A solution to energy and environmental problems of electric power system using hybrid harmony search-random search optimization algorithm

In recent years, global warming and carbon dioxide (CO2) emission reduction have become important issues in India, as CO2 emission levels are continuing to rise in accordance with the increased volume of Indian national energy consumption under the pressure of global warming, it is crucial for Indian government to impose the effective policy to promote CO2 emission reduction. Challenge of supplying the nation with high-quality and reliable electrical energy at a reasonable cost, converted government policy into deregulation and restructuring environment. This research paper presents aims to presents an effective solution for energy and environmental problems of electric power using an efficient and powerful hybrid optimization algorithm: Hybrid Harmony search-random search algorithm. The proposed algorithm is tested for standard IEEE-14 bus, -30 bus and -56 bus system. The effectiveness of proposed hybrid algorithm is compared with other well-known evolutionary, heuristics and meta-heuristics search algorithms. For multi-objective unit commitment, it is found that as there are conflicting relationship between cost and emission, if the performance in cost criterion is improved, performance in the emission is seen to deteriorate. Subjects: Electrical & Electronic Engineering; Power & Energy; Systems & Control Engineering


Introduction
Today's power system is characterized by large proportions, high interconnections and high nonlinearities, as the size of the power system is growing exponentially due to heavy demand of power

PUBLIC INTEREST STATEMENT
Global warming and carbon dioxide (CO 2 ) emission reduction are today's important research challenges for healthy environment and socioeconomic development of every country. Also, energy is essential for socioeconomic development and poverty eradication of any country. This perspective article describes some of the important aspects for energy planning and their practical utilization to reduce carbon dioxide level in environment for healthy living, which in turns helps in socioeconomic development of the country. applied to discrete variables, which uses musician's experiences as a searching direction and is free from divergence. It can handle discrete and continuous variables and do not require initial value setting for the variables. Also, it does not require differential gradients and has the ability to escape from local optima. HS has ability to overcome the drawback of GA's building block theory and explicitly considers the relationship using ensemble operation (Geem, 2006a). Geem, Tseng, and Park (2005) proposed a Multi-pitch Adjusting Rate (multiple PAR) for Generalized Orienteering Problem. They proposed three PARs that are the rates of moving to nearest, second nearest and third nearest cities, respectively. Geem (2006b) presented the use of fixed parameter values, such as HMS, HMCR, PAR and NI, while bandwidth was set to a range from 1 to 10% of the total value data range. Mahdavi, Fesanghary, and Damangir (2007) proposed Improved Harmony Search (IHS) algorithm, which includes dynamic adaptation for both pitch adjustment rate (PAR) and bandwidth (bw) values. But it faces the difficulty of determining the lower and upper bound of automatic bandwidth (bw), which was overcome by Global-best harmony search (GHS) algorithm proposed by Omran and Mahdavi (2008). GHS algorithm incorporates the PSO concept, global best particle, by replacing the bw parameter altogether and adding a randomly selected decision variables from the best harmony vector in HM. Mukhopadhyay, Roy, Das, and Abraham (2008) suggested that bw will be the standard deviation of the current population when HMCR is close to 1. Degertekin (2008) proposed a new HM initialization technique that generated two times of HMS initial harmonies but placed only the best HMS of these into the initial HM. Chakraborty, Roy, Das, Jain, and Abraham (2009) proposed Differential Harmony Search algorithm, a new improvement to HS through inspiring the Differential Evolution (DE) mutation operator, which replaces the pitch adjustment operation in classical HS with a mutation strategy borrowed from the DE (DE/rand/1/bin class) algorithm. Hasancebi, Erdal, and Saka (2009) and Saka and Hasançebi (2009) proposed a new adaptation for HS by making both HMCR and PAR change dynamically during the improvisation process of HS. This step is to make the selection of these parameter values problem independent, therefore, improves the performance of HS in finding an optimal solutions. Kattan, Abdullah, and Salam (2010) used HS as a new training technique for feed-forward artificial neural networks (ANN). Wang and Huang (2010) proposed a new variation of HS algorithm that focuses on the dynamic selection of bw and PAR parameters. Al-Betar, Khader, and Liao (2010a) also proposed a Multi-pitch Adjusting Rate strategy for enhancing the performance of HS in solving course timetabling problem. They proposed eight procedures instead of using one PAR value, each of which is controlled by its PAR value range. Each pitch adjustment procedure is responsible for a particular local change in the new harmony. Furthermore, the acceptance rule for each pitch adjustment procedure is changed to accept the adjustment that leads to a better or equal objective function. Moved from these innovative ideas, the research proposal for hybrid combination of Harmony Search (HS) and Random Search Algorithm has been taken into consideration to solve the UCP of electric power system.

Cost minimization
The foremost objective of unit commitment is to find the optimal schedule for operating the available generating units to regulate the total operating and generation cost of electric power utilities. Total operating cost of power generation includes fuel cost, shutdown and start-up costs. The fuel costs are calculated using the data of generating unit characteristics such as fuel price information, heat rate of generating utilities, turn-on, turn-off and initial status of units, which is mathematically, a quadratic, non-smooth and non-convex equation of power output of each generator at each hour and can be determined by Economic Load Dispatch (ELD) (Kerr et al., 1966), as represented below: where a i , b i and c i are the fuel cost coefficients of ith generating units.
The total fuel cost over the given time horizon "H" is (1) is the position or status of ith unit at hth hour. Start-up cost is warmth-dependent. Startup cost is that cost which occurs while bringing the thermal generating unit online. It is expressed in terms of the time (in hours) for which the units have been shut down. On the other hand, shutdown cost is a fixed amount for each unit which is shut down. Mathematically, start-up cost can be expressed as: where CSC i and HSC i are the cold start-up and hot start-up cost of ith unit, respectively, and MDT i is the minimum downtime of ith unit, MDT ON i is the number of hours that ith unit has been online since it was turned ON earlier and CSH i is the cold start hour of unit i. The various constraints linked with UCP are mentioned below.

Load balance or power balance constraints
The load balance or system power balance constraint requires that the sum of generation of all the committed units at hth hour must be greater than or equal to the demand at a particular hour "h".

Spinning reserve constraints
Considering the important aspect of reliability, there is a provision of excess capacity of generation which is required to act instantly when there is a failure of already running unit or sudden load demand. This excess capacity of generation is known as Spinning Reserve and mathematically given as:

Thermal constraints
A thermal generation unit needs to undergo gradual temperature changes and thus it takes some period of time to bring a thermal unit online. Also, the operation of a thermal unit is manually controlled. So a crew is required to perform the operation and maintenance of any thermal unit. This leads to many restrictions in the operation of thermal unit and thus it gives rise to many constraints.

Minimum uptime
If the units have already been shut down, there will be a minimum time before they can be restarted. This constraint is given as: where X on i (t) is the duration for which unit i is continuously ON (in hrs) and MU i is the unit i minimum uptime (in hrs).

Minimum down time
Once the unit is decommitted, there is a minimum time before it can be recommitted. This constraint is given as: where X off i (t) is the duration for which unit i is continuously OFF (in hrs) and MDT i minimum downtime (in hrs).

Crew constraints
If a plant consists of two or more units, they cannot be turned on at the same time since there are not enough crew members to attend both units while starting up.

Maximum and minimum power limits
Every unit has its own maximum/minimum power level of generation, beyond and below which it cannot generate.

Initial operating status of generating units
The initial operating status of every unit should take the last day's previous schedule into account, so that every unit satisfies its minimum up/downtime.

Emission minimization
To obtain the generation schedule that minimizes the total emission, the objective function described in (1) can be reformulated as: where α i , β i and γ i are the emission coefficients of ith generating units.
The total emission over the given time horizon "H" is

Multi-objective problem formulation
Many real-world applications involve simultaneous optimization of several objective functions, which are often competing or/and conflicting with each other, and subject to a number of equality and inequality constraints. In general, these multi-objective problems can be formulated as follows: where f p (U) is the pth objective function, U is a decision vector that represents a solution, P is the number of objectives, v q is the qth of the Q equality constraints and w r is the Rth of the inequality constraints.
The objective functions f p (U) must be evaluated in correspondence of each decision variable vector U in the search space. The final goal is to identify a set of optimal decision variable vectors U * m , m = 1, 2, 3, ..., M, instead of a single optimal solution. In this set of optimal solutions, no one can be regarded to be better than any other with respect to all the objective functions.
The comparison of solutions may be achieved in terms of the concepts of Pareto optimality and dominance (Mantawy et al., 1998): taking a minimization problem as example, U a solution is regarded to dominate solution U b (U a > U b ) if both the following conditions are satisfied: (11) minimize f p (U), p = 1, 2, 3, ..., P If any of the above two conditions is violated, the solution does not dominate the solution, and is said to be non-dominated by. The solutions that are non-dominated within the entire search space are denoted as Pareto-optimal and constitute the Pareto-optimal set, and the corresponding values of the objective functions form the so-called Pareto-optimal front in the objective functions space. The goal of a multi-objective optimization algorithm is to guide the search for finding solutions of the Pareto-optimal set.
MOUCP can be formulated as a non-linear mixed combinatorial and continuous multi-objective optimization problem, as follows:

Hybrid harmony search-random search algorithm
Harmony Search (HS) is a population-based meta-heuristics search algorithm inspired from the musical process of searching for a perfect state of harmony. HS has been proposed by Geem, Kim, and Loganathan (2001). The pitch of each musical instrument determines the aesthetic quality, just as the fitness function value determines the quality of decision variables. In the musical improvisation process, all players sound pitches within possible range together to make one harmony. If all the pitches make a good harmony, each player stores in his memory that experience and the possibility of making a good harmony is increased next time. The same thing in optimization, the initial solution is generated randomly from decision variables within the possible range. If the objective function values of these decision variables are good to make a promising solution, then the possibility to make a good solution is increased next time. Random Search Algorithm is a derivative-free method for continuous domain, which is based on direct search and most suitable for Stochastic and Global optimization problem. In the proposed algorithm, HS is combined with Random Search algorithm for random population search. The major steps of proposed hybrid algorithm are mentioned below: Step-I: Initialization of harmony memory (HM) The initial population HM consists of HMS vectors is generated randomly (Figure 1). The Harmony Memory (HM) matrix is filled with HMS vectors as follows: .., HMS} and j ∈ {1, 2, 3, ..., G}

Step-II: Harmony memory considering (HMC) rule
For this rule, a new random number r 1 is generated within the range [0,1].
If r 1 < HMCR, then the first decision variable in the new vector x New ij is chosen randomly from the values in the current HM as follows:  where HMCR is the Harmony Memory Consideration Rate (Figure 2).
Step-III: Pitch adjusting rate (PAR) The obtained decision variables from the harmony memory consideration rule is further examined to determine if it needs to pitch adjustment or not ( Figure 3).        If, then the pitch adjustment decision variable is calculated as follows: where, PAR is Pitch Adjustment Rate.
Pitch Adjustment Rate: where BW is a bandwidth factor, which is used to control the local search around the selected decision variable in the new vector.

Step-IV: Random initialization rule
If the condition r 1 < HMCR fails, the new first decision variable in the new vector X New ij is generated randomly as follows:     After the Harmony Vector X New ij is generated, it will replace the worst harmony vector X Worst ij in the Harmony memory if its objective function value is better than the objective function value of the worst harmony vector (Figure 4). PSEUDO code for updation of Worst Harmony Vector (WHV) with new random harmony vector is mentioned below.

Step-VI: Ensemble consideration
After the new harmony X New ij = X ij ; X ij ∈ {X 1j , X 2j , X 3j , ..., X HMSj } is obtained, one more operation can be considered from the relationship among decision variables. Just as a player has even stronger relationship with specific player in a music group, the new operation, ensemble consideration (Geem, 2006b), enables the algorithm to combine closely related variables together.

Step-VII: Violated harmony consideration
Once the new harmony is obtained using the above-mentioned rules, it is then checked whether it violates problem constraints. Although the new harmony violates the constraints, it has still Update the HM as X Worst  chance to be included in HM, just as rule-violated harmony was still used by musicians such as famous composer Ludwig van Beethoven (Geem, 2006b). Violated harmony can be considered by adding a penalty (Figures 5 and 6). The suitable penalty can be mathematically described as: • Randomization in harmony search algorithm Randomization in Harmony Search algorithm is to increase the diversity of the solutions. Although the pitch adjustment has a similar role, it is limited to certain area and thus corresponds to a local search. The use of randomization can drive the system further to explore various diverse solutions so as to attain the global optimality. The Pseudo code of Proposed Algorithm (Figure 7), the probability of randomization is  where r accept is the Harmony memory accepting rate and r pa represents the Pitch Adjustment rate. (23) P Pitch = r accept × r pa Table 8. Comparison of results for 10-generating unit system (for 5% spinning reserve)

Flow chart of proposed algorithm
In order to obtain the hybrid version of Harmony search-Random search algorithm, the general operators of harmony search algorithm and random search algorithm are integrated recursively. The flow chart of Harmony search algorithm and PSEUDO code for random search algorithm is shown in Figure 7.

Test systems
The  Khanmohammadi, Amiri, and Haque (2010) and are shown in Tables 14 and 15, respectively. The characteristics of 10-units test system are taken from Khanmohammadi et al. (2010) and are shown in Table 16 and load demand pattern is shown in   The corresponding results have been obtained using hybrid harmony search algorithm using population size of 40 and number of searches from 150 to 1,000 for 4-and 10-units test system. For multi-objective UCP, IEEE-14, 30 and 56 bus system is tested for number of searches of 30 and taking number of pareto 50. The recursive search procedure for proposed hybrid harmony search-random search algorithm is shown in Figure 7. The performance of the proposed algorithm is tested in MATLAB 2013a (8.1.0.604) software on Intel® core™ i-5-3470S CPU@ 2.90 GHz, 4.00 GB RAM system.

Results and discussion
In order to stochastic nature of Hybrid HS-random Search algorithm, 50 test trials were made for each problem set, with each run starting with different initial populations. The Population size of 40 (for 4-and 10-units test system) was taken in all runs (Figure 8). The simulation results are shown in Table 1 through and Figure 9. As shown in comparison, Table 2 for 4-units test system, Table 5 for 10-Units test system with 10% spinning reserve, Table 8 for 10-Units test system with 5% spinning reserve shows that proposed hybrid Harmony Search-Random Search algorithm gives better solution in comparison with other well-known meta-heuristics algorithms. In comparison with the results produced by reported methods, the proposed method gives satisfactory solution in reasonable  Tables 11-13, respectively, and Figure 9 shows the variation of Cost and Emission w.r.t. weights for IEEE-14, 30 and 56-Bus systems.

Conclusion and future scope
In this paper, researchers have presented the solution of multi-objective UCP using Hybrid Harmony Search-Random Search Algorithm. The results for standard IEEE-14, 30 and 56-bus systems have been successfully evaluated for multi-objective UCP and the test systems consisting of 4 and 10 units are tested for single-objective evaluation using proposed hybrid algorithm. It has been observed that performance of proposed Hybrid algorithm is much better than other well-known and recently developed evolutionary, heuristics and meta-heuristics search algorithm. For Multi-Objective criterion, it has been found that as there is a conflicting relationship between cost and emission, if the performance in cost criterion is improved, performance in the emission is seen to deteriorate. Thus, to achieve best compromising solution with respect to cost and emission, suitable adjustment in weights is required.