Power and Heat Dispatch using an Adaptive Algoritham

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Power and Heat Dispatch using an Adaptive Algoritham

Dr. J. Rameshkumar1, Dr. N. Jayakumar2

1, 2Asst. Prof. Deputed from Annamalai University, Department of Electrical Engineering, Government Polytechnic College,

Jolarpettai-635 851, Tamil Nadu, India

Abstract:- The purpose of this paper is to obtain the best feasible solutions for combined heat and power dispatch problems. The optimization tool used in this study is an Adaptive version of Teaching Learning Algorithm (ATLA). Though the Teaching Learning Algorithm (TLA) approach is a parameter free technique, the basic deficiency of the original TLA is the fact that, it gives near optimal solution rather than an optimal one in a limited run time period. Some modifications have been applied in the position of learners in order to improve its exploration and exploitation ability. Practical operational constraints such as feasible operating regions of co-generators, prohibited operating zones of thermal generators are considered. Standard test systems having non-linear and non-convex operating characteristics are chosen to show the effectiveness of ATLA. The results obtained using the ATLA algorithm are highly feasible than or as well as the best known solutions by state-of-the-art algorithms reported in the literature, suggesting that the proposed approach is capable of efficiently determining higher quality solutions addressing CHP dispatch problems.

Keywords: Combined heat and power dispatch, Economic Dispatch, Valve point effect, prohibited operating zone, Adaptive teaching learning algorithm


    1.1. Combined Heat and Power System – In brief Combined Heat and Power (CHP) system that concurrently generates electricity and useful heat from a single fuel-is a versatile technology that can generate useful energy more efficiently, and thereby significantly and economically improve energy efficiency and deliver substantial benefits for end-user facilities, utilities, and communities. As the society needs heat and power, combined heat and power generation is environmentally and economically advantageous. The objective of Combined Heat and Power Economic Dispatch (CHPED) plant is to find the heat and power generation of each unit with low fuel cost while satisfy the necessary demands and constraints. Incorporating cogeneration units into the existing utility makes economic dispatch problem further complexity to the solution methodology.


    The solution methods can be categorized into two groups: mathematical and heuristic. The mathematical approaches including direct search method [1], mesh adaptive direct search algorithm [2] and Lagrangian relaxation [3, 4]etc.,

    were applied to solve this problem. These methods require approximations in the modeling of the cost curves and are not practical as the actual cost curves are highly non linear, non-monotonic and sometimes contain discontinuities.

    The heuristic search techniques have provided alternative methods for solving CHPED problem such as, Evolutionary Programming (EP) [5], Differential Evolution (DE) [6], Genetic Algorithm (GA) [7], Harmony Search (HS) algorithm [8,9], Benders Decomposition (BD) [10], Self Adaptive Real Coded Genetic algorithm (SARGA) [11], Artificial Immune System (AIS) [12], Particle Swarm Optimization (PSO) [13], Artificial Bee colony algorithm (ABC) [14], Harmony Search-Genetic Algorithm (HSGA)

    [15] and Canonical Coordinates Method (CCM) [16] have been suggested for solving CHPED problem.

    Recently, Charged System Search Algorithm (CSSA) [17], Improved Group Search Optimization (IGSO) [18], Oppositional Teaching Learning Based Optimization (OTLBO) [19], Grey Wolf Optimization (GWO) [20] and Improved GA (IGA) [21] have also been applied to solve CHPED problem considering valve-point effects of thermal generators.


    The Teaching Learning Algorithm (TLA) is a new optimization algorithm based on learning of students from teacher through classroom teaching first introduced by Rao et al. [22]. Unlike other evolutionary algorithms, the TLA approach does not have any algorithm-particular parameters to control. In this paper, an Adaptive Teaching Learning Algorithm (ATLA) is applied for solving combined heat and power system problem. Despite the fact that the TLA algorithm is an algorithmic parameter-free technique, the fundamental deficiency of this algorithm is overwhelmed to enhance search capability and to accelerate the speed through some modifications in changing the position of learners [23]. The proposed method is tested on different scale of test systems. The obtained results are compared with the earlier reports and ETLBO emerges out to be a stout optimization technique for solving CHPED problem for linear and nonlinear models.

  4. PROBLEM FORMULATION OF CHPED Conventional power only unit, combined heat and power unit and heat only unit are considered in this study. The main issues, is to minimize the cost subjected to system and operational constraints The CHP systems total fuel cost (1) can be mathematically represented in the following form.

    Min C


    C (P )


    C (P , H


    ) C (H )


    order to economize the production. The feasible operating

    T p i

    c cj cj h k

    zones of unit can be described as follows:

    i 1

    j 1

    k 1



    P PLB

    i.e. (1) is expanded as follows

    i i



    P PLB

    j 2,3,…Np


    i, j 1 i

    i, j i

    a b P c P 2 e sin( f (P min P ))

    i i i i i i i i i




    Power only units Nc




    • P

    P 2 H

    H 2 P H

    P , j

    P P

    j Np

    T j 1 j

    j cj

    j cj

    j cj

    j cj

    1. cj


      i i i i

      4.5Feasible operating region combined heat and power

      Combined Heat and Power units



      2 Fig. 1 s s the heat power feasible operation region of a

      H H


      k1 k

    2. k k k

    combined heat and power unit, the power outputs and heat

    outputs operating region is enclosed by the boundary curve

    Heat only units

    ($/h) (2)

    The system and operating constraints are as follows:

      1. Power demand

        The eelectric power generation must be equal to the power demand.

        4.1 4.5.

        Np Nc

        P P P


        i 1 i

      2. Heat demand

        j 1 cj d


        Heat generated by the cogeneration and heat only units must be equal to the heat demand.


        j 1



        k 1

        Hk Hd



        Fig.1 Feasible operating region for the combined heat and power units

      3. Operating limits

        The power-only unit, cogeneration unit and heat-only unit has its own operating limit which is bounded by upper and lower values and is represented as:



    In the original TLA algorithm, the position of learners is not changed among the learners, which causes the

    P min P P max

    i 1,……., Np

    knowledge of learners in same level. (.e.) the learner can

    i i

    P min (H cj cj

    H min (P


    ) P


    ) H

    P max (H )

    cj cj

    H max (P )


    j 1,……., Nc


    j 1,……., Nc

    learn same level of knowledge from his/her teacher. For this reason the original TLA algorithm is modified in order to enhance the exploration and exploitation the position of learners is changed using adaptive exponential distribution inertia weight mechanism had been introduced. The purpose of this modification is to enhance the convergence speed and increase solution qualities during the early part

    cj cj


    cj cj cj



    of optimization process.

    5.1 Modified position of learners using adaptive exponential distribution inertia weight

    Hk Hk Hk

    i 1,……., Np


    In basic TLA, the teacher is identified by finding the knowledge from the best solution X teacher, k in addition, old positions of the individual are updated in the each

      1. Prohibited operating zones

    The generating units may have certain ranges where operation is restricted on the grounds of physical limitations of machine components or instability, for example, because of steam valve or vibration in shaft bearings. Consequently, discontinuities are produced in cost function according to the prohibited operating zones. So, there is a quest to avoid operation in these zones in

    iterations. As this reason, TLA can quickly trap into local search space. The old position has not yet been systematically updated the information of individuals in the TLA method. En- courage from basic TLA, we produce the learners together from the old position and best position (teacher) by new position-updating rule through inertial weight strategy on TLBO [23] using the equation

    X new i, k = *X old i, k + r 3 *(X teacher, k T f *M i,k)


    = { 1 e + 2 e }


    1 = 2 e + 1 e and 2 = 1 e 2 2


    Where X new i, k represent the updated value of current position of learner, represent the adaptive exponential distribution inertia weight, r 3 is random number lies between (0, 1); and T f is teaching factor. is the sigmoid function and the value lies between lower and upper bound.



    The performance of the proposed ATLA based CHPED problem is coded in the MATLAB 7.9 platform and is executed in the personal computer with the hardware configuration of Intel i3 processor 2.40 GHz and 4GB RAM. Numerical simulation results obtained using the ATLA for the standard test systems varying with different scale and operational characteristic are elaborated in this section.

      1. Description of the test systems

        Test system 1:

        This is the fundamental model to study the economic operation of CHP plants, Guo et al., 1996 developed this test system. This system consists of 4 units with second order cost functions are used to show the validity and effectiveness of the ATLA for non-convex problems. It has one thermal unit, two cogenerating units and a heat unit to satisfy the required demands.

        System particulars involving feasible regions and capacity limits of the aforementioned units are obtained from [3]. For the sake of comparison the economic emission dispatch is carried out for a demand of Pd=200 MW and Hd=115 MWth. The ATLA is executed and is converged to the total fuel cost of $9257.07/h. The dispatch schedules corresponding to the minimum fuel cost is presented in the Table 1. The numerical simulation results indicate the solution is feasible as the dispatches satisfy the power balance, heat balance and operational limits of generating units. The power and heat outputs settings of cogenerating units are also within the FOR region. In order to validate the numerical results obtained by the ATLA, a comparison has been made with the earlier reports and is also presented in the Table 1.

        The comparison indicates that the GWO provides the best feasible dispatches for the test system under consideration.

        The obtained numerical results are in close agreement with LR, SARGA, HS and TVAC-PSO methods. Though SPSO, SGA, RGA and EDHS have reported least cost than ATLA there are few errors in their reports such as SPSO converged with the real power mismatch of 0.4 MW; RGA attains the heat mismatch of around 2 MWth; the actual cost for the obtained dispatch using SGA is $9591.94/h; EDHS attains the zero real power output for cogenerating unit 2 but its minimum generation limit is 40 MW. Considering these errors, the solution attained by the ATLA cannot be compared with these reports. For the basic CHP plant economic operation problems, the optimal dispatches are well determined and the ATLA attains the same best feasible schedule.

        Test system 2:

        Further the ATLA is tested with a medium size CHP plant which is having 24 units. The CHP plant comprises of 13 power-only units, 6 cogenerating units and 5 heat only units. The valve point loadings are included along with quadratic cost characteristics of power-only units. Further, prohibited operating zones are included that further increases the complexity in determining the optimal operating point. The test system data is extracted from [20]. The economic operation is carried out for the power and heat demands of 2350 MW and 1250 MWth respectively. Initially, the ATLA is executed for the best feasible solution neglecting POZ. The best cost of $57773.2/h is found using ATLA and the attained desirable output settings are presented in Table 2. The applicability of ATLA can be verified by comparing the total fuel cost with the earlier reports such as CPSO, TVAC-PSO, IGSO, OTLBO and IGA, and the comparison is also presented in the Table II. It is evident that the ATLA has settled with the new least cost dispatch.

        Further, POZ of power-only units are included in the test system for economic operation that leads to multiple minimas in the search space. Due to the inclusion of POZ constraint, the total fuel cost increases and is found to be $58024.8/h. The best dispatch attained by the ATLA and numerical results comparisons with recent reports are presented in the Table II. The obtained total fuel cost using ATLA is the least when comparing with the earlier reports such as GSO, IGSO and GWO.

      2. Convergence test

    The convergence behaviour of proposed method for the two test systems is illustrated in Figs. 3(a), 3(b).

    Table: 1 CHP dispatch results for 4-unit test system and comparison with other algorithms (Pd=200MW and Hd= 115MWth)

    Methods Power Output (MW) Heat Output (MWth) Pd (MW) Hd (MWth) Cost ($/h)
    P1 P2 P3 H2 H3 H4
    IACS 0.08 150.93 49 48.84 65.79 0.37 200.1 115 9452.2
    GA-PF 0 159.23 40.77 39.94 75.06 0 200 115 9267.28
    PSO 0.05 159.43 40.57 39.97 75.03 0 200.05 115 9265.1
    IGA 0 160 40 39.99 75 0 200 114.99 9257.09
    CPSO 0 160 40 40 75 0 20 115 9257.08
    LR 0 160 40 40 75 0 200 115 9257.07
    SARGA 0 159.99 40.01 39.99 75 0 200 114.99 9257.07
    HS 0 160 40 40 75 0 200 115 9257.07
    TVAC-PSO 0 160 40 40 75 0 200 115 9257.07
    EDHS 0 200 0 0 115 0 200 115 8606.07*
    SPSO 0 159.706 39.909 40 75 0 199.6162 115 9248.17*
    SGA 0 155.867 44.420 72.622 42.37 0 200.29 115 9168.67*
    RGA 0 155.867 44.132 0.3989 112.63 0 200 113.04 9151.07*
    OTLBO 0 160 40 40 75 0 200 115 9257.07
    GWO 0 160 40 40 75 0 200 115 9257.07
    ATLA 0 160 40 40 75 0 200 115 9257.07

    Table: 2 Simulation results obtained by ATLA and other methods- 24-unit test system (Pd=2350MW and Hd= 1250MWth)

    Without POZ With POZ
    P1 680 538.558 628.152 538.565 538.584 628.318 627.943 269.750 268.943 538.524 538.519
    P2 0 224.460 299.477 299.212 299.342 299.198 298.521 360 224.152 299.277 299.142
    P3 0 224.460 154.553 299.122 299.342 299.166 300.254 77.0947 294.910 299.009 299.150
    P4 180 109.866 60.846 109.992 109.965 109.867 109.866 161.180 162.259 109.239 109.137
    P5 180 109.866 103.853 109.954 109.965 109.866 109.866 116.471 110.282 109.739 109.840
    P6 180 109.866 110.055 110.404 109.965 60 60.1120 160.118 159.055 109.739 109.740
    P7 180 109.866 159.077 109.804 109.965 109.860 109.542 123.115 158.872 141.919 141.910
    P8 180 109.866 109.825 109.686 109.965 109.823 109.852 162.264 109.653 109.864 109.968
    P9 180 109.866 159.992 109.899 109.965 109.852 109.775 161.955 109.552 109.864 109.968
    P10 50.5304 77.521 41.103 77.3992 77.6223 40.0001 40 113.852 268.943 44.6264 44.4061
    P11 50.5304 77.521 77.7055 77.8364 77.6223 77.0316 76.5420 116.989 114.639 80.1476 80.1671
    P12 55 120 94.9768 55.2225 55.0000 55.0098 55.1452 120 114.406 55.0000 55
    P13 55 120 55.7143 55.0861 55.0000 55 55 114.283 117.432 55.0000 55
    P14 117.485 88.3514 83.9536 81.7524 83.4650 81.0035 81.0010 81 118.245 81.3948 81.3952
    P15 45.9281 40.5611 40 41.7615 40.0000 40.0003 40.0100 40 81.2429 40.2800 40
    P16 117.485 88.3514 85.7133 82.273 82.7732 81.0035 81.0452 85.4377 40 81.0685 81.0710
    P17 45.9281 40.5611 40 40.5599 40.0000 40.0003 40 40 81.3534 40.2599 40.2500
    P18 10.0013 10.0245 10 10.0002 10.0000 10.0002 10.5214 10 40 10.0357 10.0357
    P19 42.1109 40.4288 35 31.4679 31.4568 35.0003 35.0002 36.4886 10 35.0084 35.0084
    H14 125.275 108.925 106.456 105.221 106.099 104.801 106.772 104.803 35 105.019 105.020
    H15 80.1175 75.4844 74.998 76.5205 75.0000 75.0001 74.9990 74.998 104.94 75.2167 75.0965
    H16 125.275 108.925 107.407 105.514 105.789 104.799 106.789 107.289 74.998 104.837 104.837
    H17 80.1174 75.484 74.998 75.4833 75.0000 74.9988 74.9980 74.998 104.99 75.223 75.2230
    H18 40.0005 40.0104 40 39.9999 40.0000 39.9993 39.9890 40.001 74.998 40.0107 40.0200
    H19 23.2322 22.4676 20 18.3944 18.3782 20 20.0010 20.6773 40.001 20.0038 20.0038
    H20 415.981 458.702 466.257 468.904 469.733 470.408 466.448 467.582 20 469.688 469.798
    H21 60 60 60 59.9994 60.0000 60 60 60 470.09 60.0000 60
    H22 60 60 60 59.9999 60.0000 60 60 60 60 60.0000 60
    H23 120 120 120 119.985 120.000 120 120 119.879 60 120.00 120
    H24 120 120 119.882 119.976 120.000 119.991 120 119.771 120 120.000 120
    Cost ($/h) 59736.2 58122.7 58049 57856.2 57846.8 57826 57773.2 58650.2 58292 58033.9 58024.8

    At beginning the acceleration speed is very high; it shows the convergence of the ATLA. The ATLA method can reach to the optimum solution more quickly than the other methods reported in literature. The proposed method is thus demonstrated to have a better convergence property. Over

    100 iterations with several initial random solutions, the ATLA has confirmed it as trustworthy solution procedure by generating the global best solution.

    Fig.2 Convergence characteristic of (a) 4-unit and (b) 24- unit systems


    This paper demonstrated the feasibility of employing adaptive TLA for efficient solving of combined heat and power economic dispatch with cogeneration sources. Two test systems have been employed to illustrate the applicability of the adaptive teaching learning algorithm for solving CHP problems. In the case of CHPED problem with second order cost functions aspects, our proposal found better solutions compared to what was known as best until now. Further the problems considering valve point effects and prohibited operating zones, our method established solutions better than so for best known results. In a nutshell considering all the results for study with different characteristic, dimensions, demands and constraints it can be concluded ATLA yields better feasible solutions mostly within the feasible operating region in terms of cost, than the previously reported results. Any advantage in this area will cause great improvement in engineering application, which by reducing generator fuel consumption, both increases the profit of Energy Company and serves the environment.

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