Abstract
The economical use of available fuel for producing electricity has been a very important challenge for power companies due to the continuously declining supply of fossil fuels. FCJHPDEED (fuel-constrained joint heat and power dynamic economic environmental dispatch) and JHPDEED (joint heat and power dynamic economic environmental dispatch) with DSM (demand-side management) integrating solar PV plants, WTGs (wind turbine generators), and PHS (pumped hydro storage) plants have been presented. Using SPEA 2 (strength Pareto evolutionary algorithm 2) and NSGA-II (non-dominated sorting genetic algorithm-II), FCJHPDEED and JHPDEED have been solved. It is seen that the results obtained without fuel constraints are more optimal than the results obtained with fuel constraints. The joint heat and power dynamic economic dispatch cost obtained with fuel constraints is approximately 2.14% more than the cost obtained without fuel constraints and joint heat and power dynamic emission dispatch, and the emission obtained with fuel constraints is approximately 6.7% more than the emission obtained without fuel constraints.
1 Introduction
The primary source of electricity production until now has been fossil fuel-based power plants. There is a chance of a fuel shortage since fossil fuel production is progressively declining. Power producers are required to reorganize power production depending on the fuel that is available since fuel suppliers have added further restrictions to their fuel-providing agreement.
With the growing debate on climate alteration and pollution-free energy, wind power and solar power are increasingly utilized today as they are free from harmful emissions. However, renewable energy sources have their own challenges due to their irregularity and intermittent nature, which can cause fluctuations in power generation scheduling. This can be overcome by assimilating PHS plants to reduce power fluctuations.
The economic dispatch problem has been described briefly in Le et al. (2019); Dashtdar et al. (2022). Trefny and Lee have explained economic dispatch, taking into account fuel restrictions (Trefny and Lee, 1981). The fuel resource arrangement in managing power systems is described in Kumar and Vemuri (1984); Vemuri et al. (1984).
The optimal generation schedule of a small sovereign system using WTGs and solar PV facilities, both of which produce no pollution, has been described in Bakirtzis and Gavanidou (1992). However, due to their limited generation capacity, the combined use of different energy-producing systems (Mondal et al., 2013; Khan et al., 2015) is increasing rapidly.
PHS plants are drawing a lot of interest throughout the world (Perez-Diaz and Jim, 2016) because of their capacity to store energy. The main purpose of a PHS plant is to pump water from the lower reservoir into the higher reservoir in order to save low-cost extra electric energy generated in off-peak power demand times (Wood and Wollenberg, 1984; Fadil and Urazel, 2013). This hoarded energy is used to generate energy throughout peak power demand periods.
Electricity is produced inefficiently using fossil fuels. Heat is the main kind of energy destroyed during the conversion process. Co-generation utilizes this heat efficiently and produces lower harmful gas emanation. Utilizing CHPDED, the production of electricity and heat is distributed in a way that minimizes the overall cost while also meeting a number of limitations. Several methods (Rooijers and van Amerongen, 1994; Guo et al., 1996; Su and Chiang, 2004; Vasebi et al., 2007; Wang and Singh, 2008; Subbaraj et al., 2009; Mohammadi-Ivatloo et al., 2013; Basu, 2016) have been described to resolve this problem.
JHPDEED optimizes the total generation cost and emission level of steam turbine generators, co-generation units, and heat-only units throughout a particular period of time, considering power ramp rate limitations of co-generation and steam turbine generating units.
Several approaches to resolve economic dispatch, assimilating WTGs and solar PV plants, are explained in Hetzer et al. (2008); Reddy et al. (2015); Tang et al. (2015); Li et al. (2016); Liu and Nair (2016); Peng et al. (2016); Yang et al. (2016); Liu et al. (2017).
According to the International Energy Agency’s strategy plan, DSM has been established as the most significant choice of the overall energy policy directives. DSM can reduce the price and boost system safety (Yousefi et al., 2013).
Here, both FCJHPDEED and JHPDEED with DSM have been described. The system comprises thermal generators, heat-only units, co-generation units, solar PV plants, WTGs, and PHS plants. The uncertainty of WTGs and solar PV plants has been considered. The primary restrictions are restrictions on different fuel types for co-generation units and thermal generators, PHS plants, time-varying load demand, and on the generation capabilities and power ramp rates. The valve-point effect and forbidden viable region of steam turbine generating units have been considered. Both FCJHPDEED and JHPDEED with DSM have been solved using SPEA 2 and NSGA-II.
2 Formulation of the problem
Here, the system considered has fuel-constrained steam turbine generating units, heat-only units, co-generation units, WTGs, PHS plants, and solar PV plants. Figure 1 demonstrates the heat-power possible range of a combined cycle co-generation unit. Power output and heat output are indivisible. Heat-power workable county is enfolded by the frontier ABCDEF.
FIGURE 1
The output power of the steam turbine generating units, WTGs, solar PV plants, and PHS plants and the heat output of heat-only units are limited by the individual minimum and maximum limits. Power is generated by steam turbine generating units, WTGs, solar PV plants, co-generation units, and PHS plants, while heat is generated by heat-only units and co-generation units.
The FCJHPDEED issue with DSM-integrating solar PV plants, WTGs, and PHS plants distributes heat and power generation among all dedicated thermal generating units, WTGs, co-generation units, PHS plants, solar PV plants, and heat-only units in a way that the emission and total price are optimized over a specific time period while satisfying a number of constraints, including generation limit restrictions, power and heat balance constraints, and dissimilar types of fuel construction. When formulating the FCJHPDEED issue, the objective functions and restrictions mentioned below are considered.
2.1 Objectives
2.1.1 Cost
The total price is expressed as
The fuel price function of the th thermal generator at hour , considering the valve-point effect (Walters and Sheble, 1993), can be expressed as
The price function of the th co-generation unit (Vemuri et al., 1984) at hour can be shown as
The price function of the th heat-only unit at time can be shown as
The reserve and penalty price of wind power (Hetzer et al., 2008) can be shown as
The reserve and penalty price of solar power (Liang and Liao, 2007) can be shown as
2.1.2 Emission
Thermal power plants are the main sources of sulfur oxides, nitrogen oxides, and carbon dioxide. Emission from a steam turbine generating unit is the addition of quadratic function and exponential function (Gent and Lamont, 1971). The total emission from steam turbine generating units, co-generation units, and heat-only units can be expressed as
2.2 Constraints
i)Power balance constraints:
Whilst power demand is cut back because of DRP,
during that time. Similar to how it is transferred to the basic power demand, the demand for electricity does not decrease at that time.
Loss in transmission is affirmed as
The number of plants
, and
is the respective steam turbine, co-generation, wind turbine, and solar PV generation.
ii) Fuel delivery constraints:
Over the course of the scheduling horizon, the total fuel provided to all co-generation units and steam turbine generating units should match the fuel that is supplied by the purveyor.
iii) Fuel storage constraints of steam turbine generators:
The residual fuel at the start of the subsequent interlude is calculated by subtracting the fuel burned at the thermal generator from the fuel volume of every steam turbine generating unit at the start of every interlude plus the fuel provided to that steam turbine generating unit.
iv) Fuel delivery limits of steam turbine generators:
Fuel that is delivered to each steam turbine generating unit at every interlude must be within its lower limit
and upper limit
.
v) Fuel storage limits of steam turbine generators:
The fuel storage limit of each steam turbine generating unit at each interlude must be within its lower limit
and upper limit
.
vi) Fuel storage constraints of co-generation units:
The amount of fuel available at the start of the subsequent interlude is determined by the fuel volume of each co-generation unit at the beginning of each interlude, fuel supplied to that co-generation unit, and fuel burned at that co-generation unit.
vii) Fuel delivery limits of co-generation units:
Fuel delivered to each co-generation unit at each interlude must be within its minimum limit
and maximum limit
.
viii) Fuel storage limits of co-generation units:
The fuel storage limit of each co-generation unit at each interlude must be within its minimum limit
and maximum limit
.
ix) Generation limits of the thermal generator:
x) Forbidden workable region of thermal generating units:
The restricted area of a steam turbine generating unit is due to the shaft bearing tremor caused by a steam valve or a flaw in the machine or supporting equipment. It is challenging to determine the input–output curve’s shape in the hinterland of a possible but restricted zone using actual routine testing. In actuality, avoiding operating in certain areas results in the biggest cost-saving strategy. The following is a possible area of operation for the
th steam turbine generator at this time
:
where
indicates the number of proscribed workable county.
is the maximum limit of the
th forbidden workable region of the
th generator. The minimum limit of the
th forbidden region of the
th generating unit is
. The number of forbidden workable regions of the
th generating unit is
.
xi) Power ramp rate limit constraints of steam turbine generators and co-generation units:
xii) Heat balance constraints:
xiii) Capacity boundary limits of co-generation units:
The heat output and power output of the co-generation unit are inseparable, and they intrude one another.
,
,
, and
are linear inequalities which depict the feasible area of the co-generation unit.
xiv) Capability boundary limits of heat-only units:
xv) Wind power model:
The WTG’s output power mostly depends on wind velocity. Cut-in pace, rated pace, and cut-out pace of wind are used to clarify the nonlinear connection between wind velocity and output power. Power output (Giorsetto and Utsurogi, 1983) of the th WTG at hour for a specific wind velocity can be signified as
Constants
,
, and
are functions of
and
and are computed utilizing the following equations:
xvi) Solar power model:
The power output (
Shilaja and Ravi, 2017) acquired from the
th solar PV power plant at hour
is signified as
xvii) Pumped hydro storage plant constraints:
Whilst the PHS unit runs in the generating type and decides to run in the pumping type or vice versa, the PHS unit must be switched off for at least 1 hour because of physical restrictions of the unit, and it is recognized as switching time.
The starting and ending volumes of the water of the upper reservoir of the PHS plant are presumed to be identical here.
Demand-side management (DSM)
DSM initiates many benefits (Yousefi et al., 2013). DSM is categorized as DRP (demand response program), planned conservation, and so on. In this manuscript, DRP is utilized, and it is shaped as the TOU (time-of-use) program (Mehdizadeh and Taghizadegan, 2017). In the TOU program, a small proportion of demand is switched from peak to off-peak hours while keeping the overall demand constant. Equation 43 explains the TOU program, while Eq. 44 restricts it (47).
3 Principle of multi-objective optimization
Most actual-world issues require concurrent optimization of various conflicting objective functions. MOO with contradictory objective functions generates a number of optimum solutions in place of one optimum solution as no solution is superior to every other relating to all objective functions. Francis Ysidro Edgeworth proposed the concept of a trade-off optimality criterion in 1881, and Vilfredo Pareto clarified it in 1896. It is usually referred to as Pareto optimum, and optimum solutions are referred to as Pareto-optimal solutions.
The following is affirmed for a MOO problem with several goals and equality and inequality constraints:
subject to
where
is denoted as the
th objective function,
is denoted as the decision vector that symbolizes a solution, and
is denoted as the number of objectives. Decision vector
dominates the decision vector
if both the conditions mentioned in (50) and (51) are attained.
a. Sufficient condition: The decision vector is better than for all the objectives.
b. Necessary condition: The decision vector is firmly superior to the decision vector as a minimum one of the objective functions.
4 Non-dominated sorting genetic algorithm-II
Srinivas and Deb (1994) ascertained NSGA for competing with MOO problems. Non-domination has been exploited as a grading decisive factor of solutions, and on the other hand, fitness distribution has been exploited for diversification control in the investigated space. Since NSGA is very receptive to fitness distribution parameters, Deb et al. (2002) initiated NSGA-II, which generates more consistent solutions swifter than its ancestor.
5 Strength Pareto evolutionary algorithm 2
Strength Pareto evolutionary algorithm 2 (SPEA 2) (Zitzler et al., 2001) is the superior edition of SPEA. It blends a well-tuned fitness assignment approach, a density assessment technique, and an improved archive truncation technique with the conventional SPEA. In SPEA 2, the fitness value assigned to every entity is computed based on the strength value and the density degree. As each individual has its own value of density, the calculation starts with sorting the values of all objectives. The density value of every entity is the same as the sum of the difference between each objective value and its nearest neighbor. The fitness value is the summation of the strength value and the density degree. SPEA 2 uses an improved archive truncation method, where the size of the external storage file is fixed. The crossover and mutation procedure only occur in the storage file.
6 Numerical results
NSGA-II and SPEA 2 have been utilized for solving FCJHPDEED and JHPDEED with DSM integrating WTGs, PHS plants, and solar PV plants.
Total price and emission are two conflicting objective functions. To elucidate contrary relationships among objective functions, each objective function, namely, total price and total emission, is lowered distinctly by using RCGA (real-coded genetic algorithm). The population size, maximum number of iterations, crossover, and mutation probabilities are chosen as 100, 300, 0.9, and 0.2, respectively.
SPEA 2 and NSGA-II are used for optimizing total price and total emission objectives concurrently. The population size, maximum number of iterations, crossover, and mutation probabilities are taken as 20, 30, 0.2, and 0.9 for SPEA 2 and NSGA-II, respectively.
An equivalent WTG, an equivalent solar PV plant, an equivalent PHS plant, 13 thermal generating units with a banned working region and valve point impact, six co-generation units, and five heat-only units are all included in the test system. The data on co-generation units, steam turbine generating units, heat-only units, and hourly heat and power demand have been taken from Basu (2019). The whole schedule is divided into six 4-h intermissions, totaling 1 day. Table A contains information on coal-burning thermal generating units, including emission coefficients, coal “consumption coefficients, fuel delivery and storage limits, and starting fuel storage. 1. Table A contains information on the co-generation unit, including coal consumption coefficients, fuel supply and storage limits, and starting fuel storage. 2. Table A lists the emission coefficients for heat-only and co-generation units. 3. Table A lists the fuel that was supplied throughout the scheduled period.
The WTG rating is denoted as = 150 MW. The direct cost coefficient for WTG is chosen as . Penalty and reserve cost coefficients for WTG are chosen as and , respectively. Cut-in, cut-out, and rated wind paces are m/s, m/s and m/s, respectively.
The solar PV plant rating is denoted as = 175 MW. The direct cost coefficient () for the solar PV plant is selected as 6. The penalty and reserve cost coefficients for the solar PV plant are selected as and , respectively. Solar radiation in the standard environment () and a certain radiation point () have been chosen as 1000 W/m2 and 150 W/m2, respectively. Solar irradiation and wind velocity’s maximum and minimum predicted limits are obtained from Walters and Sheble (1993). The reference temperature () and temperature coefficient () are chosen as and (per Kelvin), respectively. The PHS plant has subsequent features:
Generating mode:
is positive, is positive, MW, and acre-ft/hr
Pumping mode:
is negative, is negative, , acre-ft/h, and MW
Working restrictions: The PHS plant is allowed to operate only at −100 MW while pumping. The reservoir begins at 3000 acre/ft and should be at 3000 acre/ft at the ending of 24 h.
The 12, 13, and 14 hours are peak power demand hours. It is observed that 10% of 12-, 13-, and 14-hour power demands is transferred to the second, third, and fourth hour throughout DSM, respectively.
Power generation of thermal generating units, solar PV plants, WTGs, co-generation units, and PHS plants obtained from FCJHPDEED utilizing NSGA-II is portrayed in Figure 2 and Figure 3. Heat generation of heat-only units and co-generation units obtained from FCJHPDEED utilizing NSGA-II is portrayed in Figure 4. Fuel delivered to thermal generators and co-generation units obtained from FCJHPDEED using NSGA-II is mentioned in Table 1 and Table 2. TC and total emission acquired from CHPDED and joint heat and power dynamic environmental dispatch with and without fuel constraints are summarized in Table 3. Figure 5 and Figure 6 portray cost convergence characteristics, emission convergence characteristics, and the Pareto-optimal front obtained from the last iteration using SPEA 2 and NSGA-II with and without fuel constraints, respectively.
FIGURE 2
FIGURE 3
FIGURE 4
TABLE 1
| Interval | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1,582.6 | 4,986.0 | 2,684.1 | 3,045.0 | 3,494.7 | 165.1 | |
| 2,171.3 | 1,029.0 | 1,528.2 | 1,230.1 | 1,658.9 | 838.6 | |
| 131.1 | 793.6 | 1,444.7 | 2,435.6 | 213.6 | 2,295.2 | |
| 722.8 | 1,369.4 | 1496.9 | 1,294.3 | 1,446.0 | 1,482.2 | |
| 1,421.0 | 64.7 | 608.5 | 625.4 | 1,480.4 | 630.0 | |
| 1,419.9 | 9.3 | 1,220.8 | 1,214.4 | 804.3 | 248.2 | |
| 1,257.5 | 166.2 | 311.8 | 1,279.5 | 1,272.2 | 1,028.4 | |
| 1,011.6 | 502.6 | 1,500.0 | 623.7 | 1,163.4 | 674.9 | |
| 1,500.0 | 1,335.8 | 1,005.3 | 1,146.8 | 498.1 | 1,336.9 | |
| 240.6 | 888.8 | 595.6 | 530.5 | 142.3 | 856.8 | |
| 287.4 | 565.9 | 214.1 | 597.6 | 46.3 | 781.9 | |
| 553.0 | 680.6 | 504.4 | 609.8 | 716.4 | 609.3 | |
| 668.6 | 722.6 | 634.2 | 604.1 | 492.5 | 854.6 |
Fuel delivered (ton) to thermal generating units acquired from FCJHPDEED using NSGA-II.
TABLE 2
| Interval | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1,786.4 | 2,258.7 | 1,350.6 | 2,456.2 | 1,305.4 | 1,780.9 | |
| 479.3 | 16.0 | 990.0 | 233.1 | 887.0 | 1,230.1 | |
| 1,435.6 | 1,899.0 | 2,443.5 | 2,276.3 | 2,196.6 | 2,467.8 | |
| 759.9 | 421.0 | 1,329.7 | 573.1 | 1,477.5 | 1,013.5 | |
| 370.4 | 390.6 | 237.5 | 324.2 | 102.2 | 96.0 | |
| 200.9 | 900.0 | 900.0 | 900.0 | 602.2 | 609.6 |
Fuel delivered (ton) to co-generation units acquired from FCJHPDEED using NSGA-II.
TABLE 3
| Cost ($) | Emission (kg) | ||
|---|---|---|---|
| Joint heat and power dynamic economic dispatch | With fuel constraints | 3,402,717 | 3,249 |
| Without fuel constraints | 3,329,926 | 3,318 | |
| Joint heat and power dynamic environmental dispatch | With fuel constraints | 3,809,199 | 2,568 |
| Without fuel constraints | 3,851,192 | 2,396 | |
| FCJHPDEED | NSGA-II | 3,614,163 | 2,851 |
| SPEA 2 | 3,631,141 | 2,876 | |
| JHPDEED | NSGA-II | 3,595,131 | 2,863 |
| SPEA 2 | 3,607,718 | 2,840 | |
Comparison of performance.
FIGURE 5
FIGURE 6
Because of space limitations, detailed results obtained from joint heat and power dynamic economic dispatch, CHPDED with and without fuel constraints, JHPDEED without fuel constraints, and FCJHPDEED with fuel constraints using SPEA 2 cannot be given here.
7 Conclusion
In the present work, NSGA-II and SPEA 2 are used in order to solve real-world fuel-constrained joint heat and power dynamic economic environmental dispatch (FCJHPDEED) and joint heat and power dynamic economic environmental dispatch (JHPDEED) with DSM integrating the WTG, solar PV plant, and PHS plant. It is seen from numerical results that fuel consumption is satisfactorily managed for satisfying constraints inflicted by fuel purveyors utilizing the proposed techniques. It is observed that the results obtained without fuel constraints are more optimal than the results obtained with fuel constraints. In the case of joint heat and power dynamic economic emission dispatch, the cost acquired with fuel constraints is approximately 0.53% more than the cost acquired without fuel constraints, and the emission acquired with fuel constraints is approximately 0.42% lower than the emission acquired without fuel constraints. Although optimal dispatch is not achieved at all times, however, this is typically much better than the penalty imposed due to fuel constraint violations.
Statements
Data availability statement
The original contributions presented in the study are included in the article/Supplementary Material; further inquiries can be directed to the corresponding author.
Author contributions
MB: conceptualization, data curation, formal analysis, investigation, methodology, project administration, resources, software, supervision, validation, visualization, writing–original draft, and writing–review and editing. CJ: conceptualization, data curation, formal analysis, investigation, methodology, project administration, resources, software, supervision, validation, visualization, and writing–review and editing. BK: conceptualization, data curation, formal analysis, methodology, project administration, resources, software, supervision, validation, visualization, writing–original draft, and writing–review and editing. AA: conceptualization, data curation, formal analysis, investigation, methodology, project administration, resources, software, supervision, validation, visualization, and writing–review and editing. PB: data curation, formal analysis, methodology, project administration, resources, software, supervision, validation, visualization, and writing–review and editing.
Funding
The author(s) declare that no financial support was received for the research, authorship, and/or publication of this article.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Publisher’s note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
Supplementary material
The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fenrg.2023.1305076/full#supplementary-materialhttps://www.frontiersin.org/articles/10.3389/fenrg.2023.1305076/full#supplementary-material
Nomenclature
| Total price function | |
| Price function of the th thermal generator at time | |
| Price function of the th co-generation unit at time | |
| Price function of the th heat-only unit at time | |
| Price coefficients of the th thermal unit | |
| Emission coefficients of the th thermal unit | |
| Fuel utilization coefficients of the th thermal generator | |
| Delivered fuel to the th steam turbine generator in interval | |
| Lower and upper limits of the fuel delivery of the th thermal generator | |
| Fuel delivered to the th co-generation unit in interval | |
| Lower and upper limits of fuel delivery of the th co-generation unit | |
| Total fuel delivered in interval | |
| Power output of the th thermal generating unit at hour | |
| , | Lower and upper generation limits of the th thermal generator |
| , | Ramp-up and ramp-down rate limits of the th thermal generator |
| , | Power and heat generation of the th co-generation unit at time |
| Heat generation of the th heat-only unit at time | |
| , | Lower and upper heat limits of generation of the th heat-only unit |
| , | Ramp-up and ramp-down rate limits of the th co-generation unit |
| Price coefficients of the th co-generation unit | |
| Emission coefficient of the th co-generation unit | |
| Fuel utilization coefficients of the th co-generation unit | |
| Price coefficients of the th heat-only unit | |
| Emission coefficient of the th heat-only unit | |
| Obtainable power of the th wind turbine generator (WTG) at hour | |
| , | Lower and upper limits of generation for th WTG |
| Rated power of th WTG | |
| Direct price coefficient of th WTG | |
| , | Penalty price and reserve price of th WTG |
| ,and | Cut-in, cut-out, rated, and predicted wind pace at time |
| Output power from the th solar PV plant at hour | |
| Rated output power of the th solar PV plant | |
| Predicted solar irradiation | |
| , | Reference and ambient temperature |
| Coefficient of temperature | |
| Direct price coefficient of the th solar PV plant | |
| , | Penalty price and reserve price of the th solar PV plant |
| Power generation of the th pumped hydro storage (PHS) plant at hour | |
| Pumping power of the th PHS plant at hour | |
| , | Lower and upper power generation limits of the th PHS plant |
| , | Lower and upper pumping power limits of the th PHS plant |
| and | Discharge and pumping rate of the th PHS plant at hour |
| Volume of water in the upper reservoir of the th PHS plant at hour | |
| , | Minimum and maximum upper reservoir water storage limits of the th PHS plant |
| , | Specified initial and ending stored water volumes in the upper reservoir of the th PHS plant |
| Fuel storage of the th thermal generator in interval | |
| Minimum and maximum fuel storage limits of the th thermal generator | |
| Starting fuel storage of the th thermal generator | |
| Fuel storage of the th co-generation unit in intermission | |
| Lower and upper fuel storage limits of the th co-generation unit | |
| Initial fuel storage of the th co-generation unit | |
| Highest augmented load at any hour (MW) | |
| Predicted base power demand at hour | |
| Percentage of predicted based power demand partaken in DRP at hour | |
| Total augmented power demand at hour | |
| Movable power demand at hour | |
| , | Time index and the scheduling period |
| Set of all time intermissions when the PHS plant runs as the generation type | |
| Set of all time intermissions when the PHS plant runs as the pumping type | |
| Set of all time intermissions when the PHS plant runs as the idle type | |
| Duration of the subinterval | |
| Number of subintervals | |
| ,,,,and | Number of co-generation, heat-only, thermal, TTG, solar PV, and PHS units, respectively |
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Summary
Keywords
fuel-constrained co-generation units, fuel-constrained thermal generating units, demand-side management, dynamic economic environmental dispatch, optimization
Citation
Basu M, Jena C, Khan B, Ali A and Bokoro P (2023) Fuel-constrained joint heat and power dynamic economic environmental dispatch. Front. Energy Res. 11:1305076. doi: 10.3389/fenrg.2023.1305076
Received
30 September 2023
Accepted
01 December 2023
Published
20 December 2023
Volume
11 - 2023
Edited by
Deepak Kumar, Birla Institute of Technology, India
Reviewed by
Minh Quan Duong, The University of Danang, Vietnam
Masoud Dashtdar, Islamic Azad University, Iran
Updates
Copyright
© 2023 Basu, Jena, Khan, Ali and Bokoro.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Baseem Khan, baseem.khan04@gmail.com
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