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A meliorated Harris Hawks optimizer for combinatorial unit commitment problem with photovoltaic applications

Abstract

Conventional unit commitment problem (UCP) consists of thermal generating units and its participation schedule, which is a stimulating and significant responsibility of assigning produced electricity among the committed generating units matter to frequent limitations over a scheduled period view to achieve the least price of power generation. However, modern power system consists of various integrated power generating units including nuclear, thermal, hydro, solar and wind. The scheduling of these generating units in optimal condition is a tedious task and involves lot of uncertainty constraints due to time carrying weather conditions. This difficulties come to be too difficult by growing the scope of electrical power sector day by day, so that UCP has connection with problem in the field of optimization, it has both continuous and binary variables which is the furthermost exciting problem that needs to be solved. In the proposed research, a newly created optimizer, i.e., Harris Hawks optimizer (HHO), has been hybridized with sine–cosine algorithm (SCA) using memetic algorithm approach and named as meliorated Harris Hawks optimizer and it is applied to solve the photovoltaic constrained UCP of electric power system. In this research paper, sine–cosine Algorithm is used for provision of power generation (generating units which contribute in electric power generation for upload) and economic load dispatch (ELD) is completed by Harris Hawks optimizer. The feasibility and efficacy of operation of the hybrid algorithm are verified for small, medium power systems and large system considering renewable energy sources in summer and winter, and the percentage of cost saving for power generation is found. The results for 4 generating units, 5 generating units, 6 generating units, 7 generating units, 10 generating units, 19 generating units, 20 generating units, 40 generating units and 60 generating units are evaluated. The 10 generating units are evaluated with 5% and 10% spinning reserve. The efficacy of the offered optimizer has been verified for several standard benchmark problem including unit commitment problem, and it has been observed that the suggested optimizer is too effective to solve continuous, discrete and nonlinear optimization problems.

Introduction

Machine learning and artificial intelligence and so many problems are related to real world which have continuous and discrete behavior and constrained and unconstrained in nature. For this kind of attributes, there are a few challenges to handle a few sorts of issues utilizing traditional methodologies with scientific techniques [1]. A few sorts of research have tried that these all strategies are insufficient viable or effective to bargain numerous kinds of non-continuous problem and non-differentiable problem and furthermore in such huge numbers of real-world problem. In this way, meta-heuristic algorithm is considered and it is used to handle such a significant number of problems which are generally basic in nature and easily executed. Nowadays, the recent developed optimizer is Harris Hawks optimizer [HHO] [2]. Original version of Harris Hawks optimizer (HHO) had highlights that can in any case be improved as it might insight convergence problems or may effectively get caught in neighborhood optima [3]. Many variants had been developed which are discussed in Table 1 (a), which are used to improve or upgrade the existing HHO, so that the efficiency of the optimization techniques will be enhanced [4]. The procedure of optimization technique is proceeded till this can fulfill the most extreme iteration. In the present days, developing mindfulness and enthusiasm for effective, economical and fruitful utilization of such kinds of meta-heuristic calculation is under current examination. Modified version of existing algorithm was also upgraded by mutation to solve the real-world optimization problem also [5]. Nonetheless, after no free lunch theorem (NFL) [6], wide range for optimization dependent through enhancement methods prescribed and showed normal equal execution on the off chance that it is applied to every likely sort of errands dependent on optimization technique [7].

Table 1 (a) Assessment of several heuristics and meta-heuristics search optimization techniques. (b) Literature survey of unit commitment. (c) Literature survey of wind power uncertainty. (d) Literature survey of solar uncertainty

In the recent year, the electrical power sector is classified as huge proportions, vastly interconnected and highly nonlinear as dimension of electric power system is rising continuously due to huge electrical power demand in all the essential segment like commercial, agriculture, residential and industrial region. On electricity grid, the influence of overloading occurs due to rising the propensities in electrical load demand, privatization and deregulation taking place on electrical grids. For this condition, it needs progress of electric grid as the same step, as the rise in electric load demand and efficient power generation scheduling and commitment has the ability to regulate the time varying electrical load demand which is run for utilization of available grid [8]. Nowadays, recent power sector has some various sources of electrical power locations containing hydro-, thermal and nuclear power generation system; during a whole day, the electric power demand fluctuates with various peak values [9]. Thus, it is essential to determine that power generating units should be turned on, when necessary in power system network and the preparation or order in which the generating unit should kept in turn off condition is by considering the efficiency of cost for turn on and shut down for the respective power generating units. The whole procedure of constructing these assessments is known as unit commitment (UC) [10].

The main novelty of the proposed research work includes the hybrid variant of Harris Hawks optimizer, i.e., hybrid Harris Hawks–Sine–Cosine algorithm (hHHO-SCA) has been developed. The exploration phase of the existing Harris Hawks optimizer has been improved. A recently invented hybridized optimizer using memetic algorithm approach is used to solve unit commitment problem of power system. This paper offers the resolution of unit commitment optimization problems of the power system by using the hybrid algorithm, as UCP is linked optimization as it has both binary and continuous variables; the strategy adopted to tackle both variables is different. In this paper, the proposed sine–cosine algorithm searches allocation of generators (units that participate in generation to take upload) and once units are decided, allocation of generations (economic load dispatch) is done by Harris Hawks optimizer. The feasibility and efficacy of operation of the hybrid algorithm are verified for small, medium power systems and large system considering renewable energy sources in summer and winter and the percentage of cost saving for power generation is found. The results for 4 generating units, 5 generating units, 6 generating units, 7 generating units, 10 generating units, 19 generating units, 20 generating units, 40 generating units and 60 generating units are evaluated. The 10 generating units are evaluated with 5% and 10% spinning reserve.

Survey of literature

In the field of research area, the optimization method is the vastest region of research through which the research works are effectively moving forward. Nowadays, researchers are working with multiple works for various problems using different techniques and they are capable of measuring the output successfully. To discover the new algorithms, the research work is on successfully running condition and to mitigate the drawbacks of present existing techniques.

Some of the research works in the field of optimization include ant colony optimization (ACO) algorithm [11], ant lion optimizer (ALO) [12], adaptive gbest-guided search algorithm (AGG) [13], bat algorithm (BA) [14], biogeography-based optimization (BBO) [15], branch and bound (BB) [16], binary bat algorithm (BBA) [17], bird swarm algorithm (BSA) [18], bacterial foraging optimization algorithm (BFOA) [19], backtracking search optimization (BSO) [20], and binary gravitational search algorithm (BGSA) [21], colliding bodies optimization (CBO) [22], cuckoo search algorithm (CS) [23], chaotic krill herd algorithm (CKHA) [24], cultural evolution algorithm (CEA) [25], dragonfly algorithm (DA) [26], dynamic programming (DP) [27], earthworm optimization algorithm (EOA) [28], elephant herding optimization (EHO) [29], electromagnetic field optimization (EFO) [30], exchange market algorithm (EMA) [31], forest optimization algorithm (FOA) [32], fireworks algorithm (FA) [33], flower pollination algorithm (FPA) [34], gravitational search algorithm (GSA) [35], genetic algorithm (GA) [36], firefly algorithm (FFA) [37], grasshopper optimization algorithm (GOA) [38], gray wolf optimizer (GWO) [39], human group optimizer (HGO) [40], Hopfield method [41], interior search algorithm (ISA) [42], imperialist competitive algorithm (ICA) [43], krill herd algorithm (KHA) [44], invasive weed optimization (IWO) [45], lightning search algorithm (LSA) [46], league championship algorithm (LCA) [47], multi-verse optimizer (MVO) [48], mixed integer programming (MIP) [49], mine blast algorithm (MBA) [50], moth-flame optimization (MFO) [51], simulated annealing (SA) [52], monarch butterfly optimization (MBO) [53], particle swarm optimization (PSO) [54], random walk gray wolf optimizer (RW-GWO) [55], optics inspired optimization (OIO) [56], runner-root algorithm (RRA) [57], sine–cosine algorithm (SCA) [58], shuffled frog-leaping algorithm (SFLA) [59], stochastic fractal search (SFS) [60],seeker optimization algorithm (SOA) [61], teaching–learning-based optimization (TLBO) [62], symbiotic organisms search (SOS) [63], search group algorithm (SGA) [64], salp swarm algorithm (SSA) [65], and whale optimization algorithm (WOA) [66], weighted superposition attraction (WSA) [67], virus colony search (VCS) [68], water wave optimization (WWO) [69], Tabu search (TS) [70], water cycle algorithm (WCA) [71], wind-driven optimization (WDO) [72], modified sine–cosine algorithm [m-SCA] [73], and improved sine–cosine algorithm [ISCA] [74]. Leadership quality was improved by Levy flight (LF) search and gray wolf optimizer [GLF–GWO] [75], greedy differential evolution–gray wolf optimizer [gDE-GWO] [76], memory-based gray wolf optimizer [mGWO] [77], and memory-guided sine–cosine algorithm [MG-SCA] [1].

Faisal Rahiman Pazheri et al. presented scheduling of power station with energy storage facility. Utilities of power are stimulated by converting the present conventional power plant into hybrid power plant by installing available energy storage facilities and renewable electric power unit to come across the sudden increase in the power demand. Facility of energy storage maintains a level of the penetration of renewable power to 10% of required load demand throughout the period of operation for hybrid power plant [136]. Chandrasekaran et al. proposed FF algorithm to get solution of the SUC problem for thermal/solar power sector considering issues regarding smart grid. The research paper included some critical review on reliable impacts of major resources of smart grid considering demand response (DR) and solar energy. Thus, it was essential to implement method for an integration of thermal and solar generating system [144]. Selvakumar et al. implemented a new strategy for solving unit commitment problem for thermal units integrated with solar energy system. There would be changes in the cost of power generation considered solar energy. The main objective was reduction of total production price for the electricity generating unit, and this paper also explained the variances by considering solar energy and non-considering the solar power [140]. Senjyu et al. proposed a new method using genetic algorithm operated PSO to solve the thermal UCP considering wind and solar energy system. This method was able to minimize production cost and produce high-quality solutions [143]. Ma et al. discussed about appliances scheduling via cooperative multi-swarm PSO under photovoltaic (PV) generation and day-ahead prices. This research work studied about the problem including scheduling appliances in residential system unit. The model of an appliance-scheduling was established for home energy management system which was based on day-ahead electricity price and PV generation [137]. Abujarad et al. discussed a review on current methods for commitment of generating unit in existence of irregular renewable energy resource [139]. Maryam Shahbazitabar and Hamdi Abdi implemented a new priority-based stochastic unit commitment as parking lot cooperation and renewable energy sources. This paper discussed about the fastest nature of heuristic method which was established on list of priority selections to get solution for stochastic nature of the problem related to unit commitment and useful to simple 10 unit systems where the study was addition considering electrical vehicles parking allocation considering wind farm and solar farm over 24-h time horizon [135]. Quan et al. proposed a comparative review on integrated renewable energy generation uncertainties which were captured by list of prediction intervals, into stochastic unit commitment considering reserve and risk [138]. Jasmin et al. implemented an optimization technique about reinforcement learning to solve unit commitment problem considering photovoltaic sources. For stochastic behavior of the associated power and solar irradiance, the arrangement of the different types of power generating sources considering solar energy turned to be an optimization problem stochastic in nature. This paper discussed about the optimization technique and reinforcement learning that can provide uncertainty of the environment of the nature which is very effective [141]. Saniya Maghsudlu and Sirus Mohammadi proposed a method to solve the problem in optimum schedule of commitment unit as appropriate control of EVs and PV uncertainty. The meta-heuristic approach, cuckoo search algorithm, was developed by greatest convergence speed to attain the optimal solution and get solution of UCP. The research discussed about case study of IEEE 10 unit system which was used to examine the impact of PV and PEVs on scheduling of generating unit [134].

Problematic design

The generating power is distributed along with utilities of generator scheduling which will meet the time varying load demand for a specific time period known as unit commitment problem (UCP). The main objective of UCP is minimization of the overall cost for production considering different system constraints. The overall costs of production including sum of shutdown cost and start-up cost, cost of fuel are given below:

$${ \hbox{min} }({\text{TFC}}) = \sum\limits_{t = 1}^{H} {\sum\limits_{n = 1}^{N} {\left\{ {F_{{{\text{cost}}n}} (P_{nt} ) + {\text{SUC}}_{n,t} + {\text{SDC}}_{nt} } \right\}} }$$
(1)

The total cost of fuel over the scheduled time span ‘t’ is:

$${\text{TFC}} = \sum\limits_{t = 1}^{T} {\sum\limits_{n = 1}^{\text{NU}} {\left[ {F_{\text{cost}} \times U_{n,t} + {\text{SUC}}_{n,t} (1 - U_{n,(t - 1)} ) \times U_{n,t} } \right]} }$$
(2a)
$${\text{TFC}} = \sum\limits_{t = 1}^{T} {\sum\limits_{n = 1}^{\text{NU}} {[(A_{n} P_{n}^{2} + B_{n} P_{n} + C_{n} ) \times U_{n,t} + {\text{SUC}}_{n,t} (1 - U_{n,(t - 1)} ) \times U_{n,t} ]} }$$
(2b)

Here, cost for fuel \(F_{{{\text{cost}}n}} (P_{nt} )\) is stated as quadratic design that is mostly worked by researchers, also named as equation of convex function.

The cost of fuel of (n) unit at (t) hour can be mathematically represented as an equation which is given below:

$$F_{\text{cost}} \left( {P_{n} } \right) = A_{n} P_{n}^{2} + B_{n} P_{n} + C_{n}$$
(3)

where \(A_{n}\), \(B_{n}\) and \(C_{n}\) are represented as coefficients of cost that may expressed as $/h, $/MWh, and $/MWh2 correspondingly.

Start-up cost can mathematically be represented by step function which is given below:

$${\text{SUC}}_{n,t} = = \left\{ {\begin{array}{*{20}l} {{\text{HSU}}_{n} ;} \hfill & {\quad {\text{for}}\quad T_{n}^{\text{DW}} \le T_{n}^{\text{UP}} \le (T_{n}^{\text{DW}} + T_{n}^{\text{COLD}} )} \hfill \\ {{\text{CSU}}_{n} ;} \hfill & {\quad {\text{for}}\quad T_{n}^{\text{UP}} > (T_{n}^{\text{DW}} + T_{n}^{\text{COLD}} )} \hfill \\ \end{array} } \right.\quad \quad \left( {n \in {\text{NU}};\quad t = 1,2,3, \ldots ,T} \right)$$
(4)

Usual value of the shutdown cost for standard system is denoted as zero, and this can be established as fixed cost followed by the equation number (5).

$${\text{SDC}}_{nt} = {\text{KP}}_{nt}$$
(5)

where K is represented as incremental cost for shutdown.

It is subjected through some constraints followed by (1) system constraints and (2) unit constraints.

Constraints for system

System constrains are interrelated with all generating unit existing in the systems. The systems constrains are characterized into two types like:

Power balance or load balance constraints

In power system, the constraint including power balance or load balance is more important parameter consisting of summation of whole committed generating unit at tth time span which must be larger than or equivalent to the power demand for the particular time span ‘t

$$\sum\limits_{n = 1}^{\text{NU}} {P_{n,t} \times U_{n,t} = {\text{PD}}_{n} }.$$
(6)

Spinning reserve (SR) constraints

Reliability of the system can be considered as facility of extra capability of power generation that is more important to deed instantly when failure occurred due to sudden change in load demand for such power generating unit which is already running. The extra capability of power generation is recognized as spinning reserve which is exactly represented as (Fig. 1):

$$\sum\limits_{n = 1}^{\text{NU}} {P_{n,t}^{\text{MAX}} \times U_{n,t} \ge {\text{PD}}_{t} + {\text{SR}}_{t} } .$$
(7)

Constraints for power generating unit

The specific constraints related to particular power generating unit existing in the systems are called generating unit constraint which are given as:

Thermal unit constraints

Thermal power units are controlled manually. This type of unit needs to undertake the change of temperature gradually, so it takes certain time span to take the generating unit accessible. Some crew members are essential to execute the maintenance and procedure of some thermal power generating units.

Minimum up time

This constraint is defined here as the minimum period of time previously the unit can be start over when the unit has already been shut down which is mathematically defined as:

$$T_{n,t}^{\text{ON}} \ge T_{n}^{\text{UP}}$$
(8)

where \(T_{n,t}^{\text{ON}}\) is defined as interval through which the generating unit n is constantly ON (in hours) and \(T_{n}^{\text{UP}}\) is defined as minimum up time (in hours) for the generating unit n (Fig. 1).

Fig. 1
figure 1

PSEUDO code of SR repairing

Minimum down time

When the power generating units will be DE-committed, there is required least period of time for recommitment of the unit which is mathematically given as:

$$T_{n,t}^{\text{OFF}} \ge T_{n}^{\text{DW}}$$
(9)

where \(T_{n,t}^{\text{OFF}}\) is time period for which generating unit n is constantly OFF (in hours) and \(T_{n}^{\text{DW}}\) is denoted as minimum down time (in hours) for the unit.

Adequate minimum downtime and uptime repair by heuristic mechanism accepted at those stages are stated in Fig. 2.

Fig. 2
figure 2

PSEUDO code for MUD/MUT constraints

Maximum and minimum power generating limits

All power generating units have its individual maximum/minimum electric power generating limit, below and outside which it cannot produce, and this is known as maximum and minimum power limits, which is mathematically written as:

$$P_{n}^{\text{MIN}} \le P_{n,t} \le P_{n}^{\text{MAX}} .$$
(10)

Initial status for operation of electrical units

For every units, the initial operating position must proceed as the day’s earlier generation schedule is taken into consideration; thus, each and all generating units can fulfill its lowest downtime/uptime (Figs. 3, 4, 5, 6, 7).

Crew constraint

When any power plant consists of more than one units, they could not turn on at the same period of time. So there need more than one crew member to attend such units in the same time while starting up.

Unit accessibility constraint

The constraint shows accessibility of power generating unit surrounded by any of the resulting various circumstances:

  1. (A)

    Accessible or Not Accessible.

  2. (B)

    Must Out or Outage.

  3. (C)

    Must Run.

Initial status of power generation unit

It signifies value of initial grade of power generating unit. Its favorable rate signifies the position of current generating unit which is already in up condition, which means that numeral time periods of the generating units are already up, and if its negative value is an index of the integer of hours, then the generating unit has been already in down condition. The position of the generating unit ± earlier the first hour through the schedule is an essential feature to define whether its latest situation interrupts the constraint of \(T_{n}^{\text{UP}}\) and \(T_{n}^{\text{DW}}\).

Methods

The mathematical formulation of the Harris Hawks optimizer has been explained in this section. The position updating mechanism of the harris hawks optimizer has been presented in Eqs. (11), (12) and (13).  Presently, considering the equivalent possibility w for each adjusting system depends upon areas for additional individuals to approach sufficiency while confronting as a prey, given in Eq. (11) (Figs. 3 and 4)

Fig. 3
figure 3

Surprise attack

Fig. 4
figure 4

Basic of SCA

$$X(iteration + 1) = \left\{ {X_{rand} (iteration) - r_{1} \times abs(X_{rand} (iteration) - 2 \times r_{2} \times X(iteration))} \right\};\quad w \ge .5$$
(11)
$$X(iteration + 1) = \left\{ {(X_{rabbit} (iteration) - X_{m} (iteration)) - r_{3} \times ({\text{LB}} + r_{4} \times ({\text{UB}} - {\text{LB}}))} \right\};\quad w < .5$$
(12)
$$X_{m} (iteration) = \frac{1}{N}\left( {\sum\limits_{i = 1}^{N} {X_{i} } (iteration)} \right)$$
(13)

where \(r_{1,} r_{2,} r_{3,} r_{4,}\) and w are random records in the middle of (0, 1); those are upgraded in every cycle, \(X(iteration + 1)\) is denoted as Rabbit’s position and N is defined as total amount of Harris hawks

Normal area for Harris Hawks is accomplished utilizing Eq. (13) (Fig. 5).

Fig. 5
figure 5figure 5

a Pseudocode of proposed hybrid hHHO-SCA algorithm. b Flowchart for hHHO-SCA technique

Change after the period for investigation of the period of exploitation is shown:

$$E = 2 \times E{}_{0} \times \left( {1 - \frac{iteration}{iter\hbox{max} }} \right)$$
(14)

where E is the avoidance energy for rabbit, E0 the early condition for energy and \(iter\hbox{max}\) = maximum iteration

$$X(iteration + 1) = \Delta X(iteration) - E \times abs(JX_{rabbit} (iteration) - X(iteration))$$
(15)
$$\Delta X(iteration) = \left( {X_{rabbit} (iteration) - X(iteration)} \right)$$
(16)
$$X(iteration + 1) = X_{rabbit} (iteration) - E \times abs(\Delta X(iteration))$$
(17)
$$Y = X_{rabbit} (iteration) - E \times abs(JX_{rabbit} (iteration) - X(iteration))$$
(18)
$$Z = Y + S \times LF(D).$$
(19)

Along these lines, to find out the better solution of a soft enclose, the Hawks birds of prey are able to choose their development Y that depends upon standard that is shown in Eq. (18)

Established Lf (D) patterns are constructed which track the given instruction in Eq. (20),

where D = dimension of problems, S = dimension of random vectors with size 1 × D

$$LF(x) = 0.01\left( {\frac{\mu \times \sigma }{{\left| v \right|^{{\frac{1}{\beta }}} }}} \right)$$
(20)
$$\sigma = \left( {\frac{{\varGamma \left( {1 + \beta } \right) \times \sin \left( {\frac{\pi \beta }{2}} \right)}}{{\varGamma \left( {\frac{1 + \beta }{2}} \right) \times \beta \times 2\left( {\frac{\beta - 1}{2}} \right)}}} \right)^{{\frac{1}{\beta }}}$$
(21)

where \(\mu ,\sigma\) are denoted as such kind of values randomly in between (0, 1) and \(\beta\) set to 1.5 which is a constant known as default.

The final and actual positions through this period of soft encircle can be updated using Eqs. (22) and (23) shown below:

$$X(iteration + 1) = \left\{ \begin{aligned} Y\begin{array}{*{20}c} ; & {i{\text{f}}} & {F(Y) < F(X(iteration))} \\ \end{array} \hfill \\ Z\begin{array}{*{20}c} ; & {\text{if}} & {F(Z) < F(X(iteration))} \\ \end{array} \hfill \\ \end{aligned} \right.$$
(22)
$$Y = X_{rabbit} (iteration) - E \times abs(JX_{rabbit} (iteration) - X_{m} (iteration))$$
(23)
$$Z = Y + S \times Lf(D)$$
(24)

\(X_{m} (iteration)\) can be obtained from Eq. (23).

The SCA optimization technique is mathematically written as:

$$X_{i} (iteration + 1) = X_{i} (iteration) + r_{1} \times \sin (r_{2} ) \times \left| {r_{3} \times P_{i} (iteration) - X_{i} (iteration)} \right|$$
(24)
$$X_{i} (iteration + 1) = X_{i} (iteration) + r_{1} \times \cos (r_{2} ) \times \left| {r_{3} \times P_{i} (iteration) - X_{i} (iteration)} \right|$$
(25)
$$X_{i} (iteration + 1) = \left\{ \begin{aligned} X_{i} (iteration) + r_{1} \times \sin (r_{2} ) \times \left| {r_{3} \times P_{i} (iteration) - X_{i} (iteration)} \right|\begin{array}{*{20}c} ; & {\text{if}} & {r_{4} < 0.5} \\ \end{array} \hfill \\ X_{i} (iteration) + r_{1} \times \cos (r_{2} ) \times \left| {r_{3} \times P_{i} (iteration) - X_{i} (iteration)} \right|\begin{array}{*{20}c} ; & {\text{if}} & {r_{4} \ge 0.5} \\ \end{array} \hfill \\ \end{aligned} \right.$$
(26)

Here, \(r_{4}\) is denoted as random numbers [0, 1].

This method based on the suggested process may balance exploitation as well as exploration to get favorable solutions in the area of search space and lastly meet to find global optimal solutions using Eq. (27) (Fig. 6).

Fig. 6
figure 6

Flowchart of complete procedure of commitment by SCA method

$$r_{1} = \left( {2 - iteration \times \frac{2}{Iter\hbox{max} }} \right)$$
(27)

Handling of spinning reserve constraints

The simple possible solution that was obtained by SCA technique is highly unsuccessful to satisfy spinning reserve necessity (Fig. 7). Also handling of minimum uptime and downtime leads to extra spinning reserve. Thus, it is compulsory to handle/adjust spinning reserve necessity heuristically. The flowchart in Fig. 8 explains whole process to repair spinning reserve necessity.

Fig. 7
figure 7

Flowchart of handle minimum uptime–downtime constraints

Fig. 8
figure 8

Flowchart for repairing spinning reserve

De-committing of excess of units

It is obvious from the code given over that during fix of MDT, MUT, and spinning reserve we need to take generating unit status “ON” if these requirements are violated by putting it off. Since we do as such against the caution given by algorithm, obliviously it brings about additional save. This circumstance is exceptionally unwanted; thus, we need to recommit some of the units once again in order to archive economic operation. In the following, the heuristic methodology is received for de-committing the additional spinning reserve (Figs. 9, 10).

Fig. 9
figure 9

Pseudocode of decommitment for excessive power generating unit

Fig. 10
figure 10

Flowchart for the decommitment for excessive power generating units

Results and discussion

In order to validate the efficacy of the hHHO-SCA optimization technique, the outcomes of hHHO-SCA algorithm have been given below. The generating units’ data are shown in Additional file 1: Annexure-A1 to A6 and its comparative analysis considering solar energy in summer and winter are shown in Table 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2021, 22, 23, 24 and 25 (Figs. 11, 12 and 13).

Table 2 Power scheduling for 5 generating system considering renewable energy in summer
Table 3 Power scheduling for 6-generating unit system considering renewable energy in summer
Table 4 Power scheduling for 10-generating unit system (5% SR) considering renewable energy in summer
Table 5 Power scheduling for 10-generating unit system (10% SR) considering renewable energy in summer
Table 6 Power scheduling for 19-generating unit system considering renewable energy in summer
Table 7 Power scheduling for 20-generating unit system considering renewable energy in summer
Table 8 Power scheduling for 40-generating unit system considering renewable energy in summer
Table 9 Power scheduling for 60-generating unit system considering renewable energy in summer
Table 10 Power scheduling for 80-generating unit system considering renewable energy in summer
Table 11 Power scheduling for 100-generating unit system considering renewable energy in summer
Table 12 Power scheduling for 5-generating unit system considering renewable energy in winter
Table 13 Power scheduling for 6-generating unit system considering renewable energy in winter
Table 14 Power scheduling for 10-generating unit system (5% SR) considering renewable energy in winter
Table 15 Power scheduling for 10-generating unit system (10% SR) considering renewable energy in winter
Table 16 Power scheduling for 19-generating unit system considering renewable energy in winter
Table 17 Power scheduling for 20-generating unit system considering renewable energy in winter
Table 18 Power scheduling for 40-generating unit system considering renewable energy in winter
Table 19 Power scheduling for 60-generating unit system considering renewable energy in winter
Table 20 Power scheduling for 80-generating unit system considering renewable energy in winter
Table 21 Power scheduling for 100-generating unit system considering renewable energy in winter

5-Generating Unit Test Systems: The first test system contains IEEE-14 bus systems which have 24-hour power demand with 10% spinning reserve. The hHHO-SCA technique is considered for 100 iterations. Tables 2 and 12 show that optimal scheduling for this test system considering summer and winter, respectively, using the hHHO-SCA algorithm is 8226.6 $/hour and 8572.9 $/hour. Without considering the renewable energy sources, the total generation cost is 9010.1$/hour.

6-Generating Unit Test System: The second test system contains 6-generating units for IEEE-30 bus test systems with 24-hour electrical load demand including 10% SR [145]. The hHHO-SCA algorithm is assessed for 100 iterations. Tables 3 and 13 show that optimal scheduling for this test system considering summer and winter, respectively, using the hHHO-SCA algorithm is 12229 $/hour and 12977 $/hour. Without considering the renewable energy sources, the total generation cost is 13489.93957 $/hour.

10-Generating Unit Test System: The third system contains 10 units power generating units. This system has been verified for 24-hour electric power demand outline at various spinning reserve capability. Case-1 consists of spinning reserve capability of 5%, and case-2 contains spinning reserve capability of 10%.

Case-1: 10-Generating Unit Test System (SR = 5%): The system consists of 10 power generating units with 24-hour electrical load demand including 5% SR [146]. The hHHO-SCA technique is evaluated for 100 iterations. Tables 4 and 14 show that optimal scheduling for this test system considering summer and winter, respectively, using the hHHO-SCA algorithm is 529980 $/hour and 536200 $/hour. Without considering the renewable energy sources, the total generation cost is 557533.12$/hour.

Case-2: 10-Generating Unit System (SR = 10%): The system consists of 10 power generating units with 24-hour electrical load demand including 10% SR [146]. The hHHO-SCA technique is evaluated for 100 iterations. Tables 5 and 15 show that optimal scheduling for this test system considering summer and winter, respectively, using the hHHO-SCA algorithm is 534050 $/hour and 539110 $/hour. Without considering the renewable energy sources, the total generation cost is 563937.6875$/hour.

Medium-Scale and Large-Scale Electrical Power System (19-, 20-, 40-, 60-, 80- and 100-Unit System): The data for 20 and 40 generating unit test systems and the 10-unit system had been doubled and quadrupled, and electric power demand is multiplied by two and four times correspondingly [145].

19-Generating Unit System: The fourth system contains 19 power generating units of IEEE-118 bus test system with a 24-hour electricity load demand including 10% SR [145]. The hHHO-SCA technique is evaluated for 100 iterations. Tables 6 and 16 show that optimal scheduling for this test system considering summer and winter, respectively, using the hHHO-SCA algorithm is 207180 $/hour and 207560 $/hour. Without considering the renewable energy sources, the total generation cost is 208510 $/hour.

20-Generating Unit System: The fifth system contains 20-power generating units with 24-hour electricity demand including 10% SR [145]. The hHHO-SCA algorithm is assessed for 100 iterations. Tables 7 and 17 show that optimal scheduling for this test system considering summer and winter, respectively, using the hHHO-SCA algorithm is 1076400 $/hour and 1084100 $/hour. Without considering the renewable energy sources, the total generation cost is 1125200 $/hour.

40-Generating Unit System: The sixth system contains 40-power generating units having a 24-hour electricity demand including 10% SR [145]. The hHHO-SCA technique is evaluated for 100 iterations. Tables 8 and 18 show that optimal scheduling for this test system considering summer and winter, respectively, using the hHHO-SCA algorithm is 2176900 $/hour and 2189400 $/hour. Without considering the renewable energy sources, the total generation cost is 2253700 $/hour.

60-Generating Unit System: The seventh system contains 60-power generating units with 24-hour electricity demand including 10% SR [145]. The hHHO-SCA technique is evaluated for 100 iterations. Tables 9 and 19 show that optimal scheduling for this test system considering summer and winter, respectively, using the hHHO-SCA algorithm is 8226.6 $/hour and 8572.9 $/hour. Without considering the renewable energy sources, the total generation cost is 9010.1$/hour.

80-Generating Unit System: The eighth system contains 80-power generating units with 24-hour power demand including 10% SR [145]. The hHHO-SCA technique is evaluated for 100 iterations. Tables 10 and 20 show that optimal scheduling for this test system considering summer and winter, respectively, using the hHHO-SCA algorithm is 5578000 $/hour and 5591700 $/hour.

100-Generating Unit System: The ninth system contains 100-power generating units with 24-hour power demand including 10% SR [145]. The hHHO-SCA technique is evaluated for 100 iterations. Tables 11 and 21 show that optimal scheduling for this test system considering summer and winter, respectively, using the hHHO-SCA algorithm is 5530800 $/hour and 552990 $/hour (Tables 22, 23, 24, 25).

Table 22 Overall cost for generation of each unit without renewable energy sources
Table 23 Overall cost for generation of each unit with renewable energy sources in winter
Table 24 Overall cost for generation of each unit with renewable energy sources in summer
Table 25 Overall cost for generation of each unit with renewable energy sources in Autumn & Spring
Fig. 11
figure 11

Standard test systems

Fig. 12
figure 12

Percentage of cost saving for each unit considering renewable energy source in winter using hHHO-SCA optimization technique

Fig. 13
figure 13

Percentage of cost saving for each unit considering renewable energy source in winter using hHHO-SCA optimization technique

Conclusions

In this research work, the authors have successfully presented the fusion of Harris Hawks optimizer with SCA optimization technique and evaluated performance of the suggested hybrid optimized method for standard benchmark problem unit commitment problem, which consists of thermal generating units and along with PV generating units. The proposed research focuses on invention of hybrid variant of Harris Hawks optimizer (HHO) and sine–cosine algorithm (SCA) using memetic algorithm approach, named as intensify Harris Hawks optimizer. The efficacy of the suggested algorithm was tested for 4-generating unit system, 5-generating unit system, 6-generating unit system, 7-generating unit system, 10-generating unit system, 19-generating unit system, 20-generating unit system, 40-generating unit system and 60-generating unit system. After successful experiment, it was observed that the suggested optimizer is too much effective to solve continuous, discrete and nonlinear optimization problems.

After verification, it builds up the effective outcomes of the suggested hybrid improvement optimization which are more effective to other newly defined meta-heuristics, hybrid and heuristics method and advancement search calculation and suggested algorithm recommends for the efficiency of this algorithm in the search area of meta-heuristics type optimization algorithms which are nature inspired. The other existing optimization techniques have good development prospect, but their research is still at initial condition and included so many problems which need to be solved or in other instance, there are several uncertainties, such as, how to adequately stay away from nearby or local optimum? What is the most effective method to consummately consolidate the upsides of distinctive enhancement calculations? How to successfully set the boundaries or parameter of a calculation? What are the compelling cycle of iteration stop conditions? etc. The most significant issue is that it comes up short on a bound together and complete hypothetical framework. So, using this novel proposed methodology, those problems are easily solved. The proposed optimization algorithm is useful to overcome those problems.

Availability of data and material

The datasets used and/or analyzed during the current research study are available from the corresponding author on reasonable request.

Abbreviations

TFC:

Total cost of fuel

\(F_{{{\text{cost}}\,n}} (P_{nt} )\) :

Cost of fuel for a particular generating unit nth at that particular time ‘t’ hour

\({\text{SUC}}_{n,t}\) :

Cost of start-up for nth unit within ‘t’ hours

\({\text{SDC}}_{nt}\) :

Cost of Shutdown for nth unit within ‘t’ hours

\(U_{nt}\) :

Unit status at time t

\(A_{n}\) :

Coefficient of cost for nth unit

\(B_{n}\) :

Coefficient of cost for nth unit

\(C_{n}\) :

Coefficient of cost for nth unit

\({\text{HSU}}_{n}\) :

hot start for nth unit

\({\text{CSU}}_{n}\) :

cold start for nth unit

\(P_{n,t}^{\text{MAX}}\) :

Maximum electrical power generation by unit n

\(P_{n}^{\text{MIN}}\) :

Minimum electrical power which generation by unit n

\(P_{n,t}\) :

Electrical power generation of unit nth at the time span ‘t

\({\text{PD}}_{t}\) :

load demand at ‘t’ hours

INSn :

initial status of unit n at time ‘t

\(T_{n,t}^{\text{OFF}}\) :

Initial OFF status for nth unit at time ‘t

\(T_{n,t}^{\text{ON}}\) :

Initial ON status for nth unit at time ‘t

\(T_{n}^{\text{UP}}\) :

UP condition for n no. of power generating unit

\(T_{n}^{\text{DW}}\) :

DOWN condition for n no. of power generating unit

K :

incremental cost for shut down of unit

\({\text{PD}}_{n}\) :

Power demand for nth unit

\({\text{SR}}_{t}\) :

spinning reserve necessity

T COLD n :

Time span for COLD start of n no. of generating unit

Np:

Population number

t :

No. of hours

NU:

No. of generators

References

  1. Gupta S, Deep K, Engelbrecht AP (2020) Engineering applications of artificial intelligence a memory guided sine cosine algorithm for global optimization. Eng Appl Artif Intell 93:103718

    Article  Google Scholar 

  2. Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris hawks optimization: algorithm and applications. Future Gener Comput Syst 97:849–872

    Article  Google Scholar 

  3. Chen H, Asghar A, Chen H, Wang M, Pan Z, Gandomi AH (2020) Multi-population differential evolution-assisted Harris hawks optimization: framework and case studies. Future Gener Comput Syst 111:175–198

    Article  Google Scholar 

  4. Gupta S, Deep K, Moayedi H, Foong LK, Assad A (2020) Sine cosine grey wolf optimizer to solve engineering design problems. Eng Comput, no. 0123456789

  5. Gupta S, Deep K, Mirjalili S, Hoon J (2020) “A modified sine cosine algorithm with novel transition parameter and mutation operator for global optimization. Expert Syst Appl 154:113395

    Article  Google Scholar 

  6. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82

    Article  Google Scholar 

  7. Zhou W, Wang P, Heidari AA, Wang M, Chen H (2020) Multi-core sine cosine optimization: methods and inclusive analysis. Expert Syst Appl 164:113974

    Article  Google Scholar 

  8. Kerr RH, Scheidt JL, Fontanna AJ, Wiley JK (1966) Unit commitment. IEEE Trans Power Appar Syst 5:417–421

    Article  Google Scholar 

  9. Baldwin CJ, Dale KM, Dittrich RF (1959) A study of the economic shutdown of generating units in daily dispatch. AIEE Trans Power Appar Syst. 78:1272–1284

    Article  Google Scholar 

  10. Lee KD, Vierra RH, Nagel GD, Jenkins RT (1985) Problems associated with unit. Commitment in uncertainty. IEEE Trans Power Appar Syst 104(8):2072–2078

    Google Scholar 

  11. Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28–39

    Article  Google Scholar 

  12. Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80–98

    Article  Google Scholar 

  13. Mirjalili S, Lewis A (2014) Adaptive gbest-guided gravitational search algorithm. Neural Comput Appl 25(7–8):1569–1584

    Article  Google Scholar 

  14. Yang X-S (2010) New metaheuristic bat-inspired algorithm. In: Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, pp 65–74

  15. Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713

    Article  Google Scholar 

  16. Cohen AI, Yoshimura M (1983) A branch-and-bound algorithm for unit commitment. IEEE Trans Power Appar Syst 102(2):444–451

    Article  Google Scholar 

  17. Nakamura RY, Pereira LA, Costa KA, Rodrigues D, Papa JP, Yang XS (2012) BBA: a binary bat algorithm for feature selection. In: Brazilian symposium on computer graphics and image processing, pp 291–297

  18. Meng XB, Gao XZ, Lu L, Liu Y, Zhang H (2016) A new bio-inspired optimisation algorithm: Bird Swarm Algorithm. J Exp Theor Artif Intell 28(4):673–687

    Article  Google Scholar 

  19. Das S, Biswas A, Dasgupta S, Abraham A (2009) Bacterial foraging optimization algorithm: theoretical foundations, analysis, and applications. Stud Comput Intell 203:23–55

    Google Scholar 

  20. Civicioglu P (2013) Backtracking Search Optimization Algorithm for numerical optimization problems. Appl Math Comput 219(15):8121–8144

    MathSciNet  MATH  Google Scholar 

  21. Rashedi E, Nezamabadi-Pour H, Saryazdi S (2010) BGSA: binary gravitational search algorithm. Nat Comput 9(3):727–745

    MathSciNet  MATH  Article  Google Scholar 

  22. Kaveh A, Mahdavi VR (2015) Colliding bodies optimization: extensions and applications. Springer, Berlin, pp 1–284

    MATH  Book  Google Scholar 

  23. Gandomi AH, Yang X-S, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29(1):17–35

    Article  Google Scholar 

  24. Wang GG, Guo L, Gandomi AH, Hao GS, Wang H (2014) Chaotic Krill Herd algorithm. Inf Sci (NY) 274:17–34

    MathSciNet  Article  Google Scholar 

  25. Kuo HC, Lin CH (2013) Cultural evolution algorithm for global optimizations and its applications. J Appl Res Technol 11(4):510–522

    Article  Google Scholar 

  26. Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 27(4):1053–1073

    MathSciNet  Article  Google Scholar 

  27. Snyder WL, Powell HD, Rayburn JC (1987) Dynamic programming approach to unit commitment. IEEE Trans Power Syst 2:339–347

    Article  Google Scholar 

  28. Wang GG, Deb S, Coelho LDS (2015) Earthworm optimization algorithm: a bio-inspired metaheuristic algorithm for global optimization problems. Int J Bio-Inspired Comput 1(1):1

    Article  Google Scholar 

  29. Wang GG, Deb S, Coelho LDS (2016) Elephant herding optimization. In: 2015 3rd international symposium on computational and business intelligence (ISCBI 2015), pp 1–5

  30. Abedinpourshotorban H, Mariyam Shamsuddin S, Beheshti Z, Jawawi DNA (2016) Electromagnetic field optimization: a physics-inspired metaheuristic optimization algorithm. Swarm Evol Comput 26:8–22

    Article  Google Scholar 

  31. Ghorbani N, Babaei E (2014) Exchange market algorithm. Appl Soft Comput J 19(April):177–187

    Article  Google Scholar 

  32. Ghaemi M, Feizi-Derakhshi MR (2014) Forest optimization algorithm. Expert Syst Appl 41(15):6676–6687

    Article  Google Scholar 

  33. Tan Y, Tan Y, Zhu Y (2015) Fireworks algorithm for optimization fireworks algorithm for optimization, pp 355–364

  34. Yang XS (2012) Flower pollination algorithm for global optimization. In: Unconventional computation and natural computation. Springer, pp 240–249

  35. Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179:2232

    MATH  Article  Google Scholar 

  36. Kazarlis SA (1996) A genetic algorithm solution to the unit commitment problem. IEEE Trans Power Systems 11:83–92

    Article  Google Scholar 

  37. Yang XS (2010) Firefly algorithm. In: Engineering optimization, p 221

  38. Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47

    Article  Google Scholar 

  39. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey Wolf optimizer. Adv Eng Softw 69:46–61

    Article  Google Scholar 

  40. Dai C, Chen W, Ran L, Zhang Y, Du Y (2011) Human group optimizer with local search, pp 310–320

  41. Dieu VN, Ongsakul W (2008) Ramp rate constrained unit commitment by improved priority list and augmented Lagrange Hopfield network. Electr Power Syst Res 78(3):291–301

    Article  Google Scholar 

  42. Gandomi AH (2014) Interior search algorithm (ISA): a novel approach for global optimization. ISA Trans 53(4):1168–1183

    Article  Google Scholar 

  43. Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. In: Proceedings of the IEEE congress on evolutionary computation, CEC 2007, pp 4661–4667

  44. Gandomi AH, Alavi AH (2012) Krill herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul 17(12):4831–4845

    MathSciNet  MATH  Article  Google Scholar 

  45. Karimkashi S, Kishk AA (2010) Invasive weed optimization and its features in electromagnetics. IEEE Trans Antennas Propag 58(4):1269–1278

    Article  Google Scholar 

  46. Shareef H, Ibrahim AA, Mutlag AH (2015) Lightning search algorithm. Appl Soft Comput J 36:315–333

    Article  Google Scholar 

  47. Kashan AH (2014) League Championship Algorithm (LCA): an algorithm for global optimization inspired by sport championships. Appl Soft Comput J 16:171–200

    Article  Google Scholar 

  48. Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 27(2):495–513

    Article  Google Scholar 

  49. Reza Norouzi M, Ahmadi A, Esmaeel Nezhad A, Ghaedi A (2014) Mixed integer programming of multi-objective security-constrained hydro/thermal unit commitment. Renew Sustain Energy Rev 29:911–923

    Article  Google Scholar 

  50. Sadollah A, Bahreininejad A, Eskandar H, Hamdi M (2012) Mine blast algorithm: a new population based algorithm for solving constrained engineering optimization problems. Appl Soft Comput J 13:2592–2612

    Article  Google Scholar 

  51. Mirjalili S (2015) Knowledge-Based Systems Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl-Based Syst 89:228–249

    Article  Google Scholar 

  52. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680

    MathSciNet  MATH  Article  Google Scholar 

  53. Wang GG, Deb S, Cui Z (2015) Monarch butterfly optimization. Neural Comput Appl 31:1995–2014

    Article  Google Scholar 

  54. Kennedy J, Eberhart RC (1995) Particle Swarm Optimization. In: Proceedings of the IEEE international conference on neural networks, pp 1942–1948

  55. Gupta S, Deep K (2018) A novel random walk grey wolf optimizer. Swarm Evol Comput 44:101–112

    Article  Google Scholar 

  56. Husseinzadeh Kashan A (2014) A new metaheuristic for optimization: optics inspired optimization (OIO). Comput Oper Res 55:99–125

    MathSciNet  MATH  Article  Google Scholar 

  57. Merrikh-Bayat F (2015) The runner-root algorithm: a metaheuristic for solving unimodal and multimodal optimization problems inspired by runners and roots of plants in nature. Appl Soft Comput J 33:292–303

    Article  Google Scholar 

  58. Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133

    Article  Google Scholar 

  59. Anita JM, Raglend IJ (2012) Shuffled Frog Leaping Algorithm. In: International conference on computing, electronics and electrical technologies, pp 109–115

  60. Salimi H (2015) Stochastic fractal search: a powerful metaheuristic algorithm. Knowl-Based Syst 75:1–18

    Article  Google Scholar 

  61. Dai C, Zhu Y, Chen W (2007) Seeker optimization algorithm, pp 167–176

  62. Satapathy SC, Naik A, Parvathi K (2013) A teaching learning based optimization based on orthogonal design for solving global optimization problems, pp 1–12

  63. Cheng MY, Prayogo D (2014) Symbiotic organisms search: a new metaheuristic optimization algorithm. Comput Struct 139:98–112

    Article  Google Scholar 

  64. Gonçalves MS, Lopez RH, Fleck L, Miguel F (2015) Search group algorithm: a new metaheuristic method for the optimization of truss structures. Comput Struct 153:165–184

    Article  Google Scholar 

  65. Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191

    Article  Google Scholar 

  66. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67

    Article  Google Scholar 

  67. Baykasoğlu A, Akpinar Ş (2017) Weighted Superposition Attraction (WSA): a swarm intelligence algorithm for optimization problems—part 1: unconstrained optimization. Appl Soft Comput J 56:520–540

    Article  Google Scholar 

  68. Li MD, Zhao H, Weng XW, Han T (2016) A novel nature-inspired algorithm for optimization: virus colony search. Adv Eng Softw 92:65–88

    Article  Google Scholar 

  69. Zheng YJ (2015) Water wave optimization: a new nature-inspired metaheuristic. Comput Oper Res 55:1–11

    MathSciNet  MATH  Article  Google Scholar 

  70. Glover F (1989) Tabu search—part I. ORSA J Comput 1:190

    MATH  Article  Google Scholar 

  71. Eskandar H, Sadollah A, Bahreininejad A, Hamdi M (2012) Water cycle algorithm—a novel metaheuristic optimization method for solving constrained engineering optimization problems. Comput Struct 110–111:151–166

    Article  Google Scholar 

  72. Bayraktar Z, Komurcu M, Werner DH (2010) Wind driven optimization (WDO): a novel nature-inspired optimization algorithm and its application to electromagnetics, no 1, pp 0–3

  73. Gupta S, Deep K (2018) PT US CR. Expert Syst Appl

  74. Gupta S, Deep K (2018) Improved sine cosine algorithm with crossover scheme for global optimization.” Knowl-Based Syst

  75. Gupta S, Deep K (2019) Enhanced leadership—inspired grey wolf optimizer for global optimization problems. Eng Comput, no 0123456789

  76. Gupta S, Deep K (2019) Hybrid grey wolf optimizer with mutation operator. Springer, Singapore

    Book  Google Scholar 

  77. Gupta S, Deep K (2020) A memory-based grey wolf optimizer for global optimization tasks. Appl Soft Comput J 93:106367

    Article  Google Scholar 

  78. Xu Z, Hu Z, Heidari AA, Wang M, Zhao X, Chen H, Cai X (2020) Orthogonally-designed adapted grasshopper optimization: a comprehensive analysis. Expert Syst Appl 150:113282

    Article  Google Scholar 

  79. Sattar D, Salim R (2020) A smart metaheuristic algorithm for solving engineering problems. Eng Comput, no 0123456789

  80. Banerjee N (2019) HC-PSOGWO: hybrid crossover oriented PSO and GWO based co-evolution for global optimization, vol 7, pp 3–8

  81. Shahrouzi M, Salehi A (2020) Imperialist competitive learner-based optimization: a hybrid method to solve engineering problems. Iran Univ Sci Technol 10(1):155–180

    Google Scholar 

  82. Herwan M, Mustaffa Z, Mawardi M, Daniyal H (2020) Engineering applications of artificial intelligence barnacles mating optimizer: a new bio-inspired algorithm for solving engineering optimization problems. Eng Appl Artif Intell 87:103330

    Article  Google Scholar 

  83. Faramarzi A, Heidarinejad M, Stephens B, Mirjalili S (2019) Equilibrium optimizer: a novel optimization algorithm. Knowl-Based Syst 191:105190

    Article  Google Scholar 

  84. Muhammed DA, Saeed SAM, Rashid TA, Member I (2020) Improved algorithm fitness—dependent optimizer, vol XX

  85. Panda N (2019) Improved spotted hyena optimizer with space transformational search for training pi-sigma higher order neural network, pp 1–31

  86. Fan Q, Chen Z, Li Z, Xia Z, Yu J, Wang D (2020) A new improved whale optimization algorithm with joint search mechanisms for high-dimensional global optimization problems. Eng Comput, 0123456789

  87. Chen H, Wang M, Zhao X (2020) A multi-strategy enhanced sine cosine algorithm for global optimization and constrained practical engineering problems. Appl Math Comput 369:124872

    MathSciNet  MATH  Article  Google Scholar 

  88. Yimit A, Iigura K, Hagihara Y (2020) Refined selfish herd optimizer for global optimization problems. Expert Syst Appl 139:112838

    Article  Google Scholar 

  89. Kamboj VK, Nandi A, Bhadoria A, Sehgal S (2019) An intensify Harris Hawks optimizer for numerical and engineering optimization problems. Appl Soft Comput J 89:106018

    Article  Google Scholar 

  90. Zhao W, Wang L (2019) Artificial ecosystem-based optimization: a novel nature-inspired meta-heuristic algorithm, vol 0123456789. Springer, London

    Google Scholar 

  91. 2019_I-GWO and Ex-GWO.pdf

  92. Khatri A, Gaba A, Vineet KPSR (2019) A novel life choice-based optimizer. Soft Comput, 0123456789

  93. 2019_Multi-objective heat transfer search algorithm.pdf

  94. Wang R, Wang J (2019) Simplified salp swarm algorithm. In: 2019 IEEE international conference on artificial intelligence and computer applications, pp 226–230

  95. Chen X, Tianfield H, Li K (2019) Self-adaptive differential artificial bee colony algorithm for global optimization problems. Swarm Evol Comput 45:70–91

    Article  Google Scholar 

  96. Deka D, Datta D (2019) Optimization of unit commitment problem with ramp-rate constraint and wrap-around scheduling. Electr Power Syst Res 177:105948

    Article  Google Scholar 

  97. Singh HP, Brar YS, Kothari DP (2019) Solution of optimal power flow based on combined active and reactive cost using particle swarm. Int J Electr Eng Technol 10(2):98–107

    Google Scholar 

  98. Bhadoria A, Marwaha S, Kumar V (2019) An optimum forceful generation scheduling and unit commitment of thermal power system using sine cosine algorithm. Neural Comput Appl 8

  99. Srikanth K, Panwar LK, Panigrahi BK, Herrera-Viedma E, Sangaiah AK, Wang GG (2018) Unit commitment problem solution in power system using a new meta-heuristic framework: quantum inspired binary grey wolf optimizer

  100. Premrudeepreechacharn S, Siritaratiwat A (2019) Unit commitment problem, pp 1–23

  101. Bhadoria A, Kamboj VK (2018) Optimal generation scheduling and dispatch of thermal generating units considering impact of wind penetration using hGWO-RES algorithm. Appl Intell

  102. Ramu M, Srinivas LR, Kalyani ST (2017) Gravitational search algorithm for solving unit, vol 5, no Xi, pp 1497–1502

  103. Selvakumar K, Vijayakumar K, Sattianadan D, Boopathi CS (2016) Shuffled frog leaping algorithm (SFLA) for short term optimal scheduling of thermal units with emission limitation and prohibited operational zone (POZ) constraints, vol 9

  104. Shukla A, Singh SN (2016) Multi-objective unit commitment using search space-based crazy particle swarm optimisation and normal boundary intersection technique, vol 10, pp 1222–1231

  105. Saravanan B, Kumar C, Kothari DP (2016) Electrical power and energy systems a solution to unit commitment problem using fire works algorithm. Int J Electr Power Energy Syst 77:221–227

    Article  Google Scholar 

  106. Kumar V, Bath KSK (2015) Hybrid HS—random search algorithm considering ensemble and pitch violation for unit commitment problem. Neural Comput Appl 28(5):1123–1148

    Google Scholar 

  107. Shukla A, Singh SN (2016) Advanced three-stage pseudo-inspired weight-improved crazy particle swarm optimization for unit commitment problem. Energy 96:23–36

    Article  Google Scholar 

  108. Khorramdel H, Membe S, Aghaei J, Member S, Khorramdel B (2015) Optimal battery sizing in microgrids using probabilistic unit commitment. IEEE Trans Ind Inform 3203(c):1–11

    Google Scholar 

  109. Xing H, Cheng H, Zhang L (2015) Demand response based and wind farm integrated economic dispatch. CSEE J Power Energy Syst 1(4):37–41

    Article  Google Scholar 

  110. Kamboj VK, Bath SK, Dhillon JS (2017) A novel hybrid DE–random search approach for unit commitment problem. Neural Comput. Appl 28(7):1559–1581

    Article  Google Scholar 

  111. Kamboj VK (2015) A novel hybrid PSO–GWO approach for unit commitment problem. Neural Comput. Appl. 27(6):1643–1655

    Article  Google Scholar 

  112. Casolino GM, Liuzzi G, Losi A (2015) Electrical power and energy systems combined cycle unit commitment in a changing electricity market scenario. Int J Electr Power Energy Syst 73:114–123

    Article  Google Scholar 

  113. Quan H, Srinivasan D, Khambadkone AM, Khosravi A (2015) A computational framework for uncertainty integration in stochastic unit commitment with intermittent renewable energy sources. Appl Energy 152:71–82

    Article  Google Scholar 

  114. Zhang N, Hu Z, Han X, Zhang J, Zhou Y (2015) Electrical power and energy systems a fuzzy chance-constrained program for unit commitment problem considering demand response, electric vehicle and wind power. Int J Electr Power Energy Syst 65:201–209

    Article  Google Scholar 

  115. Singhal PK, Naresh R, Sharma V (2015) A modified binary artificial bee colony algorithm for ramp rate constrained unit commitment problem. Int Trans Electr Energy Syst 25(12):3472–3491

    Article  Google Scholar 

  116. Anita JM, Raglend IJ (2014) Multi objective combined emission constrained unit commitment problem using improved shuffled frog leaping algorithm Vindhya Group of Institutions mathematical modeling of emission constrained UC and, vol 13, pp 560–574

  117. Ji B, Yuan X, Li X, Huang Y, Li W (2014) Application of quantum-inspired binary gravitational search algorithm for thermal unit commitment with wind power integration. Energy Convers Manag 87:589–598

    Article  Google Scholar 

  118. Marko Č, Volkanovski A (2015) Engineering applications of artificial intelligence multi-objective unit commitment with introduction of a methodology for probabilistic assessment of generating capacities availability. Eng Appl Artif Intell 37:236–249

    Article  Google Scholar 

  119. Gharegozi A, Jahani R (2013) A new approach for solving the unit commitment problem by cuckoo search algorithm. Indian J Sci Technol 6(9):5235–5241

    Article  Google Scholar 

  120. Marko C (2013) Electrical power and energy systems a new model for optimal generation scheduling of power system considering generation units availability. Int J Electr Power Energy Syst 47:129–139

    Article  Google Scholar 

  121. Todosijevi R, Crévits I (2012) VNS based heuristic for solving the unit commitment problem. Electron Notes Discrete Math 39:153–160

    MATH  Article  Google Scholar 

  122. Anita JM, Raglend IJ, Kothari DP (2012) Solution of unit commitment problem using shuffled frog leaping algorithm, vol 1, no 4, pp 9–26

  123. Saurabh S, Ahmed M (2018) Optimization method for unit commitment in high-level wind generation and solar power. Springer, Singapore

    Book  Google Scholar 

  124. Safari A, Shahsavari H (2018) Frequency-constrained unit commitment problem with considering dynamic ramp rate limits in the presence of wind power generation. Neural Comput Appl 0123456789

  125. Varghese MP, Amudha A (2018) Artificial bee colony and cuckoo search algorithm for cost estimation with wind power energy, pp 1–8

  126. Govardhan M, Roy R, Govardhan M, Roy R (2016) Electric power components and systems comparative analysis of economic viability with distributed energy resources on unit commitment comparative analysis of economic viability with distributed energy resources on unit commitment, vol 5008

  127. Navin NK (2016) A modified differential evolution approach to PHEV integrated thermal unit commitment problem

  128. Wang W, Li C, Liao X, Qin H (2017) Study on unit commitment problem considering pumped storage and renewable energy via a novel binary artificial sheep algorithm. Appl Energy 187:612–626

    Article  Google Scholar 

  129. Banumalar K, Manikandan BV, Chandrasekaran K (2016) Security constrained unit commitment problem employing artificial computational intelligence for wind-thermal power system

  130. Govardhan M, Roy R (2015) Electrical power and energy systems economic analysis of unit commitment with distributed energy resources. Int J Electr Power Energy Syst 71:1–14

    Article  Google Scholar 

  131. Osório GJ, Lujano-rojas JM, Matias JCO, Catalão JPS (2015) Electrical power and energy systems a new scenario generation-based method to solve the unit commitment problem with high penetration of renewable energies. Int J Electr Power Energy Syst 64:1063–1072

    Article  Google Scholar 

  132. Ming Z, Kun Z, Liang W (2014) Electrical power and energy systems study on unit commitment problem considering wind power and pumped hydro energy storage. Int J Electr Power Energy Syst 63:91–96

    Article  Google Scholar 

  133. Scholar PG (2013) LR-PSO method of generation scheduling problem for thermal-wind-solar energy system in deregulated power system

  134. Maghsudlu S, Mohammadi S (2018) Optimal scheduled unit commitment considering suitable power of electric vehicle and optimal scheduled unit commitment considering suitable power of electric vehicle and photovoltaic uncertainty. J Renew Sustain Energy 10(4):043705

    Article  Google Scholar 

  135. Shahbazitabar M, Abdi H (2018) A novel priority-based stochastic unit commitment considering renewable energy sources and parking lot cooperation. Energy 161:308–324

    Article  Google Scholar 

  136. Rahiman F, Mohd P, Othman F, Ottukuloth S (2018) Power station scheduling with energy storage. J Inst Eng Ser B 100(1):77–83

    Google Scholar 

  137. Ma K, Hu S, Yang J, Xu X, Guan X (2017) Appliances scheduling via cooperative multi-swarm PSO under day-ahead prices and photovoltaic generation. Appl Soft Comput J 62:504–513

    Article  Google Scholar 

  138. Quan H, Srinivasan D, Khosravi A (2016) Integration of renewable generation uncertainties into stochastic unit commitment considering reserve and risk: a comparative study. Energy 103:735–745

    Article  Google Scholar 

  139. Abujarad SY, Mustafa MW, Jamian JJ (2017) Recent approaches of unit commitment in the presence of intermittent renewable energy resources: a review. Renew Sustain Energy Rev 70:215–223

    Article  Google Scholar 

  140. Selvakumar K, Vignesh B, Boopathi CS, Kannan T (2016) Thermal unit commitment strategy integrated with solar energy system. Int J Appl Eng Res 11(9):6856–6860

    Google Scholar 

  141. Jasmin EA, Ahamed TI, Remani T (2016) A function approximation approach to reinforcement learning for solving unit commitment problem with photo voltaic sources

  142. Chandrasekaran K, Simon SP (2012) Binary/real coded particle swarm optimization for unit commitment problem, no 3

  143. Senjyu T, Chakraborty S, Saber AY, Toyama H, Yona A (2008) Thermal unit commitment strategy with solar and wind energy systems using genetic algorithm operated particle swarm optimization, no PECon 08, pp 866–871

  144. Chandrasekaran K, Simon SP, Prasad N (2014) Electrical power and energy systems SCUC problem for solar/thermal power system addressing smart grid issues using FF algorithm. Int J Electr Power Energy Syst 62:450–460

    Article  Google Scholar 

  145. Anita JM, Raglend IJ (2013) Solution of emission constrained unit commitment problem using shuffled frog leaping algorithm. In: 2013 international conference on circuits, power and computing technologies (ICCPCT), pp 93–98

  146. Kamboj VK, Bath SK, Dhillon JS (2016) Implementation of hybrid harmony/random search algorithm considering ensemble and pitch violation for unit commitment problem. Int J Electr Power Energy Syst 77:228–249

    Article  Google Scholar 

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Acknowledgements

The corresponding author wishes to thank Dr. O.P. Malik, Professor Emeritus, Department of Electrical and Computer Engineering, Schulich School of Engineering, University of Calgary, Calgary, Alberta, CANADA for continuous support, guidance, encouragement and for providing advance research facilities for post-doctorate research at the University of Calgary, Alberta, CANADA.

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AN analyzed and interpreted the data regarding the optimal scheduling of each power generating unit during 24 h and overall cost for power generation of each unit with renewable energy sources in summer, winter, autumn and spring and also drafted the work or substantively revised it and was a major contributor in writing the manuscript. VK have made substantial contribution to the conception and design of the research work and the creation of MATLAB coding (Software) used in 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.

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Correspondence to Vikram Kumar Kamboj.

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Supplementary Information

Additional file 1.

Test data for standard Unit Commitment Problems.

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Nandi, A., Kamboj, V.K. A meliorated Harris Hawks optimizer for combinatorial unit commitment problem with photovoltaic applications. Journal of Electrical Systems and Inf Technol 8, 5 (2021). https://doi.org/10.1186/s43067-020-00026-3

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Keywords

  • Meta-heuristics
  • Harris Hawks optimizer
  • Unit commitment problem (UCP)
  • Profit-based UCP
  • Economic load dispatch (ELD)