Solving Smart Grid Operation Problems Through Variable Neighborhood Search

Transcription

1 1 Solving Smart Grid Operation Problems Through Variable Neighborhood Search Leonardo H. Macedo, São Paulo State University-Ilha Solteira (Brazil) John F. Franco, São Paulo State University-Rosana (Brazil) Rubén Romero, São Paulo State University-Ilha Solteira (Brazil) Miguel A. Ortega-Vazquez, University of Washington-Seattle (USA) Marcos J. Rider, University of Campinas-Campinas (Brazil) Chicago - IL, July 17, 2017

2 2 Table of contents Introduction Variable neighborhood search Stochastic OPF based active-reactive power dispatch Cyclic coordinated method Nelder-Mead simplex method Local search for taps and shunts Optimal scheduling of distributed energy resources Codification Solution approach Conclusion

3 3 Introduction Stochastic OPF based active-reactive power dispatch MINLP Minimize the cost of generation and the uncertainty cost Optimal scheduling of distributed energy resources Large and complex problem Maximize the profit Proposed solution approach: variable neighborhood search Variable neighborhood descent (VND) Several methods to explore the neighborhoods

4 4 Variable neighborhood descent [1] Initialization. Select the set of neighborhood structures N k, k = 1,, k max, that will be used in the descent; find an initial solution x. Repeat the following until no improvement is obtained: (1) Set k 1; (2) Until k = k max, repeat the following steps: (a) (b) Exploration of the neighborhood. Find the best neighbor x of x; Move or not. If the solution thus obtained x is better than x, set x x and k 1; otherwise, set k k + 1.

5 5 Characteristics of the VNS algorithm Extensively used to solve problems in operations research Almost not applied to power systems problems Does not require defining parameters Population size Mutation rate Does not require tuning the algorithm to every instance of the problem Easy to implement and understand

6 6 Stochastic OPF based active-reactive power dispatch

7 7 Proposed VND algorithm Each type of control defines a neighborhood P N 1 V N 2 Tap N 3 Shunt N 4 N 5 When a neighborhood is being explored, the other controls remain fixed Several methods are used to explore each neighborhood The exploration of the neighborhoods is performed in a sequence [1] Even if an improvement is achieved in N k, the sequence is maintained

8 8 Exploration of each neighborhood Based on the following methods Cyclic coordinated method (CCM) with a line search performed by Fibonacci s algorithm [3] to explore: N 1, N 2, N 3, and N 5 Nelder-Mead simplex method with adaptive parameters [4], [5] to explore: N 1, N 2, and N 3 A local search to explore N 3 A heuristic to reduce the infeasibility due to violations in the reactive power capacity of the generators by performing a search in N 2 A simple strategy to change the status of each shunt (explore N 4 )

9 9 Cyclic coordinated method (CCM) [3] Minimizes a function in a sequence of directions Uses Fibonacci Line Search Method [3] Minimizes a strictly quasiconvex function over a bounded interval One of the most efficient algorithm for performing a line search

10 10 Nelder-Mead simplex method [4] For nonlinear unconstrained optimization Performs a sequence of reflection, expansion, contraction, and shrink operations to a initial simplex The order of these operations depends on the value of the evaluation function obtained for the vertices after each step The initial simplex is randomly generated The method is adapted to deal with a bounded search space: fix the limits at the bounds if a violation is observed The implemented version includes adaptive parameters [5] Not suitable for large problems!

11 11 Nelder-Mead simplex method [4]

12 12 Local search to adjust the taps and shunts Taps (optap) Select a tap randomly Try to increase the value of the position If this leads to an improvement of the solution, in the next time this tap is chosen, try to increase the value again Else, if this operation leads to a worse solution, then try to decrease the value of the position the next time this tap is chosen Repeat this for all taps, and until no improvement is obtained Shunts (opsh) Simple change the status from 0 to 1 or from 1 to 0

13 13 Heuristic to reduce the infeasibility Performed only in the beginning Only the infeasibility related to the reactive capacity of the generators is considered Steps If the reactive power of a generator is violating the upper bound Reduce the voltage of this generator Else, if the reactive power of a generator is violating the lower bound: Increase the voltage of this generator Repeat these steps for all generators with violations, until no improvement is obtained

14 14 Evaluation function (SOPF) For the stochastic OPF based active-reactive power dispatch problem iter: current iteration k: current neighborhood μ i k 0,1. F iter, k = f + α iter μ i k g i 2 i

15 15 Proposed algorithm 1. Generate D initial random solutions and use the best one considering α iter 0; 2. Apply the heuristic to reduce the infeasibility related to the violation of the reactive capacity of the generators; 3. Apply the CCM to N 5, then the simplex method to N 1, N 3, N 2, and N 1, with α iter 0; 2 4. Iterative process (consider F iter, k = f + α iter i μ i k g i ), it 0: while 1 if it 4 or it 10 μ i k 1 for all constraints; If it 4, α iter 0, else, (α iter 10 7 and update the incumbent with the best solution found so far considering the original evaluation function); explore N 3 (simplext), N 3 (optap), N 4 (opsh), N 2 (simplexv), N 1 (simplexp), and N 5 (ccm). else (reactive problem) α iter 10 7 ; μ i k 1 for Qgen constraints only; explore N 2 (simplexv) ; μ i k 1 for Vload constraints only; explore N 3 (optap), N 3 (simplext), and N 3 (ccm); μ i k 1 for Vload and Qgen constraints only; explore N 2 (ccm). end it it + 1. end

16 Convergence of the method 16

17 17 Optimal scheduling of distributed energy resources

18 18 Evaluation function (OSDER) Optimal scheduling of distributed energy resources F = f + α μ i g i 2 i Ω 1 i Ω 2 + μ i 2 max max g i, 0, g i Ω 1 : Constraints related to the voltage magnitudes limits on nodes and current limits on branches Ω 2 : Constraints related to the capacity of the substation α: 10000

19 19 Group of variables Large number of variables the local search strategies presented are not suitable to be applied directly To apply the VNS algorithm to this problem, the variables were grouped in different forms, for each hour of the day Only the CCM method is used as local search strategy N 1 N 2 N 3 N 4 N 5 N 6 N 7 N 8 Pdg Qdg Xdg V2G DR ESS Market Tap First form of grouping: only eight variables are used to represent all variables of the problem, one variable for each type of control Second form of grouping: eight variables are used for each hour of the day Third form of grouping: all variables are considered separately, except the V2G: one variable per node of the system per hour

20 20 Proposed algorithm 1. Generate a random initial solution; 2. Considering the first group of variables, adjust each group to optimize F; 3. Iterative process: while 1 for i=1:2 Optimize each group of variable for each hour of the day using the CCM; Use a intelligent strategy to transform each group of variable to individual variables Consider the costs of generation, for example; The order of the neighborhoods is the natural order that they appear in the vector. end Use the CCM to optimize the variables, for each hour, according to the third type of grouping. end

21 21 Results 33-node system (49,920 variables): Average fitness: [m.u.] 180-node system (154,800 variables): Average fitness: [m.u.]

22 22 Conclusion A simple VND algorithm was proposed to solve each problem Several strategies were implemented for the Exploration of the neighborhood step For the problem of optimal scheduling of distributed energy resources a codification strategy was used to reduce the number of variables Consistent results were obtained for each problem

23 23 References [1] P. Hansen and N. Mladenović, Variable neighborhood search: principles and applications, European Journal of Operational Research, vol. 130, no. 3, 2001, pp [2] N. Mladenović, M. Dražić, V. Kovačevic-Vujčić, and M. Čangalović, General variable neighborhood search for the continuous optimization, European Journal of Operational Research, vol. 191, no. 3, 2008, pp [3] M. S. Bazaraa, H. D. Sherali, and C. M. Shetty, Nonlinear programming: theory and algorithms, 3 rd Edition, Wiley-Interscience, [4] J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, Convergence properties of the Nelder-Mead simplex method in low dimensions, SIAM Journal on Optimization, vol. 9, no. 1, pp [5] F. Gao and L. Han, Implementing the Nelder-Mead simplex algorithm with adaptive parameters, Computational Optimization and Applications, vol. 51, no. 1, 2012, pp

24 24 Thank you!