The Economic load dispatch (ELD) is a large scale non-linear allocation problem in power system operation. ELD is allocating the number of committed generators to the given load demand economically while meeting the various operating constraints [1]. Multi-area economic dispatch (MAED) is an extension of the Economic load dispatch. MAED determines the generation level and the interchange power between areas such that the fuel cost in all areas is minimized while satisfying power balance constraints, generating limits and tieline constraints.
The ELD is traditionally solved by considering the cost function for the generating units has been approximated as a quadratic function. The lambda-iteration method and gradient method were used to solve the ELD problem. The study of MAED was first done by Shoults in 1980. He solved economic dispatch considering import and export constraints between areas [2]. Romano proposed a decomposition principle to solve constrained economic dispatch with multi area systems [3]. An algorithm based on newton-raphson's method for multi-area economic dispatch and calculation of short range margin cost based prices was presented by Wernerus and Soder [4]. Streiffert proposed Network flow models for solving the multi-area economic dispatch [5]. Yalcinoz and short used Hopfield neural network approach for solving multi-area economic dispatch [6].
Stochastic search techniques like genetic algorithm, simulated annealing are being employed in recent days to find the global optimal solution. Jeyakumar, Jayabarathi and Raghunathan solved various types of economic dispatch problems by Particle swarm optimization [7]. Manoharan solved the multi-area economic dispatch problems by various evolutionary algorithms [8]. Artificial bee colony optimization for MAED was proposed by M Basu [9]. A differential evolution particle swarm optimizer for various types of MAED problems was presented by Ghasemi [10]. Jain and Pandit discussed on reserve constrained MAED employing differential evolution and time-varying mutation [11]. Prasanna et al. [12] solved the Security Constrained Economic Dispatch in interconnected power system by using Fuzzy logic strategy incorporated with Evolutionary Programming and with Tabu-Search algorithms.
In the present paper, Particle swarm optimization (PSO) with constriction factor has been used to solve various MAED problems. The PSO method is a member of the wide category of swarm intelligence methods, which was first introduced by American social psychologist James Kennedy and electrical engineer Russel C. Eberhart in 1995 [13]. PSO 𝑖𝑡𝑒𝑟 is the current position of ith particle in the dth dimension at the iteration iter By suitably selecting the inertia weight w, we can provide a balance between global and local explorations, thus requiring lesser number of iteration on average to find an optimal solution. As originally developed, w is often linearly decreased from 0.9 to 0.4 during a run. It is generally put by following equation 𝑤 = 𝑤 𝑚𝑎𝑥 -𝑤 𝑚𝑎𝑥 -𝑤 𝑚𝑖𝑛 𝑖𝑡𝑒𝑟 𝑚𝑎𝑥 * 𝑖𝑡𝑒𝑟(9)
Where 𝑖𝑡𝑒𝑟 𝑚𝑎𝑥 isthe maximum number of iterations and iter is the current iteration. The acceleration constants c 1 andc 2 represent the weighting of the stochastic acceleration terms that pull each particle toward the Pbest and gbest positions. Low values allow particles to roam far from the target regions before being tugged back. On the other hand, high values result in abrupt movement toward, or past, target regions. Hence, the acceleration constants c 1 andc 2 were often set to be 2.0 according to the past experience.
Clerc [14] in his study on stability and convergence of PSO have introduced a constriction factor K. Clerc indicates that the use of a constriction factor may be necessary to insure convergence of the particle swarm algorithm.The basic system equations of the PSO (7-8) can be considered as a kind of difference equations. Therefore, the system dynamics, namely, the search procedure, can be analysed by the Eigen value analysis and can be controlled so that the system has the following features. a) The system converges, b) The system can search different regions efficiently by avoiding premature convergence. In order to insure convergence of the PSO algorithm, the velocity of the constriction factor based approach can be expressed as follows
Where ∅ = c 1 +c 2 , ∅ > 4
The convergence characteristic of the system can be controlled by ϕ. In the constriction factor approach, the ϕ must be greater than 4.0 to guarantee stability.
In this paper, MAED problem is solved using a PSO algorithm with constriction factor within power system operation. Its implementation is given in following steps STEP1 Let P n =[(P 11 ,P 12 ,…P 1N1 ),…(P i1 ,P i2 ,…P iN2 ),…(P M1 ,P M2 ,. …P NM ),(T 12 ,T 13 …T 1N ),(T 23 ,T 34 …T 2N )….
T (N-1)N ] be the nth particle of a population n=1,2,….I. The elements of the P n are real power outputs of the generators of all areas and tie-line power flows. The particles must be generated in the range following equations (4) to (6). STEP 2 The particle velocities are generated randomly in the range [-V d max ,V d max ]. The maximum velocity limit in the dth dimension is computed as follows
Where R is the chosen number of intervals in the dth dimension.
Objective function values of the particles are evaluated using equation (1). These are recognised as Pbest of the particles. STEP 4
The best value among all the Pbest are identified as gbest.
STEP 5 New velocities of all dimensions are calculated using equation (10). STEP 6
The positions of each particle is updated using equation ( 8). STEP 7
The objective function values are calculated for the updated positions of the particles.
If the new value is better than the previous Pbest, the new value is set to be Pbest. If the stopping criteria is met, the positions of particles represented by gbest are the optimal solution. Otherwise the procedure is repeated from step 4.
The performance of PSO with constriction factor for MAED has been evaluated by using two test systems.
Test system 1 is a small power system network with two areas and each areas contains three generators. All the generators have prohibited operating zones (POZ). Transmission loss is considered. The generator data has been taken from [4]. The total real power load demand is 1263 MW and that the percentage of load demands in area 1 and area 2 are 60% and 40% respectively. The tieline power flow limit is 100 MW. The results obtained by the proposed method are presented in Table 1.
Table1. Simulation results for the test system 1
UNIT GENERATION (MW) The results are compared with other algorithms which are tested on the same test system. For comparison, artificial bee colony optimization (ABCO) and differential evolution (DE) methods are chosen. Results obtained are validated in the Table 2.
This test system consists of a four area system interconnected by six tie lines. The cost coefficients, generator data and tie line limits are taken from [5].The system is a medium scale test system with sixteen generating units divided into four areas with four generators in each and six tie lines interconnecting them. The active load demand are set to 400MW for area 1, 200MW for area 2, 350MW for area 3 and 300MW for area 4. The obtained results of PSO with constriction factor algorithm for the test system 2 are tabulated in Table 3. Here negative tie-line power in T 24 indicates that power is being imported to area 2 from area 4. Similarly, negative T 34 indicates power is imported to area 3 from area 4.The results are compared with other algorithms which are tested on the same test system. For comparison, classical evolutionary programming (CEP) and network flow programming method (NFP) algorithms are chosen. Results obtained are validated in the Table 4. The results show that the PSO with constriction factor algorithm has been successfully implemented to solve the MAED problem with generator constraints.
In this paper, PSO with constriction factor algorithm is proposed for solving MAED problem. In this study, a two area system with six generators and a four area system with sixteen generators are evaluated using the proposed algorithm and the results are compared with existing algorithms. It is seen from the comparisons that PSO with constriction factor has the ability to converge with better quality for MAED problem. (X) -Can NOT be fixed by PDF/A-1b conversion. (!X) -Could be fixed by PDF/A-1b conversion. User chose to be warned in PDF/A settings.
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Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed -203 more not displayed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed -41 more not displayed Page 4 Results (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed Page 4 Results (contd.) (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Arial,Bold is not embedded. Font Arial,Bold can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed Page 4 Results (contd.) (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed -367 more not displayed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed -1 more not displayed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed -23 more not displayed Page 5 Results (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed Page 5 Results (contd.) (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Arial,Bold is not embedded. Font Arial,Bold can not be embedded because: Could not find matching font to embed Page 5 Results (contd.) (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Arial is not embedded. Font Arial can not be embedded because: Could not find matching font to embed (X) Font Arial is not embedded. Font Arial can not be embedded because: Could not find matching font to embed (X) Font Arial is not embedded. Font Arial can not be embedded because: Could not find matching font to embed (X) Font Arial is not embedded. Font Arial can not be embedded because: Could not find matching font to embed (X) Font Arial is not embedded. Font Arial can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed -440 more not displayed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed -4 more not displayed Page 6 Results (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Italic is not embedded. Font Times New Roman,Italic can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed Page 6 Results (contd.) (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,Bold is not embedded. Font Times New Roman,Bold can not be embedded because:
Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Arial is not embedded. Font Arial can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Times New Roman is not embedded. Font Times New Roman can not be embedded because: Could not find matching font to embed (X) Font Arial is not embedded. Font Arial can not be embedded because: Could not find matching font to embed (X) Font Arial is not embedded. Font Arial can not be embedded because: Could not find matching font to embed (X) Font Arial is not embedded. Font Arial can not be embedded because: Could not find matching font to embed (X) Font Arial is not embedded. Font Arial can not be embedded because: Could not find matching font to embed (X) Font Arial is not embedded. Font Arial can not be embedded because: Could not find matching font to embed (X) Font Arial is not embedded. Font Arial can not be embedded because: Could not find matching font to embed (X) Font Arial is not embedded. Font Arial can not be embedded because: Could not find matching font to embed (X) Font Arial is not embedded. Font Arial can not be embedded because: Could not find matching font to embed (X) Font Times New Roman,BoldItalic is not embedded. Font Times New Roman,BoldItalic can not be embedded because: Could not find matching font to embed
www.ijera.com DOI: 10.9790/9622-1009020611