Fuzzy Unit Commitment for Cost Minimization in Power ... - IEEE Xplore

2013 IEEE 7th International Power Engineering and Optimization Conference (PEOCO2013), Langkawi, Malaysia. 3-4 June 2013

Fuzzy Unit Commitment for Cost Minimization in Power System Planning N. A. Rahmat, I. Musirin, A. F. Abidin Faculty of Electrical Engineering Universiti Teknologi MARA Shah Alam, Malaysia simple yet provide fast convergence towards the optimal solution. The ineffectiveness of the conventional methods has encouraged researches to develop new approaches to solve unit commitment problem. More recent development on power system optimization brought to the employment of artificial intelligence and meta-heuristic techniques into unit commitment problem. Among them are the Genetic Algorithm [7]-[8], Evolutionary Programming [9]-[10], Harmonic Search Algorithm [11], Artificial Bee Colony [12], Bacteria Foraging Optimization [13]-[14], and Differential Evolution [15], and Particle Swarm Optimization [16]-[17]. Method [16]-[17] has the ability to memorize the best solution of search agent at each search space. However, in [18], the algorithm was claimed to disrupt the inequality constraint. Method [15] offers simplicity in the algorithm construction. However, in [19] it is revealed that the algorithm only provide near-optimal solution despite its fast convergence speed. Another concern during unit commitment optimization process is the existence of several uncertainty constraints [20]. The uncertainties includes fuel price and the load forecast. The uncertainties were introduced due to the difficulties of future forecasting. Several constraints such as the fuel cost and load demand might be different and sometimes unpredictable during the next time horizon [21]. The uncertainties affect the output of each generating unit and the production cost. In the deregulated electrical power industry, any negligence towards these uncertainties by the generating company may raise unwanted issues such as an additional cost of purchasing extra amount of power from neighboring or rivaling companies [22]. Hence, this research proposes the implementation of fuzzy modeling to incorporate the uncertainty constraints into the unit commitment problem. Introduced by Zadeh in 1965 [23], fuzzy modeling is a class of a probabilistic logic that deals with approximation process [24]. Fuzzy modeling can be characterized by its membership function that relates fuzzy set with the degree of satisfaction. In this research, fuzzy modeling is used to determine the fuel price and the load demand. Hence, the problem will be termed as fuzzy unit commitment (FUC) optimization problem. This research proposes the implementation of Differential Evolution Immunized Ant Colony Optimization (DEIANT) technique to solve fuzzy unit commitment problem. DEIANT is the hybrid of Differential Evolution and Ant Colony

Abstract- Unit commitment is among of the key elements in power system planning. Unit commitment is extensively applied by the power utilities to plan the optimal dispatch of generating units in the system. In the deregulated power system industry, it is important to consider several uncertainty constraints during the planning process. This research proposes the application of fuzzy set modeling to determine the uncertainty constraints. Several intelligence techniques including Particle Swarm Optimization, Ant Colony Optimization, and Differential Evolution Immunized Ant Colony Optimization approaches have been used to optimize the fuzzy unit commitment problem. The verification process was performed on IEEE 30-Bus Reliable Test System (RTS). Comparative studies among PSO, ACO and DEIANT indicate the superiority of DEIANT in solving the fuzzy unit commitment problem. Index Terms – Ant Colony Optimization (ACO), Differential Evolution Immunized Ant Colony Optimization (DEIANT), Fuzzy Unit Commitment (FUC), Particle Swarm Optimization (PSO).

I. INTRODUCTION Several ranges of power system simulations are now aided with numerous computer simulation programs. The programs are broadly utilized by the utilities to simulate several power system operational situations such as grid expansion, price forecasting, and system contingencies. Centered on mathematical techniques that include linear, quadratic and mixed-integer programming, the computer simulation programs have assisted the utilities to solve several key elements of power systems namely; load flow study, transient stability, optimal power flow, and unit commitment. Similar to economic dispatch optimization problem, unit commitment is categorized under mixed-integer optimization problem [1]. Unit commitment concentrates on the scheduling of optimal power dispatch without violating any unit constraints. However, according to [2], several constraints can be breached to a certain amount. Load forecasting and fuel price create uncertainties in the constraints. The uncertainties can render the unit commitment solutions to unwanted solution if ignored [3]. Therefore the uncertainties of unit commitment problem should be incorporated into the optimization problem. Numerous approaches have been introduced to solve optimal dispatch problem which include deterministic, meta-heuristic, and combinatorial techniques. Deterministic approaches comprise of dynamic programming [4], Lagrangian Relaxation [5], mixed-integer programming [6]. These methods are

978-1-4673-5074-7/13/$31.00 ©2013 IEEE

680

2013 IEEE 7th International Power Engineering and Optimization Conference (PEOCO2013), Langkawi, Malaysia. 3-4 June 2013

Optimization Technique. Cloning process that was based on Artificial Immune System was also embedded into the algorithm to enhance the performance of the algorithm. Comparative studies between several approaches, including the conventional method, Particle Swarm Optimization, and Ant Colony Optimization were conducted to verify the performance of DEIANT.

Where: MC Cf C ΔC1, ΔC2 MC 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

II. FUZZY UNIT COMMITMENT FORMULATION The objective of unit commitment operation is to plan the optimal power dispatch while satisfying several constraints. There are several uncertainty constrains within the unit commitment. This research uses fuzzy modeling to determine the uncertainty constraints including load demand forecasting and fuel cost. Fuzzy theory [25] put into use the membership function. Membership function is denoted by Mx and the function will correspond to the characteristic function Xi with figures varies between zero to one. It is desired to get the membership function as close to 1.0 as possible. The mapping characteristics are based on triangular fuzzy set. Equation (1) describes the characteristic and graphically explained by figure I: 0 if PD < (D - ΔD1 ) ⎧ ⎪ PD − ( D − ΔD1 ) if (D - ΔD1 ) ≤ PD < D ⎪ ΔD1 ⎪⎪ MD⎨ 1 if PD = D ⎪ ( D + ΔD2 ) − PD if D < PD ≤ (D + ΔD2 ) ⎪ ΔD2 ⎪ ⎪⎩ 0 if PD > ( D + ΔD2 ) Where: MD PD D ΔD1, ΔD2 MC 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

C Fuel price, Cf

C+ΔC2

The determined constraint will be used to perform the unit commitment optimal dispatch. Unit commitment can be described as in equation (3):

Ci ( Pi ) = ai Pi 2 + bi Pi + c

(3)

Where Ci is the operating cost for unit i. ai, bi, and ci are the cost factor of unit i. Pi is the vector of generated output. Another aim of optimal load dispatch is to cut down the total operating cost to the lowest. The summation of unit commitment in the system is shown by equation (4) below:

(1)

Ng

CTotal =

∑C ( P ) i

(4)

i

i

Equation (5) below represents the inequality constraint of generation limits for each unit:

Demand membership Calculated power demand Actual demand Demand changes

Pi min ≤ Pi ≤ Pi max

(5)

Where Pimin and Pimax is the minimum and maximum generation limit respectively. Equation (6) is the power balance constraints: Ng

∑P

gi

= PD + Ploss

(6)

i

D-ΔD1

D Fuel price, Cf

Equation (6) explains that the total generation is the summation of power demand, PD and total system loss, Ploss. Ploss can be computed by using the following equation:

D+ΔD2

n

Ploss =

The fuel cost is also determined by triangular fuzzy set as shown by equation (2) and depicted by figure 2:

C

C-ΔC1

Fig. 2. Triangular fuzzy set for fuel price

Fig. 1. Triangular fuzzy set for load demand

M

Fuel price membership Calculated fuel price Actual fuel cost Fuel cost changes

0 if C f < (C - Δ C 1 ) ⎧ ⎪ C − (C − ΔC ) f 1 ⎪ if (C - Δ C 1 ) ≤ C f < C ΔC1 ⎪ ⎪ 1 if C f = C ⎨ ⎪(C + ΔC2 )− C f if C < C f ≤ ( C + Δ C 2 ) ⎪ ΔC2 ⎪ ⎪⎩ 0 if C f > ( C + Δ C 2 )

n

∑∑ i

j

n

Pi Bij Pj +

∑B

0 i Pi

+ B00

(7)

i

Where Bij, B0i and B00 is the elements of loss coefficient matrix.

(2)

III. DIFFERENTIAL EVOLUTION IMMUNIZED ANT COLONY OPTIMIZATION FORMULATION The applications of Ant Colony Optimization (ACO) technique in cracking many optimization problems have been

681

2013 IEEE 7th International Power Engineering and Optimization Conference (PEOCO2013), Langkawi, Malaysia. 3-4 June 2013

very vast in the past few decades. However, despite the good performance, robustness and capable of solving parallel processes [26] the algorithm tends to get caught in long computation time and unfitting to solve problem with large matrix size [27]. Hence, this research will put forward the hybrid of Differential Evolution and Ant Colony Optimization. Cloning process was extracted from Artificial Immune System algorithm and imposed into the new algorithm. Differential Evolution process will mutate, crossover and perform selection process to the pheromone level of ACO. Meanwhile, the cloning process will enhance and diversify the number of search agent of ACO. The improvement of ACO with the elements of DE and AIS will be known as Differential Evolution Immunized Ant Colony Optimization (DEIANT). The following steps are the briefing on DEIANT processes. Figure 3 depicts the entire pheromone modification process.

1 1 1 1 Cloning

1 1

1 1 1 1

1 1

1 1

1 1

1 1

1 1

Mutation

1 1 0 0

Mutation

1 0 1 0

1 1 1 0

Crossover

A. Initialization DEIANT is based on ACO algorithm. Therefore, several of its parameters initialized according to ACO parameters such as the number of ants, number of nodes, and pheromone decay factor. These parameters are heuristically determined. The algorithm also encompasses of DE and AIS parameters. Hence, additional parameters such as scout-ant cloning factor, pheromone mutation factor, and crossover constant need to be initialized.

1 1 0 1 Crossover

1 1

1 1

0 0

1 0

1 0

1 1

1 0

0 1 Selection

1 1 1 0 1 1

B. Transition Rule Each ant will tour from a node to another unvisited node. The next node is chosen according to the transition rule as described by the following equation: ⎧⎪ Pk ( r , s ) = ⎨ ⎪⎩

[ τ ( r , s ) ⋅ [η ( r , s )β ]

∑ μεJ

k ( r ) [ τ ( r , s )] ⋅ [η ( r ,u )

β

]

0 1

Fig. 3. Pheromone modification process

E. Pheromone Mutation Mutation coefficient can either be user-defined or calculated by using several types of distribution functions. In this research, Gaussian Distribution Equation was revised to create the pheromone mutation function as shown by equation (9):

(8)

Where r is the current point, s is the next node, and u is the unvisited node.

C. First Update Pheromones are traced during the ant’s travels. In this research, the shortest route will have plenty of pheromone traces and vice versa. Each ant will update the pheromone level according to the evaporation factor, ρ. This factor is vital to avoid pre-mature convergence. The evaporation rate will decrease the pheromone level during each iteration. The evaporation rate is numbered between 0 and 1. The closer the number to one, the faster the evaporation rate.

X i + m = X i , j + N ( 0 , β ( X j max − X j min ) ⋅

fi ) f max

(9)

Where: Xi+m : Pheromone mutation function Xjmin : Smallest node number Xjmin : Largest node number fi : Travelled distance fmax : Maximum distance Equation (9) was used to increase the variations of pheromone layer by altering the elements of the pheromone matrix, ρmat.

D. Cloning This process was adopted from Artificial Immune System. In DEIANT, the pheromone matrix will be replicated to create several copies of the original matrix. The replicated matrix will go through mutation process afterwards.

F. Crossover Crossover operation will combine pheromone parents, ρ0i to produce pheromone offspring ρci. The parents are produced via the mutation process. The mutated pheromone matrix will be combined with the original pheromone matrix.

682

2013 IEEE 7th International Power Engineering and Optimization Conference (PEOCO2013), Langkawi, Malaysia. 3-4 June 2013

The merged matrices (offspring) will be arranged in descending order. Figure 3 portrays the mutation and crossover process.

TABLE I OPERATION LIMITS AND COST COEFFICIENT OF IEEE 30-BUS SYSTEM

G. Selection This roulette-wheel selection procedure will terminate its process only when there are sufficient selected individuals. Also known as the fitness proportionate selection, this method will select the fittest matrix after the crossover operations. The unselected matrix will be eliminated. Equation (10) below describe selection process: ⎧ ρ sel ,if pheromone level , ρ < ρ sel ρ ,otherwise ⎩

ρ sel = ⎨

Pmin (MW)

1 2 3 4 5 6

200 80 50 10 10 10

50 20 15 35 30 30

Cost Coefficient ai bi ($/MW2hr) ($/MWhr) 0.00375 2.00 0.00175 1.75 0.06250 1.00 0.00834 3.25 0.00250 3.00 0.00250 3.00

ci ($/hr) 0 0 0 0 0 0

TABLE II COMPARISON OF UNIT COMMITMENT SOLUTION BEFORE AND AFTER FUZZY SET MODELING

H. Control Variable Calculation The control variable x will be used to find the objective function. The control variable can be calculated by equation (11) :

d ⋅ x max d max

Pmax (MW)

A. Fuzzy Modeling Verification The unit commitment optimal dispatch were solved by using the conventional (without fuzzy modeling) method and compared with the fuzzy set modeling. Table II tabulates the comparison between the two methods:

(10)

Where ρsel is the selected pheromone and ρ is the original pheromone. If ρsel is fitter than ρ, therefore, ρsel will be selected and vice versa.

x=

Generating Unit

Units 1 2 3 4 5 6 Total Demand (MW) Total Dispatch (MW) PLoss (MW) Total Cost ($/hr)

(11)

Where: d : distance of ant tour dmax : maximum distance xmax : maximum value of x

I. Second Update The best ant from the colony that carries the best solution will be selected during the global updating rule. The solution will be assigned as the first node for the next iteration.

Without Fuzzy (MW) 447.548 173.087 263.363 138.716 166.099 86.939

With Fuzzy (MW) 446.979 172.518 261.153 140.209 165.361 87.297

1263

1263

1275.752

1273.518

12.752

10.5181

15447

15417.91

The data from table II indicates that there are several differences between the generation outputs of the two methods. The total dispatch calculated by fuzzy modeling (1273.518MW) is smaller than the one without fuzzy modeling (1275.752MW). By referring to the total demand (1263MW), the fuzzy modeling dispatches output at a closer value to the total demand than the conventional method does. As a result, the power loss, PLoss (10.5181MW) is smaller than the one calculated by the conventional method (12.752MW). Moreover, the fuzzy modeling has cut down the total operating cost from 15447$/hr to 15417.91$/hr. Therefore, the fuzzy modeling can help the utilities to save their investment around 29.09$/hr. A smaller power loss and smaller cost indicates that the fuzzy modeling approach has better performance than the conventional method.

J. Termination The algorithm will terminate its processes either when it hits the maximum number of iteration (Itmax), or when the best solution has been obtained. IV. RESULTS & DISCUSSION The development of Differential Evolution Immunized Ant Colony Optimization algorithm and fuzzy unit commitment problem were implemented on MATLAB. In this research, the algorithm was employed to determine the optimal dispatch of unit commitment problem on IEEE 30-Bus system with 6 generating units. However, the optimization problems were bounded by several constraints and uncertainties that can be determined by using fuzzy set modeling. Table I tabulates the operation limits and operating cost coefficient for each generator.

683

2013 IEEE 7th International Power Engineering and Optimization Conference (PEOCO2013), Langkawi, Malaysia. 3-4 June 2013

B. Fuzzy Unit Commitment Optimization In this research, the fuzzy unit commitment problems were optimized with several techniques including Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), and Differential Evolution Immunized Ant Colony Optimization (DEIANT) technique. Table III tabulates the comparisons among these three approaches:

implements several approaches including PSO, ACO, and DEIANT optimization techniques. Comparative studies indicate that fuzzy unit commitment produces better solution than the conventional methods. Moreover, DEIANT optimization technique has been verified to bear the best solution for unit commitment among the other two techniques. Future works will focus on the development of fuzzy unit commitment that will consider environment and pollutant level as constraints.

Table III COMPARISON OF FUZZY UNIT COMMITMENT OPTIMIZATION TECHNIQUES

Techniques

PSO

ACO

DEIANT

U1 U2 U3 U4 U5 U6 Total Demand (MW) Total Dispatch (MW) PLoss (MW) Total Cost ($/hr) Computation Time (s)

446.819 172.287 261.034 139.677 166.410 86.325

446.833 172.311 261.200 140.532 165.279 86.433

446.706 172.352 261.114 139.870 165.439 86.995

1263

1263

1263

1272.552

1272.588

1272.476

9.552

9.588

9.476

15404.83

15405.64

15403.99

27.1149

20.6207

1.7360

ACKNOWLEDGEMENT The authors would like to acknowledge The Research Management Institute (RMI) UiTM Shah Alam, Ministry of Higher Education Malaysia (MOHE) and Faculty of Electrical Engineering UiTM for the financial support of this research. This research is partly supported by MOHE under the Research Acculturation Grant Scheme (RAGS) with project code: 600-RMI/RAGS 5/3(49/2012). REFERENCES [1] [2] [3]

Where U1 to U6 represents the generation unit 1 to unit 6. The fuzzy modeling produces better solutions after the employment of optimization techniques. By referring to table III, ACO approach computes the largest loss (9.588MW) and cost (15405.64$/hr). However, the computation time (20.6207s) is slightly faster than PSO (27.1149s) but lags behind DEIANT (1.7360s). PSO offers better dispatch solution (1272.552MW), lower loss (9.552MW) and lower operating cost (15404.83$/hr) than ACO. However, PSO computation time is slower than ACO. The comparison between PSO and ACO brought up clearer understanding on the behavior and characteristic of both algorithms. PSO technique offers better fitness solutions despite its slow computation time. On the other hand, ACO offers fast computation time over fitness computation. Nonetheless, DEIANT algorithm came up with the best solution among the three techniques. Within 1.7360s, it calculates the lowest power loss (9.476MW) and minimizes the operating cost (15403.99$/hr). Altogether, DEIANT provides the best solution among the three algorithms

[4]

[5]

[6]

[7]

[8]

[9] [10]

V. CONCLUSION

[11]

This research emphasizes on the implementation of fuzzy set modeling to determine the uncertainty constraints in solving unit commitment problems. Ignoring the uncertainty constraints, especially in the deregulated power industry, may give rise to unwanted issues. Furthermore, in an effort to optimize the solution of fuzzy unit commitment, this research

[12]

684

M. Y. El-Sharkh, et al., "Fuzzy unit commitment using the Ant Colony Search Algorithm," in Electric Power and Energy Conference (EPEC), 2010 IEEE, 2010, pp. 1-6. A. K. B. P.K. Hota, R. Chakrabarti, "Economic Emission Load Dispatch Through Fuzzy Based Bacterial Foraging Algorithm," Electric Power and Energy Systems, vol. 32, pp. 794-803, 2010. Hatim Y. Yamin, ‘‘Fuzzy Self-Scheduling for GenCos,’’ IEEE Trans. Power Sys, vol. 20, no. 1, pp. 503---505, Feb. 2005. S. S. Balamurugan R, "Hybrid Integer Coded Differential Evolution Dynamic Programming Approach for Economic Load Dispatch With Multiple Fuel Options " International Journal of Energy Convers Manage, vol. 49, pp. 608-614, 2008. S. Krishnamurthy and R. Tzoneva, "Impact of price penalty factors on the solution of the combined economic emission dispatch problem using cubic criterion functions," in Power and Energy Society General Meeting, 2012 IEEE, 2012, pp. 1-9. T.S. Dillon, K.W. Edwin, H.D. Kochs, and R.J. Taud, “Integer programming approach to the problem of optimal unit commitment with probabilistic reserve determination,” IEEE Transaction on Power Apparatus and Systems, vol. 97, pp. 2154-2166, 1978. A. B. M. Nasiruzzaman and M. G. Rabbani, "Implementation of Genetic Algorithm and fuzzy logic in economic dispatch problem," in Electrical and Computer Engineering, 2008. ICECE 2008. International Conference on, 2008, pp. 360-365. B. Goswami and V. Agrawal, "Security Constrained Economic Dispatch using a hybrid Fuzzy Genetic Algorithm approach," in Computer Communication and Informatics (ICCCI), 2013 International Conference on, 2013, pp. 1-6. J. Y. K.P Wang, "Evolutionary Programming Based Algorithm for Environmentally Constrained Economic Dispatch," IEEE Transection on Power System, vol. 13, pp. 301-306, 1998. T. S. Prasanna and P. Somasundaram, "Fuzzy mutated evolutionary programming based algorithm for combined economic and emission dispatch," in TENCON 2008 - 2008 IEEE Region 10 Conference, 2008, pp. 1-5. V. Ravikumar Pandi and B. K. Panigrahi, "Dynamic economic load dispatch using hybrid swarm intelligence based harmony search algorithm," Expert Systems with Applications, vol. 38, pp. 8509-8514, 2011. R. Gopalakrishnan and A. Krishnan, "Intelligence technique to solve combined economic and emission dispatch," in Pattern Recognition, Informatics and Medical Engineering (PRIME), 2012 International Conference on, 2012, pp. 347-352.

2013 IEEE 7th International Power Engineering and Optimization Conference (PEOCO2013), Langkawi, Malaysia. 3-4 June 2013

[13] I. A. Farhat and M. E. El-Hawary, "Bacterial foraging algorithm for optimum economic-emission dispatch," in Electrical Power and Energy Conference (EPEC), 2011 IEEE, 2011, pp. 182-186. [14] R.-A. Hooshmand, et al., "Emission, reserve and economic load dispatch problem with non-smooth and non-convex cost functions using the hybrid bacterial foraging-Nelder–Mead algorithm," Applied Energy, vol. 89, pp. 443-453, 2012. [15] Y. Wang, et al., "Estimation of distribution and differential evolution cooperation for large scale economic load dispatch optimization of power systems," Information Sciences, vol. 180, pp. 2405-2420, 2010. [16] Z. Zhisheng, "Quantum-behaved particle swarm optimization algorithm for economic load dispatch of power system," Expert Systems with Applications, vol. 37, pp. 1800-1803, 2010. [17] K. K. Swarnkar, et al., "Optimal Power Flow of large distribution system solution for Combined Economic Emission Dispatch Problem using Partical Swarm Optimization," in Power Systems, 2009. ICPS '09. International Conference on, 2009, pp. 1-5. [18] A. S. Xiaohui Yuan, Yanbin Yuan, Hao Nie, Liang Wang, "An improved PSO for dynamic load dispatch of generators with valve-point effects," Energy Conversion and Management, vol. 34, pp. 67-74, 17 October 2008 2009. [19] T. Sum-Im, "Self-adaptive differential evolution algorithm for economic dispatch with transmission losses consideration," in TENCON 2010 2010 IEEE Region 10 Conference, 2010, pp. 90-95. [20] P. K. Hota, R. Chakrabarti, and P. K. Chattopadhyay ‘‘Economic emission load dispatch through an interactive fuzzy satisfying method,’’ Electric Power Syst. Res., vol. 1, no. 3, pp. 100---103, 2005. [21] S.M. Shahidepour and K.H. Abdul-Rahman, “A Fuzzy-Based Optimal Reactive Power Control,” IEEE Transactions on Power Systems, vol. 8, no. 2, pp. 665-669, May 1993. [22] Z. Li, M. Shahidehpour, ’’Security-constraint unit commitment for simultaneous clearing of energy and ancillary services markets,’’ IEEE rans on Power Systems, vol. 20, no. 2, pp. 1079---88, April 2005. [23] M. F. Bedrifiana, et al., "Decisions in Power System Operation based on Fuzzy Economic and Environmental Dispatch," in Power Tech, 2007 IEEE Lausanne, 2007, pp. 1296-1301. [24] J. C. Y. Lai, et al., "Economic load dispatch using intelligent optimization with fuzzy control," in Fuzzy Systems (FUZZ), 2011 IEEE International Conference on, 2011, pp. 2219-2224. [25] V. Miranda and H. Pun Sio, "Economic dispatch model with fuzzy wind constraints and attitudes of dispatchers," Power Systems, IEEE Transactions on, vol. 20, pp. 2143-2145, 2005. [26] G. Hongyuan and D. Ming, "Multiuser Detection Using Immune Ant Colony Optimization," in Artificial Intelligence and Computational Intelligence, 2009. AICI '09. International Conference on, 2009, pp. 109-113. [27] S. T. A. Kaveh, "An Improved Ant Colony Optimization for Constrained Engineering Design Problems," International Journal for Computer Aided Engineering and Software, vol. 27, pp. 155-182, 2010.

685