 Research
 Open access
 Published:
An optimal solution to unit commitment problem of realistic integrated power system involving wind and electric vehicles using chaotic slime mould optimizer
Journal of Electrical Systems and Information Technology volumeÂ 10, ArticleÂ number:Â 4 (2023)
Abstract
Plugin electric vehicles (PEVs) could be integrated into power networks to meet rising demand as well as provide mobile storage to help the electric grid operate more efficiently. The most efficient charging and discharging of PEVs are required for the effective utilization of this potential. PEVs with poor charging management may see a spike in peak demand, resulting in increased generation. To take advantage of offpeak charging benefits and avoid load shedding, PEVs charging and discharging must be intelligently scheduled. This paper offers a solution to optimal generation scheduling and the impact of vehicle to grid (V2G) operation in the presence of wind as a renewable energy source using the chaotic slime mould algorithm (CSMA). Further, the effectiveness of the proposed simulation results for a 10unit system incorporating V2G operation has been compared with other wellknown optimization techniques such as harmony search algorithm (HAS), chemical reaction optimization(CRO), genetic algorithm and artificial neural network(GAANN), particle swarm optimization (PSO), and cuckoo search (CS). The comparative analysis of the results reveals a significant cost savings in power generation.
Background
The majority of existing generation and transportation systems rely solely on fossil fuels, resulting in massive pollution and adverse impacts on the atmosphere. To ensure the longterm viability of these finite energy sources, it is essential to use them very precisely and economically. The incorporation of electric vehicles (EVs) has resulted in a decrease in the use of conventional petroleumbased transportation systems during the last few years. The main sources of battery charging are electric power utilities. A wellcoordinated charging and discharging cycle, on the other hand, could help to reduce overall fossil fuel usage and pollutant emissions. Meanwhile, due to progress in power electronics, battery technology, and controller topologies, surplus power stored in batteries might be sent back to utilities via a convertor plant at the consumer's location. V2G technology has various advantages, including (i)Â alternative energy sources, (ii) energy diversification, (iii) pollution reduction, and (iv) increased performance and efficiencies. It also provides voltage regulation, harmonic filtering, and primary frequency control.
Overview of wind power and electric vehicles
Power developed by a wind turbine depends upon wind speed. As wind velocity continuously changes, power generated is always fluctuating. A large number of methods are available for predicting the uncertainties associated with wind power. In this study, Weibull function [1] is used for evaluating uncertainties in wind and mathematically represented as,
As the power generated by wind is uncertain, variable due to randomness of wind velocity expressed as,
From Eq.Â (2), when wind speed \(c^{h}\) is less than or equal to minimum rated velocity, wind power is zero. Wind power is equal to the rated wind power, when wind speed is greater than rated speed. So, this shows that wind power is a discrete variable. The probability of wind power being 0,\(P_{wr}\) is calculated as per Eqs. (3) & (4), respectively, and described below:
The probability density function depends upon \(v_{in\,\,} {\text{and}}\,v_{r}\) as the wind power is a continuous variable and it can be written as,
The facility of the spinning reserve to meet the sudden demand may be fulfilled by the empirical formulas shown in Eq. (4). The base section of the load curve is considered for maximum wind power generation. A typical load pattern for maximum wind power supplied is plotted for a 24hour duration as shown in Fig. 1.
EVs operate by consuming the stored energy in batteries and act as an excess load on existing system [3]. EVs may be broadly classified as: battery operated vehicles, PEVs and hybrid electric vehicles. With the advancement in battery technologies, a large variety of EVs are being recently manufactured on a large scale. Some of the electrochemical battery categories are given in Table 1. In [4], a systematic approach towards V2G planning is explored for cost minimization. Further, availability of large number of charging facilities either while transportation or during parking bounds huge attraction of consumers. A typical charging/discharging pattern is selected as shown in Fig. 2
Overview of vehicle to grid operation
EVs can store or generate 4 KW to 80 KWHr on average, and if a wellcoordinated system is available, widespread use of these vehicles may be viable. The unplanned charging and discharging of such a huge number of EVs could disturb the power system's dynamics and stability. However, a common power aggregator that can bring together a group of EVs and present the entire system to the grid as a single system could result in significant power contribution. The power aggregator should keep a keen watch on performanceÂ so that a large enough number of vehicles may engage in V2G operations. FigureÂ 3 depicts a simplified model that explains the various operations that fall under the V2G framework [7].
Optimization approaches for UCV2G
The concept of smart grid technology enables a large number of consumers to take participate in energy conservation by selling back excessive power to grid. Advancement in battery technology enables to design desired sizing and providing efficient facilities for controlled charging and discharging. The UC problem becomes rather more complex by this increased power injection. Thus, it becomes necessary to have proper coordination of UCV2G operation by fixing various UC and V2G constraints. The complexities of intermittent nature of wind energy and electric vehicles are coordinated, and unit commitment problem is resolved using mixed integer linear programming [8]. A power dispatch with 15 conventional units and 3 wind farms along PEV is incorporated in shifting of EV and wind power injection effectively to reduce the generation cost. Chemical reaction optimization technique is employed for economic generation scheduling incorporating V2G operation [9]. The charging and discharging patterns of electric vehicles were correctly formulated for cost minimization and enhancing system reliability by using genetic algorithm [10]. Virtual power of parking lot is fed back to grid using GAANN method for removing additional cost of small units required for reserve [11]. Complexities in conventional UC due to large number of gridable electric vehicles were effectively resolved by using particle swarm optimizer algorithm. PSO enables to provide solution for cost minimization and low emission [12].The subsequent section presents construction of unit commitment problem using proposed CSMA algorithm.
Construction of unit commitment problem
Mathematical formulation
The generation schedule must be planned well in advance such that sufficient power is always available to meet forecasted load demand with reliability. This could be more effective if a sufficient amount of power is contributed by renewable energy sources. Various mathematical equations satisfying system constraints are formulated to meet load demand including the cost of fuel, starting cost, and shunt down cost. The total fuel cost (F_{T}) is determined by summing up generation cost of each individual unit for a defined time interval. It can be mathematically represented as:
where \(a_{i} \,b_{i} \,{\text{and }}\,c_{i}\) are the fuel cost function expressed in \(\$ /{\text{h}}\,,\,\$ /{\text{MWh}}\,,\,\,{\text{and}}\,\,\,\$ /{\text{MWh}}^{2} \,\), respectively.
Mathematically, startup cost \(ST_{c(i)}\) can be expressed as the sum of cold startup \(({\text{CSch}}(i))\) and hot startup cost \(({\text{HSch}})\) of ith unit, respectively.
Unit commitment problem needs to provide optimum solution within certain constraints. The major constraints involved in UC problem are:

(i)
Operating limit constraints

(ii)
Load balance constraints

(iii)
V2G constraints

(iv)
Spinning reserve constraints
Operating limits constraints
There is a limit below which power generation is not economical due to some technical limitations. Similarly, power generation should not be more maximum power generation limit. These power generation limits for a particular unit are calculated from the heat rate curve and fuel cost coefficient limits.
Load balance constraints
The load demand is found to never remain constant, and it continuously changes over the entire span of the considered time interval. It is desired that the overall power generated by all the committed units (N) for a particular duration (h) should always satisfy the connected load demand (DL). Therefore, at any instant of time, the power supplied by thermal unit and additional wind power should always be equal to power demand.
Case1: During charging of vehicle (grid to vehicle)
Case2: During discharging (vehicle to grid)
The power outputs of the NG generating units at a particular time period have to satisfy the forecasted load. For arbitrary free unit power outputs Phi, (i=1, 2, NG), it is assumed that the Rth reference unit power output is constrained by the power balance equation as:
Case1: During charging of vehicle
Case2: During discharging
V2G constraint
V2G technology enables a fixed number of registered vehicle to participate in UC. EVs are assumed to be charged during offload period by utility grid or from renewable energy sources. Chargingâ€“discharging duration depends upon battery size and charging facilities. It is assumed that all vehicles charged by standalone system available at the parking slot.
Spinning reserve constraints
Unpredictable disturbances, such as sudden load demand or unexpected tripping of lines or generators, necessitate the availability of additional generation capacity. Spinning reserve is the term given to this additional generation capability. To meet demand while maintaining an adequate reserve margin, optimal generation allocation must be planned ahead of time. Wind penetration adds additional electricity, which assists to contribute towards total power generation. As a result of the additional power provided by wind energy, the load on thermal units may be reduced. Mathematically, spinning reserve is given as:
Grid to vehicle
Vehicle to grid
CSMA mathematical formulation
Slime moulds have received a level of admiration in recent times. The slime mould mentioned in this article is usually Physarum polycephalum. Typically, the plasmodium forms a network of protoplasmic tubes connecting the masses of protoplasm at the food sources, which is efficient in terms of network length and elasticity [13]. The slime mould even flows vibrantly in the situation of food scarcity, which aids in comprehending how slime mould search, move, and connect food in a changing environment. It can judge positive and negative feedback, when a secretion approaches the target and determines the most effective approach to capture food. While foraging, slime mould uses empirical principles based on currently available insufficient data to decide whether to start a fresh search and leave the existing place.
Mould may divide its biomass to exploit other resources on the information of some other rich highquality food information, even if a food source is abundant. It may modify their search patterns dynamically depending on the quality of food sources [14].The concept of probability distribution is captured by lot of metaheuristics algorithms to gain randomness. Chaotic maps could be beneficial if randomness due to ergodicity, idleness and randomness properties are properly utilized. These chaotic criteriaâ€™s are fulfilled by Eq.Â (18).
In Eq.Â (1), \(O_{k + 1} \,\& f(O_{k} )\) are the \((\,k + 1){\text{th}}\,\,\& \,k{\text{th}}\) chaotic number, respectively. The action of chaotic function is dependent on initial value \(O_{0}\). In the proposed work, from the 10 most commonly used chaotic strategies presented in Table 2, Tent chaotic function has been combined with basic CSMA algorithm to search space more enthusiastically and comprehensively.
The optimization procedure for the CSMA algorithm consists of the following eight steps:
 Step 1:

Specify the input parameters required by SMA and random chaotic function to solve the optimization problem defined by Eq. (21). Moulds position, population size, maximum iteration and smell index associated food searching, random iteration, random variables r, mean position of moulds, upper bound and lower bound (Ub), (Lb) are according initiated.
 Step 2:

Initialization of stochastic population (X_{i}â€‰=â€‰1, 2, 3â€¦..,N) and maximum iteration number is taken as ier_max.
 Step 3:

Calculate the fitness of all slime mould and estimating the updated position of moulds.
$$\overrightarrow {{X\left( {t + 1} \right)}} = \left\{ {\begin{array}{*{20}c} {\overrightarrow {{X_{b} \left( t \right)}} + \overrightarrow {{v_{b} }} .\left( {\overrightarrow {{\text{W}}} .\overrightarrow {{X_{A} \left( t \right)}}  \overrightarrow {{X_{B} \left( t \right)}} } \right),} & {r < p} \\ {\overrightarrow {{v_{c} }} .\overrightarrow {X\left( t \right)} ,} & {r \ge p} \\ \end{array} } \right.$$(19)  Step 4:

Enhancing the search process by clubbing chaotic strategy.
 Step 5:

Calculating the
$$\overrightarrow {{{\text{W}}\left( {{\text{smell}}\,{\text{index}}\left( {\text{i}} \right)} \right)}} = \left\{ {\begin{array}{*{20}c} {1 + r.\log \left( {\frac{bF  S\left( i \right)}{{bF  wF}} + 1} \right),} & {{\text{condition}}} \\ {1  r.\log \left( {\frac{bF  S\left( i \right)}{{bF  wF}} + 1} \right),} & {others} \\ \end{array} } \right.$$(20)  Step 6:

For each search iteration using sinusoidal chaotic function, the positions of \(p,vb, vc\) are updated
$$\begin{gathered} r_{o} = rand; \hfill \\ r_{o} \left( {t + 1} \right) = 2.3 \times r_{0}^{2} \times {\text{Sin}} \left( {Pi.r_{0} } \right) \hfill \\ r_{1} = r_{0} \left( {t + 1} \right); \hfill \\ \end{gathered}$$(21)  Step 7:

The eqn. for upgrading the positions of agents (i.e. to wrap food) is given as:
$$\overrightarrow {{X^{*} }} = \left\{ {\begin{array}{*{20}l} {rand.\left( {UB  LB} \right) + LB,\,rand < z} \hfill \\ {\overrightarrow {{X_{b} \left( t \right)}} + \overrightarrow {{v_{b} }} .\left( {{\text{W}}.\overrightarrow {{X_{A} \left( t \right)}}  \overrightarrow {{X_{B} \left( t \right)}} ,\,r < p} \right)} \hfill \\ {\overrightarrow {{v_{c} }} .\overrightarrow {X\left( t \right)} ,\,r \ge p} \hfill \\ \end{array} } \right.$$(22)  Step 8:

With the up gradation in the search process, the value of \(\overrightarrow {{v_{b} }}\) vibrantly changes between [âˆ’â€‰a,a] and \(\overrightarrow {{v_{c} }}\) varies between [âˆ’â€‰1,1] and at last shrinks to zero. This is known to be as â€˜grabbling of foodâ€™.
The flow chart for optimization procedure for the CSMA algorithm is shown in fig. 4.
Implementation of proposed CSMA algorithm for unit commitment problem
The CSMA method is an innovative metaheuristic algorithm that has an excellent ability of exploration and exploitation and effectively utilized to solve the unit commitment problem of a hybrid system. For a particular test system, the proposed algorithm selects an optimal generating schedule as a binary variable showing ON/OFF status. The following steps elucidate the procedure of a unit commitment problem [15].
 Step 1:

The status of a unit for generation scheduling is expressed through their position. In this study, we define the status of a unit as a binary number: 0 indicates decommitted unit, and 1 is for committed unit. Once the generation schedule is for a particular load demand is selected, the data of units are stored in integer matrix \(U_{NG}\) as,
$$U_{NG} = \left[ {\begin{array}{*{20}c} \begin{gathered} u_{1}^{1} \hfill \\ u_{2}^{1} \hfill \\ \vdots \hfill \\ u_{G}^{1} \hfill \\ \end{gathered} & \begin{gathered} u_{1}^{2} \hfill \\ u_{2}^{2} \hfill \\ \vdots \hfill \\ u_{G}^{2} \hfill \\ \end{gathered} & \begin{gathered} \cdots \hfill \\ \cdots \hfill \\ \vdots \hfill \\ \cdots \hfill \\ \end{gathered} & \begin{gathered} u_{1}^{H} \hfill \\ u_{2}^{H} \hfill \\ \vdots \hfill \\ u_{G}^{H} \hfill \\ \end{gathered} \\ \end{array} } \right]$$  Step 2:

Enter UCP input parameters, i.e. Maximum power limit, minimum power limit, fuel cost coefficient
 Step 3:

Set iteration counter, i =0 and initialize random position of search agents.
 Step 4:

Calculate the priority list of each search generator according to characteristics of each generating units.
 Step 5:

Modify search agent position to satisfy reserve constraints.
 Step 6:

Repair each search agent position for minimum Up/Down time violation.
 Step 7:

Verify generator output power or else increment iteration count by 1 and go to step 5.
Constraints repair strategy
Typically unit commitment programmes are designed to represent the operations of a centrally dispatched power system that is the portfolio of generators all scheduled in a coordinated way to meet aggregated electricity demand. The goal is always to minimize the cost of doing this subjected to constraints. During the major scheduling by CSMA, there may be a possibility that CSMA may fail to fulfill essential constraints such as minimum up/downtime, and spinning reserve. So, deviations in these constraints are needed to be repaired. In this paper, the strategy adopted is a heuristic search to tackle the UC problem.
Constraints related to minimum up /minimum downtime
Once a unit is started, it should not be turned off immediately before reaching MUT. This is required to satisfy economic, mechanical, and design limitations. Similarly, any unit which is once decommitted should not put online immediately. These constraints are required to be calculated in advance by using the following recursive relation:
Handling of spinning reserve constraints
The CSMA algorithm may sometimes perform unenviably to satisfy spinning reserve constraint. This happens to handle minimum up/down constraint, and excessive spinning reserve is needed. Thus, this spinning reserve constraint requirement should be handled heuristically. The PSEUDO code is shown in appendix1, and whole process to repair spinning reserve requirement is represented in Fig.Â 5
Decommitting of excess of units
During repair process of MDT/MUT and spinning reserve, some of the units may get unnecessarily ON. To avoid this situation that could result in excessive cost for running those units, some of the units need to be shutdown. The PSEUDO code is shown in appendix2, and flow chart for decommitting of excessive units is shown in fig. 6.
Results & discussion for unit commitment problem
In this section, results of standard IEEE test system with conventional UC and UCEV system are presented. The test systems are simulated MATLAB 2018a Windows 10, CPU@2.10Ghz4GB RAM Core i5. To check the performance of the CSMA method for solving the unit commitment, standard test system of IEEE is taken into concern.
Overview of assumptions

(i)
It is assumed that system is considered as lossless.

(ii)
Operating cost of V2G is omitted in this study

(iii)
A fleet of 40,000 electric vehicles are taken into consideration. Out of which 8000 vehicles are assumed to wire for V2G operation at any instant.

(iv)
Wind power forecasting error cost is not considered as it is out of scope in the present research

(v)
Simulation with different wind penetration levels, capacity of thermal generation and participation of PEVs are kept fixed
A standard IEEE 10unit system presented in Table 3 is considered for simulation study with 40000 PEVs. Spinning reserve requirement is assumed to be 10% of the hourly load demand in 24 hour scheduling time period. Parameters of PEV are depicted in Table 4. Table 5 shows unit allocation and active power scheduling for 10unit system. Figure 7 shows convergence curve for 10 unit system with 10% SR.Table 6 illustrates unit allocation and active power scheduling for 10unit system with wind. Figure 8 shows convergence curve for 10 unit system with 10% SR with wind using CSMA. Table 7 shows unit allocation and active power scheduling for 10unit system with V2G penetration using CSMA. Figure 9 shows convergence curve for 10 units system with EV penetration. Figure 10 shows cost comparison for 10 unit system with EV penetration using CSMA method.Further, effectiveness of the proposed simulation results for a 10 unit system incorporating wind and V2G operation has been compared with other wellknown optimization techniques such as HSA[8], CRO[8], GAANN[8], PSO[8] and CS[8]. The comparative analysis of the results shows a significant cost reduction for V2G operation using proposed CSMA method (Table 8).
Conclusion
In this paper, standard IEEE 10 unit system has been simulated with and without V2G by applying CSMA method for minimizing the overall cost. Results revealed that proposed method is effective in solving economic despatch problem very precisely. To check the effectiveness of proposed algorithm, results are compared with other methods. The comparative analysis reveals that proposed method outperforms in all aspects. Thus, proposed method is a cost effective solution for solving UC problem with due effect of renewables and EV.
Availability of data and materials
The data sets used and /or analysed during current research study are available from the corresponding author on reasonable request.
Abbreviations
 \(a_{i} ,\,b_{i} \,{\text{and}}\,c_{i}\) :

Fuel cost coefficients
 \({\text{CS}}({\text{h}})\) :

Cold starting hour of the ith unit
 \({\text{CSc}}_{{i,{\text{h}}}}\) :

Cold startup cost
 \(D_{L}\) :

Demand at â€˜hâ€™ hour
 \(F_{T}\) :

Total fuel cost
 \(itn_{\max }\) :

Maximum iterations
 \({\text{NG}}\) :

Number of generators
 \({\text{MUT}}\) :

Minimum uptime
 \({\text{MDT}}\) :

Minimum downtime
 \(P_{g\,\max \,(i)}\) :

Maximum generation by ith unit
 \(P_{g\,\min \,(i)}\) :

Minimum generation by ith unit
 \(P_{g\,(i)}\) :

Minimum generation by ith unit
 \(P_{g}^{w}\) :

Power contributed by renewable energy
 \(P_{{R({\text{h}})}}\) :

Output power available at Rth unit at â€˜hâ€™ hours
 \({\text{ST}}_{{C_{i} }}\) :

Startup cost of ith generating unit
 \({\text{SD}}_{{C_{i} }}\) :

Shutdown cost of ith generating unit
 \({\text{SR}}_{{({\text{h}})}}\) :

Spinning reserve at â€˜hâ€™ hour
 \(T_{{i.{\text{h}}}}^{{{\text{ON}}}}\) :

Time for which ith unit is continuously ON
 \(T_{{i.{\text{h}}}}^{{{\text{OFF}}}}\) :

Time for which ith unit is continuously OFF
 \(U_{{i,{\text{h}}}}\) :

Status of ith unit
References
Hetzer J, Yu DC, Bhattarai K (2008) An economic dispatch model incorporating wind power. IEEE Trans Energy Convers 23:603â€“611. https://doi.org/10.1109/TEC.2007.914171
Purwadi A, Ikhsan M, Hariyanto N, Heryana N, Haroen Y (2013) Wind speed calculation by using electrical output and wind turbine power curve, In: Proceedings of2013 international conference on informanation and technology electrical engineering, Intelligent green technology sustainable development. ICITEE 2013, pp 420â€“423. https://doi.org/10.1109/ICITEED.2013.6676279.
Dai S, Gao F, Guan X, Yan CB, Liu K, Dong J, Yang L (2020) Robust energy management for a corporate energy system with shiftworking V2G. IEEE Trans Autom Sci Eng. https://doi.org/10.1109/TASE.2020.2980356
Gnann T, PlÃ¶tz P, KÃ¼hn A, Wietschel M (2015) Modelling market diffusion of electric vehicles with real world driving data â€“ German market and policy options. Transp. Res. Part A Policy Pract. 77:95â€“112. https://doi.org/10.1016/j.tra.2015.04.001
Huda M, Tokimatsu K, Aziz M (2020) Techno economic analysis of vehicle to grid (V2G) integration as distributed energy resources in Indonesia power system. Energies. https://doi.org/10.3390/en13051162
Maghsudlu S, Mohammadi S (2018) Optimal scheduled unit commitment considering suitable power of electric vehicle and photovoltaic uncertainty. J Renew Sustain Energy. https://doi.org/10.1063/1.5009247
Haque ANMM, Ibn Saif AUN, Nguyen PH, Torbaghan SS (2016) Exploration of dispatch model integrating wind generators and electric vehicles. Appl Energy 183:1441â€“1451. https://doi.org/10.1016/j.apenergy.2016.09.078
MousaviTaghiabadi SM, Sedighizadeh M, Zangiabadi M, Fini AS (2020) Integration of wind generation uncertainties into frequency dynamic constrained unit commitment considering reserve and plug in electric vehicles. J Clean Prod 276:124272. https://doi.org/10.1016/j.jclepro.2020.124272
Yu JJQ, Li VOK, Lam AYS (2013) Optimal V2G scheduling of electric vehicles and unit commitment using chemical reaction optimization. 2013 IEEE Congr Evol Comput CEC 2013. https://doi.org/10.1109/CEC.2013.6557596
Wang Q, Gao Y, Zhang J (2014) Research on electric vehicle orderly charging and discharging considering unit running cost and effectiveness of power system operation, In: POWERCON 2014  2014 international conference on power system technology towards Green, efficiency of Smart Power System Proceedings. pp 996â€“1000. https://doi.org/10.1109/POWERCON.2014.6993936.
Bioki MMH, Jahromi MZ, Rashidinejad M (2013) A combinatorial artificial intelligence realtime solution to the unit commitment problem incorporating V2G. Electr. Eng. 95:341â€“355. https://doi.org/10.1007/s0020201202635
Saber AY, Venayagamoorthy GK (2010) Intelligent unit commitment with vehicletogrid A costemission optimization. J Power Sources 195:898â€“911. https://doi.org/10.1016/j.jpowsour.2009.08.035
Adamatzky A (2012) Slime mold solves maze in one pass, assisted by gradient of chemoattractants. IEEE Trans Nanobioscience. 11:131â€“134. https://doi.org/10.1109/TNB.2011.2181978
Dhawale D, Kamboj VK, Anand P (2021) An effective solution to numerical and multidisciplinary design optimization problems using chaotic slime mold algorithm. Springer, London. https://doi.org/10.1007/s00366021014094
Dhawale D, Kamboj VK (2020) A new hybrid harris hawks optimizer for solving global optimization problems, In: HHHOIGWO: Proceedings of international conference on computation, automation and knowledge management ICCAKM 2020, pp 52â€“57. https://doi.org/10.1109/ICCAKM46823.2020.9051509.
Dhawale D, Kamboj VK (2020) An effective solution to unit commitment problem in presence of sustainable energy using hybrid Harris Hawkâ€™s optimizer, In: 2020 international conferenceÂ onÂ decision aidÂ sciences andÂ applications DASA 2020, pp 469â€“472. https://doi.org/10.1109/DASA51403.2020.9317057.
Priya RP (2015) A solution to unit commitment problem with V2G using harmony search algorithm. Int. J. Adv. Res. Electr. Electron. Instrum. Eng. 04:1208â€“1214. https://doi.org/10.15662/ijareeie.2015.0403005
Saber AY, Venayagamoorthy GK (2009) Unit commitment with vehicletogrid using particle swarm optimization. 2009 IEEE Bucharest PowerTech Innov Ideas Towar Electr Grid Futur. https://doi.org/10.1109/PTC.2009.5282201
Amel Terki HB (2019) Cuckoo search algorithm for solving the problem of unitcommitment with vehicletogrid, In: Proceedings of the 4th international conference on electrical engineering and control applications, pp 77â€“92
Acknowledgements
Not applicable.
Funding
This research work has not been funded by any source or agencies.
Author information
Authors and Affiliations
Contributions
DD has analysed and interpreted the data regarding the scheduling of each power generating units for 24Â h duration and also drafted the work or substantively revised it and act as major contributor in writing the manuscript. VK has made substantial contribution to research design and handled all MATLAB coding in the work. PA has contributed in renewables data analysis and overall reformation of the work. All authors have read and approved the manuscript, and the content of the manuscript has not been published or submitted for publication elsewhere.
Corresponding author
Ethics declarations
Competing interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The authors declare that they have no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix
Appendix
(1) Pseudo code for satisfying minimum up and down using heuristic repair mechanism.
(2) PSEUDO code for spinning reserve repairing.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Dhawale, D., Kamboj, V.K. & Anand, P. An optimal solution to unit commitment problem of realistic integrated power system involving wind and electric vehicles using chaotic slime mould optimizer. Journal of Electrical Systems and Inf Technol 10, 4 (2023). https://doi.org/10.1186/s43067023000692
Received:
Accepted:
Published:
DOI: https://doi.org/10.1186/s43067023000692