Multi-objective unit commitment with spinning reserve cost using hybrid method

ABSTRACT


INTRODUCTION
In power systems, thermal power plants are a pivotal source in the entire world.In the modern span, the unmatched power demand is enhancing day to day of life.In meeting the desired load demand, thermal units are addressed with a major portion of the power demand in the power network.Based on the realization of environmental protection and draining of fossil fuels requirements are targeted to enhance performance and clean environment.In enhancing the requirements of operational strategies, the economy concerned with fuel consumption and the clean air act related to the environment are added to the account at the instant of time.To address the objectives mathematical concepts are applied that focus on the optimization problem.The computational procedure of predicting the best solution of the objective, among all feasible solutions is termed optimization.Optimization problems are categorized into two types mono-objective [1] and multi-objective optimization problems [2], [3].Over several decades research is carried out on unit commitment extensively based on optimization.Unit commitment (UC) is used to predict optimal value by the line-up of thermal units to increase the performance with the minimization of objectives to avoid the wastage of fuel [4].The major task in handling complex systems requires computational efforts in achieving the solution to a problem of optimization.The results of the UC problem gives information, on which unit should work and which unit turned off, and how much power to generate from each thermal unit concerned to power over a period of short interval [5].A committed unit is termed as the unit which is decided to be connected to the network for contributing to load demand.Scheduling the on/off status of power units with a reduction in fuel cost for twenty-four hours while maintaining all the systems constraints [6] is termed as UC.The size of the problem increases by enhancing the objectives and constraints.There are two types of constraints namely inequality constraints and equality constraints [7].The more the number of constraints as consequence the more complexity of the problem increases and becomes tedious in evaluating the optimal solution of a UC optimization problem.The criteria of UC are to reduce the total production cost for one week or one day with many constraints like spinning reserve, power balance, minimum downtime, minimum uptime and ramp rate limits [8].In a mono objective problem, the total cost is the amalgamation of fuel cost, startup cost, and shutdown cost.More than one objective of UC is termed a multi-objective unit commitment (MOUC) optimization problem [9].Many strategies were applied for achieving the optimal values of UC over several decades.Still, there are further many more paths for predicting the best optimal values.
In this paper, a new hybrid technique is introduced which is the amalgamation of the cuckoo search method with the flower pollination algorithm.The contribution of this paper, in general, the spinning reserve is considered a constraint by many of the researchers.In this paper along with constraints, the cost of spinning reserve is also considered and amalgamated with the total cost and applied to two test systems.The remaining paper is as follows, the section 2 presents the formulation of two objectives minimization, the section 3 deals with the proposed hybrid technique is a union of two algorithms, and the section 4 discusses the simulation results which are applied to the mono and multi-objective problem and the finally, section 5 presents the conclusion.

PROBLEM FORMULATION
The mathematical expression for minimization of total cost is given as: () is the active power of u th power unit at '' hour,  is the start-up cost, M indicates the total no of units, T for 24 hours,   prescribes the status of the u th thermal unit.SRC is spinning reserve cost,   is the unit cost of spinning reserve at an hour 'v'.  represent the cost function which is represented in (3). .
Where   ,   ,   is the cost coefficient of thermal unit 'u'.
EF represents the emission function which is represented in quadratic form as follows:   ,   ,   represent emission coefficients.The startup cost is expressed in terms of hot startup cost or cold startup cost is presented in (6).
= (, ) + () (), ()are termed as cold and hot start-up cost of u th thermal unit.TC(u) represents the online status of unit u. (, ) represents the minimum downtime of thermal unit  at hour .The constraits are as follows.

Balanced power constraints:
This constraint in which the sum of generated power must meet the demand at hour.The mathematical expression is presented as (7).
() represents the demand at hour .

Spinning reserve (SR)
Spinning reserve is considered and maintained at each time interval of one hour and is mathematically expressed as (8).

Real power range
The real power generation from the thermal units lie in the range of minimum and maximum power which indicate the inequality constraints.
, ,  , are the low and high-power generation limits of thermal unit 'u'.

Minimum uptime and downtime
Based on the de-commitment and commitment of the thermal unit there will be associated minimum times with each unit for commitment and de-commitment.

METHODOLOGY
The combination of cuckoo search and flower pollination technique is implemented for solving optimization problem of UC.

Cuckoo search algorithm (CSA)
CSA is a meta-heuristic algorithm and it is a nature-inspired one, found on the cuckoo species behavior.This species lay its egg in the nest of host bird's.There is a probability of 0.1 percent of identifying the other species egg by the host bird.There are two chances to be done by the host bird after predicting the cuckoo's egg.The host bird may throw off the cuckoo's egg or it may abandoned the nest by replacing the new one.In CSA the egg is the solution and the host nest is the concern to the population whose size is fixed.The CS is endured with three major basic rules [30].i) Individual cuckoo bird lay only egg and places it in the host bird's nest stochastically.ii) Host bird nest with superior quality eggs is taken for the next production.
iii) The chances of detecting egg of the cuckoo by host bird is considered as Pb Є (0, 1).CS commences with an initial population that represents cuckoos.These cuckoo's lay eggs in the host bird's nests.The egg is analogous to host bird's egg there will be more probability to grow as the young chick otherwise the egg is thrown.The area where more cuckoo's eggs survive the area is more profitable.After the cuckoo chicks hatch from the eggs and grow as adults, groups and communities are formed.Each group has its own identity of habitat.Among all the groups the best habitat will be considered as the next location and migrate towards it.
The current location of habitat is prescribed as {y1^g,y2^g,y3^g,y4^g,…yn^g} where n represents the no of host bird nests and 'g' is the no of generations.By using the Levy flight, the random walk of the cuckoo's bird for the new solution is given by: ⊕ is the entry-wise multiplication, (⋋) is the stochastic number taken from  distribution. is the step size and is evaluated using (13).
The scaling factor is represented as   and present the best solution prescribed as    .The (⋋) value is predicted by a procedure [31].
presents the value of (⋋) after simulation.The x and zare the numbers selected randomly from the normal distribution with a mean zero. is the parameter of Levy distribution.
The random walk based on the local is given by (16).
,    are selected randomly from the given population and  ˈ ,  are the arbitrarily number between (0,1).
The best value is sort-out for each iteration process.CSA is mainly focused on the minimization of an optimization problem.

Flower pollination algorithm
Flowers have played a pivotal role in the development of flowering plants over the past years that is impossible to imagine without them.Through pollination, there will be subsequent reproduction with the purpose of the flower.Pollen is usually transferred when flowers are pollinated and this transfer is frequently attributed to pollinators like birds, insects, bats, and other animals.Two categories of pollination exist namely biotic and abiotic [32].Figure 1 shows the hybrid technique flowchart.
The majority of flowering plants are related to pollination of biotic which is approximately about 90%.Cross-pollination occurs from the pollen of a flower with a various plant.Abiotic pollination which doesn't requires any pollinators it's about approximately 10%.Self-pollination is when pollen of the same or different flowers of the similar plant is considered for fertilization.Pollen carriers are also termed pollinators, which are wide in variety.Almost 2 lakhs of different pollinators exist in nature.The following rules are applied for pollinator behaviour and flower consistency.

SIMULATION RESULTS DISCUSSION
The mono objective and multi-objective problem related to UC is solved using a hybrid method which is the amalgamation of two meta-heuristic methods.The cuckoo search method and flower pollination method are amalgamated to form a hybrid method.Two test systems are considered to predict the potential of the proposed technique i.e. four unit system and IEEE 39 bus system.
-Case (i) In this case, a four-unit system is implemented.The initial parameters of are cuckoo search algorithm is initialized.The population was considered as 40, the number of iterations is 20, the cost coefficients, minimum and maximum power limits, start-up cost, minimum uptime and downtime, and a number of decision variables are initialized [33].
The on/off status of the thermal units is shown in Table 1.The scheduling of thermal units and their startup cost, fuel cost, and total cost value is shown in Table 2.The comparison of total cost value without spinning reserve cost is shown in Table 3 and with spinning, the reserve is shown in Table 4.
Table 1.Four thermal units for eight-hour status In this case, the multiobjective problem is considered in which cost and emission are considered as two clash objectives.The test case IEEE 39 bus with 10 units is considered to find the effectiveness of the proposed technique.The optimization problem is subjected to constraints.
The respective data of the IEEE thirty-nine bus with 10 units is considered [34]- [38].The initial parameters are assigned the same as in a single objective problem.The spinning reserve was considered as 10 percent.The commitment status of the ten thermal units is illustrated in Table 5 and the corresponding sharing of load demand for twenty-four hours among ten units is shown in Table 6. Figure 2 shows the load curve for twenty-four hours.Table 3.Comparison of total cost value with the proposed method

Method
Total Cost($) Method Total Cost($) ILR [35] 75,231 BDE [37] 74,676 B. SMP [36] 74,812 Proposed Method 73,452 LRPSO [35] 74,808 Table 5. Scheduling of ten-unit system of IEEE 39 bus system  The respective startup cost, total cost, fuel cost and emission are illustrated in Table 7.The total cost is the addition of operating cost and startup cost.From Table 7 it can be illustrated that the total cost was 5,64,018 ($) and the emission value is 20,267.69(lb).With the observation of Table 8 the optimal values are better that other existing methods.
The total cost with the incorporation of the spinning reserve cost can be illustrated in

CONCLUSION
The single and multi-objective optimization problem related to UC is solved using the hybrid method.The amalgamation of cuckoo's search and flower pollination techniques is applied as a hybrid method.Two conflicting objectives cost and emission is considered.In addition to the cost, the spinning reserve cost is also amalgamated.The two systems are implemented to predict the potential of the proposed technique.The outcome of the two systems shows better optimal values in comparison with the other existing methods.Total cost and emission get modified with the effect of spinning reserve cost.

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Global pollination process in which cross-pollination takes place where pollinators with pollen perform levy fights.-Localpollination process where self-pollination takes place.-Whentwo flowers are involved, flower constancy can be thought of as the reproduction chance being proportional to the resemblance of two flowers.-Switching probability controls the global and local pollination.
unit commitment with spinning reserve cost using hybrid method (Rajasekhar Vatambeti) 2541 L is the Levy distribution which represents the pollination strength.Γ() is the function of gamma which is applicable for large step sizes q>0.There is the existence of global and local pollination.Both global scale and local scale is taken place in the flower pollination and are controlled by switching probability.

Table 4 .
Scheduling of thermal units with spinning reserve cost of four unit system

Table 6 .
Dispatching of load demand among thermal units of IEEE 39 bus system

Table 9 (
see in Appendix).The total spinning reserve cost for different load demands of twenty-four hours is 24,033 ($).The 2543 total cost is the sum of the startup cost, spinning reserve cost, and operating cost.With the incorporation of SRC the total cost is enhanced but there is a miniature reduction in the value of emission.
Multi-objective unit commitment with spinning reserve cost using hybrid method(Rajasekhar Vatambeti)

Table 7 .
Total cost and emission of IEEE 39 bus system without SRC

Table 8 .
Comparison of emission and total cost values with the hybrid technique