An Improved DA-PSO Optimization Approach for Unit Commitment Problem
Abstract
:1. Introduction
2. Formulation of the UC Problem
2.1. Objective Function
2.2. Constraints
2.2.1. Power Balance Constraint
2.2.2. Spinning Reserve Constraint
2.2.3. Generation Limit Constraints
2.2.4. Minimum Up-Time Constraint
2.2.5. Minimum Down-time Constraint
3. Overview of DA-PSO Optimization Algorithm and Related Algorithms
3.1. DA
3.2. PSO
3.3. DA-PSO
4. An Improved DA-PSO Optimization Approach (iDA-PSO) for UC Problem
4.1. An Approach of Improving DA-PSO to Solve a Binary Problem
4.2. Priority List
4.3. Spinning Reserve Constraint Satisfaction
- Step 1.
- At each hour t, calculate αi by using (26) for all uncommitted unit at hour t, and sort them in an ascending order.
- Step 2.
- Calculate the spinning reserve requirement at t as in (5)
- Step 3.
- If the result from step 2 satisfies the spinning reserve constraint, go to step 5; otherwise, go to step 4.
- Step 4.
- Commit one uncommitted unit with the least αi from step 1.
- Step 5.
- If t < T, t = t + 1 and go to step 1; otherwise, stop this process.
4.4. Minimum Up-Time and Down-Time Constraints Satisfaction
- Step 1.
- At each hour t, calculate the accumulated current on/off hours of the ith unit at hour t, Tti,cur by referring to the accumulated hours of the previous state, Tti,prev. If t = 1, Tti, prev = initial state; else Tti,prev = accumulated on/off hours of the previous state, Tt−1i,cur.
- Step 2.
- At each unit i
- Step 2.1.
- If uit = 1 and Tti,prev ≥ 1, Tti,cur = Tti,prev + 1
- Step 2.2.
- If uit = 1 and Tti,prev ≤ −MDTi, Tti,cur = 1
- Step 2.3.
- If uit = 0 and Tti,prev ≤ −1, Tti,cur = Tti,prev − 1
- Step 2.4.
- If uit = 0 and Tti,prev ≥ MUTi, Tti,cur = −1
- Step 2.5.
- If uit = 0 and Tti,prev < MUTi, set uit = 1 and Tti,cur = Tti,prev + 1
- Step 2.6.
- If uit = 1 and Tti,prev > −MDTi, set uit = 0 and Tti,cur = Tti,prev − 1
- Step 3.
- If i < Ng, i =i + 1 and go to step 2; otherwise, go to step 4.
- Step 4.
- If t < T, t = t + 1 and go to step 1; otherwise, stop this process.
4.5. Economic Dispatch
- Step 1.
- At each hour t, check if , go to step 2; otherwise, go to step 8.
- Step 2.
- Calculate αi by using (26) for all committed unit at hour t, sort them in a descending order, and name it descending order list (DOLt). Name the first unit in the DOLt to be the lowest priority (LPt).
- Step 3.
- Compute the excessive spinning reserve by .
- Step 4.
- Check if ExcessReserve is higher than the maximum power output of the LPt go to step 5; otherwise, go to step 6.
- Step 5.
- Check if decommitting the LPt does not violate its minimum up- or down-time constraint, decommit the LPt, and update the Tti,cur.
- Step 6.
- Delete the LPt from the DOLt.
- Step 7.
- Check if the DOLt is not empty, set the new LPt to be the first unit of the DOLt and go to step 3; otherwise, go to step 13.
- Step 8.
- Calculate αi by using (26) for all uncommitted units at hour t, sort them in an ascending order, and name it ascending order list (AOLt). Name the first unit in the AOLt to be the highest priority (HPt).
- Step 9.
- Compute the lacking spinning reserve by .
- Step 10.
- Check if the LackReserve < 0, go to step 11; otherwise, go to step 13.
- Step 11.
- Check if committing the HPt does not violate its minimum up- or down-time constraint, commit the HPt, and update the Tti,cur.
- Step 12.
- Let the HPt be the next unit in the AOLt, and go to step 9.
- Step 13.
- Solve the ED problem by a lambda-iteration method, which finds the optimal value of Ptgi of all on-line units to meet the load demand while satisfying the power balance and generation limit constraints.
- Step 14.
- If t < T, t = t + 1 and go to step 1; otherwise, stop this process.
4.6. The Application of the iDA-PSO Approach for Solving the UC Problem
- Step 1.
- Produce the initial population of dragonflies and particles by randomly generating them to be on or off status (1 or 0) over the time horizon T.
- Step 2.
- Calculate the objective function of each dragonfly, and set the best one to be the first personal best (Xpbesti) of PSO.
- Step 3.
- Compute the coefficients used in DA (s, a, c, f, e and ω).
- Step 4.
- Update the food source and enemy of DA.
- Step 5.
- Compute the representative behavior factors of DA, namely S, A, C, F, and E by (9)–(13).
- Step 6.
- If each dragonfly consists of at least one neighboring, update the step vector (ΔX) of a dragonfly by (14), and check whether any element of each population violates its limit, then move ΔX of that population into its minimum/maximum limit. Then, update the position of dragonfly (XDA) by sigmoid function as in (25), as described in Section 4.1. However, if a dragonfly does not have any neighboring, calculate the Levy flight as in (18) and multiply it by XDA, then update XDA by the sigmoid function, (25), and set ΔX to be zero.
- Step 7.
- Set the best position provided by DA to be the global best position of PSO (Xgbest).
- Step 8.
- Update the velocity of each particle (V) by (22), and check whether any element of each population violates its limit, then move V of that population into its minimum/maximum limit. Then, apply the sigmoid function, Equation (25), to update the position of each particle (XPSO) as described in Section 4.1.
- Step 9.
- Change the status of units of the newly generated population to satisfy the spinning reserve constraint as presented in Section 4.3.
- Step 10.
- Repair the newly generated population violating the minimum up- or down-time constraint as explained in Section 4.4.
- Step 11.
- Solve ED problem as expressed in Section 4.5 to find the optimal Ptgi of all on-line units of the newly generated population.
- Step 12.
- Calculate start-up costs, which are hot or cold starts, of the units started in each hour by comparing with the status of the previous hour. For the first hour, compare the status with that of the initial status of each unit.
- Step 13.
- Calculate the objective function of the newly generated population.
- Step 14.
- Test whether any obtained objective function from an individual is better than that of the previous Xpbesti, then the newly generated population is set to be a new Xpbesti. Likewise, if the best Xpbesti is better than Xgbest, that Xpbesti is set to be new Xgbest.
- Step 15.
- If the maximum number of iterations is not reached, go to step 3; otherwise, stop the implementation and the optimal solution of UC problem is the particle with the non-dominated Xgbest.
5. Numerical Results
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
- Wood, A.J.; Wollenberg, B.F. Power Generation, Operation, and Control, 2nd ed.; Wiley: Hoboken, NJ, USA, 1996; ISBN 9780471790556. [Google Scholar]
- Padhy, N.P. Unit commitment—A bibliographical survey. IEEE Trans. Power Syst. 2004, 19, 1196–1205. [Google Scholar] [CrossRef]
- Dillon, T.S.; Edwin, K.W.; Kochs, H.-D.; Taud, R.J. Integer Programming Approach to the Problem of Optimal Unit Commitment with Probabilistic Reserve Determination. IEEE Trans. Power Appar. Syst. 1978, PAS-97, 2154–2166. [Google Scholar] [CrossRef]
- Garver, L.L. Power Generation Scheduling by Integer Programming—Development of Theory. Trans. Am. Inst. Electr. Eng. Part III Power Appar. Syst. 1962, 81, 730–734. [Google Scholar] [CrossRef]
- Cohen, A.; Yoshimura, M. A Branch-and-Bound Algorithm for Unit Commitment. IEEE Trans. Power Appar. Syst. 1983, PAS-102, 444–451. [Google Scholar] [CrossRef]
- Snyder, W.L.; Powell, H.D.; Rayburn, J.C. Dynamic programming approach to unit commitment. IEEE Trans. Power Syst. 1987, 2, 339–348. [Google Scholar] [CrossRef]
- Lowery, P.G. Generating Unit Commitment by Dynamic Programming. IEEE Trans. Power Appar. Syst. 1966, PAS-85, 422–426. [Google Scholar] [CrossRef]
- Pang, C.K.; Chen, H.C. Optimal short-term thermal unit commitment. IEEE Trans. Power Appar. Syst. 1976, 95, 1336–1346. [Google Scholar] [CrossRef]
- Pang, C.K.; Sheble, G.B.; Albuyeh, F. Evaluation of dynamic programming based methods and multiple area representation for thermal unit commitments. IEEE Trans. Power Appar. Syst. 1981, PAS-100, 1212–1218. [Google Scholar] [CrossRef]
- Su, M.-C.; Hsu, Y.-Y. Fuzzy Dynamic Programming: An Application to Unit Commitment. IEEE Trans. Power Syst. 1991, 6, 1231–1237. [Google Scholar] [CrossRef]
- Ouyang, Z.; Shahidehpour, S.M. An intelligent dynamic programming for unit commitment application. IEEE Trans. Power Syst. 1991, 6, 1203–1209. [Google Scholar] [CrossRef] [Green Version]
- Muckstadt, J.A.; Wilson, R.C. An Application of Mixed-Integer Programming Duality to Scheduling Thermal Generating Systems. IEEE Trans. Power Appar. Syst. 1968, PAS-87, 1968–1978. [Google Scholar] [CrossRef]
- André, M.; Sandrin, P. A New Method for Unit Commitment at Electricité de France. IEEE Power Eng. Rev. 1983, 5, 38–39. [Google Scholar]
- Zhuang, F.; Galiana, F.D. Towards a more rigorous and practical unit commitment by lagrangian relaxation. IEEE Trans. Power Syst. 1988, 3, 763–773. [Google Scholar] [CrossRef]
- Sheble, G.B. Solution of the unit commitment problem by the method of unit periods. IEEE Trans. Power Syst. 1990, 5, 257–260. [Google Scholar] [CrossRef]
- Kazarlis, S.A.; Bakirtzis, A.G.; Petridis, V. A genetic algorithm solution to the unit commitment problem. IEEE Trans. Power Syst. 1996, 11, 83–92. [Google Scholar] [CrossRef]
- Balci, H.; Valenzuela, J. Scheduling electric power generators using particle swarm optimization combined with the Lagrangian relaxation method. Int. J. Appl. Math. Comput. Sci. 2004, 14, 411–422. [Google Scholar]
- Juste, K.A.; Kita, H.; Tanaka, E.; Hasegawa, J. An evolutionary programming solution to the unit commitment problem. IEEE Trans. Power Syst. 1999, 14, 1452–1459. [Google Scholar] [CrossRef]
- Ganguly, D.; Sarkar, V.; Pal, J. A new genetic approach for solving the unit commitment problem. In Proceedings of the 2004 International Conference on Power System Technology, Singapore, 21–24 November 2004; Volume 1, pp. 542–547. [Google Scholar]
- Wang, B.; Li, Y.; Watada, J. Re-Scheduling the Unit Commitment Problem in Fuzzy Environment. In Proceedings of the 2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011), Taipei, Taiwan, 27–30 June 2011; pp. 1090–1095. [Google Scholar]
- Eldin, A.S.; El-sayed, M.A.H.; Youssef, H.K.M. A two-stage genetic based technique for the unit commitment optimization problem. In Proceedings of the 2008 12th International Middle-East Power System Conference, Aswan, Egypt, 12–15 March 2008; pp. 425–430. [Google Scholar] [CrossRef]
- Damousis, I.G.; Bakirtzis, A.G.; Dokopoulos, P.S. A solution to the unit-commitment problem using integer-coded genetic algorithm. IEEE Trans. Power Syst. 2004, 19, 1165–1172. [Google Scholar] [CrossRef]
- Simopoulos, D.N.; Kavatza, S.D.; Vournas, C.D. Unit Commitment by an Enhanced Simulated Annealing Algorithm. IEEE Trans. Power Syst. 2006, 21, 68–76. [Google Scholar] [CrossRef]
- Kamboj, V.K. A novel hybrid PSO–GWO approach for unit commitment problem. Neural Comput. Appl. 2016, 27, 1643–1655. [Google Scholar] [CrossRef]
- Sriyanyong, P.; Song, Y.H. Unit commitment using particle swarm optimization combined with Lagrange relaxation. In Proceedings of the 2005 IEEE Power Engineering Society General Meeting, San Francisco, CA, USA, 16 June 2005; Volume 3, pp. 2752–2759. [Google Scholar] [CrossRef]
- Kanellos, F.D.; Anvari-Moghaddam, A.; Guerrero, J.M. A cost-effective and emission-aware power management system for ships with integrated full electric propulsion. Electr. Power Syst. Res. 2017, 150, 63–75. [Google Scholar] [CrossRef] [Green Version]
- Vahedipour-Dahraie, M.; Anvari-Moghaddam, A.; Guerrero, J.M. Evaluation of reliability in risk-constrained scheduling of autonomous microgrids with demand response and renewable resources. IET Renew. Power Gener. 2018, 12, 657–667. [Google Scholar] [CrossRef]
- Yaprakdal, F.; Baysal, M.; Anvari-Moghaddam, A. Optimal Operational Scheduling of Reconfigurable Microgrids in Presence of Renewable Energy Sources. Energies 2019, 12, 1858. [Google Scholar] [CrossRef]
- Esmaeili, S.; Anvari-Moghaddam, A.; Jadid, S.; Guerrero, J.M. Optimal simultaneous day-ahead scheduling and hourly reconfiguration of distribution systems considering responsive loads. Int. J. Electr. Power Energy Syst. 2019, 104, 537–548. [Google Scholar] [CrossRef]
- Vahedipour-Dahraei, M.; Najafi, H.R.; Anvari-Moghaddam, A.; Guerrero, J.M. Security-constrained unit commitment in AC microgrids considering stochastic price-based demand response and renewable generation. Int. Trans. Electr. Energy Syst. 2018, 28, e2596. [Google Scholar] [CrossRef]
- Vahedipour-Dahraie, M.; Najafi, H.; Anvari-Moghaddam, A.; Guerrero, J. Study of the Effect of Time-Based Rate Demand Response Programs on Stochastic Day-Ahead Energy and Reserve Scheduling in Islanded Residential Microgrids. Appl. Sci. 2017, 7, 378. [Google Scholar] [CrossRef]
- Moghaddam, A.A.; Seifi, A.; Niknam, T. Multi-operation management of a typical micro-grids using Particle Swarm Optimization: A comparative study. Renew. Sustain. Energy Rev. 2012, 16, 1268–1281. [Google Scholar] [CrossRef]
- Moghaddam, A.A.; Seifi, A.; Niknam, T.; Alizadeh Pahlavani, M.R. Multi-objective operation management of a renewable MG (micro-grid) with back-up micro-turbine/fuel cell/battery hybrid power source. Energy 2011, 36, 6490–6507. [Google Scholar] [CrossRef]
- El-Fergany, A.A.; Hasanien, H.M. Single and Multi-objective Optimal Power Flow Using Grey Wolf Optimizer and Differential Evolution Algorithms. Electr. Power Compon. Syst. 2015, 43, 1548–1559. [Google Scholar] [CrossRef]
- Mirjalili, S. Dragonfly algorithm: A new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput. Appl. 2016, 27, 1053–1073. [Google Scholar] [CrossRef]
- Sliman, L.; Bouktir, T. Economic Power Dispatch of Power System with Pollution Control using Multiobjective Ant Colony Optimization. Int. J. Comput. Intell. Res. 2007, 3, 145–153. [Google Scholar] [CrossRef]
- Rezaei Adaryani, M.; Karami, A. Artificial bee colony algorithm for solving multi-objective optimal power flow problem. Int. J. Electr. Power Energy Syst. 2013, 53, 219–230. [Google Scholar] [CrossRef]
- Khunkitti, S.; Siritaratiwat, A.; Premrudeepreechacharn, S.; Chatthaworn, R.; Watson, N. A Hybrid DA-PSO Optimization Algorithm for Multiobjective Optimal Power Flow Problems. Energies 2018, 11, 2270. [Google Scholar] [CrossRef]
- Bashishtha, T.K. Nature Inspired Meta-heuristic dragonfly Algorithms for Solving Optimal Power Flow Problem. Int. J. Electron. Electr. Comput. Syst. 2016, 5, 111–120. [Google Scholar]
- Reynolds, C.W. Flocks, herds and schools: A distributed behavioral model. ACM SIGGRAPH Comput. Graph. 1987, 21, 25–34. [Google Scholar] [CrossRef] [Green Version]
- Hu, X.; Shi, Y.; Eberhart, R. Recent advances in particle swarm. In Proceedings of the 2004 Congress on Evolutionary Computation, Portland, OR, USA, 19–23 June 2004; Volume 1, pp. 90–97. [Google Scholar] [CrossRef]
- Banks, A.; Vincent, J.; Anyakoha, C. A review of particle swarm optimization. Part I: Background and development. Nat. Comput. 2007, 6, 467–484. [Google Scholar] [CrossRef]
- Niknam, T.; Narimani, M.R.; Aghaei, J.; Azizipanah-Abarghooee, R. Improved particle swarm optimisation for multi-objective optimal power flow considering the cost, loss, emission and voltage stability index. IET Gener. Transm. Distrib. 2012, 6, 515. [Google Scholar] [CrossRef]
- Narimani, M.R.; Azizipanah-Abarghooee, R.; Zoghdar-Moghadam-Shahrekohne, B.; Gholami, K. A novel approach to multi-objective optimal power flow by a new hybrid optimization algorithm considering generator constraints and multi-fuel type. Energy 2013, 49, 119–136. [Google Scholar] [CrossRef]
- Eberhart, R.; Kennedy, J. A New Optimizer Using Particle Swarm Theory. In Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, 4–6 October 1995; pp. 39–43. [Google Scholar]
- Kennedy, J.; Eberhart, R.C. A discrete binary version of the particle swarm algorithm. In Proceedings of the 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation, Orlando, FL, USA, 12–15 October 1997; Volume 5, pp. 4104–4108. [Google Scholar] [CrossRef]
- De Jong, K.A. Analysis of the Behavior of a Class of Genetic Adaptive Systems; University of Michigan: Ann Arbor, MI, USA, 1975. [Google Scholar]
- Anita, J.M.; Raglend, I.J. Solution of Unit Commitment Problem Using Shuffled Frog Leaping Algorithm. In Proceedings of the 2012 International Conference on Computing, Electronics and Electrical Technologies (ICCEET), Kumaracoil, India, 21–22 March 2012; pp. 109–115. [Google Scholar]
- Gaing, Z.-L. Discrete particle swarm optimization algorithm for unit commitment. In Proceedings of the 2003 IEEE Power Engineering Society General Meeting, Toronto, ON, Canada, 13–17 July 2003; Volume 1, pp. 418–424. [Google Scholar] [CrossRef]
- Viana, A.; De Sousa, J.P.; Matos, M. Using GRASP to Solve the Unit Commitment Problem. Ann. Oper. Res. 2003, 120, 117–132. [Google Scholar] [CrossRef]
- Moussa, A.M.; Gammal, M.E.; Attia, A.I. An Improved Particle Swarm Optimization Technique for Solving the Unit Commitment Problem. Online J. Power Energy Eng. 2011, 2, 217–222. [Google Scholar]
Unit No. | Pgimax | Pgimin | a ($/MW2) | b ($/MW) | c ($/h) | MUTi | MDTi | HSCi | CSCi | CSHi | ISi |
---|---|---|---|---|---|---|---|---|---|---|---|
U1 | 250 | 10 | 0.00315 | 2 | 0 | 1 | 1 | 70 | 176 | 2 | 1 |
U2 | 140 | 20 | 0.0175 | 1.75 | 0 | 2 | 1 | 74 | 187 | 2 | −3 |
U3 | 100 | 15 | 0.0625 | 1 | 0 | 1 | 1 | 50 | 113 | 1 | −2 |
U4 | 120 | 10 | 0.00834 | 3.25 | 0 | 2 | 2 | 110 | 267 | 1 | −3 |
U5 | 45 | 10 | 0.025 | 3 | 0 | 1 | 1 | 72 | 180 | 1 | −2 |
Unit No. | Pgimax | Pgimin | a ($/MW2) | b ($/MW) | c ($/h) | MUTi | MDTi | HSCi | CSCi | CSHi | ISi |
---|---|---|---|---|---|---|---|---|---|---|---|
U1 | 200 | 50 | 0.00375 | 2 | 0 | 1 | 1 | 70 | 176 | 2 | 1 |
U2 | 80 | 20 | 0.0175 | 1.7 | 0 | 2 | 2 | 74 | 187 | 1 | −3 |
U3 | 50 | 15 | 0.0625 | 1 | 0 | 1 | 1 | 50 | 113 | 1 | −2 |
U4 | 35 | 10 | 0.00834 | 3.25 | 0 | 1 | 2 | 110 | 267 | 1 | −3 |
U5 | 30 | 10 | 0.025 | 3 | 0 | 2 | 1 | 72 | 180 | 1 | −2 |
U6 | 40 | 12 | 0.025 | 3 | 0 | 1 | 1 | 40 | 113 | 1 | −2 |
Unit No. | Pgimax | Pgimin | a ($/MW2) | b ($/MW) | c ($/h) | MUTi | MDTi | HSCi | CSCi | CSHi | ISi |
---|---|---|---|---|---|---|---|---|---|---|---|
U1 | 455 | 150 | 0.00048 | 16.19 | 1000 | 8 | 8 | 4500 | 9000 | 5 | 8 |
U2 | 455 | 150 | 0.00031 | 17.26 | 970 | 8 | 8 | 5000 | 10000 | 5 | 8 |
U3 | 130 | 20 | 0.002 | 16.6 | 700 | 5 | 5 | 550 | 1100 | 4 | −5 |
U4 | 130 | 20 | 0.00211 | 16.5 | 680 | 5 | 5 | 560 | 1120 | 4 | −5 |
U5 | 162 | 25 | 0.0398 | 19.7 | 450 | 6 | 6 | 900 | 1800 | 4 | −6 |
U6 | 80 | 20 | 0.00712 | 22.26 | 370 | 3 | 3 | 170 | 340 | 2 | -3 |
U7 | 85 | 25 | 0.00079 | 27.74 | 480 | 3 | 3 | 260 | 520 | 2 | −3 |
U8 | 55 | 10 | 0.00413 | 25.92 | 660 | 1 | 1 | 30 | 60 | 0 | −1 |
U9 | 55 | 10 | 0.00222 | 27.27 | 665 | 1 | 1 | 30 | 60 | 0 | −1 |
U10 | 55 | 10 | 0.00173 | 27.79 | 670 | 1 | 1 | 30 | 60 | 0 | −1 |
Unit No. | Pgimax | Pgimin | a ($/MW2) | b ($/MW) | c ($/h) | MUTi | MDTi | HSCi | CSCi | CSHi | ISi |
---|---|---|---|---|---|---|---|---|---|---|---|
U1 | 400 | 100 | 0.0019 | 7.5031 | 311.9102 | 8 | 5 | 500 | 500 | 10 | 10 |
U2 | 400 | 100 | 0.0019 | 7.4921 | 310.0021 | 8 | 5 | 500 | 500 | 10 | 10 |
U3 | 350 | 140 | 0.0015 | 10.8616 | 177.0575 | 8 | 5 | 300 | 200 | 8 | 10 |
U4 | 197 | 68.95 | 0.0026 | 23.2000 | 260.1760 | 5 | 4 | 200 | 200 | 8 | −4 |
U5 | 197 | 68.95 | 0.0026 | 23.1000 | 259.6490 | 5 | 4 | 200 | 200 | 8 | −4 |
U6 | 197 | 68.95 | 0.0026 | 23.0000 | 259.1310 | 5 | 4 | 200 | 200 | 8 | −4 |
U7 | 155 | 54.25 | 0.0049 | 10.7583 | 143.5972 | 5 | 3 | 150 | 150 | 6 | 5 |
U8 | 155 | 54.25 | 0.0048 | 10.7367 | 134.3719 | 5 | 3 | 150 | 150 | 6 | 5 |
U9 | 155 | 54.25 | 0.0047 | 10.7154 | 143.0288 | 5 | 3 | 150 | 150 | 6 | 5 |
U10 | 155 | 54.25 | 0.0046 | 10.6940 | 142.7348 | 5 | 3 | 150 | 150 | 6 | 5 |
U11 | 100 | 25 | 0.0060 | 18.2000 | 218.7752 | 4 | 2 | 70 | 70 | 4 | −3 |
U12 | 100 | 25 | 0.0061 | 18.1000 | 218.3350 | 4 | 2 | 70 | 70 | 4 | −3 |
U13 | 100 | 25 | 0.0062 | 18.0000 | 217.8952 | 4 | 2 | 70 | 70 | 4 | −3 |
U14 | 76 | 15.2 | 0.0093 | 13.4073 | 81.6259 | 3 | 2 | 50 | 50 | 3 | 3 |
U15 | 76 | 15.2 | 0.0091 | 13.3805 | 81.4641 | 3 | 2 | 50 | 50 | 3 | 3 |
U16 | 76 | 15.2 | 0.0089 | 13.3538 | 81.2980 | 3 | 2 | 50 | 50 | 3 | 3 |
U17 | 76 | 15.2 | 0.0088 | 13.3272 | 81.1364 | 3 | 0 | 50 | 50 | 3 | 3 |
U18 | 20 | 4 | 0.0143 | 37.8896 | 118.8206 | 0 | 0 | 20 | 20 | 2 | −1 |
U19 | 20 | 4 | 0.0136 | 37.7770 | 118.4576 | 0 | 0 | 20 | 20 | 2 | −1 |
U20 | 20 | 4 | 0.0126 | 37.6637 | 118.1083 | 0 | 0 | 20 | 20 | 2 | −1 |
U21 | 20 | 4 | 0.0120 | 37.5510 | 117.7551 | 0 | 0 | 20 | 20 | 2 | −1 |
U22 | 12 | 2.4 | 0.0285 | 26.0611 | 24.8882 | 0 | 0 | 0 | 0 | 1 | −1 |
U23 | 12 | 2.4 | 0.0284 | 25.9318 | 24.7605 | 0 | 0 | 0 | 0 | 1 | −1 |
U24 | 12 | 2.4 | 0.0280 | 25.8027 | 24.6382 | 0 | 0 | 0 | 0 | 1 | −1 |
U25 | 12 | 2.4 | 0.0265 | 25.6753 | 24.4110 | 0 | 0 | 0 | 0 | 1 | −1 |
U26 | 12 | 2.4 | 0.0253 | 25.5472 | 24.3891 | 0 | 0 | 0 | 0 | 1 | −1 |
Hour | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
Demand | 148 | 173 | 220 | 244 | 259 | 248 | 227 | 202 | 176 | 134 | 100 | 130 |
Hour | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
Demand | 157 | 168 | 195 | 225 | 244 | 241 | 230 | 210 | 176 | 157 | 138 | 103 |
Hour | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
Demand | 166 | 196 | 229 | 267 | 283.4 | 272 | 246 | 213 | 192 | 161 | 147 | 160 |
Hour | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
Demand | 170 | 185 | 208 | 232 | 246 | 241 | 236 | 225 | 204 | 182 | 161 | 131 |
Hour | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
Demand | 700 | 750 | 850 | 950 | 1000 | 1100 | 1150 | 1200 | 1300 | 1400 | 1450 | 1500 |
Hour | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
Demand | 1400 | 1300 | 1200 | 1050 | 1000 | 1100 | 1200 | 1400 | 1300 | 1100 | 900 | 800 |
Hour | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
Dmd. | 2223 | 2052 | 1938 | 1881 | 1824 | 1825.5 | 1881 | 1995 | 2280 | 2508 | 2565 | 2593.5 |
Hour | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
Dmd. | 2565 | 2508 | 2479.5 | 2479.5 | 2593.5 | 2850 | 2821.5 | 2764.5 | 2679 | 2662 | 2479.5 | 2308.5 |
Hour | Unit Schedule | Generation Schedule | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
U1 | U2 | U3 | U4 | U5 | U1 | U2 | U3 | U4 | U5 | |
1 | 1 | 0 | 1 | 0 | 0 | 133 | 0 | 15 | 0 | 0 |
2 | 1 | 0 | 0 | 0 | 0 | 173 | 0 | 0 | 0 | 0 |
3 | 1 | 0 | 1 | 0 | 0 | 205 | 0 | 15 | 0 | 0 |
4 | 1 | 0 | 1 | 0 | 0 | 229 | 0 | 15 | 0 | 0 |
5 | 1 | 0 | 1 | 0 | 0 | 244 | 0 | 15 | 0 | 0 |
6 | 1 | 0 | 1 | 0 | 0 | 233 | 0 | 15 | 0 | 0 |
7 | 1 | 0 | 0 | 0 | 0 | 227 | 0 | 0 | 0 | 0 |
8 | 1 | 0 | 0 | 0 | 0 | 202 | 0 | 0 | 0 | 0 |
9 | 1 | 0 | 1 | 0 | 0 | 161 | 0 | 15 | 0 | 0 |
10 | 1 | 0 | 1 | 0 | 0 | 119 | 0 | 15 | 0 | 0 |
11 | 1 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0 |
12 | 1 | 0 | 1 | 0 | 0 | 115 | 0 | 15 | 0 | 0 |
13 | 1 | 0 | 0 | 0 | 0 | 157 | 0 | 0 | 0 | 0 |
14 | 1 | 0 | 0 | 0 | 0 | 168 | 0 | 0 | 0 | 0 |
15 | 1 | 0 | 1 | 0 | 0 | 180 | 0 | 15 | 0 | 0 |
16 | 1 | 0 | 1 | 0 | 0 | 210 | 0 | 15 | 0 | 0 |
17 | 1 | 0 | 1 | 0 | 0 | 229 | 0 | 15 | 0 | 0 |
18 | 1 | 0 | 1 | 0 | 0 | 226 | 0 | 15 | 0 | 0 |
19 | 1 | 0 | 1 | 0 | 0 | 215 | 0 | 15 | 0 | 0 |
20 | 1 | 0 | 0 | 0 | 0 | 210 | 0 | 0 | 0 | 0 |
21 | 1 | 0 | 0 | 0 | 0 | 176 | 0 | 0 | 0 | 0 |
22 | 1 | 0 | 0 | 0 | 0 | 157 | 0 | 0 | 0 | 0 |
23 | 1 | 0 | 0 | 0 | 0 | 138 | 0 | 0 | 0 | 0 |
24 | 1 | 0 | 0 | 0 | 0 | 103 | 0 | 0 | 0 | 0 |
Total Cost ($) 11,830.94 |
Hour | Unit Schedule | Generation Schedule | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
U1 | U2 | U3 | U4 | U5 | U6 | U1 | U2 | U3 | U4 | U5 | U6 | |
1 | 1 | 1 | 1 | 0 | 0 | 0 | 131 | 20 | 15 | 0 | 0 | 0 |
2 | 1 | 1 | 0 | 0 | 0 | 0 | 176 | 20 | 0 | 0 | 0 | 0 |
3 | 1 | 1 | 1 | 0 | 0 | 0 | 194 | 20 | 15 | 0 | 0 | 0 |
4 | 1 | 1 | 1 | 0 | 0 | 0 | 200 | 52 | 15 | 0 | 0 | 0 |
5 | 1 | 1 | 1 | 0 | 0 | 0 | 200 | 68.4 | 15 | 0 | 0 | 0 |
6 | 1 | 1 | 1 | 0 | 0 | 0 | 200 | 57 | 15 | 0 | 0 | 0 |
7 | 1 | 1 | 0 | 0 | 0 | 0 | 200 | 46 | 0 | 0 | 0 | 0 |
8 | 1 | 1 | 0 | 0 | 0 | 0 | 193 | 20 | 0 | 0 | 0 | 0 |
9 | 1 | 1 | 0 | 0 | 0 | 0 | 172 | 20 | 0 | 0 | 0 | 0 |
10 | 1 | 0 | 0 | 0 | 0 | 0 | 161 | 0 | 0 | 0 | 0 | 0 |
11 | 1 | 0 | 0 | 0 | 0 | 0 | 147 | 0 | 0 | 0 | 0 | 0 |
12 | 1 | 1 | 0 | 0 | 0 | 0 | 140 | 20 | 0 | 0 | 0 | 0 |
13 | 1 | 1 | 0 | 0 | 0 | 0 | 150 | 20 | 0 | 0 | 0 | 0 |
14 | 1 | 1 | 0 | 0 | 0 | 0 | 165 | 20 | 0 | 0 | 0 | 0 |
15 | 1 | 1 | 0 | 0 | 0 | 0 | 188 | 20 | 0 | 0 | 0 | 0 |
16 | 1 | 1 | 0 | 0 | 0 | 0 | 200 | 32 | 0 | 0 | 0 | 0 |
17 | 1 | 1 | 0 | 0 | 0 | 0 | 200 | 46 | 0 | 0 | 0 | 0 |
18 | 1 | 1 | 0 | 0 | 0 | 0 | 200 | 41 | 0 | 0 | 0 | 0 |
19 | 1 | 1 | 0 | 0 | 0 | 0 | 200 | 36 | 0 | 0 | 0 | 0 |
20 | 1 | 1 | 0 | 0 | 0 | 0 | 200 | 25 | 0 | 0 | 0 | 0 |
21 | 1 | 1 | 0 | 0 | 0 | 0 | 184 | 20 | 0 | 0 | 0 | 0 |
22 | 1 | 1 | 0 | 0 | 0 | 0 | 162 | 20 | 0 | 0 | 0 | 0 |
23 | 1 | 0 | 0 | 0 | 0 | 0 | 161 | 0 | 0 | 0 | 0 | 0 |
24 | 1 | 0 | 0 | 0 | 0 | 0 | 131 | 0 | 0 | 0 | 0 | 0 |
Total Cost ($) 13,292.28 |
Unit Schedule | Generation Schedule | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
U1 | U2 | U3 | U4 | U5 | U6 | U7 | U8 | U9 | U10 | U1 | U2 | U3 | U4 | U5 | U6 | U7 | U8 | U9 | U10 |
1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 455 | 245 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 455 | 295 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 455 | 370 | 0 | 0 | 25 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 455 | 455 | 0 | 0 | 40 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 455 | 455 | 0 | 65 | 25 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 455 | 455 | 35 | 130 | 25 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 455 | 455 | 85 | 130 | 25 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 455 | 455 | 130 | 130 | 30 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 455 | 455 | 130 | 130 | 85 | 20 | 25 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 455 | 455 | 130 | 130 | 162 | 33 | 25 | 10 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 455 | 455 | 130 | 130 | 162 | 73 | 25 | 10 | 10 | 0 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 455 | 455 | 130 | 130 | 162 | 80 | 58 | 10 | 10 | 10 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 455 | 455 | 130 | 130 | 162 | 33 | 25 | 10 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 455 | 455 | 130 | 130 | 85 | 20 | 25 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 455 | 455 | 0 | 130 | 115 | 20 | 25 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 455 | 455 | 0 | 115 | 25 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 455 | 455 | 0 | 65 | 25 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 455 | 455 | 0 | 130 | 50 | 0 | 0 | 10 | 0 | 0 |
1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 455 | 455 | 0 | 130 | 115 | 20 | 25 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 455 | 455 | 130 | 130 | 162 | 33 | 25 | 10 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 455 | 455 | 130 | 130 | 85 | 20 | 25 | 0 | 0 | 0 |
1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 455 | 455 | 130 | 0 | 40 | 20 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 455 | 425 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 455 | 325 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Total Cost ($) 565,807.3094 |
Methods | Total Generation Cost ($) | Time (s) | ||
---|---|---|---|---|
Best | Average | Worst | ||
GA [16] | 565,825 | - | 570,032 | 221 |
DP [16] | 565,825 | - | - | - |
LR [16] | 565,825 | - | - | 257 |
PSO-LR [17] | 565,869 | - | - | 42 |
EP [18] | 564,551 | - | 566,231 | 100 |
NGA [19] | 591,715 | - | - | 677 |
LCA-PSO [20] | 570,006 | - | - | 18.34 |
IPSO [20] | 599,782 | - | - | 14.48 |
MPSO [20] | 574,905 | - | - | 15.73 |
TSGA [21] | 568,314.56 | - | - | - |
ICGA [22] | - | 566,404 | - | 7.4 |
BCGA [22] | 567,367 | - | - | 3.7 |
SA [23] | 565,828 | 565,988 | 566,260 | 3.35 |
SM [23] | 566,686 | 566,787 | 567,022 | - |
PSO-GWO [24] | 565,210.2564 | - | - | - |
HPSO [25] | 574,153 | - | - | - |
ILR [25] | 565,823 | - | - | - |
GRASP [50] | 565,825 | - | - | 17 |
iDA-PSO | 565,807.3094 | 565,827.0145 | 565,891.7599 | 231.31 |
Generation Schedule (Units 1–13) | ||||||||||||
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
400 | 400 | 350 | 0 | 0 | 0 | 155 | 155 | 155 | 155 | 0 | 35.4 | 100 |
400 | 400 | 350 | 0 | 0 | 0 | 155 | 155 | 155 | 155 | 0 | 25 | 29 |
400 | 400 | 350 | 0 | 0 | 0 | 155 | 155 | 155 | 155 | 0 | 25 | 67 |
400 | 400 | 350 | 0 | 0 | 0 | 155 | 155 | 155 | 155 | 0 | 25 | 25 |
400 | 400 | 350 | 0 | 0 | 0 | 155 | 155 | 155 | 155 | 0 | 0 | 0 |
400 | 400 | 350 | 0 | 0 | 0 | 155 | 155 | 155 | 155 | 0 | 0 | 0 |
400 | 400 | 350 | 0 | 0 | 0 | 155 | 155 | 155 | 155 | 0 | 0 | 0 |
400 | 400 | 350 | 0 | 0 | 0 | 155 | 155 | 155 | 155 | 0 | 0 | 0 |
400 | 400 | 350 | 0 | 0 | 101.2 | 155 | 155 | 155 | 155 | 0 | 0 | 100 |
400 | 400 | 350 | 0 | 0 | 120.4 | 155 | 155 | 155 | 155 | 100 | 100 | 100 |
400 | 400 | 350 | 0 | 68.95 | 122.05 | 155 | 155 | 155 | 155 | 100 | 100 | 100 |
400 | 400 | 350 | 0 | 68.95 | 150.55 | 155 | 155 | 155 | 155 | 100 | 100 | 100 |
400 | 400 | 350 | 0 | 68.95 | 122.05 | 155 | 155 | 155 | 155 | 100 | 100 | 100 |
400 | 400 | 350 | 0 | 120.4 | 0 | 155 | 155 | 155 | 155 | 100 | 100 | 100 |
400 | 400 | 350 | 0 | 98.3 | 0 | 155 | 155 | 155 | 155 | 100 | 100 | 100 |
400 | 400 | 350 | 0 | 98.3 | 0 | 155 | 155 | 155 | 155 | 100 | 100 | 100 |
400 | 400 | 350 | 68.95 | 150.55 | 0 | 155 | 155 | 155 | 155 | 100 | 100 | 100 |
400 | 400 | 350 | 74.8 | 197 | 197 | 155 | 155 | 155 | 155 | 100 | 100 | 100 |
400 | 400 | 350 | 68.95 | 181.55 | 197 | 155 | 155 | 155 | 155 | 100 | 100 | 100 |
400 | 400 | 350 | 68.95 | 124.55 | 197 | 155 | 155 | 155 | 155 | 100 | 100 | 100 |
400 | 400 | 350 | 98.4 | 0 | 197 | 155 | 155 | 155 | 155 | 100 | 100 | 100 |
400 | 400 | 350 | 83.8 | 0 | 197 | 155 | 155 | 155 | 155 | 100 | 100 | 100 |
400 | 400 | 350 | 0 | 0 | 98.3 | 155 | 155 | 155 | 155 | 100 | 100 | 100 |
400 | 400 | 350 | 0 | 0 | 0 | 155 | 155 | 155 | 155 | 25 | 97.5 | 100 |
Generation Schedule (Units 14–26) | ||||||||||||
14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |
76 | 76 | 76 | 76 | 0 | 0 | 0 | 4 | 0 | 2.4 | 2.4 | 2.4 | 2.4 |
0 | 76 | 76 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 61 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 15.2 | 38.8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 15.2 | 40.3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 15.2 | 19.8 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
15.2 | 53 | 76 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2.4 | 2.4 |
76 | 76 | 76 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2.4 | 2.4 |
76 | 76 | 76 | 76 | 0 | 0 | 0 | 4 | 0 | 2.4 | 2.4 | 2.4 | 2.4 |
76 | 76 | 76 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
76 | 76 | 76 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
76 | 76 | 76 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
76 | 76 | 76 | 76 | 0 | 0 | 0 | 4 | 0 | 2.4 | 2.4 | 2.4 | 2.4 |
76 | 76 | 76 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 2.4 | 2.4 | 2.4 |
76 | 76 | 76 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 2.4 | 2.4 | 2.4 |
76 | 76 | 76 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
76 | 76 | 76 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 2.4 | 2.4 | 2.4 |
76 | 76 | 76 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
76 | 76 | 76 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
76 | 76 | 76 | 76 | 0 | 0 | 0 | 0 | 0 | 2.4 | 2.4 | 2.4 | 2.4 |
76 | 76 | 76 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 2.4 | 2.4 | 2.4 |
76 | 76 | 76 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 2.4 | 2.4 | 2.4 |
76 | 76 | 76 | 76 | 0 | 0 | 0 | 0 | 2.4 | 2.4 | 2.4 | 2.4 | 2.4 |
Total Cost ($) 741,587.7088 |
© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Khunkitti, S.; R. Watson, N.; Chatthaworn, R.; Premrudeepreechacharn, S.; Siritaratiwat, A. An Improved DA-PSO Optimization Approach for Unit Commitment Problem. Energies 2019, 12, 2335. https://doi.org/10.3390/en12122335
Khunkitti S, R. Watson N, Chatthaworn R, Premrudeepreechacharn S, Siritaratiwat A. An Improved DA-PSO Optimization Approach for Unit Commitment Problem. Energies. 2019; 12(12):2335. https://doi.org/10.3390/en12122335
Chicago/Turabian StyleKhunkitti, Sirote, Neville R. Watson, Rongrit Chatthaworn, Suttichai Premrudeepreechacharn, and Apirat Siritaratiwat. 2019. "An Improved DA-PSO Optimization Approach for Unit Commitment Problem" Energies 12, no. 12: 2335. https://doi.org/10.3390/en12122335