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. INTRODUCTION

    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.

  2. REVIEW OF EXISTING METHODS

    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.

  3. ATLA AS AN OPTIMIZATION TOOL

    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

    Np

    C (P )

    Nc

    C (P , H

    Nh

    ) C (H )

    ($/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

    (1)

    Pmin

    P PLB

    i.e. (1) is expanded as follows

    i i

    PUB

    i,1

    P PLB

    j 2,3,…Np

    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

    (9)

    i1

     

    Power only units Nc

    UB

    max

    C

    • 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

      cj

      i i i i

      4.5Feasible operating region combined heat and power

      Combined Heat and Power units

      units

      Nh

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

      H H

      how

      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

        (MW)

        i 1 i

      2. Heat demand

        j 1 cj d

        (3)

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

        Nc

        j 1

        Hcj

        Nh

        k 1

        Hk Hd

        (MWth)

        (4)

        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:

  5. ADAPTIVE TEACHING LEARNING ALGORITHM

    (ATLA)

    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

    i

    ) P

    cj

    ) H

    P max (H )

    cj cj

    H max (P )

    (5)

    j 1,……., Nc

    (6)

    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

    min

    cj cj cj

    max

    (7)

    of optimization process.

    5.1 Modified position of learners using adaptive exponential distribution inertia weight

    Hk Hk Hk

    i 1,……., Np

    (8)

    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)

    (10)

    = { 1 e + 2 e }

    (11)

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

    (12)

    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.

  6. NUMERICAL SIMULATION RESULTS AND

    DISCUSSION

    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)

    MethodsPower Output (MW)Heat Output (MWth)Pd (MW)Hd (MWth)Cost ($/h)
    P1P2P3H2H3H4
    IACS0.08150.934948.8465.790.37200.11159452.2
    GA-PF0159.2340.7739.9475.0602001159267.28
    PSO0.05159.4340.5739.9775.030200.051159265.1
    IGA01604039.99750200114.999257.09
    CPSO01604040750201159257.08
    LR016040407502001159257.07
    SARGA0159.9940.0139.99750200114.999257.07
    HS016040407502001159257.07
    TVAC-PSO016040407502001159257.07
    EDHS02000011502001158606.07*
    SPSO0159.70639.90940750199.61621159248.17*
    SGA0155.86744.42072.62242.370200.291159168.67*
    RGA0155.86744.1320.3989112.630200113.049151.07*
    OTLBO016040407502001159257.07
    GWO016040407502001159257.07
    ATLA016040407502001159257.07

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

    Without POZWith POZ
    OutputCPSOTVAC- PSOIGSOOTLBOGWOIGAATLAGSOIGSOGWOATLA
    P1680538.558628.152538.565538.584628.318627.943269.750268.943538.524538.519
    P20224.460299.477299.212299.342299.198298.521360224.152299.277299.142
    P30224.460154.553299.122299.342299.166300.25477.0947294.910299.009299.150
    P4180109.86660.846109.992109.965109.867109.866161.180162.259109.239109.137
    P5180109.866103.853109.954109.965109.866109.866116.471110.282109.739109.840
    P6180109.866110.055110.404109.9656060.1120160.118159.055109.739109.740
    P7180109.866159.077109.804109.965109.860109.542123.115158.872141.919141.910
    P8180109.866109.825109.686109.965109.823109.852162.264109.653109.864109.968
    P9180109.866159.992109.899109.965109.852109.775161.955109.552109.864109.968
    P1050.530477.52141.10377.399277.622340.000140113.852268.94344.626444.4061
    P1150.530477.52177.705577.836477.622377.031676.5420116.989114.63980.147680.1671
    P125512094.976855.222555.000055.009855.1452120114.40655.000055
    P135512055.714355.086155.00005555114.283117.43255.000055
    P14117.48588.351483.953681.752483.465081.003581.001081118.24581.394881.3952
    P1545.928140.56114041.761540.000040.000340.01004081.242940.280040
    P16117.48588.351485.713382.27382.773281.003581.045285.43774081.068581.0710
    P1745.928140.56114040.559940.000040.0003404081.353440.259940.2500
    P1810.001310.02451010.000210.000010.000210.5214104010.035710.0357
    P1942.110940.42883531.467931.456835.000335.000236.48861035.008435.0084
    H14125.275108.925106.456105.221106.099104.801106.772104.80335105.019105.020
    H1580.117575.484474.99876.520575.000075.000174.999074.998104.9475.216775.0965
    H16125.275108.925107.407105.514105.789104.799106.789107.28974.998104.837104.837
    H1780.117475.48474.99875.483375.000074.998874.998074.998104.9975.22375.2230
    H1840.000540.01044039.999940.000039.999339.989040.00174.99840.010740.0200
    H1923.232222.46762018.394418.37822020.001020.677340.00120.003820.0038
    H20415.981458.702466.257468.904469.733470.408466.448467.58220469.688469.798
    H2160606059.999460.0000606060470.0960.000060
    H2260606059.999960.00006060606060.000060
    H23120120120119.985120.000120120119.87960120.00120
    H24120120119.882119.976120.000119.991120119.771120120.000120
    Cost ($/h)59736.258122.75804957856.257846.85782657773.258650.25829258033.958024.8

    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

  7. CONCLUSION

    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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