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In the present deregulated electricity market, power system congestion is the main complication that an independent system operator (ISO) faces on a regular basis. Transmission line congestion trigger serious problems for smooth functioning in restructured power system causing an increase in the cost of transmission hence affecting market efficiency. Thus, it is of utmost importance for the investigation of various techniques in order to relieve congestion in the transmission network. Generation rescheduling is one of the most efficacious techniques to do away with the problem of congestion. For optimiz ing the congestion cost, this work suggests a hybrid optimization based on two effective algorithms viz Teaching learning-based optimization (TLBO) algorithm and Particle swarm optimization (PSO) algorithm. For binding the constraints, the traditional penalty function technique is incorporated. Modified IEEE 30-bus test system and modified IEEE 57-bus test system are used to inspect the usefulness of the suggested methodology.

In the present world, restructuring and deregulation have allowed equal availability of transmission system to all electricity buyers and sellers [

Congestion problem in an electrical network averts the coveted transaction of power resulting in buyers getting forced to buy power at higher costs from other providers [

Various techniques for CM have been elaborated in the articles provided in recent years for addressing the CM problem. Various methods have been proposed by the researchers like physically curtail transactions, rescheduling of real and reactive power, flexible AC transmission systems (FACTS) along with various optimization techniques. The transmission congestion related economy and cost aspect have been highlighted in [

This paper suggests a hybrid optimization technique established on TLBO and PSO algorithms for solving this congestion management problem. The conventional penalty function technique is also introduced in the system in order to bind the system constraints. The proposed hybrid optimization technique is tested on IEEE 30-bus system and IEEE 57-bus system and the desired results are discussed.

By the technique of rescheduling i.e., increase or decrease in the real power generated by the participating generators, the main objective of congestion management (CM) is achieved while fulfilling the network constraints [

C c = ∑ j ∈ N g ( C k Δ P G j + + D k Δ P G j − ) $ / h (1)

where the coefficients.

C c = Total cost acquired for altering the real power output of participating generators in $/h.

C k = incremented price bids proposed by GENCOs in $/MWh.

D k = decremented price bids proposed by GENCOs in $/MWh.

Δ P G j + = increment in the real power generation of generators in MW.

Δ P G j − = decrement in the real power generation of generators in MW.

Certain inequality and equality constraints are imposed on the above-given optimization problem and are mentioned in the below sections.

In [

P G k − P D k = | V j | | V k | | Y K j | cos ( δ k − δ j − θ k j ) ; j = 1 , 2 , ⋯ , N b (2)

Q G k − Q D k = | V j | | V k | | Y K j | sin ( δ k − δ j − θ k j ) ; j = 1 , 2 , ⋯ , N b (3)

P G k = P G k c + Δ P G k + − Δ P G k − ; k = 1 , 2 , ⋯ , N g (4)

P D j = P D j c ; j = 1 , 2 , ⋯ , N d (5)

where;

P G k = real power produced at bus k.

Q G k = reactive power produced at bus k.

P D k = real power available at bus k.

Q D k = reactive power available at bus k.

V j , V k = voltages at busj and k.

δ j , δ k = voltage angle of busesj and k.

θ k j = admittance angle of the line between bus j and k.

N b , N g , N d = number of buses, generators and loads.

P G k c = real power provided by generator k.

P D j c = real power employed by load bus j.

The Equation (2) represents active power while the Equation (3) represents the reactive power of respective nodes similarly the Equations (4) and (5) are related to power market prices.

The Equations (6)-(9) give the inequality constraints which describe the maximum permissible limits under which the power system components like transformers, transmission lines, and generators must be operated for efficient operation. If these limits are violated, it is consequences are very serious causing serious damage to the power system element.

P G k min ≤ P G k ≤ P G k max , ∀ k ∈ N g (6)

Q G k min ≤ Q G k ≤ Q G k max , ∀ k ∈ N g (7)

( P G k − P G k min ) = Δ P G k min ≤ Δ P G k ≤ Δ P G k max = ( P G k max − P G k ) (8)

V n min ≤ V n ≤ V n max , ∀ n ∈ N l (9)

P i j ≤ P i j max (10)

where max and min represent maximum and minimum values and N_{1} denote the number of transmission lines.

Developed in [

TLBO algorithm is motivated by the process of knowledge sharing in the classroom. The process of teaching-learning is very important to bring fruitful changes in the students. The grades or marks of the learners i.e., the students are considered as the product of the TLBO algorithm. In this approach, the teacher is presumed to be a highly knowledgeable person who imparts his knowledge to his students. Students are considered as learners whose aim is to try to acquire knowledge in order to ameliorate their grades. Thus, if grades got ameliorated, the process of learning gets enhanced. Besides learning from the teacher, the students also improve their learning by interacting with other fellow students in the classroom to enhance their grades.

TLBO is a metaheuristic family member algorithm based on population. In this approach, a batch of students in the class is treated as a population while design variables are taken as the subjects learned by the students in the classroom. The objective of our work i.e., the fitness function is comparable to the grades obtained by students. TLBO algorithm operates in two phases which are elaborated in the below sections.

In the teaching phase, teacher who is presumed as the knowledgeable person who tries to pass on its knowledge to the students in order to help them in achieving better grades. His main objective is to improve the mean knowledge of the students in the class. Let us assume there are “m” design variables which have been assigned to “n” number of students. Let T_{i} denote the outcome of the teacher and M_{i} be the mean outcome at any instanti. The object of the teacher is to match T_{i} to M_{i} and thus M_{new} is described as the new mean. The mean difference is given as:

d i f f e r e n c e m e a n i = r i ( M n e w − T F ⋅ M i ) (11)

where r i is a random number ranging between 0 to1 and TF is the teaching factor having a value of 1 or 2. The coefficient TF is given as:

T F = r o u n d [ 1 + r a n d ( 0 , 1 ) × ( 2 − 1 ) ] (12)

The adjustment to the current solution is accomplished by the equation given below:

X n e w , i = X o l d , i + d i f f e r e n c e m e a n (13)

In the second phase viz. learning phase, the learners improve their learning by communicating with other fellow learners in the classroom to enhance their grades. Knowledge is shared with each other by constantly interacting with other fellow learners. The process of learning is explained as below:

PSO algorithm, developed in 1995 was introduced by Dr. Kennedy and Dr. Eberhart [

V i j + 1 = W V i j + c 1 ∗ r 1 ∗ ( P i j − X i j ) + c 2 ∗ r 2 ∗ ( G B j − X i j ) (14)

X i j + 1 = X i j + V i j + 1 (15)

where the coefficient w represents inertia weight, c_{1} and c_{2} are cognitive and social parameters and value of both c_{1} and c_{2} are equal to 2, r_{1} and r_{2} indicate random numbers lying in the range of 0 and 1, and the coefficient j denotes the iteration number.

Acceleration constant c_{1} helps the particles to attain the local best position quickly while the acceleration constant c_{2} aids the particles to attain the global best position quickly. The appropriate choice of the inertia weight factor “w” helps in quick convergence. Sensibly, the maximum velocity Vmax of each particle should be selected otherwise the particle may not be able to find the best solution [

In our proposed work, each particle consists of N design variables where N gives the total number of participating generators in CM. Each design variable serves as the output of the generators indulging in congestion management. The objective function generally treated as the fitness function is used to assess the pre-eminence of the particle. To meet with the system constraints, the evolution of the particles based on the fitness and choice of global best (GB) and local best (P_{i}) are used. The conventional method of penalty functions is used in which the inequality constraints are changed into penalty factors and the effect of these penalty factors is taken into account by adding them in the fitness function [

Minimize F F = C c + P F 1 × ∑ i = 1 o v l ( P i j − P i j max ) 2 + P F 2 × ∑ j = 1 V B ( Δ V j ) 2 + P F 3 × ( Δ P G ) 2 (16)

where,

Δ V j = { ( V j min − V j ) ; if V j ≤ V j min ( V j − V j max ) ; if V j ≥ V j max (17)

Δ P G = { ( P G min − P G ) ; if P G ≤ P G min ( P G − P G max ) ; if P G ≥ P G max (18)

Here, FF represents the fitness or evaluation function whose minimization is our objective, ovl is an array of overloaded lines, VB is the group of load buses violating voltage limits and PF_{i} (i = 1 to 3) are the penalty factors. The general value of penalty factors taken throughout is equal to 10,000.

The strategy for applying the hybrid optimization technique for congestion management solution is mentioned below:

Step 1: Generate an initial population of the particles randomly within the limits. The dimensions of each particle generated are equal to N where N represents the number of generators. The value of N gives the total of rescheduling needed by participating generators for managing the CM problem.

Step 2: The selection of the teacher is done by evaluating the fitness function of the learners. Among learners, one having the best fitness value is being selected as the teacher (Teaching phase).

Step 3: The values of position best (X_{i}) and global best (GB) are determined which provide a new fitness (Expert).

Step 4: New fitness (Expert) is compared with the previously attained best fitness function (Teacher). The particle having the best fitness value is selected (as a teacher) while the other is rejected. Position and velocity of the individual particles are updated until the best particle (Teacher) is obtained.

Step 5: The remaining learners are modified in the quotation with the mean (teacher). From the remaining learners, the algorithm randomly selects two learners for their fitness values to be compared. The learner having the best fitness is selected while rejecting the other (Learning phase).

Step 6: Repeat step 5, until from the remaining learners, no two learners are left to repeat the test.

Step 7: The program will be halted in the case when the count of iterations is exceeded else it will go to step 2.

The TLBO-PSO hybrid algorithm for obtaining the solution for congestion management problem is realized employing MATLAB (version 9.4.0) software on a CPU powered by Intel Core i3 processor operating @ 1.80 GHz with 4 GB of RAM. Investigation of the proposed method is done by executing it on the modified IEEE 30 bus and modified IEEE 57 test system. The generator, bus and line data of the test bus systems are given in Appendix A (Tables A1-A6). Load buses have been assigned number 1, generator buses as number 2 while the slack bus has been assigned number 3. The performance of suggested hybrid technique is contrasted with [

Incremental and decremental price bids proposed by GENCOs for modifying their generation are also given in Appendix A (TableA1 and TableA4). The incremental cost is assumed more than marginal cost value while the decremental cost is assumed less than the marginal cost value. The significant observations of the work are presented below.

To validate our work, we have firstly chosen modified IEEE 30 bus test system. This bus system combines generator buses six in number, load buses twenty-four in number, and transmission lines forty-one in number. The total active power of the load is 283.4 MW, and the total reactive power is 126.2 MVAR. PG and PD are taken as the values for generation and load are also given in Appendix A as the initial market clearing values. In a power system, contingencies are mainly due to the line outages and hence for the purpose of simulation, we have taken line outages along with load variations. Two cases are studied for this purpose:

Case 1.1: Considering the unavailability of the line between bus 1&2 with normal loading.

When the line between bus 1&2 is being outed, the lines between bus 1&7, and 7&8 are overloaded. For obtaining the information about the amount of overloading in the congested lines, Newton-Raphson algorithm of power flow [

The results obtained by implementing the TLBO-PSO hybrid optimization technique for managing the CM problem for case 1.1 are mentioned in

Case No. | Contingency type | Congested lines | Power flow in line (MW) | Overload % | Total power violation (MW) |
---|---|---|---|---|---|

Case 1.1 | Unavailability of the line between bus 1&2 | 1 - 7 7 - 8 | 150.46 138.78 | 15.74 6.75 | 29.24 |

Case 1.2 | unavailability of the line between bus 1&7 and load increment of 50% at all buses | 1 - 2 2 - 8 2 - 9 | 202.57 66.11 69.46 | 55.82 1.70 6.86 | 92.745 |

Parameters | Approaches | ||
---|---|---|---|

Hybrid TLBO-PSO [Proposed] | TLBO [ | PSO [ | |

Congestion cost ($/h) | 100.69 | 494.66 | 538.95 |

ΔP_{G}_{1} | −16.3312 | −8.5876 | −8.6123 |

ΔP_{G}_{2} | −4.0577 | +12.9855 | +10.4059 |

ΔP_{G}_{3} | −2.0659 | +0.4598 | +3.0344 |

ΔP_{G}_{4} | −7.2759 | +0.7289 | +0.0170 |

ΔP_{G}_{5} | −2.5654 | −0.0093 | +0.8547 |

ΔP_{G}_{6} | −2.6203 | +0.3988 | −0.0122 |

Total power rescheduled (MW) | 34.9165 | 23.169 | 22.936 |

It is worthy to note that the solution obtained from the suggested method as given in

Case 1.2: Considering the unavailability of the transmission line between bus 1&7 and load increment of 50% at all buses.

When the line between bus 1&7 is being outed and 50% increment in load at each bus is done, the effect is that the lines between bus 1&2, bus 2&8 and bus 2&9 are overloaded. The actual power flowing in these lines is 202.57 MW, 66.11 MW, and 69.46 MW, respectively, while 130 MW is the net power flow limit in line between bus 1&2 and for lines between buses 2&8 and 2&9, it is 65 MW for both. Thus, the total power violation encountered is 92.745 MW (

mentioned in

Thus, it is noticeable that the cost of managing congestion is lower for the proposed hybrid technique when compared with the other methods mentioned. The total losses in the system have also decreased to 9.8123 MW from the initial value of 15.2915 MW during congestion. The proposed hybrid algorithm-based convergence of fitness function with the iteration number is shown in

Further to validate our work, we have also chosen a modified IEEE 57 bus test

Parameters | Approaches | ||
---|---|---|---|

Hybrid TLBO-PSO [Proposed] | TLBO [ | PSO [ | |

Congestion cost ($/h) | 1347.5 | 5306.5 | 5335.5 |

ΔP_{G}_{1} | +71.0241 | −8.5876 | NR |

ΔP_{G}_{2} | −15.9882 | +75.65 | NR |

ΔP_{G}_{3} | −7.1258 | +0.012 | NR |

ΔP_{G}_{4} | −5.5115 | +34.357 | NR |

ΔP_{G}_{5} | −23.2332 | +31.4791 | NR |

ΔP_{G}_{6} | −17.1719 | +17.83 | NR |

Total power rescheduled (MW) | 140.0547 | 168.088 | 168.03 |

system. This bus system combines generator buses seven in number, load buses fifty in number, and transmission lines eighty in number. The total active power of the load is 1250.8 MW, and the total reactive power is 336 MVAR. Two cases are also studied for this purpose. For obtaining the information about the measure of overloading in the congested lines, Newton-Raphson power flow [

Case 2.1: Simulating overload of lines between buses 5&6 and 6&12 by reducing their capacity.

In the present case, the real power flowing in the line between bus 5&6 is 184.62 MW and in line between bus 6&12 is 46.985 MW. The baseload power limit of the line between bus 5&6 is 200 MW while that of the line between bus 6&12 is 50 MW. To perform overload simulation, the limit of the line between bus 5&6 is taken as 175 MW while that of the line between bus 6&12 as 35 MW.

The effect of reducing the capacity of lines is that the line between bus 5&6 gets overloaded by 5.49% while the line between bus 6&12 gets overloaded by 34.24% and net power violation encountered is 21.605 MW. To manage this overload of 21.605 MW, optimal rescheduling of generation is accomplished using the proposed hybrid algorithm. The results obtained are tabulated in

From

Case 2.2: Simulating overload of the line between bus 2&3 by reducing its capacity.

To simulate the overload in this case, the capacity of the line between bus 2&3

Case No. | Contingency type | Congested lines | Power flow in line (MW) | percentage overload | Net power violation (MW) |
---|---|---|---|---|---|

Case 2.1 | Simulating overload by capacity reduction of the lines between buses 5&6 and 6&12. | 5 - 6 6 - 12 | 184.62 46.985 | 5.49 34.24 | 21.605 |

Case 2.2 | Simulating overload by capacity reduction of the-lines between buses 5&6 and 6&12. | 2 - 3 | 38.6 | 93 | 18.6 |

Parameters | Approaches | ||
---|---|---|---|

Hybrid TLBO-PSO [Proposed] | TLBO [ | PSO [ | |

Congestion cost ($/h) | 2787.70 | 5981.3 | 6951.9 |

ΔP_{G}_{1} | −297.5807 | +38.1219 | +23.135 |

ΔP_{G}_{2} | −12.1838 | +0.7801 | +12.447 |

ΔP_{G}_{3} | −3.275 | +9.0766 | +7.493 |

ΔP_{G}_{4} | −2.441 | −0.0179 | −5.385 |

ΔP_{G}_{5} | +28.7574 | −432018 | −81.216 |

ΔP_{G}_{6} | +28.5324 | −29.9082 | 0 |

ΔP_{G}_{7} | −45.4485 | +22.8093 | +39.03 |

Total power rescheduled (MW) | 418.2188 | 143.9158 | 168.70 |

is reduced from an outset value of 85 MW to an ending value of 20 MW. The baseload power flow in the line is 38.6 MW and for that reason, the line is overloaded by 93%. The net power violation in the line is 18.6 MW. To manage this congestion of 18.6 MW, optimal rescheduling of generation is done according to the suggested method. The results obtained along with other comparative methods are presented in

From

Parameters | Approaches | ||
---|---|---|---|

Hybrid TLBO-PSO [Proposed] | TLBO [ | PSO [ | |

Congestion cost ($/h) | 939.3927 | 2916.4 | 3117.6 |

ΔP_{G}_{1} | −429.3075 | −1.0174 | NR |

ΔP_{G}_{2} | +39.0969 | −24.6365 | NR |

ΔP_{G}_{3} | −4.6236 | +36.0991 | NR |

ΔP_{G}_{4} | −27.158 | −6.2282 | NR |

ΔP_{G}_{5} | −2.0455 | −0.2811 | NR |

ΔP_{G}_{6} | +3.2447 | −1.2540 | NR |

ΔP_{G}_{7} | −29.7139 | −2.5732 | NR |

Total power rescheduled (MW) | 535.1899 | 72.089 | 76.314 |

The present paper demonstrates a TLBO-PSO hybrid technique of CM employing the optimal rescheduling of power generation units in the pool-based electricity market. Transmission line outage due to overload and sudden variation in the load are considered for validating the effectiveness of this work. This technique has been evaluated on modified IEEE 30 bus and modified IEEE 57 bus test systems successfully. The results achieved are correlated with [

The authors declare no conflicts of interest regarding the publication of this paper.

Ul Bashir, M., Ul Hijaz Paul, W., Ahmad, M., Ali, D. and Ali, Md.S. (2021) An Efficient Hybrid TLBO-PSO Approach for Congestion Management Employing Real Power Generation Rescheduling. Smart Grid and Renewable Energy, 12, 113-135. https://doi.org/10.4236/sgre.2021.128008

Tables A1-A3 presents the generator data, bus data and line data for the modified IEEE 30 bus test system while Tables A4-A6 give the generator, bus, and line data for the modified IEEE 57 bus test system. Price bids submitted by GENCOs for the modified IEEE 30 bus and modified IEEE 57 bus test system are also presented in TableA1 and TableA4, respectively.

Bus no. | P G min (MW) | P G max (MW) | P G C (MW) | Price bids submitted by GENCOs | |
---|---|---|---|---|---|

C_{k} | D_{k} | ||||

1 | 0 | 360.2 | 138.59 | 22 | 18 |

2 | 20 | 140 | 57.56 | 21 | 19 |

3 | 15 | 100 | 24.56 | 42 | 38 |

4 | 10 | 100 | 35.00 | 43 | 37 |

5 | 10 | 100 | 17.93 | 43 | 35 |

6 | 12 | 100 | 16.91 | 41 | 39 |

Bus No. | Bus code | Voltage (V) | MW | MVAR | Bus no. | Bus code | Voltage (V) | MW | MVAR |
---|---|---|---|---|---|---|---|---|---|

1 | 3 | 1.06 | 0 | 0 | 16 | 1 | 1.00 | 3.5 | 1.8 |

2 | 2 | 1.043 | 21.7 | 12.7 | 17 | 1 | 1.00 | 9.0 | 5.8 |

3 | 2 | 1.01 | 94.2 | 19.0 | 18 | 1 | 1.00 | 3.2 | 0.9 |

4 | 2 | 1.01 | 30.0 | 30.0 | 19 | 1 | 1.00 | 9.5 | 3.4 |

5 | 2 | 1.082 | 0.0 | 0.0 | 20 | 1 | 1.00 | 2.2 | 0.7 |

6 | 2 | 1.071 | 0.0 | 0.0 | 21 | 1 | 1.00 | 17.5 | 11.2 |

7 | 1 | 1.00 | 2.4 | 1.2 | 22 | 1 | 1.00 | 0.0 | 0.0 |

8 | 1 | 1.01 | 7.6 | 1.6 | 23 | 1 | 1.00 | 3.2 | 1.6 |

9 | 1 | 1.00 | 0.0 | 0.0 | 24 | 1 | 1.00 | 8.7 | 6.7 |

10 | 1 | 1.00 | 22.8 | 10.9 | 25 | 1 | 1.00 | 0.0 | 0.0 |

11 | 1 | 1.082 | 0.0 | 0.0 | 26 | 1 | 1.00 | 3.5 | 2.3 |

12 | 1 | 1.00 | 5.8 | 2.0 | 27 | 1 | 1.00 | 0.0 | 0.0 |

13 | 1 | 1.071 | 11.2 | 7.5 | 28 | 1 | 1.00 | 0.0 | 0.0 |

14 | 1 | 1.00 | 6.2 | 6.2 | 29 | 1 | 1.00 | 2.4 | 0.9 |

15 | 1 | 1.00 | 8.2 | 2.5 | 30 | 1 | 1.00 | 10.6 | 1.9 |

Line no. | Between Buses | R (p.u) | X (p.u) | B (p.u) | Line Limit (MW) | Line no. | Between Buses | R (p.u) | X (p.u) | B (p.u) | Line Limit (MW) |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1 - 2 | 0.0192 | 0.0575 | 0.0264 | 130 | 13 | 11 - 5 | 0.00 | 0.2080 | 0.00 | 65 |

2 | 1 - 7 | 0.0452 | 0.1652 | 0.0204 | 130 | 14 | 11 - 12 | 0.00 | 0.1100 | 0.00 | 65 |

3 | 2 - 8 | 0.0570 | 0.1737 | 0.0184 | 65 | 15 | 8 - 13 | 0.00 | 0.2560 | 0.00 | 65 |

4 | 7 - 8 | 0.0132 | 0.0379 | 0.0042 | 130 | 16 | 13 - 6 | 0.00 | 0.1400 | 0.00 | 65 |

5 | 2 - 3 | 0.0472 | 0.1983 | 0.0209 | 130 | 17 | 13 - 14 | 0.1231 | 0.2559 | 0.00 | 32 |

6 | 2 - 9 | 0.0581 | 0.1763 | 0.0187 | 65 | 18 | 13 - 15 | 0.0662 | 0.1304 | 0.00 | 32 |

7 | 8 - 9 | 0.0119 | 0.0414 | 0.0045 | 90 | 19 | 13 - 16 | 0.0945 | 0.1987 | 0.00 | 32 |

8 | 3 - 10 | 0.0460 | 0.1160 | 0.0102 | 70 | 20 | 14 - 15 | 0.2210 | 0.1997 | 0.00 | 16 |

9 | 9 - 10 | 0.0267 | 0.0820 | 0.0085 | 130 | 21 | 16 - 17 | 0.0824 | 0.1923 | 0.00 | 16 |

10 | 9 - 4 | 0.0120 | 0.0420 | 0.0045 | 32 | 22 | 15 - 18 | 0.1073 | 0.2185 | 0.00 | 16 |

11 | 9 - 11 | 0.00 | 0.2080 | 0.00 | 65 | 23 | 18 - 19 | 0.0639 | 0.1292 | 0.00 | 16 |

12 | 9 - 12 | 0.00 | 0.5560 | 0.00 | 32 | 24 | 19 - 20 | 0.0340 | 0.0680 | 0.00 | 32 |

25 | 12 - 20 | 0.0936 | 0.2090 | 0.00 | 32 | 34 | 25 - 26 | 0.2544 | 0.3800 | 0.00 | 16 |

26 | 12 - 17 | 0.0324 | 0.0845 | 0.00 | 32 | 35 | 25 - 27 | 0.1093 | 0.2087 | 0.00 | 16 |

27 | 12 - 21 | 0.0348 | 0.0749 | 0.00 | 32 | 36 | 28 - 27 | 0.0000 | 0.3960 | 0.00 | 65 |

28 | 12 - 22 | 0.0727 | 0.1499 | 0.00 | 32 | 37 | 27 - 29 | 0.2198 | 0.4153 | 0.00 | 16 |

29 | 21 - 22 | 0.0116 | 0.0236 | 0.00 | 32 | 38 | 27 - 30 | 0.3202 | 0.6027 | 0.00 | 16 |

30 | 15 - 23 | 0.1000 | 0.2020 | 0.00 | 16 | 39 | 29 - 30 | 0.2399 | 0.4533 | 0.00 | 16 |

31 | 22 - 24 | 0.1150 | 0.1790 | 0.00 | 16 | 40 | 4 - 28 | 0.0636 | 0.2000 | 0.0214 | 32 |

32 | 23 - 24 | 0.1320 | 0.2700 | 0.00 | 16 | 41 | 9 - 28 | 0.0169 | 0.0599 | 0.065 | 32 |

33 | 24 - 25 | 0.1885 | 0.3292 | 0.00 | 16 |

Bus no. | P G min (MW) | P G max (MW) | P G C (MW) | Price bids submitted by GENCOs | |
---|---|---|---|---|---|

C_{k} | D_{k} | ||||

1 | 0 | 575.88 | 146.39 | 44 | 41 |

2 | 0 | 100 | 87.55 | 43 | 39 |

3 | 0 | 140 | 41.97 | 42 | 38 |

4 | 0 | 100 | 89.67 | 43 | 37 |

5 | 0 | 550 | 461.21 | 42 | 39 |

6 | 0 | 100 | 100 | 44 | 40 |

7 | 0 | 410 | 344.95 | 44 | 41 |

Bus No. | Bus code | Voltage (V) | MW | MVAR | Bus no. | Bus code | Voltage (V) | MW | MVAR |
---|---|---|---|---|---|---|---|---|---|

1 | 3 | 1.04 | 55 | 17 | 30 | 1 | 1.00 | 3.6 | 1.8 |

2 | 2 | 1.01 | 3.0 | 88 | 31 | 1 | 1.00 | 5.8 | 2.9 |

3 | 2 | 0.99 | 41 | 21 | 32 | 1 | 1.00 | 1.6 | 0.8 |

4 | 2 | 0.98 | 75 | 2.0 | 33 | 1 | 1.00 | 3.8 | 1.9 |

5 | 2 | 1.01 | 150 | 22 | 34 | 1 | 1.00 | 0.0 | 0.0 |

6 | 2 | 0.98 | 121 | 26 | 35 | 1 | 1.00 | 6.0 | 3.0 |

7 | 2 | 1.02 | 377 | 24 | 36 | 1 | 1.00 | 0.0 | 0.0 |

8 | 1 | 1.00 | 0.0 | 0.0 | 37 | 1 | 1.00 | 0.0 | 0.0 |

9 | 1 | 1.00 | 13.0 | 4.0 | 38 | 1 | 1.00 | 14 | 7.0 |

10 | 1 | 1.00 | 0.0 | 0.0 | 39 | 1 | 1.00 | 0.0 | 0.0 |

11 | 1 | 1.00 | 5.0 | 2.0 | 40 | 1 | 1.00 | 0.0 | 0.0 |

12 | 1 | 1.00 | 0.0 | 0.0 | 41 | 1 | 1.00 | 6.3 | 3.0 |

13 | 1 | 1.00 | 18 | 2.3 | 42 | 1 | 1.00 | 7.1 | 4.0 |

14 | 1 | 1.00 | 10.5 | 5.3 | 43 | 1 | 1.00 | 2.0 | 1.0 |

15 | 1 | 1.00 | 22 | 5.0 | 44 | 1 | 1.00 | 12 | 1.8 |

16 | 1 | 1.00 | 43 | 3.0 | 45 | 1 | 1.00 | 0.0 | 0.0 |

17 | 1 | 1.00 | 42 | 8.0 | 46 | 1 | 1.00 | 0.0 | 0.0 |

18 | 1 | 1.00 | 27.2 | 9.8 | 47 | 1 | 1.00 | 29.7 | 11.6 |

19 | 1 | 1.00 | 3.3 | 0.6 | 48 | 1 | 1.00 | 0.0 | 0.0 |

20 | 1 | 1.00 | 2.3 | 1.0 | 49 | 1 | 1.00 | 18 | 8.5 |

21 | 1 | 1.00 | 0.0 | 0.0 | 50 | 1 | 1.00 | 21 | 10.5 |

22 | 1 | 1.00 | 0.0 | 0.0 | 51 | 1 | 1.00 | 18 | 5.3 |

23 | 1 | 1.00 | 6.3 | 2.1 | 52 | 1 | 1.00 | 4.9 | 2.2 |

24 | 1 | 1.00 | 0.0 | 0.0 | 53 | 1 | 1.00 | 20 | 10 |

25 | 1 | 1.00 | 6.3 | 3.2 | 54 | 1 | 1.00 | 4.1 | 1.4 |

26 | 1 | 1.00 | 0.0 | 0.0 | 55 | 1 | 1.00 | 6.8 | 3.4 |

27 | 1 | 1.00 | 9.3 | 0.5 | 56 | 1 | 1.00 | 7.6 | 2.2 |

28 | 1 | 1.00 | 4.6 | 2.3 | 57 | 1 | 1.00 | 6.7 | 2.0 |

29 | 1 | 1.00 | 17 | 2.6 |

Line no. | Between Buses | R (p.u) | X (p.u) | B (p.u) | Line Limit (MW) | Line no. | Between Buses | R (p.u) | X (p.u) | B (p.u) | Line Limit (MW) |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1 - 2 | 0.0083 | 0.028 | 0.129 | 150 | 40 | 28 - 29 | 0.0418 | 0.0587 | 0.00 | 100 |

2 | 2 - 3 | 0.0298 | 0.085 | 0.0818 | 85 | 41 | 10 - 29 | 0.000 | 0.0648 | 0.00 | 100 |

3 | 3 - 8 | 0.0112 | 0.0366 | 0.038 | 100 | 42 | 25 - 30 | 0.1350 | 0.202 | 0.00 | 100 |

4 | 8 - 9 | 0.0625 | 0.132 | 0.0258 | 100 | 43 | 30 - 31 | 0.3260 | 0.497 | 0.00 | 100 |

5 | 8 - 4 | 0.0430 | 0.148 | 0.0348 | 50 | 44 | 31 - 32 | 0.5070 | 0.755 | 0.00 | 100 |

6 | 4 - 10 | 0.0200 | 0.102 | 0.0276 | 40 | 45 | 32 - 33 | 0.0392 | 0.036 | 0.00 | 100 |

7 | 4 - 5 | 0.0339 | 0.173 | 0.047 | 100 | 46 | 34 - 32 | 0.0000 | 0.953 | 0.00 | 100 |

8 | 5 - 6 | 0.0099 | 0.0505 | 0.0548 | 200 | 47 | 34 - 35 | 0.0520 | 0.078 | 0.0032 | 100 |

9 | 6 - 11 | 0.0369 | 0.1679 | 0.044 | 50 | 48 | 35 - 36 | 0.0430 | 0.0537 | 0.0016 | 100 |

10 | 6 - 12 | 0.0258 | 0.0848 | 0.0218 | 50 | 49 | 36 - 37 | 0.0290 | 0.0366 | 0.00 | 100 |

11 | 6 - 7 | 0.0648 | 0.295 | 0.0772 | 50 | 50 | 37 - 38 | 0.0651 | 0.1009 | 0.002 | 100 |

12 | 6 - 13 | 0.0481 | 0.158 | 0.0406 | 50 | 51 | 37 - 39 | 0.0239 | 0.0379 | 0.00 | 100 |

13 | 13 - 14 | 0.0132 | 0.0434 | 0.011 | 50 | 52 | 36 - 40 | 0.0300 | 0.0466 | 0.00 | 100 |

14 | 13 - 15 | 0.0269 | 0.0869 | 0.023 | 100 | 53 | 22 - 38 | 0.0192 | 0.0295 | 0.00 | 100 |

15 | 1 - 15 | 0.00178 | 0.091 | 0.0988 | 200 | 54 | 12 - 41 | 0.0000 | 0.749 | 0.00 | 100 |

16 | 1 - 16 | 0.0454 | 0206 | 0.0546 | 100 | 55 | 41 - 42 | 0.2070 | 0.352 | 0.00 | 100 |

17 | 1 - 17 | 0.0238 | 0.108 | 0.0286 | 100 | 56 | 41 - 43 | 0.0000 | 0.412 | 0.00 | 100 |

18 | 3 - 15 | 0.0162 | 0.053 | 0.0544 | 100 | 57 | 38 - 44 | 0.0289 | 0.0585 | 0.002 | 100 |

19 | 8 - 18 | 0.0000 | 0.555 | 0.00 | 100 | 58 | 15 - 45 | 0.0000 | 0.1042 | 0.00 | 100 |

20 | 8 - 18 | 0.0000 | 0.43 | 0.00 | 100 | 59 | 14 - 46 | 0.0000 | 0.0735 | 0.00 | 100 |

21 | 9 - 4 | 0.0302 | 0.0641 | 0.0124 | 100 | 60 | 46 - 47 | 0.0230 | 0.068 | 0.0032 | 100 |

22 | 10 - 5 | 0.0139 | 0.0712 | 0.0194 | 100 | 61 | 47 - 48 | 0.0182 | 0.0233 | 0.00 | 100 |

23 | 11 - 7 | 0.0277 | 0.1262 | 0.0328 | 100 | 62 | 48 - 49 | 0.0834 | 0.129 | 0.0048 | 100 |

24 | 12 - 13 | 0.0233 | 0.0732 | 0.0188 | 100 | 63 | 49 - 50 | 0.0801 | 0.128 | 0.00 | 100 |

25 | 7 - 13 | 0.0178 | 0.058 | 0.0604 | 100 | 64 | 50 - 51 | 0.1386 | 0.22 | 0.00 | 100 |

26 | 7 - 16 | 0.0180 | 0.0813 | 0.0216 | 100 | 65 | 11 - 51 | 0.0000 | 0.0712 | 0.00 | 100 |

27 | 7 - 17 | 0.0397 | 0.179 | 0.0476 | 100 | 66 | 13 - 49 | 0.0000 | 0.191 | 0.00 | 100 |

28 | 14 - 15 | 0.0171 | 0.0547 | 0.0148 | 100 | 67 | 29 - 52 | 0.1442 | 0.187 | 0.00 | 100 |

29 | 18 - 19 | 0.4610 | 0.685 | 0.00 | 100 | 68 | 52 - 53 | 0.0762 | 0.0984 | 0.00 | 100 |

30 | 19 - 20 | 0.2830 | 0.434 | 0.00 | 100 | 69 | 53 - 54 | 0.1878 | 0.232 | 0.00 | 100 |

31 | 21 - 20 | 0.0000 | 0.7767 | 0.00 | 100 | 70 | 54 - 55 | 0.1732 | 0.2265 | 0.00 | 100 |

32 | 21 - 22 | 0.0736 | 0.117 | 0.00 | 100 | 71 | 12 - 43 | 0.0000 | 0.153 | 0.00 | 100 |

33 | 22 - 23 | 0.0099 | 0.0152 | 0.00 | 100 | 72 | 44 - 45 | 0.0624 | 0.1242 | 0.004 | 100 |

34 | 23 - 24 | 0.1660 | 0.256 | 0.0084 | 100 | 73 | 40 - 56 | 0.0000 | 1.195 | 0.00 | 100 |

35 | 24 - 25 | 0.0000 | 1.182 | 0.00 | 100 | 74 | 56 - 41 | 0.5530 | 0.549 | 0.00 | 100 |

36 | 24 - 25 | 0.0000 | 1.23 | 0.00 | 100 | 75 | 56 - 42 | 0.2125 | 0.354 | 0.00 | 100 |

37 | 24 - 26 | 0.0000 | 0.0473 | 0.00 | 100 | 76 | 39 - 57 | 0.0000 | 1.355 | 0.00 | 100 |

38 | 26 - 27 | 0.1650 | 0.254 | 0.00 | 100 | 77 | 57 - 56 | 0.1740 | 0.26 | 0.00 | 100 |

39 | 27 - 28 | 0.0618 | 0.0954 | 0.00 | 100 |