Short Term Economic Emission Power Scheduling of Hydrothermal Energy Systems Using Improved Water Cycle Algorithm

Due to the increasing environmental concerns, the demand of clean and green energy and concern of atmospheric pollution is increasing. Hence, the power utilities are forced to limit their emissions within the prescribed limits. Therefore, the minimization of fuel cost as well as exhaust gas emissions is becoming an important and challenging task in the short-term scheduling of hydro-thermal energy systems. This paper proposes a novel algorithm known as WCA-ER (Water Cycle Algorithm with Evaporation Rate) to inspect the short term EEPSHES (Economic Emission Power Scheduling of Hydrothermal Energy Systems). WCA has its ancestries from the natural hydrologic cycle i.e. the raining process forms streams and these streams start flowing towards the rivers which finally flow towards the sea. The worth of WCA-ER has been tested on the standard economic emission power scheduling of hydrothermal energy test system consisting of four hydropower and three thermal plants. The problem has been investigated for the three case studies (i) ECS (Economic Cost Scheduling), (ii) ES (Economic Emission Scheduling) and (iii) ECES (Economic Cost & Emission Scheduling). The results obtained show that WCA-ER is superior to many other methods in the literature in bringing lower fuel cost and emissions.

other, hence a cost penalty method has been proposed to find a trade-off between these two contradictory objectives.
In the developed countries, due to the vitality of the environmental concerns, EEPSHES problem is being extensively investigated and it is under active research due to stronger needs of economical operating schedules.
Several methods have been proposed and discussed in [4] to reduce the exhaust gas emission levels of thermal plants. These exhaust gas emissions may be taken as an objective function in economic dispatch problem. Besides them various other techniques such as Fuzzy Satisfaction Decision Approach [5], Improved Back-Propagation Neural Network [6], Maximizing Decision Recursive Technique [7], Multi-objective Approach using Evolutionary Algorithm [8], Improved GA (Genetic Algorithm) [9,10], PSO (Particle Swarm Optimization) [11,12], DE (Differential Evolution) [13,14] and Gravitational Search Algorithm [15,16] have been previously applied to reduce the emissions.
In this paper an improved form of WCA, known as WCA-ER presented by Sadollah, et. al. [17] has been used to solve the non-linear and non-convex EEPSHES problem. This algorithm has its ancestries from the water cycle process of the nature that how the rain process forms streams and these streams flow towards rivers and then these rivers finally drops into sea. The performance of WCA-ER was compared with GA, PSO and DE for several bench mark constrained optimization problems and WCA-ER was found out to be superior than these [17]. The WCA-ER has not yet been investigated to solve the problem of power system operation. In the proposed work, short-term hydrothermal scheduling problem has been investigated using WCA-ER while taking into account the non-convexity of thermal plants' fuel cost characteristics that arise due to valve point effect. The effectiveness of WCA-ER has been tested on a standard test system of EEPSHES problem for different cases.
The contribution of the proposed work is, the highly nonconvex and complex problem of EEPSHES has completely been modelled for the environment of WCA-ER and a complete algorithm has been developed whose parameters have effectively been tuned so as to achieve the optimum results for all the three cases of ECS, EES and ECES. The comparison of the results with other strong techniques shows that WCA-ER has been successful in finding lower fuel costs and lesser exhaust gas emissions in all the three cases.

Economic Cost Scheduling
The objective of pure ECS (Economic Fuel Cost Scheduling) problem is the minimization of total fuel cost of thermal plants. Mathematically it is represented as [3]: where, F is the total fuel cost, f x is the fuel cost of thermal plant, PG sxt is the power generation of xth thermal generating unit at time t,M are the total number of time intervals for the scheduled period and N s are the total number of thermal plants.
The objective function of both convex and non-convex nature will be handled in this research work:

Convex Objective Function
Conventionally, the fuel cost function of thermal plants can be represented as a quadratic function as follows: where, a x , b x , c x are the fuel cost coefficients of xth thermal plant.

Non-Convex Objective Function
For the precise and real-world modeling of problem, the above mentioned fuel cost function needs to be reviewed.
The real-world characteristics involve valve point effect and the objective function is re-written as: where, d x , g x are the fuel cost coefficients of xth thermal plant showing valve point effect.

Economic Emission Scheduling
The EES problem is to minimize the amount of exhaust gas emissions from thermal plants due to burning of fossil fuels used for generation of electricity. The emission released by thermal plant can be formulated as summation of an exponential function with a quadratic one [8]. The EES problem is written mathematically as: (4) where, E is the total fuel emissions, and e xt are the total amount of exhaust gases released by xth thermal plant.
where, α x , β x , γ x , η x , ρ x are the emission coefficients of xth thermal plant.

Economic Cost and Emission Scheduling
The mutual ECES problem seeks a trade-off relation between exhaust gas emissions and fuel cost. Emission scheduling is incorporated in pure economic dispatch problem by adding emission cost in conventional cost scheduling. This becomes a multi-objective ECES problem, converted into a single one by introducing a cost penalty approach as follows [6]: The trade-off relation between fuel cost and exhaust gas emission is developed as: where, CPF t cost penalty factor at time interval t and K 1 , K 2 are the weight factors.
Re-arrange the computed values of h sx in an ascending order.
(iv) Starting from the smallest h sx add max loading limit of each generating unit one at a time until ΣPG sx max > PD t is achieved.
(v) At this phase, h sx related with last unit is the cost penalty factor CPF t for a given power demand at time t.
From above procedure it is obvious that the value of cost penalty factor CPF t depends on the power demand during each interval t and it varies according to power demand.

Constraints
The above described objective functions are to be minimized subject to various hydraulic and thermal constraints [3], which can be written mathematically as:

Power Balance Constraint
The total hydropower and thermal generations at each time interval t should meet the forecasted load demand. (9) where, PG hyt is the generated power of yth hydropower unit at interval t, PD t is the power demand at interval t and N h is the total number of hydropower plants where, A 1y , A 2y , A 3y , A 4y , A 5y , A 6y are the generation coefficients of yth hydropower plant, U hyt is the reservoir storage volume of yth plant at time t and D hyt is the water release of yth plant at time t.

Generation Capacity Constraint
where, D hy min , D hy max are the minimum and maximum discharge limits of yth reservoir.  (15) where, lnf hyt is the natural inflow of yth hydropower plant respectively at time t, S hyt is the spillage discharge rate of yth hydropower plant respectively at time t, R uy is the number of upstream hydropower generating units immediately above the yth reservoir and τ ny is the water transport time delay from reservoir n to reservoir y.

Basic Concept
WCA-ER mimics the natural water cycle as formation of streams from rain and then their flow towards rivers and then flow of these rivers towards the sea. The first step is the assumption of rain so that a population of streams is generated randomly.

Initialization
A population of design variables i.e. the population of streams is initially generated randomly. The individual having the best fitness value i.e. the best stream is chosen as sea and some next as rivers. The remaining streams flow towards rivers and sea [17]. Initially N pop streams are created. Each stream created is a candidate solution. The total population of stream as mentioned in [17] is: The stream having the lowermost value is marked as the sea. N sr (a predefined parameter) is the sum of a sea and total of number of rivers as per Equation (18). The remaining number of streams N stream might start flowing towards the rivers or directly towards the sea will be calculated as per Equation (19) as follows: The sea absorbs the water from river and every river absorbs the water from the streams. Some streams will might directly flow towards the sea as well. The intensity of flow of streams determines the amount of water entering a specific river or sea depends. The number of streams entering the sea and the no. of streams entering the river are calculated using the Equation (20).
Where CV n is the fitness value or the cost function. The absolute sign is used to eliminate the negative sign and round operator is used because any value other than positive integers cannot be assigned to a river or sea. e.g.
1.5 or 1.7 streams flow to the river.

Movement of Streams to the Rivers or Sea
Fig. 1 [17] but modified& redrawn) shows a stream flowing towards a specific river. The connection lines are also shown. The distance Z between the river and the stream is updated as: The value of C is such that, 1 < C < 2, and the finest value for C may be 2; is the distance between stream and river. Keeping C > 1 bounds streams to flow in various directions towards rivers. Same concept is also used to indicate rivers flowing towards the sea [17]. The latest positions of streams, rivers and sea are given using the following equations: where, rnd is a uniformly distributed random number between 0 and 1. Equation (22) depicts streams flowing towards the corresponding river and Equation (23) depicts streams flowing directly towards the sea. If the fitness of the streams comes out to be better than its connecting rivers then the streams and river is swapped with each other. The same is done for the river and sea.

Evaporation and Raining Process
In the evaporation process sea water vaporizes as the streams or rivers flow towards the sea. This results in rainfall to form new streams. It is therefore checked if the rivers or streams have advanced up to the sea to make the evaporation process occur [17]. This avoids premature convergence of this algorithm. The following condition is used to check this evaporation condition: if the above condition in Case 1 becomes true then start the raining process as per Equation (25), where dist max is a small number (very near to zero).

Mehran University Research
The same condition of evaporation is checked for those streams which start flowing directly to the sea. The condition for evaporation for the streams directly flowing towards the sea is: If the above condition in Case 2 becomes true, then start the raining process as per Equation (26): where, σ depicts the area being searched around the sea.
After the evaporation the created streams with σ variance are disseminated around the sea. rndn(1,N) is a vector of N standard Gaussian numbers. The smaller σ helps to search in minor region near the sea. The optimized value of σ is found to be 0.1 [17].
The value of dist max is calculated from Equation (27) and is decreasing adaptively. If a higher value of dist max is selected it avoids extra searches and its smaller value intensify the search closer to the sea.
This raining process is analogous to mutation in GA.
The streams and rivers which have low flow intensity and are not able to reach the sea will definitely evaporate after some time. The evaporation process in WCA-ER is altered slightly by adding the concept of evaporation rate [17]. Therefore, the evaporation rate (ε) is defined as: The Equation (28) If the above conditions in Case 3 are satisfied, then the raining process is started again using Equation (25). If the evaporation condition is satisfied for any river, then that specific river along with its streams will be removed and new streams and a river will be created but in a different position.

Initialization
The structure of solution for the hydro-thermal scheduling problem consists of two control variables; where, rnd is the random number generated in (0,1). A candidate population of streams will be initialized as: where, X k is the kth stream or candidate solution.

Constraint Handling
Hydrothermal scheduling problem is more convoluted due to the involvement of many equality and inequality constraints. And, the fulfillment of all these constraints is very important and tedious task in this problem. In the proposed technique, pragmatic set of rules have been developed to fulfill these constraints.

Constraint Handling for Equality Constraints
The equality constraints are more convoluted to be handled problem. The water balance constraint and power balance constraint are required to be handled after the initialization and every time whenever the raining process starts. A pragmatic method to balance these constraints is devised as follows:

Water Balance Constraint Handling
To meet exactly the limits on reservoir storage as per Equation (10) the water discharge rate of the yth hydro plant D hyj in the dependent interval j is then calculated by:

Power Balance Constraint Handling
To fulfill the power balance constraint exactly as per Equation (4), the dependent thermal unit j from the thermal plants is randomly selected and dependent thermal generation PG t s,j is calculated using the following Equation (34):

Flowchart of Proposed WCA-ER for EEPSHES Problem
The detailed flowchart of the proposed WCA-ER for EEPSHES problem is shown in Fig. (2).

SIMULATION RESULTS
The EEPSHES problem has been mapped as per proposed WCA-ER algorithm in Microsoft Visual C++ 6.0

Case Study-1 (Economic Cost Scheduling)
In this case the only fuel cost objective as per Equation (7) is considered. Here the objective is to only curtail the fuel cost of thermal plants. The value of weight factors in this case will be K 1 = 1, K 2 = 0. For satisfaction of active power balance constraint, the priority list of thermal plants is same over the whole scheduling horizon in this case. Table 2 shows the optimal discharges of hydropower plants. Table 3 shows the hourly optimal hydropower and thermal power schedules obtained from proposed WCA-ER method.

Case Study-2 (Economic Emission Scheduling)
In this case the objective is to only curtail the exhaust gas emission of thermal plants. So, the value of weight factors will be K 1 = 0, K 2 = 1/CPF t . In this case the priority sequence of thermal plants is also same for whole scheduled period for the satisfaction of active power balance constraint. Table 4 shows the optimal discharges of hydropower plants. Table 5 shows the hourly optimal hydropower and thermal power schedules obtained from proposed WCA-ER method.

Case Study-3 (Economic Cost & Emission Scheduling)
In this case an amalgamated objective function with attempt to optimize both fuel cost and exhaust gas emission is engaged. The value of weight factors for this case is K 1 = 1, K 2 = 1. The optimal hydropower discharges and optimal hourly dispatch schedules of hydropower and thermal plants for this case study are presented in Tables   6-7 respectively. The fuel cost and exhaust gas emissions for the above three studies have been collectively summarized in Table   8. In Table 8, the second and third column are of ECS, in which the objective function is to minimize only the fuel cost without considering fuel emissions. However, fuel emissions are written against the fuel costs. In this case, the minimum generation cost is achieved by WCA-ER but the amount of exhaust gas emission is higher than EES and ECES because emissions are not considered here, while they are just written against the fuel cost.   The last two columns of Table 8 are of ECES. In this case both the minimization of fuel cost and fuel emissions has been taken into account in the objective function. Even then the fuel costs and fuel emissions obtained by WCA-ER are found to be lowest. However, they are a bit higher than the independent cases ECS and EES indicating that cost is compromised when both conflicting objective    The results of proposed WCA-ER method have been compared with the results obtained by PSO [19], IQPSO [20], DE [13], QADEVT [21] and SOHPSO_TVAC [22] in Table 8. The results clearly depict the superiority of WCA-ER over others in terms of reduction in both of the fuel cost and exhaust gas emission for all of the three cases.  The cost obtained for ECS is lowest and the emissions obtained in EES are lowest but for the combined case of ECES, which is a multi-objective optimization problem of two conflicting objectives, a compromise between the fuel costs and fuel emissions has been obtained, which is also optimum as compared to other strong techniques in the literature. Therefore, the proposed WCA-ER algorithm is an effective method to find an optimal solution for the multi-objective EEPSHES problem.