Fwc is the estimation of cost associated with wind curtailment, STCi,t and SDCi,t are the start-up and shutdown cost, respectively. Fwc is a function of wind curtailment power \({\mathrm{P}}_{\mathrm{t}}^{\mathrm{wc}}\) at the ith bus during tth hour [29].

$${F}^{wc} =EWC\times {P}_{t}^{wc}$$
(2)

EWC is the estimate of wind curtailment. Linearized cost-based UC problem is expressed here and the fuel cost is assumed to be in the form of a quadratic expression of produced real power of the thermal units Pg,t considered an acceptable estimation of fuel curve for more accurate results [27]. Parameters, a [$/(MW2)], b [$/(MW)], and c [$] for the cost function of generators, may be drawn from the measurement statistics of heat run tests.

The linear version of fuel cost calculation as provided in [28] is described in Eq. (3–11).

$$0\le {p}_{\mathrm{i},\mathrm{t}}^{k}\le \Delta {P}_{\mathrm{i}}^{k}{u}_{i,t}, \forall k=1:n$$
(3)
$$\Delta {P}_{\mathrm{i}}^{k}=\frac{{P}_{\mathrm{i}}^{max}-{P}_{\mathrm{i}}^{min}}{n}$$
(4)
$${P}_{i,ini}^{k}=\left(k-1\right)\Delta {P}_{i}^{k}+{P}_{i}^{min}$$
(5)
$${P}_{i,fin}^{k}=\Delta {P}_{i}^{k}+{P}_{i,ini}^{k}$$
(6)
$${P}_{\mathrm{i},\mathrm{t}}={P}_{i}^{min}{u}_{i,t}+\sum_{k}{p}_{i,t}^{k}$$
(7)
$${C}_{i,ini}^{k}={a}_{i}{\left({P}_{i,ini}^{k}\right)}^{2}+{b}_{i}{P}_{i,ini}^{k}+{c}_{i}$$
(8)
$${C}_{i,fin}^{k}={a}_{i}{\left({P}_{i,fin}^{k}\right)}^{2}+{b}_{i}{P}_{i,fin}^{k}+{c}_{i}$$
(9)
$${s}_{i}^{k}=\frac{{C}_{i,fin}^{k}-{C}_{i,ini}^{k}}{\Delta {P}_{i}^{k}}$$
(10)
$$F{C}_{i,t}={a}_{i}{\left({P}_{i}^{min}\right)}^{2}+{b}_{i}{P}_{i}^{min}+{c}_{i}{u}_{i,t}+\sum_{k}{s}_{i}^{k}{P}_{i,t}^{k}$$
(11)

Wind curtailment considers that the system operators must not be allowed to use the thermal generation when wind energy is available. Wind curtailment occurs under lightly loaded condition when the load on the system is less than the lowest limits that the thermal generators are running and rest of the energy sources are also available including wind energy.

Modeling for Thermal Generators

The capacity constraints of a thermal generator are as follows:

Constraint for Ramp Rate: The generated power of ith thermal generator at tth time should be within the limits as given by (12–16). The ramp up/down constraints as given in [28] are modeled as follows:

$${P}_{i,t}^{tmin}\le {P}_{i,t}\le {P}_{i,t}^{tmax}$$
(12)
$${P}_{i,t}^{tmax}\le {P}_{i}^{max}\left[{u}_{i,t}-{z}_{i,t+1}\right]+S{D}_{i}{z}_{i,t+1}$$
(13)
$${P}_{i,t}^{tmax}\le {P}_{i,t-1}+R{U}_{i}{u}_{i,t-1}+S{U}_{i}{y}_{i,t}$$
(14)
$${P}_{i,t}^{tmin}\ge {P}_{i,t}^{min}{u}_{i,t}$$
(15)
$${P}_{i,t}^{tmin}\ge {P}_{i,t-1}-R{D}_{i}{u}_{i,t}-S{D}_{i}{z}_{i,t}$$
(16)

Constraints for Minimum Up/Down Time: The operation status of ith thermal generator at tth time is given by ui,t. Also, shutdown and start-up statuses are given as yi,t, zi,t as in Eq. (17, 18, and 19).

$${y}_{i,t}-{z}_{i,t}={u}_{i,t}-{u}_{i,t-1}$$
(17)
$${y}_{i,t}+{z}_{i,t}\le 1$$
(18)
$${y}_{i,t},{z}_{i,t},{u}_{i,t}\in \left\{\mathrm{0,1}\right\}$$
(19)

The min uptime (UTi) of ith thermal generator is given in (20 to 23) as proposed in [28]

$$\sum\nolimits_{{t = 1}}^{{\mu _{i} }} {1 - u_{{i,t}} } = 0$$
(20)
$$\sum\nolimits_{t=k}^{k+U{T}_{i}-1}{u}_{i,t}\ge U{T}_{i}{y}_{i,k},\forall k={\upmu }_{i}+1 . . .T-U{T}_{i}+1$$
(21)
$$\sum\nolimits_{t=k}^{T}{u}_{i,t}-{y}_{i,t}\ge 0 , \forall k=T-U{T}_{i}+2 . . .T$$
(22)
$${\upmu }_{i}=\mathrm{min}\{T,\left(U{T}_{i}-{U}_{i}^{0}\right){u}_{i,t=0}\}$$
(23)

The minimum downtime (DTi) of an ith thermal generator is given in (24, 25, and 26) as proposed in [28]

$$\sum\nolimits_{t=1}^{{\mu }_{i}}{u}_{i,t}=0$$
(24)
$$\sum\nolimits_{t=k}^{k+D{T}_{i}-1}1-{u}_{i,t}\ge D{T}_{i}{z}_{i,k}, \forall k=T-D{T}_{i}+2 . . .$$
(25)
$${\upmu }_{i}=\mathrm{min}\{T,(D{T}_{i}-{S}_{i}^{0})[1-{u}_{i,t=0}]\}$$
(26)

The viable cost for shutdown and start-up of thermal generator depends on the duration for which the generator has been on or off, respectively. Here, costs for shutdown (Sdi) and start-up (Csi) are taken as constants as given in Eq. (27 and 28)

$$ST{C}_{i,t}=C{s}_{i}{y}_{i,t}$$
(27)
$$SD{C}_{i,t}=S{d}_{i}{z}_{i,t}$$
(28)

Power Balance Equation

The total power demand should be equal to the total generation for every time slot:

$${P}_{t}^{s}+{P}_{t}^{w}+{P}_{t}^{dis}+\sum_{i}{P}_{i,t}\ge {L}_{t}+{P}_{t}^{ch}$$
(29)

Modeling for Wind Energy

The wind turbine power output curve [30] is shown in Fig. 3, and it is modeled as given by Eq. (30).

$${P}^{w}=\left\{\begin{array}{c}{P}^{r}\times {\left(\frac{v-{v}_{in}}{{v}_{r}-{v}_{in}}\right)}^{3} ; {v}_{c}\le v\le {v}_{r}\\ {P}^{r}; {v}_{r}\le v\le {v}_{f}\\ 0; v<{v}_{c} or v>{v}_{f}\end{array}\right.$$
(30)

Here, v,\({\mathrm{v}}_{\mathrm{f}},\) and \({\mathrm{v}}_{\mathrm{c}}\) are wind speed, cut out, and cut in speed, respectively. vr is the lowest speed at which rated power \({P}^{r}\) is produced.

Fig. 3
figure 3

Wind power output curve

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Wind curtailment is represented as

$${\mathrm{P}}_{\mathrm{t}}^{\mathrm{wc}}={\mathrm{W}}_{\mathrm{t}}-{\mathrm{ P}}_{\mathrm{t}}^{\mathrm{w}}$$
(31)

It is beneficial to utilize most of the generated wind energy, because it will lead to a reduction in fuel cost and it is environmentally sustainable due to low emissions, hence, \({\mathrm{P}}_{\mathrm{t}}^{\mathrm{wc}}\) should be small. The power generation constraint of the wind turbine is given by

$$0\le {\mathrm{P}}_{\mathrm{t}}^{\mathrm{w}}\le {\mathrm{W}}_{\mathrm{t}}$$
(32)

Modeling for Solar PV

Solar PV power generation involves irradiance. The irradiance equation [31, 34] is written as

$${\mathrm{I}}_{\mathrm{t}}={\mathrm{I}}_{\mathrm{d}}\times {\mathrm{cos\theta }}_{\upbeta }+{\mathrm{I}}_{\mathrm{dif}}\times \frac{(1+\mathrm{cos\beta })}{2}+\uprho \times {\mathrm{I}}_{\mathrm{g}}\times \frac{(1-\mathrm{cos\beta })}{2}$$
(33)

where Id, Idif, and Ig are direct, diffuse, and global irradiance, respectively. ρ is nearby local reflection. \(\upbeta\) and \({\uptheta }_{\upbeta }\) are tilt and incidence angle. Solar PV power \({\mathrm{P}}_{\mathrm{i},\mathrm{t}}^{\mathrm{PV}}\) [32] is stated as:

$${\mathrm{P}}_{\mathrm{t}}^{\mathrm{PV}}={\mathrm{P}}_{\mathrm{stc}}^{\mathrm{PV}}{\times \mathrm{n}}_{\mathrm{s}}^{\mathrm{PV}}\times {\mathrm{n}}_{\mathrm{p}}^{\mathrm{PV}}\times ({\mathrm{I}}_{\mathrm{t}}/1000)\times [1-\in \left({\mathrm{T}}_{\mathrm{t}}^{\mathrm{c}}-25\right)]$$
(34)

where \({\mathrm{P}}_{\mathrm{stc}}^{\mathrm{PV}}\) is the output of PV module under standard parameters and at the maximum powerpoint. \({\mathrm{n}}_{\mathrm{p}}^{\mathrm{PV}}\) and \({\mathrm{n}}_{\mathrm{s}}^{\mathrm{PV}}\) represent the required series–parallel combination of solar cells., \({\mathrm{T}}_{\mathrm{t}}^{\mathrm{c}}\) and \(\in\) are PV module temperature and its numerical multiplier, respectively [32].

Cell temperature is stated as

$${\mathrm{T}}_{\mathrm{t}}^{\mathrm{c}}={\mathrm{T}}_{\mathrm{t}}^{\mathrm{a}}+({\mathrm{I}}_{\mathrm{t}}/800)\times (\mathrm{NOTC}-20)$$
(35)

where \({\mathrm{T}}_{\mathrm{t}}^{\mathrm{a}}\) is ambient and NOTC is nominal temperature. The values of \({\mathrm{s}}_{\mathrm{t}}\) for each time are determined with the given model. Limiting power of solar PV is modeled as

$$0\le {\mathrm{P}}_{\mathrm{t}}^{\mathrm{s}}\le {\mathrm{S}}_{\mathrm{t}}$$
(36)

Battery Modeling

The parameters of the battery are given in Table 2. The relationship between charging power, discharging power, SOC, and depth of discharge (DOD) [13, 34] is given in Eq. (39).

$${\mathrm{SOC}}^{\mathrm{min}}={\mathrm{C}}^{\mathrm{nb}}\left(1-{\mathrm{DOD}}^{\mathrm{max}}\right)$$
(37)
$${\mathrm{SOC}}^{\mathrm{max}}={\mathrm{C}}^{\mathrm{nb}}$$
(38)

where \({\mathrm{C}}^{\mathrm{nb}}\) is the nominal capacity of the battery.

Table 2 Data for BESS
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$${\mathrm{SOC}}_{\mathrm{t}}={\mathrm{SOC}}_{\mathrm{t}-\Delta \mathrm{t}}.\left(1-{\mathrm{DOD}}_{\mathrm{t}}\right)+\left({\mathrm{P}}_{\mathrm{t}}^{\mathrm{ch}}.{\upeta }_{\mathrm{ch}}-{\mathrm{P}}_{\mathrm{t}}^{\mathrm{dis}}.\frac{1}{{\upeta }_{\mathrm{dis}}}\right).\Delta \mathrm{t}$$
(39)

The battery storage limits and state of charge are expressed as

$${\mathrm{SOC}}^{\mathrm{min}}\le {\mathrm{SOC}}_{\mathrm{t}} \le {\mathrm{SOC}}^{\mathrm{max}}$$
(40)
$${\mathrm{P}}_{\mathrm{t}}^{\mathrm{ch},\mathrm{min}}\le {\mathrm{P}}_{\mathrm{t}}^{\mathrm{ch}}\le {\mathrm{P}}_{\mathrm{t}}^{\mathrm{ch},\mathrm{max}}$$
(41)
$${\mathrm{P}}_{\mathrm{t}}^{\mathrm{dis},\mathrm{min}}\le {\mathrm{P}}_{\mathrm{t}}^{\mathrm{dis}}\le {\mathrm{P}}_{\mathrm{t}}^{\mathrm{dis},\mathrm{max}}$$
(42)

Constraints for Demand Response Flexibility

For improving the performance and validity of the MG operation, the unit commitment optimization model should be solved with more constraints like demand flexibility. Conventionally, the generator scheduling was used to make a balance of power between demand and generation which is now changing with time. To increase the performance of the unit commitment problem, the demand is also sometimes changed deliberately and it can be dispatched according to the system requirement. The unit commitment problem considering demand response flexibility is modeled as

$$\sum_{i}{P}_{i,t}\ge {D}_{t}$$
(43)
$$\left( {1 - \alpha _{{min}} } \right)\;L_{t} \le D_{t} \le \left( {1 + \alpha _{{max}} } \right)\;L_{t}$$
(44)
$$\sum\nolimits_{t}{D}_{t}=\sum\nolimits_{t}{L}_{t}$$
(45)

Equation (44) shows the range for the variation in demand. αmax/min gives the minimum or maximum demand response. Equation (43) tells that the overall power requirement cannot change with time. The αmax/min is taken to be varying from 0 to 12%.

Data used for the Analysis

Ten thermal generators have been considered for the purpose. The generator characteristics, operating constraints for generator, and data for BESS are inspired from [29]. The simulation parameters for BESS for the unit commitment problem are given in Table 2. Solar and wind power generation and the energy requirements are drawn and displayed in Fig. 4. As can be seen in the figure, solar energy is available for a certain duration of the day, i.e., from 5 to 19th duration and wind energy is accessible twenty-four hours, the highest availability of solar and wind energy is at 13th and 16th hours separately. The maximum demand occurs at 10th and 11th hour.

Fig. 4
figure 4

Variation in fractional load, wind, and solar power availability w.r.t. time

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Results and Discussions

Windows 10 operating system with i7 processor having 8 GB RAM is used for the study. GAMS version 24.4.3 [33] is employed for the coding purpose to obtain the results. The UC problem is solved majorly using stochastic, deterministic, and evolutionary algorithms. But in case of high complexity, evolutionary algorithms may not give a global optimal solution. Considering this, the UC model is solved as MILP using CPLEX optimization solver in GAMS. GAMS allows high-level mathematical optimization using various deterministic techniques. The problem of UC in microgrid operating in islanded mode is arranged into four separate cases. Case 1, When exclusively conventional thermal generators (DGs) are operating. Case 2, Wind turbine is operational along with DG. Case 3, PV generator along with wind turbine and DG is operational. Case 4, Battery energy storage system (BESS) is operational alongside DG, wind technology, and solar technology.

Case study 1: This is a base case including DG sets only. Figure 5 shows the number of generators to be turned on, the generation schedule, and the level of generation of each unit to provide for the electricity demand by local generation consisting of thermal generators. The total operating cost of the microgrid is $233,154.2 for a period of 24 h and the cost of fuel, shutdown and start-up costs are $232,685, $269.8, and $199.4, respectively, as shown in Figs. 13 and 10.

Fig. 5
figure 5

Hourly power generation schedule for thermal generator (MW) under case 1, 2, 3, and 4

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Case study 2: Fig. 5 shows that there is a reduction in the commitment status and increment in the de-commitment of DG units when wind technology is integrated into the system. It will further reduce when we consider solar and BESS technology. It is noteworthy that the system operator will have to pay wind curtailment costs for using the generators instead of utilizing the full capacity of wind generation. The total operating cost is $202,733.7 which is composed of $129,909 fuel cost for DG, $72,285 wind curtailment cost of the wind turbine, $184.9 start-up, and $355 for shutdown costs. It is seen that the overall operation cost and fuel cost have been reduced by 13% and 44.1%, respectively, as compared to case 1. This is mainly because the wind turbine is supplying an appreciable portion of the total energy requirements of the MG which is evident from Fig. 6.

Fig. 6
figure 6

Total power generation schedule under case 2

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Case study 3: In this case, renewable generation including both solar and wind technology is modeled to see the relation between power generation by renewable and non-renewable sources and its impacts on the scheduling of conventional thermal generator. As it is shown in Fig. 7, to supply the electric power demand, power generation is divided among thermal units, wind turbine, and solar PV. The number of thermal generating units has been further reduced which is seen from Fig. 5. The overall cost of operation has reduced to $189,538.9 and the fuel cost of DG unit to $116,998.5 which is shown in Figs. 12 and 13.

Fig. 7
figure 7

Total power generation schedule under case 3

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Case study 4: The application of energy storage systems into the microgrid has seen a growing trend in the recent past. It facilitates the incorporation of renewable power sources into the power system by storing a certain amount of energy and then reinjecting it into the system to facilitate power exchange and improve overall system characteristics. Firstly, when peak demand is more than the generation, it helps in reducing increased energy supply and thus reduces generation cost and network installations. Secondly, it helps in reducing uncertainty arising due to power generation from renewable sources and makes the system more robust. Considering these advantages, battery storage technology is integrated into the system. It will charge the battery during off-peak loads and discharge it during peak loads to reduce the overall operating cost which can be seen from Fig. 8. The charging and discharging patterns can be seen from Fig. 9. Variation in start-up and shutdown cost can be seen from Fig. 10. Start-up cost first increases and then decreases due to operating constraints, while shutdown cost will only decrease as we move from case 1 to case 4. Considering this case, wind curtailment cost further gets reduced to a minimum value as given in Fig. 11. Reduction in fuel cost for thermal generators is shown in Fig. 12. Total operating cost as compared to case 1 has been reduced by 22% as shown in Fig. 13.

Fig. 8
figure 8

Total power generation schedule under case 4

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Fig. 9
figure 9

Power despatch of BESS in case 4

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Fig. 10
figure 10

Variation in start-up and shutdown cost

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Fig. 11
figure 11

Variation in wind curtailment cost

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Fig. 12
figure 12

Variation in fuel cost for DG

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Fig. 13
figure 13

Variation in total operating cost for the microgrid

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The minimum/maximum flexibility of demand response is changed from 0 to 12% in steps of 3, and the response to demand flexibility is analyzed. The average demand response is calculated and drawn for each case as shown in Fig. 14. It can be seen that the demand response is changing from t3 to t7 and from t13 to t18 for individual cases. Figure 15 shows that if the flexibility in demand despatch is given to the system operator, then the total cost of operation would decrease for each case. Table 3 summarizes the outcomes of the simulation performed. A comparison of base case results obtained from the proposed system using MILP under CPLEX optimization solver available in GAMS has been made using different optimization methods such as dynamic programming and Lagrangian relaxation as mentioned in Table 4. Comparison of base case shows better results for MILP technique under CPLEX solver compared to other optimization techniques such as dynamic programming and Lagrangian relaxation.

Fig. 14
figure 14

Average demand response pattern change under each case and sensitivity toward demand flexibility in unit commitment problem

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Fig. 15
figure 15

Variation in total operation cost with demand response flexibility

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Table 3 COMPARISON OF RESULTS FOR THE GIVEN CASES
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Table 4 Comparison of optimization results for base case unit commitment
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Conclusions

Optimization framework for the unit commitment of hybrid energy MG is developed in this paper. The model presented is developed based on literature review for unit commitment models. The model is analyzed using the MILP technique considering its high accuracy and flexibility. MG consisting of energy resources such as thermal generator, solar PV, wind energy and battery storage is modeled and investigated with grid islanded scheme of operation. The method is described in a twenty-four hour time duration using GAMS software, and a comparison of simulation results is made for each case. It is observed that increased renewable energy generation leads to reduced non-renewable energy generation and lower operating costs. This involves efficient UC models to overcome irregularity and unreliability. It is observed that renewable power and energy storage systems are crucial parts of MG considering the UC models. Energy storage becomes important both from demand and generation perspective particularly during the incorporation of large renewable power generation into the electrical system. The contribution to battery storage and renewable generation in boosting demand response flexibility of the microgrid has been explained. The decrease in cost of fuel for thermal generation is also very large due to high renewable energy penetration. This also helps in mitigating the environmental impacts of using conventional sources of energy and improved energy security. Demand response is studied for all the four cases as mentioned in section III. A comparison of simulation results is provided for four scenarios, and it is observed that case 4 provides promising results than rest of the cases. MILP technique shows better performance compared to other techniques discussed in this paper.

Scope of Improvement

Firstly, the given results are achieved without taking into account energy loss which can be modeled using AC/DC power flow constraints. Secondly, uncertainty modeling of renewable sources using various meta-heuristic techniques can be performed to achieve more accurate results and make the system more robust. Third, to overcome unexpected demand increase or generating unit outage, the UC-reserve constrained modeling of thermal generators connected to the system can be done. Fourth, a problem involving a grid-connected mode of operation considering variable market price may be formulated and compared with an islanded mode of operation of MG.