International Journal of Communication, Science and Technology (eISSN:3049-0650)

vol.1,no.3(June – July,2025),pp.7-15

Economic and Green Dispatch in Multi-Area Power Systems: An Approach of using NDSGA-II

 

 

Abhik Hazra

Electrical Engineering Department (Gargi Memorial Institute of Technology)

Kolkata, India

 

 

Mihir Kumar Manna

Electrical Engineering Department (Gargi Memorial Institute of Technology)

Kolkata, India

Arnab Ganguly

Electrical Engineering Department (Gargi Memorial Institute of Technology)

Kolkata, India

 

 

Rakesh Naskar

Electrical Engineering Department (Gargi Memorial Institute of Technology)

Kolkata, India

Amartya Roy

Electrical Engineering Department (Gargi Memorial Institute of Technology)

Kolkata, India

 

Abstract— This paper introduces an improved strategy for multi- area economic and environmental dispatch (MAEED) utilizing the Non-Dominated Sorting Genetic Algorithm II (NSGA-II). As the global push for sustainable energy solutions intensifies, optimizing power distribution to minimize both cost and emissions has become essential. This work formulates MAEED as a bi-goal nonlinear constrained optimization problem incorporating power balance, generation capacity, and tie-line limits. The proposed NSGA-II is benchmarked against Strength Pareto Evolutionary Algorithm II (SPEA-II) and other contemporary methods. Simulation results on a four-area power system illustrate that NSGA-II consistently outperforms alternatives by offering superior trade-offs between cost and emissions. Recent studies support these findings, highlighting the robustness of evolutionary approaches in multi-goal dispatch problems.

 

1. Introduction

 

Power generation from fossil fuels continues to be a major contributor to air pollution, releasing harmful gases like sulfur oxides, carbon oxides, and nitrogen oxides into the atmosphere. These pollutants not only pose serious risks to human health and other living organisms but also contribute to vegetation damage, acid rain, reduced visibility, and global warming.

 

Growing environmental awareness, along with regulatory frameworks like the Clean Air Act Amendments of 1990, have pushed power stations to actively work towards reducing emissions. However, this creates a challenging trade-off: producing electricity at the lowest cost while also minimizing environmental impact.

 

More than a few methods have been projected to reduce emissions—such as installing post-combustion cleaning systems, using cleaner fuels, replacing older fuel burners, and optimizing how power is dispatched. Among these, power dispatch optimization within emission limits is often seen as the most practical and cost-effective strategy, especially since the other approaches usually require substantial capital investment and infrastructure changes.

The dual goals of minimizing both fuel cost and emissions often conflict, and must be addressed together to find a balanced, feasible solution. Initially, classical optimization techniques like linear programming were employed, but they struggled with the complexity of real-world systems[1-17]. As a result, more sophisticated methods—like evolutionary and swarm-based algorithms—have gained popularity. These modern techniques are better equipped to navigate the complicated landscape of multi- objective optimization problems [18-25].

 

Over the years, many such methods have been developed and tested for Economic Emission Dispatch (EED) in single-area systems, taking into account real-world constraints [27]. More recently, Multi-Objective Evolutionary Algorithms (MOEVAs) have emerged, providing effective solutions via Pareto-optimal fronts obtained in a single execution, using techniques such as the Strength Pareto Evolutionary Algorithm II (SPEA II), Non- Dominated Sorting Genetic Algorithm (NSGA), its improved version NSGA-II, Multi-Objective Particle Swarm Optimization (MOPSO), and others have shown promising results in this space [26-30].

 

However, modern power systems are rarely isolated. They are usually part of interconnected multi-area networks, where power generation and distribution happen across different regions linked via tie-lines. This adds another layer of complexity. While earlier research mostly focused on profitable dispatch in these multi-area systems, recent attention has turned to Multi-Area Economic Environmental Dispatch Strategies (MAEEDS), which consider both cost and environmental factors [31-48].

 

In MAEEDS, the goal is to determine how much power should be generated in each area, and how much should be exchanged across regions, so that both total cost and emissions are minimized— while still respecting operational constraints like generation capacity, tie-line limits, and demand-supply balance[45-55].

 

Solving such complex, constraint-heavy optimization problems is no easy task. There’s no one-size-fits-all key solution, and choosing the right optimization technique is critical.

 

 

 

 

 

 

 

In this context, the present work focuses on applying NSGA-II to solve the MAEEDS problem, modeled as a nonlinear, constrained, multi-objective optimization challenge.

 

A four-area test system has been used to validate this approach. For comparison, the same system is also analyzed using SPEA

1. Benchmark results from other methods—such as multi- objective particle swarm optimization(PSO), differential evolution(DE), and the Jaya algorithm—are taken from the

 

Results from the study show that NSGA-II provides superior performance in subsequent monetary and ecological goals, making it a strong candidate for real-world MAEEDS applications.

 

 

1. PROBLEM FORMULATION

This MAEED is formulated here as in convention. The set of governing equations and constraints are summed up below

 

Objectives Cost

NA NCg

f1 =ååf1gh (pgh )                                  (1)

g=1 h=1

• SOLUTION METHODOLOGY

 

To solve complex multi-objective and constraint-laden problems like Multi-Area Economic Emission Dispatch (MAEED), the real- coded NDSGA-II has been used in this study. The step-by-step workflow of the algorithm is described below in a simplified and structured manner:

 

Step-by-Step Process of NDSGA-II

 

1. Initialization: The algorithm begins by randomly generating an initial parent population (PAPOP) consisting of N1 members. These represent potential solutions to the optimization problem.

 

2. Fast Non-Dominated Sorting: Each solution in the population is ranked based on non-dominance. Solutions that are not dominated by any others are assigned to the first front (rank 1), the next set to the second front (rank 2), and so on. This helps prioritize better solutions during selection.

 

3. Tournament Selection: From the current population, two individuals are randomly selected and compared based on their front ranking and crowding distance (a measure of solution diversity). The better of the two is chosen and added to the mating pool.

 

4. Crossover and Mutation: Next, the mating pool undergoes Polynomial transmutation and Simulated Binary Crossover (SBX) to generate a new child population (CHPOP). This population is the same size (N1) as the parent population.

 

 

 

f1gh

(pgh

)=agh

+b_gh

pgh

+c_gh ²

5. Merging of Populations: The parent (PAPOP) and child (CHPOP) populations are merged to create a combined population

 

p

gh

+ d_gh´siníe_gh´(p^min–p_gh)ý                            (2)

Emission

 

NA NCg

f1’=ååf1’gh (pgh )                                 (3)

g=1 h=1

f1’gh (pgh ) =agh+bgh pgh+γghp2+ ηgh exp(δgh pgh )           (4)

 

 

Constraints

Production-demand balance

NCg

åpgh =pDg +pLg +åTgo         “gÎNA                       (5)

h=1                                   o,o¹1

Tie line capacity

RESPOP of size 2N1.

 

6. Fast Non-Dominated Sorting on RESPOP: This combined population is then sorted again based on non-dominance. This step includes both parents and children, ensuring elitism (the best solutions are preserved). The algorithm selects the best individuals from the top fronts (starting with the first front, then second, and so on) until the new parent population reaches size N1.

 

If the number of individuals in the last front exceeds the required number of spots, solutions in that front are sorted based on crowding distance (in descending order), and the top solutions are selected to fill the remaining slots.

 

The result is a new generation of PAPOP containing N1 high- quality solutions.

 

7. Repeat Until Termination: The process—tournament selection → crossover → mutation → merging → sorting → selection—is repeated for a predefined number of After each

 

−𝑇𝑚𝑎𝑥 ≤ 𝑇  ≤ 𝑇𝑚𝑎𝑥                                                                                                          (6)     generation, the termination condition is checked.

 

g𝑜

g𝑜

g𝑜

 

Power production capacity

−𝑃^𝑚𝑖𝑛 ≤ 𝑃  ≤ 𝑃^𝑚𝑎𝑥                         “gÎNA, hÎNC_g                   (7)

If the stopping condition is not met, the newly created PAPOP is used as the parent for the next iteration.

 

g𝑜

g𝑜

g𝑜

 

 

 

8. Final Selection: Once the termination criterion is satisfied, the

                                                                                                       best solution is chosen from the first non-dominated front,

 

 

 

representing the most optimal trade-off among objectives.

 

9. End of Execution: At this point, the NDSGA-II algorithm

 

A flowchart representing this entire process is shown in Figure I, followed by a detailed explanation.

 

 

Fig. NDSGAII

RES_POP= PA_POPÈ (Merging of the PA_POP and the CH_POP)

·        F_S denotes     fast    non-dominance   based    sorting (RES_POP).

F_S=(ND_B1, ND_B2, …, ND_Bl)

Where NDB_i denotes a non-dominance based front corresponding to the RES_POP.

PA_POP=fand p = 1

Until |PA_POP| + |FN_P| £N₁ (i.e., the PA_POP fills)

• Assigning of p_dist(FN_p)

RES_POP = PA_POPÈFN_p (Inclusion of p^th non-dominance based facade in the PA_POP) p = p + 1 (examination of the following front in order to include)

·        Sorting (FNp,>)

‘>gets utilized for sorting in the decreasing order.

PA_POP‘ = PA_POP‘ ÈFN_pëé1:(N₁– |PA_POP|)ùû

Selecting the starting (N₁ – |PA_POP|) elements corresponding to

FN_p.

CH_POP’ represents child population corresponding to the PA_POP’.

Figure II delineates flowchart of the STPEA II algorithm.

 

 

Fig. 2 SPEA II

 

 

1. SIMULATION RESULTS

 

Evaluating NDSGA-II on a Multi-Area Power System: Performance and Comparisons: To demonstrate the effectiveness of the NDSGA-II, a four-area power system was used, with each area containing four generators. The model includes complex, non-smooth fuel cost functions and emission characteristics for pollutants. Detailed generator data and tie-line power exchange limits are provided in Appendix Tables A1 through A4. The load demands for areas 1 to 4 were set at 30 MWt, 50 MWt, 40 MWt, and 60 MWt, respectively.

 

The simulations were executed using custom-developed code in MATLAB R2013a. To determine the extreme points of the trade- off surface (between cost and emission), a real-coded genetic algorithm (RECGA) was used, based on the work by Herrera et al. (1998). Results showing area-wise power generation, associated operating costs, and emissions are visualized in Figures 3 through 6.

 

 

 

During the RECGA simulations, parameters were set as follows: population size = 100, number of generations = 500, mutation probability = 0.2, and crossover probability = 0.9. Under the cost-minimization objective, the fuel cost reached

$1,521.92/hour with an emission level of 2.511944 tons/hour. When the focus shifted to minimizing emissions, the cost rose to $2,858.45/hour while emissions dropped to 2.255910 tons/hour. These trade-offs are further illustrated through the convergence curves in Figures 7 and 8.

 

To simultaneously optimize both cost and emissions, the NDSGA-II method was employed. For this scenario, the algorithm parameters were: population size = 20, generations = 50, mutation probability = 0.2, and crossover probability = 0.9. The results revealed a balanced outcome: fuel cost of

$2,306.15/hour and emissions of 2.367206 tons/hour. These values lie between the extremes achieved when cost and emissions were optimized individually, demonstrating the method’s effectiveness in achieving a good compromise.

 

To benchmark NDSGA-II’s performance, another well- regarded method—Strength Pareto Evolutionary Algorithm II (STPEA-II)—was also applied to the same problem. Both algorithms were run with identical settings for a fair comparison: population size = 20, generations = 50, mutation = 0.2, crossover = 0.9.

 

Table I summarizes the best results from both NDSGA-II and STPEA-II, including the most cost-effective and least-polluting solutions, with RECGA results included for reference. Figure 9 presents 20 non-dominated solutions obtained at the final generation by both NDSGA-II and STPEA-II.

 

In Table II, the results from NDSGA-II are compared against those from other widely-used optimization techniques such as Particle Swarm Optimization (PSO), Differential Evolution (DE), and the Jaya Algorithm (JA), based on literature sources. Notably, the minimum fuel cost achieved by NDSGA-II was:

 

10.10% lower than PSO (Wang & Singh, 2009), 8.84% lower than DE (Pandit et al., 2015), and

8.80% lower than JA (Azizipanah-Abarghooee et al., 2016). Similarly, the minimum emission level was reduced by: 28.03% compared to PSO,

5.98% compared to DE, and 4.84% compared to JA.

These significant improvements highlight the strength of NDSGA-II in solving complex multi-objective problems like MAEEDS. One of the key advantages of NDSGA-II is that it avoids favoring any single solution during its search process. Every solution on the Pareto front is treated with equal importance, which minimizes the chances of getting trapped in local optima. As a result, NDSGA-II is capable of uncovering superior solutions that other particle-based optimization methods might miss.

 

 

Fig. 3  Power/cost/emission character for area 1

 

 

Fig. 4  Power/cost/emission character for area 2

 

 

 

Fig. 5 Power-cost-emission characteristics for area 3 (see online version for colours)

 

 

 

 

 

Minimum

TABLE 1 REPRODUCTION RESULTS

 

fuel cost ($/hr) Level (Ton/hr) NDSGA II STPEA II P11 (MWt) 6.2199 0.000524 4.2767 3.7801 P12 (MWt) 0.0500 0.000450 2.4432 1.9565 P13 (MWt) 0.0675 0.117000 5.0288 9.0004 P14 (MWt) 11.6650 0.107682 10.2873 9.0604 P21 (MWt) 8.6814 0.225000 15.6294 13.9816 P22 (MWt) 0.3559 0.108000 9.1385 8.0030 P23 (MWt) 20.0000 0.084093 12.1516 17.5303 P24 (MWt) 17.9797 0.089201 16.1274 15.6876 P31 (MWt) 0.0500 0.084356 11.1128 14.2898 P32 (MWt) 30.0000 0.082287 11.5027 6.8935 P33 (MWt) 8.0818 0.107455 9.2512 3.3478 P34 (MWt) 10.0555 0.115771 11.5776 18.2130 P41 (MWt) 1.4822 0.099000 7.8041 7.1157 P42 (MWt) 14.0633 0.151746 14.1608 13.0403 P43 (MWt) 30.0000 0.129198 21.1647 18.8948 P44 (MWt) 21.2478 0.118237 18.3432 19.2051 T21 (MWt) 6.0000 0.054000 4.4186 4.3529 T13 (MWt) –3.9976 –0.006468 –2.5100 –1.5756 T41 (MWt) 2.0000 –0.016125 1.0355 0.2741 T32 (MWt) 3.5000 0.031500 1.4146 1.0910 T24 (MWt) –5.4830 0.033794 0.0429 1.9407 T34 (MWt) 0.6898 –0.008100 –0.4802 0.0775

Minimum emission

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 6  Power/cost/emission character for area 4

 

 

Fig. 7  Performance curve for the fuel cost

 

 

Fig. 8  Performance for the emission

 

 

 

 

 

Fig. 9 Final optimal pareto

 

 

TABLE II RELATIVE ANALYSIS

 

 

 

V  CONCLUSIONS

 

Strategy of MAEED is a critical optimization challenge in power system operations. This study proposes the use of the Non- Dominated Sorting Genetic Algorithm II (NDSGA-II) to address this bi-objective problem—minimizing both fuel cost and emissions—across a four-area power network, while accounting for real-world constraints such as load-generation balance, generator capacity, and tie-line transmission limits.

 

A detailed comparison between the results obtained using NDSGA- II, Strength Pareto Evolutionary Algorithm II (STPEA-II), and other established methods highlights the effectiveness of both NDSGA-II and STPEA-II for solving such dual-objective optimization tasks. Among these, NDSGA-II demonstrates superior performance in achieving better trade-off solutions in this particular setup.

 

However, it’s important to recognize that the true global optimal

Real-world systems often involve more areas, diverse constraints, and non-linear characteristics, making it uncertain whether the same algorithm will consistently perform best across all scenarios.

 

Therefore, while this work validates NDSGA-II for the chosen case, future research should focus on testing and developing newer, more advanced multi-objective optimization algorithms on a wider range of MAEEDS models. Exploring their adaptability and robustness in more complex, real-world configurations will be key to advancing this field

 

 

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APPENDIX

 

TABLEA1  GENERATOR CHARACTERISTICS (PRODUCTION CAPACITY LIMITS)

 

 

 

 

TABLEA2     GENERATOR CHARACTERISTICS (COST COEFFICIENTS)

 

Generator(GNgh)		agh($/hr)	bgh($/MWt.hr)	cgh($/MWt2.hr)	dgh($/hr)	egh(rad/MWt)
GN11	0		38.53900	0.15247	100	0.084
GN12	0		46.15916	0.10587	150	0.063
GN13	0		40.39655	0.02803	120	0.077
GN14	0		38.30553	0.03546	200	0.042
GN21	0		36.32782	0.02111	300	0.035
GN22	0		38.27041	0.01799	150	0.063
GN23	0		2.000000	0.00375	18.0	0.037
GN24	0		1.750000	0.01750	16.0	0.038
GN31	0		3.000000	0.02500	13.5	0.041
GN32	0		2.000000	0.00375	18.0	0.037
GN33	0		1.000000	0.06250	14.0	0.040
GN34	0		1.750000	0.01950	15.0	0.039
GN41	0		3.250000	0.06250	12.0	0.045
GN42	0		3.250000	0.00834	12.0	0.045
GN43	0		1.750000	0.01950	15.0	0.039
GN44	0		1.000000	0.00834	14.0	0.040

 

 

 

TABLEA3     GENERATOR CHARACTERISTICS (EMISSION COEFFICIENTS)

 

 

 

 

TABLEA4      TIE LINE POWER TRANSFERRING CAPACITY LIMITS

 

 

Tie line (T  ) –T  max (MWt ) T max (MWt ) go T12 T13 –6.0 –4.0 6.0 4.0 T14 –2.0 2.0 T23 –3.5 3.5 T24 –5.5 5.5 T34 –0.9 0.9

go                                          go