American Journal of Engineering and Technology Management
Volume 1, Issue 2, August 2016, Pages: 12-24

Dynamic Economic Dispatch for Combined Heat and Power (Steam and Gas) Units Using Seeker and Bacteria Foraging Optimization Algorithms

Mohamed Ahmed Sadeek Mohamed

East Delta Electricity Production Company, Ismailia, Egypt

Email address:

To cite this article:

Mohamed Ahmed Sadeek Mohamed. Dynamic Economic Dispatch for Combined Heat and Power (Steam and Gas) Units Using Seeker and Bacteria Foraging Optimization Algorithms. American Journal of Engineering and Technology Management. Vol. 1, No. 2, 2016, pp. 12-24. doi: 10.11648/j.ajetm.20160102.12

Received: July 13, 2016; Accepted: July 21, 2016; Published: August 6, 2016


Abstract: In this paper, combined heat and power units are incorporated in dynamic economic dispatch to minimize total production costs considering realistic constraints such as ramp rate and spinning reserve limits effects over a short time span. Three evolutionary approaches, namely seeker optimization Algorithm (SOA), Seeker optimization with inertia weight factor (SOAIW) and Bacteria Foraging Optimization Algorithms (BFOA) are successfully implemented to solve the combined heat and power economic dispatch (CHPED) problem. These approaches have been tested on 12-generation units system with two steam, four gas and six cogeneration units. In addition, the performance tests are applied to measure the actual power output and the fuel consumption in every point tests for achieving different curves such as input/output, incremental heat rate and heat rate curves for the twelve units. The results of the four approaches are compared to obtain the best solution. The results show that the seeker optimization with improved inertia weight is able to achieve the best solution at less computational time.

Keywords: Combined Heat and Power Economic Dispatch (CHPED), Seeker Optimization Algorithm (SOA), Bacteria Foraging Optimization Algorithm (BFOA)


1. Introduction

Combined heat and power unit (CHPU) known as cogeneration has the ability of creating simultaneous generation of two types of energy: useful heat and electricity. It improves efficiency and therefore, is more environmental friendly [1]. It also reduces the generation cost between 10 and 40% [2]. In Thermal Units, all the thermal energy is not converted into electricity and large quantities of energy are wasted in the form of heat [3]. CHPU uses the heat and can potentially achieve the energy conversion efficiency of up to 80% [4]. This means that less fuel needs to be consumed to produce the same amount of useful energy.

In order to utilize the CHPUs more efficiently, economic dispatch must be applied to achieve their optimal combination of power and heat output subject to system equality and inequality operational constraints. Hence, the combined heat and power economic dispatch (CHPED) problem is formulated as an optimization problem [5]. A practical CHPED problem should include ramp rate limits, spinning reserve to overcome the sudden fault in the system and joint characteristic of electricity power heat which makes finding the optimal dispatching a challenging problem [6,7].

In the recent researches, global optimization techniques like genetic algorithms (GA) [8], harmony search algorithm (HAS) [9], and particle swarm optimization (PSO) [10], have been applied for optimal tuning of CHPED based restructure schemes. These evolutionary algorithms are heuristic population-based search procedures that incorporate random variation and selection operators. Although, these methods seem to be good methods for the solution of CHPED parameter optimization problem, they have degraded efficiency to obtain global optimum solution when the system has a highly epistatic objective function (i.e. where parameters being optimized are highly correlated), and number of parameters to be optimized are large, then. In order to overcome these drawbacks, different modifications of particle swarm optimization approach are proposed for solution of the CHPED problem [10,11,12].

In this work, heat and power output of each generating unit and optimum fuel cost are obtained by using Three approaches; Seeker optimization Algorithm (SOA), Seeker optimization Algorithm with inertia weight factor (SOAIW) and Bacteria Foraging Optimization Algorithms (BFOA). The results of the three approaches are compared. Simulation results show that the SOAIW approach is superior to the other existing methods.

2. CHPED Problem Formulation

The proposed CHPED problem is an optimization problem like economic load dispatch (ELD) problem, but it considers some types of production units such as pure heat units, cogenerating combined heat and power units. The cogeneration is a role to produce heat and power with feasible operation region according to Figure 1, where the boundary curve ABCDEF determines the feasible region. Along the boundary there is a trade-off between power generation and heat production delivered by the unit. It can be seen that along the curve AB the unit reaches maximum output power. On the contrary, the unit reaches maximum heat production along the curve CD. Therefore, power generation limits of cogeneration units are determined by combined functions incorporating the unit heat production, and vice versa [9]. Mathematically, the problem is formulated as:

Figure 1. Typical heat-power region for cogeneration units.

2.1. Objective Function

Minimize:

Cost =    (1)

2.2. Constraints

2.2.1. Equality Constraints

(2)

(3)

2.2.2. Inequality Constraints

, i = 1,…………………, np    (4)

, j = 1,…………, nc   (5)

, j = 1,…….….., nc   (6)

where:

Cost: Total heat and power production cost,

α: Unit production cost,

P: Unit power generation,

h: cogeneration heat production,

HD: System heat demand,

PD: System power demand,

np, nc are the numbers of the of conventional power units and cogeneration units, respectively.

pmin and pmax are the unit power capacity limits,

hmin and hmax are the cogeneration heat capacity limits.

2.3. In Addition, up and down Ramp Rate Limits can Be Formulated as

(7)

where,

Pi is the output power at time 't', Pio is the initial output power, URi & DRi are the ramp up & down rate limits of the ith generator, respectively [13].

2.4. Spinning Reserve Requirements

The Mid American Interconnected Network (MAIN) requires 1.1% of peak demand for regulation. MAIN's additional requirement for spinning reserve is 1.5% of it as peak demand. Thus, the total spinning reserve is allocated among as many units as is practical because it is easier to get the required rapid response by adjusting several units by small amounts rather than by adjusting a single unit by a large amount. The MAIN's non spinning reserve requirement is 1.9% of the peak demand [14].

3. Proposed Approaches of SOA

SOA is a population- based heuristic search algorithm. It regards optimization process as an optimal solution obtained by a seeker population. Each individual of this population is called a seeker. The total population is randomly categorized into three subpopulations. These subpopulations search over several different domains of the search space. All the seekers in the same subpopulation constitute a neighborhood. This neighborhood represents the social component for the social sharing of information.

3.1. Egotistic Behavior

Swarms (i.e., seeker population) are a class of entities found in nature which specialize in mutual cooperation among them in executing their routine needs and roles. There are two extreme types of cooperative behavior. One, egotistic, is entirely pro-self and another, altruistic, is entirely pro-group [15]. Every person, as a single sophisticated agent, is uniformly egotistic, believing that he should go toward his personal best position; Īi, best through cognitive learning [16].

Figure 2. Flowchart of the seeker optimization algorithm [17].

3.2. Altruistic Behavior

The altruistic behavior means that the swarms co-operate explicitly, communicate with each other and adjust their behaviors in response to others to achieve the desired goal. Hence, the individuals exhibit entirely pro-group behavior through social learning and simultaneously move to the neighborhood’s historical best position or the neighborhood’s current best position. As a result, the move expresses a self-organized aggregation behavior of swarms. The aggregation is one of the fundamental self-organization behaviors of swarms in nature and is observed in organisms ranging from unicellular organisms to social insects and mammals [17]. The positive feedback of self-organized aggregation behaviors usually takes the form of attraction toward a given signal source. For a "black-box" problem in which the ideal global minimum value is unknown, the neighborhood’s historical best position or the neighbor-hood's current best position is used as the only attraction signal source for the self organized aggregation behavior.

3.3. Pro-activeness Behavior

Agents (i.e., seekers) enjoy the properties of pro-activeness: agents do not simply act in response to their environment; they are able to exhibit goal-directed behavior by taking the initiative. Furthermore, future behavior can be predicted and guided by past behavior [18]. As a result, the seekers may be pro-active to change their search directions and exhibit goal-directed behaviors according to the response to his past behaviors.

3.4. Steps of Seeker Optimization Algorithm

In SOA, a search direction λij(t) and a step length αij(t) are computed separately for each ith seeker on each jth variable at each time step t, two extreme types of cooperative behavior prevailing in swarm dynamics. One, egotistic, is entirely pro-self and another, altruistic, is entirely pro-group. Every seeker, as a single sophisticated agent, is uniformly egotistic. He believes that he should go towards his historical best position according to his own judgment. This attitude of ith seeker may be modeled by an empirical direction vector

 as shown: [17].

(8)

4. Seeker Optimization Algorithm with Inertia Weight Factor Approach (SOAIW)

In SOAIW the parameter ω is used to decrease the step length with increasing time step so as to gradually improve the search precision. In the present experiments, ω is linearly decreased from 0.9 to 0.1 [18].

5. The Bacteria Foraging Optimization Algorithm (BFOA)

During foraging of the real bacteria, locomotion is achieved by a set of tensile flagella. Flagella help an E.coli bacterium to tumble or swim, which are two basic operations performed by a bacterium at the time of foraging. When they rotate the flagella in the clockwise direction, each flagellum pulls on the cell. That results in the moving of flagella independently and finally the bacterium tumbles with lesser number of tumbling whereas in a harmful place it tumbles frequently to find a nutrient gradient. Moving the flagella in the counterclockwise direction helps the bacterium to swim at a very fast rate. In the above mentioned algorithm the bacteria undergoes chemotaxis, where they like to move towards a nutrient gradient and avoid noxious environment. Generally the bacteria move for a longer distance in a friendly environment. Figure 3 depicts how clockwise and counter clockwise movement of a bacterium take place in a nutrient solution.

When they get food in sufficient, they are increased in length and in presence of suitable temperature they break in the middle to form an exact replica of itself. This phenomenon inspired Passino to introduce an event of reproduction in BFOA. Due to the occurrence of sudden environmental changes or attack, the chemotactic progress may be destroyed and a group of bacteria may move to some other places or some other may be introduced in the swarm of concern.

This constitutes the event of elimination-dispersal in the real bacterial population, where all the bacteria in a region are killed or a group is dispersed into a new part of the environment [19].

Now suppose that we want to find the minimum of chemotactic "", where "" is the position of each bacteria at chemotactic step G-dimensional vector of real numbers, and we do not have measurements or an analytical description of the gradient "". BFOA mimics the four principal mechanisms observed in a real bacterial system: chemotaxis, swarming, reproduction, and elimination-dispersal to solve this non-gradient optimization problem.

Let us define a chemotactic step to be a tumble followed by a tumble or a tumble followed by a run. Let "g" be the index for the chemotactic step. Let "k" be the index for the reproduction step. Let "L" be the index of the elimination-dispersal event. Also let [20-21].

G: Dimension "position" of the search space,

S: Total number of bacteria in the population,

Nc: The number of chemotactic steps,

Ns: The swimming length.

Nre: The number of reproduction steps,

Ned: The number of elimination-dispersal events,

Ged: Elimination-dispersal probability,

Y (e): The size of the step taken in the random direction

specified by the tumble.

Figure 3. Flowchart of the BFOA algorithm [20-21].

6. Performance Tests

Testing and monitoring programs are developed to find out where the efficiency problems are and what improvements can be made. The objective of these performance tests is to provide uniform test methods to obtain the best points of the units operation (optimal power with maximum efficiency). In addition, they help determine the thermal performance and electrical output (capacity or efficiency) of heat cycle for electric power plants and cogeneration facilities according to the specifications [22,23]. Twelve generation units (two steam units of Ayoun Mousa steam power plant, four gas units of West Damietta power plant and six cogeneration units of Damietta combined power plant) with data given in Appendix A are used in this study in order to assess the performance of the four approaches.

In this study, the performance tests are applied to measure the actual power output and the fuel consumption in every point tests to achieve different curves such as input/ output, incremental heat rate and heat rate curves for the 12 units. It has been proved that the intersection of both the hate rate and incremental heat rate curves occurs at the minimum heat rate value. The results of the performance tests for the 12 units are as follow:

a)  Power only units:

- Two steam units

F(Pi) =

Limit: and URi = 65, DRi = 100

Figure 4. Illustrate performance test for 2 steam units.

The fuel costs of the two steam units according to Figure 4 can be expressed as:

b)  Four gas units:

Figure 5. Illustrate performance test for 4 gas units.

From Figure 5 the fuel costs of the four gas units can be expressed as:

F(Pi)=

Limit: , URi = 125, DRi = 125

where, PGTi is the power limits of gas units.

c)  Cogeneration units:

Figure 6. Illustrate performance test for 6 cogeneration units.

The combined heat and power cost equation is expressed as follow:

where, a, b, c, d, e, and f are the combined heat and power cost equation coefficients and J is the number of cogeneration units.

Figure 6 shows the heat rate and incremental heat rate characteristics for cogeneration units. From this figure, the combined heat and cost is expressed as:

Limit: , , , URi = 60, DRi = 100.

where,

(P, H)COGJ: total power and heat limits of cogeneration units,

PJ: cogeneration power limits and HJ: cogeneration heat limits

Figure 7. The heat-power operating region for 6 cogeneration units.

Figure 7 shows heat-power feasible region for the six cogeneration units. The maximum and minimum fuel is 200 and 100 MW; respectively.

7. Simulation Results

CHPED problem is solved using the SOA, SOAIW, and BFOA approaches. To assess the units efficiency when applying each approach, two case-study are proposed. First, the approaches are tested with a load demand equals to 2148 MW which is the reference of the performance test for the twelve generating units. Second, they are applied to a daily load curve. On both cases, twelve units (two steam, four gas and six cogeneration units) are used.

7.1. First Case Study

Figure 8 shows the convergence behavior of the SOA and the other two approaches for the twelve generating units at a load 2148 MW. It is shown that SOAIW approach can reach to the best solution with minimum cost. The convergence behavior of the SOAIW is the best.

Table 1 shows the comparison of the results of the performance of the three approaches at a load of 2148 MW. From these results, it can be seen that the results of SOAIW approach provides lower total operation cost at less computation time compared with those obtained from the other two approaches.

Therefore, SOAIW is more effective in providing better solutions and shows a more robust performance.

Figure 8. The convergence behavior of the SOA, SOAIW and BFOA for 12 units at load 2148MW.

Table 1. Comparison results between the SOA, SOAIW and BFOA approaches.

Units output SOA BFOA SOA-IW
ST1 318.859 292.644 319.997
ST2 316.339 319.998 311.024
GA1 101.271 114.823 104.003
GA2 123.840 94.640 106.429
GA3 87.025 95.872 76.917
GA4 114.075 112.042 117.873
COG-P1 123.680 125.450 130.680
COG-H1 60.700 61.500 64.100
COG-P2 127.980 129.220 100.250
COG-H2 60.420 60.810 54.440
COG-P3 122.700 133.850 134.470
COG-H3 56.980 63.950 64.400
COG-P4 117.440 129.930 137.340
COG-H4 53.690 58.790 61.830
COG-P5 133.640 125.510 130.670
COG-H5 58.330 56.570 57.700
COG-P6 116.610 117.680 120.400
COG-H6 54.430 54.720 55.470
Total power (MW) 2148.000 2148.000 2148.000
Total heat (MW) 344.55 356.34 357.94
Total cost ($/h) 29043.457 29039.763 29025.411
CPU Time (sec) 4.6 4.56 4.42

The total cost of SOAIW with heat and load demands ($29025.41) is lower than those of SAO, and BFOA ($29043.457 and $29039.763, respectively). In addition, the total heat production which is the sum of the total heat production of the six cogeneration units (357.94 MW) is higher than those of the other approaches (344.55 MW and 356.34 MW; respectively). The same conclusion can be concluded from Figure 9.

Figure 9. The comparison between SOA, SOAIW and BFOA methods for case 1.

7.2. Second Case Study

Figure 10 shows the daily load curve used in the study. The four approaches are applied to the twelve units and Figure 11 shows the comparison between the results. It is evident that the SOAIW algorithm has the advantage of cost saving that is around 1.00058 and 1.002016 times from SOA and BFOA, respectively.

Figure 10. The daily load curve.

Figure 11. The total cost for 12 generation units of all approaches for case 2.

8. Conclusions

Comparative study based on SOA, SOAIW and BFOA approaches applied to solve CHPED problem has been presented. The approaches are tested on 12 generation units (two steam, four gas and six cogeneration units) taking into consideration the system and units constraints. The results of the Three approaches are compared. From the results, it is clear that SOAIW approach is more effective than other approaches discussed. This gives the best global optimum solution with less computation time than the SOA and BFOA techniques.

Appendix A

The system data of twelve units (two steam, four gas and six cogeneration units) are used.

a)  two steam units x 320 MW:

Steam unit 1:

item unit Test1 Test2 Test3 Test4 Best point
Fuel (input) (K cal/hr) x1000 664730 582015 502997 404351 647770
IHR K cal /kwh 2110.89 2023.02 1974.08 1966.12 2090.09
Heat rate K cal /kwh 2090.35 2094.18 2110.60 2149.43 2090.09
Power (output) MW 318 277.92 238.32 188.12 309.925

Steam unit 2:

item unit Test1 Test2 Test3 Test4 Best point
Fuel (input) (K cal/hr) x1000 665668 584642 505425 405604 656558
IHR K cal /kwh 2094.24 2020.01 1978.29 1973.07 2084.43
Heat rate K cal /kwh 2084.51 2088.75 2104.01 2139.49 2084.44
Power (output) MW 319.34 279.9 240.22 189.58 314.98

b)  four gas units x 125 MW:

Gas unit 1

item unit Test1 Test2 Test3 Test4 Best point
Fuel (input) (K cal/hr) x1000 317324.7 263822.2 227770.346 209663.12 273909.9
IHR K cal /kwh 3555.20 2235.32 1481.63 1351.32 2483.71
Heat rate K cal /kwh 2542.67 2488.89 2648.49 2872.10 2483.77
Power (output) MW 124.8 106 86 73 110.28

Gas unit 2:

item unit Test1 Test2 Test3 Test4 Best point
Fuel (input) (K cal/hr) x1000 323031.3 260072.6 230865.235 213659.53 278393.5
IHR K cal /kwh 3511.88 2098.95 1596.01 1482.11 2497.74
Heat rate K cal /kwh 2584.25 2549.73 2687.60 2864.07 2530.85
Power (output) MW 125 102 85.9 74.6 110

Gas unit 3:

item unit Test1 Test2 Test3 Test4 Best point
Fuel (input) (K cal/hr) x1000 320071.9 247676.1 224654.549 207196.88 260931.5
IHR K cal /kwh 4007.42 2134.01 1597.85 1356.38 2478.83
Heat rate K cal /kwh 2585.40 2489.21 2582.24 2762.63 2478.92
Power (output) MW 123.8 99.5 87 75 105.26

Gas unit 4:

item unit Test1 Test2 Test3 Test4 Best point
Fuel (input) (K cal/hr) x1000 308690.8 250392.3 219403.641 210814.23 276286.1
IHR K cal /kwh 3275.93 1782.22 1254.95 1248.11 2440.70
Heat rate K cal /kwh 2477.45 2484.05 2759.79 2903.78 2440.91
Power (output) MW 124.6 100.8 79.5 72.6 113.19

c)  six cogeneration units x 200MW:

Cogeneration unit 1:

item unit Test1 Test2 Test3 Test4 Best point
Fuel (input) (K cal/hr) x1000 404353.91 356572.29 315138.28 281644.22 363973.43
IHR K cal /kwh 2286.44 1983.85 1784.71 1690.33 2026.6
Heat rate K cal /kwh 2038.37 2027.09 2048.76 2094.43 2026.6
Power (output) MW 132 116.95 100.36 84.54  
heat (output) MW 198.371 175.904 153.819 134.473 179.595

Cogeneration unit 2:

item unit Test1 Test2 Test3 Test4 Best point
Fuel (input) (K cal/hr) x1000 391443.43 360134.47 316518.59 289141.83 357111.94
IHR K cal /kwh 2260.04 2015.55 1733.91 1615.87 1993.39
Heat rate K cal /kwh 2004.00 1993.48 2012.81 2052.78 1993.39
Power (output) MW 131.5 120.6 101.34 86.91  
heat (output) MW 195.33 180.66 157.25 140.85 179.148

Cogeneration unit 3:

item unit Test1 Test2 Test3 Test4 Best point
Fuel (input) (K cal/hr) x1000 410491.102 363411.374 304327.356 291457.797 406550.15
IHR K cal /kwh 2153.21 1910.48 1746.90 1738.49 2130.2
Heat rate K cal /kwh 2130.31 2145.03 2224.55 2252.11 2130.20
Power (output) MW 131.8 116.6 91.8 85.7  
heat (output) MW 192.69 169.42 136.80 129.42 190.851

Cogeneration unit 4:

item unit Test1 Test2 Test3 Test4 Best point
Fuel (input) (K cal/hr) x1000 401156.933 368562.154 302906.047 281493.663 387648.65
IHR K cal /kwh 2237.59 1938.97 1537.40 1509.88 2109.6
Heat rate K cal /kwh 2111.69 2114.38 2232.94 2315.85 2109.6
Power (output) MW 130.64 119.6 92.05 82.05  
heat (output) MW 189.97 174.31 135.65 121.55 183.752

Cogeneration unit 5:

item unit Test1 Test2 Test3 Test4 Best point
Fuel (input) (K cal/hr) x1000 396773.48 375003.52 319707.01 299629.20 355356.1
IHR K cal /kwh 2496.34 2272.08 1772.19 1640.61 2079.110
Heat rate K cal /kwh 2108.47 2094.51 2111.82 2146.42 2090.330
Power (output) MW 131.86 124.34 101.61 92.25  
heat (output) MW 188.181 179.041 151.389 139.595 170.00

Cogeneration unit 6:

item unit Test1 Test2 Test3 Test4 Best point
Fuel (input) (K cal/hr) x1000 392372.53 373151.982 314787.229 294693.019 370725.07
IHR K cal /kwh 2224.51 2059.95 1656.48 1574.69 2039.92
Heat rate K cal /kwh 2044.68 2039.99 2083.16 2125.52 2039.9212
Power (output) MW 132 125.23 100.24 90.33  
heat (output) MW 191.899 182.919 151.111 138.645 181.735

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