stochastic programming for hydropower operations
play

Stochastic Programming for Hydropower Operations Modeling and - PowerPoint PPT Presentation

Mar 27, 2023 •253 likes •1.46k views

Stochastic Programming for Hydropower Operations Modeling and Algorithms Martin Biel KTH - Royal Institute of Technology JUNE 28, 2018 Price forecasts Irregular power production: solar and wind Nuclear power phase-out Common:

  1. • No clearcut way to calculate stochastic measures: EVPI, VSS • The model creation is somewhat infmexible • Parallel L-shaped using the Distributed module in Julia… • …but StructJuMP relies on MPI • Creating a new hydromodel involves reimplementing a new type Initial Approach - Issues Martin Biel (KTH) Stochastic Programming for Hydropower 7 / 25 • A lot of code repetition

  2. • The model creation is somewhat infmexible • Parallel L-shaped using the Distributed module in Julia… • …but StructJuMP relies on MPI • Creating a new hydromodel involves reimplementing a new type Initial Approach - Issues Martin Biel (KTH) Stochastic Programming for Hydropower 7 / 25 • A lot of code repetition • No clearcut way to calculate stochastic measures: EVPI, VSS

  3. • Parallel L-shaped using the Distributed module in Julia… • …but StructJuMP relies on MPI • Creating a new hydromodel involves reimplementing a new type Initial Approach - Issues Martin Biel (KTH) Stochastic Programming for Hydropower 7 / 25 • A lot of code repetition • No clearcut way to calculate stochastic measures: EVPI, VSS • The model creation is somewhat infmexible

  4. • …but StructJuMP relies on MPI • Creating a new hydromodel involves reimplementing a new type Initial Approach - Issues Martin Biel (KTH) Stochastic Programming for Hydropower 7 / 25 • A lot of code repetition • No clearcut way to calculate stochastic measures: EVPI, VSS • The model creation is somewhat infmexible • Parallel L-shaped using the Distributed module in Julia…

  5. • Creating a new hydromodel involves reimplementing a new type Initial Approach - Issues Martin Biel (KTH) Stochastic Programming for Hydropower 7 / 25 • A lot of code repetition • No clearcut way to calculate stochastic measures: EVPI, VSS • The model creation is somewhat infmexible • Parallel L-shaped using the Distributed module in Julia… • …but StructJuMP relies on MPI

  6. Initial Approach - Issues Martin Biel (KTH) Stochastic Programming for Hydropower 7 / 25 • A lot of code repetition • No clearcut way to calculate stochastic measures: EVPI, VSS • The model creation is somewhat infmexible • Parallel L-shaped using the Distributed module in Julia… • …but StructJuMP relies on MPI • Creating a new hydromodel involves reimplementing a new type

  7. ∘ Flexible model creation ∘ Parallel capabilities based on the Distributed module ∘ Stochastic programming constructs ∘ Model creation focused on data and optimization formulation ∘ Effjcient model reinitialization ∘ Predefjned models • Short-term production planning • Optimal orders on the day-ahead market New Approach Martin Biel (KTH) Stochastic Programming for Hydropower 8 / 25 • StochasticPrograms.jl • HydroModels.jl

  8. ∘ Parallel capabilities based on the Distributed module ∘ Stochastic programming constructs ∘ Model creation focused on data and optimization formulation ∘ Effjcient model reinitialization ∘ Predefjned models • Short-term production planning • Optimal orders on the day-ahead market New Approach Martin Biel (KTH) Stochastic Programming for Hydropower 8 / 25 • StochasticPrograms.jl ∘ Flexible model creation • HydroModels.jl

  9. ∘ Stochastic programming constructs ∘ Model creation focused on data and optimization formulation ∘ Effjcient model reinitialization ∘ Predefjned models • Short-term production planning • Optimal orders on the day-ahead market New Approach Martin Biel (KTH) Stochastic Programming for Hydropower 8 / 25 • StochasticPrograms.jl ∘ Flexible model creation ∘ Parallel capabilities based on the Distributed module • HydroModels.jl

  10. ∘ Model creation focused on data and optimization formulation ∘ Effjcient model reinitialization ∘ Predefjned models • Short-term production planning • Optimal orders on the day-ahead market New Approach Martin Biel (KTH) Stochastic Programming for Hydropower 8 / 25 • StochasticPrograms.jl ∘ Flexible model creation ∘ Parallel capabilities based on the Distributed module ∘ Stochastic programming constructs • HydroModels.jl

  11. ∘ Effjcient model reinitialization ∘ Predefjned models • Short-term production planning • Optimal orders on the day-ahead market New Approach Martin Biel (KTH) Stochastic Programming for Hydropower 8 / 25 • StochasticPrograms.jl ∘ Flexible model creation ∘ Parallel capabilities based on the Distributed module ∘ Stochastic programming constructs • HydroModels.jl ∘ Model creation focused on data and optimization formulation

  12. ∘ Predefjned models • Short-term production planning • Optimal orders on the day-ahead market New Approach Martin Biel (KTH) Stochastic Programming for Hydropower 8 / 25 • StochasticPrograms.jl ∘ Flexible model creation ∘ Parallel capabilities based on the Distributed module ∘ Stochastic programming constructs • HydroModels.jl ∘ Model creation focused on data and optimization formulation ∘ Effjcient model reinitialization

  13. New Approach Martin Biel (KTH) Stochastic Programming for Hydropower 8 / 25 • StochasticPrograms.jl ∘ Flexible model creation ∘ Parallel capabilities based on the Distributed module ∘ Stochastic programming constructs • HydroModels.jl ∘ Model creation focused on data and optimization formulation ∘ Effjcient model reinitialization ∘ Predefjned models • Short-term production planning • Optimal orders on the day-ahead market

  14. StochasticPrograms.jl - Simple Example where Stochastic Programming for Hydropower Martin Biel (KTH) s.t. minimize Q ( x 1 , x 2 , 𝜊) = min y 1 , y 2 ∈ℝ x 1 , x 2 ∈ℝ s.t. 9 / 25 100 x 1 + 150 x 2 + 𝔽 𝜕 [ Q ( x 1 , x 2 , 𝜊)] x 1 + x 2 ≤ 120 x 1 ≥ 40 x 2 ≥ 20 q 1 (𝜊) y 1 + q 2 (𝜊) y 2 6 y 1 + 10 y 2 ≤ 60 x 1 8 y 1 + 5 y 2 ≤ 80 x 2 0 ≤ y 1 ≤ d 1 (𝜊) 0 ≤ y 2 ≤ d 2 (𝜊)

  15. StochasticPrograms.jl - Simple Example Martin Biel (KTH) Stochastic Programming for Hydropower 10 / 25 sp = StochasticProgram(solver=ClpSolver()) @first_stage sp = begin @variable(model, x₁ >= 40) @variable(model, x₂ >= 20) @objective(model, Min, 100*x₁ + 150*x₂) @constraint(model, x₁+x₂ <= 120) end @second_stage sp = begin @decision x₁ x₂ s = scenario @variable(model, 0 <= y₁ <= s.d[1]) @variable(model, 0 <= y₂ <= s.d[2]) @objective(model, Min, s.q[1]*y₁ + s.q[2]*y₂) @constraint(model, 6*y₁ + 10*y₂ <= 60*x₁) @constraint(model, 8*y₁ + 5*y₂ <= 80*x₂) end

  16. StochasticPrograms.jl - Simple Example Creates a generator function for the fjrst stage model Stochastic Programming for Hydropower Martin Biel (KTH) 10 / 25 sp = StochasticProgram(solver=ClpSolver()) @first_stage sp = begin @variable(model, x₁ >= 40) @variable(model, x₂ >= 20) @objective(model, Min, 100*x₁ + 150*x₂) @constraint(model, x₁+x₂ <= 120) end @second_stage sp = begin @decision x₁ x₂ s = scenario @variable(model, 0 <= y₁ <= s.d[1]) @variable(model, 0 <= y₂ <= s.d[2]) @objective(model, Min, s.q[1]*y₁ + s.q[2]*y₂) @constraint(model, 6*y₁ + 10*y₂ <= 60*x₁) @constraint(model, 8*y₁ + 5*y₂ <= 80*x₂) end

  17. StochasticPrograms.jl - Simple Example Creates a generator function for the second stage model Stochastic Programming for Hydropower Martin Biel (KTH) 10 / 25 sp = StochasticProgram(solver=ClpSolver()) @first_stage sp = begin @variable(model, x₁ >= 40) @variable(model, x₂ >= 20) @objective(model, Min, 100*x₁ + 150*x₂) @constraint(model, x₁+x₂ <= 120) end @second_stage sp = begin @decision x₁ x₂ s = scenario @variable(model, 0 <= y₁ <= s.d[1]) @variable(model, 0 <= y₂ <= s.d[2]) @objective(model, Min, s.q[1]*y₁ + s.q[2]*y₂) @constraint(model, 6*y₁ + 10*y₂ <= 60*x₁) @constraint(model, 8*y₁ + 5*y₂ <= 80*x₂) end

  18. StochasticPrograms.jl - Simple Example Explicitly denote that some variables originate from the fjrst stage Stochastic Programming for Hydropower Martin Biel (KTH) 10 / 25 sp = StochasticProgram(solver=ClpSolver()) @first_stage sp = begin @variable(model, x₁ >= 40) @variable(model, x₂ >= 20) @objective(model, Min, 100*x₁ + 150*x₂) @constraint(model, x₁+x₂ <= 120) end @second_stage sp = begin @decision x₁ x₂ s = scenario @variable(model, 0 <= y₁ <= s.d[1]) @variable(model, 0 <= y₂ <= s.d[2]) @objective(model, Min, s.q[1]*y₁ + s.q[2]*y₂) @constraint(model, 6*y₁ + 10*y₂ <= 60*x₁) @constraint(model, 8*y₁ + 5*y₂ <= 80*x₂) end

  19. StochasticPrograms.jl - Simple Example Injection point for scenario data Stochastic Programming for Hydropower Martin Biel (KTH) 10 / 25 sp = StochasticProgram(solver=ClpSolver()) @first_stage sp = begin @variable(model, x₁ >= 40) @variable(model, x₂ >= 20) @objective(model, Min, 100*x₁ + 150*x₂) @constraint(model, x₁+x₂ <= 120) end @second_stage sp = begin @decision x₁ x₂ s = scenario @variable(model, 0 <= y₁ <= s.d[1]) @variable(model, 0 <= y₂ <= s.d[2]) @objective(model, Min, s.q[1]*y₁ + s.q[2]*y₂) @constraint(model, 6*y₁ + 10*y₂ <= 60*x₁) @constraint(model, 8*y₁ + 5*y₂ <= 80*x₂) end

  20. StochasticPrograms.jl - Simple Example Martin Biel (KTH) Stochastic Programming for Hydropower 11 / 25 struct SimpleScenario <: AbstractScenarioData p:: Float64 d:: Vector { Float64 } q:: Vector { Float64 } end StochasticPrograms.probability(s::SimpleScenario) = s.p

  21. StochasticPrograms.jl - Simple Example Add two scenarios to the stochastic program Martin Biel (KTH) Stochastic Programming for Hydropower 11 / 25 struct SimpleScenario <: AbstractScenarioData p:: Float64 d:: Vector { Float64 } q:: Vector { Float64 } end StochasticPrograms.probability(s::SimpleScenario) = s.p s1 = SimpleScenario(0.4,[500.0,100],[-24.0,-28]) s2 = SimpleScenario(0.6,[300.0,300],[-28.0,-32]) append!(sp,[s1,s2])

  22. StochasticPrograms.jl - Simple Example Martin Biel (KTH) Stochastic Programming for Hydropower 11 / 25 print(sp)

  23. StochasticPrograms.jl - Simple Example Martin Biel (KTH) Stochastic Programming for Hydropower 11 / 25 print(sp) First-stage ============== Min 100 x₁ + 150 x₂ Subject to x₁ + x₂ ≤ 120 x₁ ≥ 40 x₂ ≥ 20 Second-stage ============== Subproblem 1: Min -24 y₁ - 28 y₂ Subject to 6 y₁ + 10 y₂ - 60 x₁ ≤ 0 8 y₁ + 5 y₂ - 80 x₂ ≤ 0 0 ≤ y₁ ≤ 500 0 ≤ y₂ ≤ 100 Subproblem 2: Min -28 y₁ - 32 y₂ Subject to 6 y₁ + 10 y₂ - 60 x₁ ≤ 0 8 y₁ + 5 y₂ - 80 x₂ ≤ 0 0 ≤ y₁ ≤ 300 0 ≤ y₂ ≤ 300

  24. • JuMP models are not created instantly • Model defjnitions are stored in generating lambda functions • These model recipes are then used as building blocks • The generating functions contain certain placeholders keywords • Upon model creation, the keywords contain the required data fjelds • Flexible model creation and reformulation • Effjcient parallel implementation • Versatility Implementation Details Deferred model creation Data injection Implications Martin Biel (KTH) Stochastic Programming for Hydropower 12 / 25

  25. • Model defjnitions are stored in generating lambda functions • These model recipes are then used as building blocks • The generating functions contain certain placeholders keywords • Upon model creation, the keywords contain the required data fjelds • Flexible model creation and reformulation • Effjcient parallel implementation • Versatility Implementation Details Deferred model creation Data injection Implications Martin Biel (KTH) Stochastic Programming for Hydropower 12 / 25 • JuMP models are not created instantly

  26. • These model recipes are then used as building blocks • The generating functions contain certain placeholders keywords • Upon model creation, the keywords contain the required data fjelds • Flexible model creation and reformulation • Effjcient parallel implementation • Versatility Implementation Details Deferred model creation Data injection Implications Martin Biel (KTH) Stochastic Programming for Hydropower 12 / 25 • JuMP models are not created instantly • Model defjnitions are stored in generating lambda functions

  27. • The generating functions contain certain placeholders keywords • Upon model creation, the keywords contain the required data fjelds • Flexible model creation and reformulation • Effjcient parallel implementation • Versatility Implementation Details Deferred model creation Data injection Implications Martin Biel (KTH) Stochastic Programming for Hydropower 12 / 25 • JuMP models are not created instantly • Model defjnitions are stored in generating lambda functions • These model recipes are then used as building blocks

  28. • The generating functions contain certain placeholders keywords • Upon model creation, the keywords contain the required data fjelds • Flexible model creation and reformulation • Effjcient parallel implementation • Versatility Implementation Details Deferred model creation Data injection Implications Martin Biel (KTH) Stochastic Programming for Hydropower 12 / 25 • JuMP models are not created instantly • Model defjnitions are stored in generating lambda functions • These model recipes are then used as building blocks

  29. • Upon model creation, the keywords contain the required data fjelds • Flexible model creation and reformulation • Effjcient parallel implementation • Versatility Implementation Details Deferred model creation Data injection Implications Martin Biel (KTH) Stochastic Programming for Hydropower 12 / 25 • JuMP models are not created instantly • Model defjnitions are stored in generating lambda functions • These model recipes are then used as building blocks • The generating functions contain certain placeholders keywords

  30. • Flexible model creation and reformulation • Effjcient parallel implementation • Versatility Implementation Details Deferred model creation Data injection Implications Martin Biel (KTH) Stochastic Programming for Hydropower 12 / 25 • JuMP models are not created instantly • Model defjnitions are stored in generating lambda functions • These model recipes are then used as building blocks • The generating functions contain certain placeholders keywords • Upon model creation, the keywords contain the required data fjelds

  31. • Flexible model creation and reformulation • Effjcient parallel implementation • Versatility Implementation Details Deferred model creation Data injection Implications Martin Biel (KTH) Stochastic Programming for Hydropower 12 / 25 • JuMP models are not created instantly • Model defjnitions are stored in generating lambda functions • These model recipes are then used as building blocks • The generating functions contain certain placeholders keywords • Upon model creation, the keywords contain the required data fjelds

  32. • Effjcient parallel implementation • Versatility Implementation Details Deferred model creation Data injection Implications Martin Biel (KTH) Stochastic Programming for Hydropower 12 / 25 • JuMP models are not created instantly • Model defjnitions are stored in generating lambda functions • These model recipes are then used as building blocks • The generating functions contain certain placeholders keywords • Upon model creation, the keywords contain the required data fjelds • Flexible model creation and reformulation

  33. • Versatility Implementation Details Deferred model creation Data injection Implications Martin Biel (KTH) Stochastic Programming for Hydropower 12 / 25 • JuMP models are not created instantly • Model defjnitions are stored in generating lambda functions • These model recipes are then used as building blocks • The generating functions contain certain placeholders keywords • Upon model creation, the keywords contain the required data fjelds • Flexible model creation and reformulation • Effjcient parallel implementation

  34. Implementation Details Deferred model creation Data injection Implications Martin Biel (KTH) Stochastic Programming for Hydropower 12 / 25 • JuMP models are not created instantly • Model defjnitions are stored in generating lambda functions • These model recipes are then used as building blocks • The generating functions contain certain placeholders keywords • Upon model creation, the keywords contain the required data fjelds • Flexible model creation and reformulation • Effjcient parallel implementation • Versatility

  35. dep = DEP(sp) Minimization problem with: * 5 linear constraints * 6 variables Solver is ClpMathProg • First stage generator • Second stage generator on all available scenarios • Connections possible due to the @decision annotation • DEP model is cached internally until new scenarios are added Stochastic Programming for Hydropower Martin Biel (KTH) StochasticPrograms.jl - Deterministically Equivalent Model minimize Ax = b s.t. c T x + 𝔽 𝜕 [ Q ( x , 𝜊(𝜕))] x ∈ℝ n 13 / 25

  36. • First stage generator • Second stage generator on all available scenarios • Connections possible due to the @decision annotation • DEP model is cached internally until new scenarios are added StochasticPrograms.jl - Deterministically Equivalent Model minimize Stochastic Programming for Hydropower Martin Biel (KTH) 13 / 25 Ax = b s.t. c T x + 𝔽 𝜕 [ Q ( x , 𝜊(𝜕))] x ∈ℝ n dep = DEP(sp) Minimization problem with: * 5 linear constraints * 6 variables Solver is ClpMathProg

  37. • Second stage generator on all available scenarios • Connections possible due to the @decision annotation • DEP model is cached internally until new scenarios are added StochasticPrograms.jl - Deterministically Equivalent Model minimize Stochastic Programming for Hydropower Martin Biel (KTH) 13 / 25 s.t. Ax = b c T x + 𝔽 𝜕 [ Q ( x , 𝜊(𝜕))] x ∈ℝ n dep = DEP(sp) Minimization problem with: * 5 linear constraints * 6 variables Solver is ClpMathProg • First stage generator

  38. • Connections possible due to the @decision annotation • DEP model is cached internally until new scenarios are added StochasticPrograms.jl - Deterministically Equivalent Model minimize Stochastic Programming for Hydropower Martin Biel (KTH) 13 / 25 Ax = b s.t. c T x + 𝔽 𝜕 [ Q ( x , 𝜊(𝜕))] x ∈ℝ n dep = DEP(sp) Minimization problem with: * 5 linear constraints * 6 variables Solver is ClpMathProg • First stage generator • Second stage generator on all available scenarios

  39. • DEP model is cached internally until new scenarios are added StochasticPrograms.jl - Deterministically Equivalent Model minimize Stochastic Programming for Hydropower Martin Biel (KTH) 13 / 25 s.t. Ax = b c T x + 𝔽 𝜕 [ Q ( x , 𝜊(𝜕))] x ∈ℝ n dep = DEP(sp) Minimization problem with: * 5 linear constraints * 6 variables Solver is ClpMathProg • First stage generator • Second stage generator on all available scenarios • Connections possible due to the @decision annotation

  40. StochasticPrograms.jl - Deterministically Equivalent Model minimize Stochastic Programming for Hydropower Martin Biel (KTH) 13 / 25 Ax = b s.t. c T x + 𝔽 𝜕 [ Q ( x , 𝜊(𝜕))] x ∈ℝ n dep = DEP(sp) Minimization problem with: * 5 linear constraints * 6 variables Solver is ClpMathProg • First stage generator • Second stage generator on all available scenarios • Connections possible due to the @decision annotation • DEP model is cached internally until new scenarios are added

  41. StochasticPrograms.jl - Deterministically Equivalent Model Martin Biel (KTH) Stochastic Programming for Hydropower 13 / 25 print(dep)

  42. StochasticPrograms.jl - Deterministically Equivalent Model Martin Biel (KTH) Stochastic Programming for Hydropower 13 / 25 print(dep) Min 100 x₁ + 150 x₂ - 9.6 y₁_1 - 11.2 y₂_1 - 16.8 y₁_2 - 19.2 y₂_2 Subject to x₁ + x₂ ≤ 120 6 y₁_1 + 10 y₂_1 - 60 x₁ ≤ 0 8 y₁_1 + 5 y₂_1 - 80 x₂ ≤ 0 6 y₁_2 + 10 y₂_2 - 60 x₁ ≤ 0 8 y₁_2 + 5 y₂_2 - 80 x₂ ≤ 0 x₁ ≥ 40 x₂ ≥ 20 0 ≤ y₁_1 ≤ 500 0 ≤ y₂_1 ≤ 100 0 ≤ y₁_2 ≤ 300 0 ≤ y₂_2 ≤ 300

  43. • Extended form solve(sp,solver=ClpSolver()) :Optimal getobjectivevalue(sp) -855.83 • L-shaped solve(sp,solver=LShapedSolver(:ls,ClpSolver())) L-Shaped Gap Time: 0:00:01 (4 iterations) Objective: -855.8333333333358 Gap: 2.1229209144670507e-15 Number of cuts: 5 :Optimal • Convenience function (Value of the recourse problem) VRP(sp,solver=ClpSolver()) -855.83 Stochastic Programming for Hydropower StochasticPrograms.jl - Solving Models Martin Biel (KTH) 14 / 25

  44. • L-shaped solve(sp,solver=LShapedSolver(:ls,ClpSolver())) L-Shaped Gap Time: 0:00:01 (4 iterations) Objective: -855.8333333333358 Gap: 2.1229209144670507e-15 Number of cuts: 5 :Optimal • Convenience function (Value of the recourse problem) VRP(sp,solver=ClpSolver()) -855.83 Stochastic Programming for Hydropower Martin Biel (KTH) StochasticPrograms.jl - Solving Models 14 / 25 • Extended form solve(sp,solver=ClpSolver()) :Optimal getobjectivevalue(sp) -855.83

  45. • Convenience function (Value of the recourse problem) VRP(sp,solver=ClpSolver()) -855.83 StochasticPrograms.jl - Solving Models Stochastic Programming for Hydropower Martin Biel (KTH) 14 / 25 • Extended form solve(sp,solver=ClpSolver()) :Optimal getobjectivevalue(sp) -855.83 • L-shaped solve(sp,solver=LShapedSolver(:ls,ClpSolver())) L-Shaped Gap Time: 0:00:01 (4 iterations) Objective: -855.8333333333358 Gap: 2.1229209144670507e-15 Number of cuts: 5 :Optimal

  46. StochasticPrograms.jl - Solving Models Martin Biel (KTH) Stochastic Programming for Hydropower 14 / 25 • Extended form solve(sp,solver=ClpSolver()) :Optimal getobjectivevalue(sp) -855.83 • L-shaped solve(sp,solver=LShapedSolver(:ls,ClpSolver())) L-Shaped Gap Time: 0:00:01 (4 iterations) Objective: -855.8333333333358 Gap: 2.1229209144670507e-15 Number of cuts: 5 :Optimal • Convenience function (Value of the recourse problem) VRP(sp,solver=ClpSolver()) -855.83

  47. ws = WS(sp,s1) Minimization problem with: * 3 linear constraints * 4 variables Solver is ClpMathProg • First stage generator • Second stage generator on the given scenario StochasticPrograms.jl - Wait-And-See Models Stochastic Programming for Hydropower Martin Biel (KTH) 𝜊 minimize ̃ for given x ≥ 0 Ax = b s.t. 𝜊) x ∈ℝ n 15 / 25 c T x + Q ( x , ̃

  48. • First stage generator • Second stage generator on the given scenario StochasticPrograms.jl - Wait-And-See Models ̃ Stochastic Programming for Hydropower Martin Biel (KTH) minimize 𝜊 for given x ≥ 0 Ax = b s.t. 𝜊) x ∈ℝ n 15 / 25 c T x + Q ( x , ̃ ws = WS(sp,s1) Minimization problem with: * 3 linear constraints * 4 variables Solver is ClpMathProg

  49. • Second stage generator on the given scenario StochasticPrograms.jl - Wait-And-See Models for given Stochastic Programming for Hydropower Martin Biel (KTH) minimize ̃ 𝜊 x ≥ 0 Ax = b s.t. 𝜊) x ∈ℝ n 15 / 25 c T x + Q ( x , ̃ ws = WS(sp,s1) Minimization problem with: * 3 linear constraints * 4 variables Solver is ClpMathProg • First stage generator

  50. StochasticPrograms.jl - Wait-And-See Models for given Stochastic Programming for Hydropower Martin Biel (KTH) minimize ̃ 𝜊 x ≥ 0 Ax = b s.t. 𝜊) x ∈ℝ n 15 / 25 c T x + Q ( x , ̃ ws = WS(sp,s1) Minimization problem with: * 3 linear constraints * 4 variables Solver is ClpMathProg • First stage generator • Second stage generator on the given scenario

  51. StochasticPrograms.jl - Wait-And-See Models Martin Biel (KTH) Stochastic Programming for Hydropower 15 / 25 print(ws)

  52. StochasticPrograms.jl - Wait-And-See Models Martin Biel (KTH) Stochastic Programming for Hydropower 15 / 25 print(ws) Min 100 x₁ + 150 x₂ - 24 y₁ - 28 y₂ Subject to x₁ + x₂ ≤ 120 6 y₁ + 10 y₂ - 60 x₁ ≤ 0 8 y₁ + 5 y₂ - 80 x₂ ≤ 0 x₁ ≥ 40 x₂ ≥ 20 0 ≤ y₁ ≤ 500 0 ≤ y₂ ≤ 100

  53. function expected(scenarios:: Vector {SimpleScenario}) return SimpleScenario(sum([s.p for s in scenarios]), sum([s.p*s.d for s in scenarios]), sum([s.p*s.q for s in scenarios])) end StochasticPrograms.jl - Expected Value Problems Must be possible to take expectation over scenarios Stochastic Programming for Hydropower Martin Biel (KTH) 𝜊 = 𝔽 𝜕 [𝜊(𝜕)] minimize ̄ where x ≥ 0 Ax = b s.t. 𝜊) x ∈ℝ n 16 / 25 c T x + Q ( x , ̄

  54. StochasticPrograms.jl - Expected Value Problems where Stochastic Programming for Hydropower Martin Biel (KTH) Must be possible to take expectation over scenarios minimize ̄ 𝜊 = 𝔽 𝜕 [𝜊(𝜕)] x ≥ 0 Ax = b s.t. 𝜊) x ∈ℝ n 16 / 25 c T x + Q ( x , ̄ function expected(scenarios:: Vector {SimpleScenario}) return SimpleScenario(sum([s.p for s in scenarios]), sum([s.p*s.d for s in scenarios]), sum([s.p*s.q for s in scenarios])) end

  55. StochasticPrograms.jl - Expected Value Problems Martin Biel (KTH) Stochastic Programming for Hydropower 16 / 25 evp = EVP(sp) Minimization problem with: * 3 linear constraints * 4 variables Solver is ClpMathProg print(evp)

  56. StochasticPrograms.jl - Expected Value Problems Martin Biel (KTH) Stochastic Programming for Hydropower 16 / 25 evp = EVP(sp) Minimization problem with: * 3 linear constraints * 4 variables Solver is ClpMathProg print(evp) Min 100 x₁ + 150 x₂ - 26.4 y₁ - 30.4 y₂ Subject to x₁ + x₂ ≤ 120 6 y₁ + 10 y₂ - 60 x₁ ≤ 0 8 y₁ + 5 y₂ - 80 x₂ ≤ 0 x₁ ≥ 40 x₂ ≥ 20 0 ≤ y₁ ≤ 380 0 ≤ y₂ ≤ 220

  57. x ̂ = [50,50]; eval_decision(sp,x ̂ ,solver=ClpSolver()) 356.0 • Create fjrst stage variables using generator • Fixate them to the given values • Generate the second stage problems • Again, linking handled through @decision • Solve resulting JuMP model Stochastic Programming for Hydropower Martin Biel (KTH) StochasticPrograms.jl - Decision Evaulation x + 𝔽 𝜕 [ Q ( ̂ x , 𝜊(𝜕))] 17 / 25 c T ̂

  58. • Fixate them to the given values • Generate the second stage problems • Again, linking handled through @decision • Solve resulting JuMP model StochasticPrograms.jl - Decision Evaulation Stochastic Programming for Hydropower Martin Biel (KTH) 17 / 25 x + 𝔽 𝜕 [ Q ( ̂ x , 𝜊(𝜕))] c T ̂ ̂ x = [50,50]; eval_decision(sp,x ̂ ,solver=ClpSolver()) 356.0 • Create fjrst stage variables using generator

  59. • Generate the second stage problems • Again, linking handled through @decision • Solve resulting JuMP model StochasticPrograms.jl - Decision Evaulation Stochastic Programming for Hydropower Martin Biel (KTH) 17 / 25 x , 𝜊(𝜕))] x + 𝔽 𝜕 [ Q ( ̂ c T ̂ ̂ x = [50,50]; eval_decision(sp,x ̂ ,solver=ClpSolver()) 356.0 • Create fjrst stage variables using generator • Fixate them to the given values

  60. • Again, linking handled through @decision • Solve resulting JuMP model StochasticPrograms.jl - Decision Evaulation Stochastic Programming for Hydropower Martin Biel (KTH) 17 / 25 x + 𝔽 𝜕 [ Q ( ̂ x , 𝜊(𝜕))] c T ̂ ̂ x = [50,50]; eval_decision(sp,x ̂ ,solver=ClpSolver()) 356.0 • Create fjrst stage variables using generator • Fixate them to the given values • Generate the second stage problems

  61. • Solve resulting JuMP model StochasticPrograms.jl - Decision Evaulation Stochastic Programming for Hydropower Martin Biel (KTH) 17 / 25 x , 𝜊(𝜕))] x + 𝔽 𝜕 [ Q ( ̂ c T ̂ ̂ x = [50,50]; eval_decision(sp,x ̂ ,solver=ClpSolver()) 356.0 • Create fjrst stage variables using generator • Fixate them to the given values • Generate the second stage problems • Again, linking handled through @decision

  62. StochasticPrograms.jl - Decision Evaulation Martin Biel (KTH) Stochastic Programming for Hydropower 17 / 25 x + 𝔽 𝜕 [ Q ( ̂ x , 𝜊(𝜕))] c T ̂ x ̂ = [50,50]; eval_decision(sp,x ̂ ,solver=ClpSolver()) 356.0 • Create fjrst stage variables using generator • Fixate them to the given values • Generate the second stage problems • Again, linking handled through @decision • Solve resulting JuMP model

  63. • Expected wait-and-see solution (EWS) EWS(sp,solver=ClpSolver()) -1518.75 • Expected value of perfect information (EVPI = VRP - EWS) EVPI(sp,solver=ClpSolver()) 662.92 • Value of the stochastic solution (VSS = EEV - VRP) VSS(sp,solver=ClpSolver()) 286.92 Stochastic Programming for Hydropower Martin Biel (KTH) Many of the required calculations are embarassingly parallel StochasticPrograms.jl - Stochastic Measures 18 / 25 • Expected value of using the expected solution (EEV) EEV(sp,solver=ClpSolver()) -568.92

  64. • Expected value of perfect information (EVPI = VRP - EWS) EVPI(sp,solver=ClpSolver()) 662.92 • Value of the stochastic solution (VSS = EEV - VRP) VSS(sp,solver=ClpSolver()) 286.92 Stochastic Programming for Hydropower Martin Biel (KTH) Many of the required calculations are embarassingly parallel StochasticPrograms.jl - Stochastic Measures 18 / 25 • Expected value of using the expected solution (EEV) EEV(sp,solver=ClpSolver()) -568.92 • Expected wait-and-see solution (EWS) EWS(sp,solver=ClpSolver()) -1518.75

  65. • Value of the stochastic solution (VSS = EEV - VRP) VSS(sp,solver=ClpSolver()) 286.92 StochasticPrograms.jl - Stochastic Measures Stochastic Programming for Hydropower Martin Biel (KTH) Many of the required calculations are embarassingly parallel 18 / 25 • Expected value of using the expected solution (EEV) EEV(sp,solver=ClpSolver()) -568.92 • Expected wait-and-see solution (EWS) EWS(sp,solver=ClpSolver()) -1518.75 • Expected value of perfect information (EVPI = VRP - EWS) EVPI(sp,solver=ClpSolver()) 662.92

  66. StochasticPrograms.jl - Stochastic Measures Many of the required calculations are embarassingly parallel Stochastic Programming for Hydropower Martin Biel (KTH) 18 / 25 • Expected value of using the expected solution (EEV) EEV(sp,solver=ClpSolver()) -568.92 • Expected wait-and-see solution (EWS) EWS(sp,solver=ClpSolver()) -1518.75 • Expected value of perfect information (EVPI = VRP - EWS) EVPI(sp,solver=ClpSolver()) 662.92 • Value of the stochastic solution (VSS = EEV - VRP) VSS(sp,solver=ClpSolver()) 286.92

  67. StochasticPrograms.jl - Stochastic Measures Many of the required calculations are embarassingly parallel Stochastic Programming for Hydropower Martin Biel (KTH) 18 / 25 • Expected value of using the expected solution (EEV) EEV(sp,solver=ClpSolver()) -568.92 • Expected wait-and-see solution (EWS) EWS(sp,solver=ClpSolver()) -1518.75 • Expected value of perfect information (EVPI = VRP - EWS) EVPI(sp,solver=ClpSolver()) 662.92 • Value of the stochastic solution (VSS = EEV - VRP) VSS(sp,solver=ClpSolver()) 286.92

  68. LShapedSolvers.jl L-shaped algorithm variants Martin Biel (KTH) Stochastic Programming for Hydropower 19 / 25 • L-shaped [Van Slyke,Wets] • Multicut L-shaped [Birge,Louveaux] • Regularized decomposition [Ruszczyński] • Trust-region L-shaped [Linderoth,Wright] • Level-set [Fábián,Szőke]

  69. • Distributed L-shaped variants 1. Distributed L-shaped with multiple cuts: LShapedSolver(:dls) 2. Distributed regularized L-shaped: LShapedSolver(:drd) 3. Distributed L-shaped with trust region: LShapedSolver(:dtr) 4. Distributed L-shaped with level sets: LShapedSolver(:dlv) • Trait based implementation. Every solver is a combination of a: ∘ Regularization trait ∘ Parallelization trait • Subproblems are solved using MathProgBase solvers Stochastic Programming for Hydropower Martin Biel (KTH) LShapedSolvers.jl 20 / 25 • L-shaped variants 1. L-shaped with multiple cuts (default): LShapedSolver(:ls) 2. L-shaped with regularized decomposition: LShapedSolver(:rd) 3. L-shaped with trust region: LShapedSolver(:tr) 4. L-shaped with level sets: LShapedSolver(:lv)

  70. • Trait based implementation. Every solver is a combination of a: ∘ Regularization trait ∘ Parallelization trait • Subproblems are solved using MathProgBase solvers LShapedSolvers.jl Stochastic Programming for Hydropower Martin Biel (KTH) 20 / 25 • L-shaped variants 1. L-shaped with multiple cuts (default): LShapedSolver(:ls) 2. L-shaped with regularized decomposition: LShapedSolver(:rd) 3. L-shaped with trust region: LShapedSolver(:tr) 4. L-shaped with level sets: LShapedSolver(:lv) • Distributed L-shaped variants 1. Distributed L-shaped with multiple cuts: LShapedSolver(:dls) 2. Distributed regularized L-shaped: LShapedSolver(:drd) 3. Distributed L-shaped with trust region: LShapedSolver(:dtr) 4. Distributed L-shaped with level sets: LShapedSolver(:dlv)

  71. • Subproblems are solved using MathProgBase solvers LShapedSolvers.jl Stochastic Programming for Hydropower Martin Biel (KTH) 20 / 25 • L-shaped variants 1. L-shaped with multiple cuts (default): LShapedSolver(:ls) 2. L-shaped with regularized decomposition: LShapedSolver(:rd) 3. L-shaped with trust region: LShapedSolver(:tr) 4. L-shaped with level sets: LShapedSolver(:lv) • Distributed L-shaped variants 1. Distributed L-shaped with multiple cuts: LShapedSolver(:dls) 2. Distributed regularized L-shaped: LShapedSolver(:drd) 3. Distributed L-shaped with trust region: LShapedSolver(:dtr) 4. Distributed L-shaped with level sets: LShapedSolver(:dlv) • Trait based implementation. Every solver is a combination of a: ∘ Regularization trait ∘ Parallelization trait

  72. LShapedSolvers.jl Martin Biel (KTH) Stochastic Programming for Hydropower 20 / 25 • L-shaped variants 1. L-shaped with multiple cuts (default): LShapedSolver(:ls) 2. L-shaped with regularized decomposition: LShapedSolver(:rd) 3. L-shaped with trust region: LShapedSolver(:tr) 4. L-shaped with level sets: LShapedSolver(:lv) • Distributed L-shaped variants 1. Distributed L-shaped with multiple cuts: LShapedSolver(:dls) 2. Distributed regularized L-shaped: LShapedSolver(:drd) 3. Distributed L-shaped with trust region: LShapedSolver(:dtr) 4. Distributed L-shaped with level sets: LShapedSolver(:dlv) • Trait based implementation. Every solver is a combination of a: ∘ Regularization trait ∘ Parallelization trait • Subproblems are solved using MathProgBase solvers

  73. • The user creates a model recipe using the @hydromodel macro • Defjne model indices • Defjne model data • Defjne modelindices(::AbstractHydroModelData, ::Horizon, args...) • Defjne optimization problem • horizon : the time horizon if the model • indices : structure with model indices • data : structure with model data HydroModels.jl Creating a Planning Problem Data injection keywords Martin Biel (KTH) Stochastic Programming for Hydropower 21 / 25 • Also based on deferred model creation and data injection

  74. • Defjne model indices • Defjne model data • Defjne modelindices(::AbstractHydroModelData, ::Horizon, args...) • Defjne optimization problem • horizon : the time horizon if the model • indices : structure with model indices • data : structure with model data HydroModels.jl Creating a Planning Problem Data injection keywords Martin Biel (KTH) Stochastic Programming for Hydropower 21 / 25 • Also based on deferred model creation and data injection • The user creates a model recipe using the @hydromodel macro

  75. • horizon : the time horizon if the model • indices : structure with model indices • data : structure with model data HydroModels.jl Creating a Planning Problem Data injection keywords Martin Biel (KTH) Stochastic Programming for Hydropower 21 / 25 • Also based on deferred model creation and data injection • The user creates a model recipe using the @hydromodel macro • Defjne model indices • Defjne model data • Defjne modelindices(::AbstractHydroModelData, ::Horizon, args...) • Defjne optimization problem

  76. HydroModels.jl Creating a Planning Problem Data injection keywords Martin Biel (KTH) Stochastic Programming for Hydropower 21 / 25 • Also based on deferred model creation and data injection • The user creates a model recipe using the @hydromodel macro • Defjne model indices • Defjne model data • Defjne modelindices(::AbstractHydroModelData, ::Horizon, args...) • Defjne optimization problem • horizon : the time horizon if the model • indices : structure with model indices • data : structure with model data

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Hydropower services and Climate Change 4 December 2019 Hydropower in the world

Hydropower services and Climate Change 4 December 2019 Hydropower in the world

IEA Hydro kick-off workshop: Hydropower services and Climate Change 4 December 2019 Hydropower in the world www.hydropower.org/status2019 www.hydropower.org/status2019 Hydropower A&amp;R services Operational flexibility and efficiency

400 views • 29 slides
NORWEP Webinar on the Covid19 situation in Hydropower markets Eddie Rich Chief Executive

NORWEP Webinar on the Covid19 situation in Hydropower markets Eddie Rich Chief Executive

NORWEP Webinar on the Covid19 situation in Hydropower markets Eddie Rich Chief Executive International Hydropower Association 22 April 2020 www.hydropower.org HYDROPOWER GROWTH IN DECADES hydropower.org/statusreport ELECTRICITY GENERATION

577 views • 14 slides
Some References P. Carpentier Master MMMEF Cours MNOS 2014-2015 263 / 263 Stochastic

Some References P. Carpentier Master MMMEF Cours MNOS 2014-2015 263 / 263 Stochastic

Stochastic Approximation and Stochastic Gradient Optimization Theory and Large Scale Systems Dual Effect and Discretization Stochastic Programming and Stochastic Optimal Control Some References P. Carpentier Master MMMEF Cours MNOS

385 views • 9 slides
Fishfriendly Innovative Technologies for Hydropower (FIThydro) IEA Hydropower, Brussels, Belgium

Fishfriendly Innovative Technologies for Hydropower (FIThydro) IEA Hydropower, Brussels, Belgium

Fishfriendly Innovative Technologies for Hydropower (FIThydro) IEA Hydropower, Brussels, Belgium 29-30 May, 2017 Peter Rutschmann Technical University Munich Key Facts Partners - 26 partners (13 research, 13 industrial) in 10 European

1k views • 24 slides
Calmness in stochastic programming exact penalization and sample approximation techniques

Calmness in stochastic programming exact penalization and sample approximation techniques

Calmness in stochastic programming exact penalization and sample approximation techniques Martin Branda Charles University in Prague Faculty of Mathematics and Physics Department of Probability and Mathematical Statistics Stochastic

940 views • 69 slides
Case study: The Benefits of Small Hydropower Bogdan Popa President of Romanian Small Hydropower

Case study: The Benefits of Small Hydropower Bogdan Popa President of Romanian Small Hydropower

Supported by the Case study: The Benefits of Small Hydropower Bogdan Popa President of Romanian Small Hydropower Association, member of EREF The Benefits of Small Hydropower Hy Hydr dropo opower in er in Eur Europe ope today and today and

381 views • 25 slides
Optimizing Infrastructure Design and Recovery Operations Under Stochastic Disruptions Siqian Shen

Optimizing Infrastructure Design and Recovery Operations Under Stochastic Disruptions Siqian Shen

Optimizing Infrastructure Design and Recovery Operations Under Stochastic Disruptions Siqian Shen Department of Industrial and Operations Engineering University of Michigan The 13th INFORMS Computing Society Conference January 07, 2013 Shen,

632 views • 34 slides
1. What is Operations Research (OR) 2 What is Operations Research? It is an application of

1. What is Operations Research (OR) 2 What is Operations Research? It is an application of

Unit 4 Systems Engineering Tools Deterministic Operations Research, Linear Programming Source: Introduction to Operations Research, 9th edition, Frederick S. Hillier, McGraw-Hill 1 1. What is Operations Research (OR) 2 What is Operations

905 views • 61 slides
Stochastic Optimization and Discretization January 06, 2021 P. Carpentier Master Optimization

Stochastic Optimization and Discretization January 06, 2021 P. Carpentier Master Optimization

Stochastic Programming: the Scenario Tree Method Stochastic Optimal Control and Discretization Puzzles A General Convergence Result Stochastic Optimization and Discretization January 06, 2021 P. Carpentier Master Optimization Stochastic

1.04k views • 59 slides
Understanding the Value of Hydropower and Pumped Storage ABHISHEK SOMANI, PNNL Feb 21, 2018 DOE

Understanding the Value of Hydropower and Pumped Storage ABHISHEK SOMANI, PNNL Feb 21, 2018 DOE

NWHA 2018, Portland - OR Understanding the Value of Hydropower and Pumped Storage ABHISHEK SOMANI, PNNL Feb 21, 2018 DOE Initiatives on Valuation of Pumped Storage and Hydropower In July 2016, the Hydropower Vision Report illustrated some

295 views • 11 slides
REGIONAL STRATEGY FOR SUSTAINABLE HYDROPOWER IN THE WESTERN BALKANS On Gap Analysis of the

REGIONAL STRATEGY FOR SUSTAINABLE HYDROPOWER IN THE WESTERN BALKANS On Gap Analysis of the

This project is funded by the European Union REGIONAL STRATEGY FOR SUSTAINABLE HYDROPOWER IN THE WESTERN BALKANS On Gap Analysis of the Legal-Regulatory and Institutional-Organisational Framework Relevant for Hydropower Development

320 views • 14 slides
Overview of Bhutan Power Sector Karma Namgyel Department of Hydropower &amp; Power Systems

Overview of Bhutan Power Sector Karma Namgyel Department of Hydropower &amp; Power Systems

Overview of Bhutan Power Sector Karma Namgyel Department of Hydropower &amp; Power Systems Ministry of Economic Affairs 1 8/24/2017 * Power Sector reforms * Role of Hydropower in the Bhutan Economy * Current Scenario (existing hydropower

1.04k views • 14 slides
Benefits from technological advances in hydropower Fredrik Ringnes April 25th 2017 About

Benefits from technological advances in hydropower Fredrik Ringnes April 25th 2017 About

&quot; Hydropower Norway 2017 Make Hydropower Great Again &quot;! Benefits from technological advances in hydropower Fredrik Ringnes April 25th 2017 About Rainpower Rainpower is an experienced project organisation based on Norwegian

352 views • 12 slides
Regional Operations Forum Planning and Programming for Operations Todays Agenda 1.

Regional Operations Forum Planning and Programming for Operations Todays Agenda 1.

Accelerating solutions for highway safety, renewal, reliability, and capacity Regional Operations Forum Planning and Programming for Operations Todays Agenda 1. Indentify the kind of program planning needed to guide TSM&amp;O improvements

746 views • 52 slides
From Stochastic Search to Programming by Optimisation: My Quest for Automating the Design of

From Stochastic Search to Programming by Optimisation: My Quest for Automating the Design of

From Stochastic Search to Programming by Optimisation: My Quest for Automating the Design of High-Performance Algorithms Holger H. Hoos Department of Computer Science University of British Columbia Canada TAO Seminar Universit e de Paris

1.22k views • 97 slides
What If We Only Have Stochastic . . . What if the Stochastic . . . Approximate Stochastic

What If We Only Have Stochastic . . . What if the Stochastic . . . Approximate Stochastic

In Finance, We Need . . . How to Make . . . From a Theoretical . . . How to Make . . . What If We Only Have Stochastic . . . What if the Stochastic . . . Approximate Stochastic Additional Reasonable . . . Dominance? The Assumption 0 &lt; .

550 views • 15 slides
Ramanujan congruences for infinite family of partition functions Shashika Petta Mestrige

Ramanujan congruences for infinite family of partition functions Shashika Petta Mestrige

Ramanujan congruences for infinite family of partition functions Shashika Petta Mestrige Louisiana State University April 13, 2019 Shashika Petta Mestrige (Louisiana State University) Ramanujan congruences for infinite family of partition

1.01k views • 61 slides
Outin, Edouard, et al. &quot; Enhancing cloud energy models for optimizing datacenters efficiency.

Outin, Edouard, et al. &quot; Enhancing cloud energy models for optimizing datacenters efficiency.

Outin, Edouard, et al. &quot; Enhancing cloud energy models for optimizing datacenters efficiency. &quot; Cloud and Autonomic Computing (ICCAC), 2015 International Conference on. IEEE, 2015. Reviewed by Cristopher Flagg December 6, 2017

331 views • 29 slides
Spe c ie s Distrib utio n Mo de ling L E CT URE 25 SPE CI E S DI ST RI BUT I ON MODE

Spe c ie s Distrib utio n Mo de ling L E CT URE 25 SPE CI E S DI ST RI BUT I ON MODE

Spe c ie s Distrib utio n Mo de ling L E CT URE 25 SPE CI E S DI ST RI BUT I ON MODE L I NG UNI T 3: ST UF F Ob je c tive s At the e nd o f this se rie s o f le c ture s, yo u sho uld b e a b le to : De fine te rms

259 views • 8 slides
pecan trees Clive H. Bock USDA-ARS-SEFTNRL, 21 Dunbar Rd., Byron, GA 31008 Overview of

pecan trees Clive H. Bock USDA-ARS-SEFTNRL, 21 Dunbar Rd., Byron, GA 31008 Overview of

Disease and spray coverage in pecan trees Clive H. Bock USDA-ARS-SEFTNRL, 21 Dunbar Rd., Byron, GA 31008 Overview of presentation Background, challenges to good fungicide coverage (particularly in relation to pecan scab) Describe

516 views • 18 slides
On quasitrivial and associative operations University of Zielona G ora Jimmy Devillet in

On quasitrivial and associative operations University of Zielona G ora Jimmy Devillet in

On quasitrivial and associative operations University of Zielona G ora Jimmy Devillet in collaboration with Miguel Couceiro and Jean-Luc Marichal University of Luxembourg Connectedness and Contour Plots Let X be a nonempty set and let F : X

460 views • 34 slides
Low-lying excitations of quantum spin-glasses Koh Yang Wei International workshop on numerical

Low-lying excitations of quantum spin-glasses Koh Yang Wei International workshop on numerical

Low-lying excitations of quantum spin-glasses Koh Yang Wei International workshop on numerical methods and simulations for materials design and strongly correlated quantum matters March 24-25, 2017. Kobe, Japan. A Personal Motivation

841 views • 25 slides
Child Welfare: parents G.S. 7B 911 &amp; Guardianship Respect right to family autonomy

Child Welfare: parents G.S. 7B 911 &amp; Guardianship Respect right to family autonomy

June 2019 Purpose Protect constitutional rights of juveniles &amp; Child Welfare: parents G.S. 7B 911 &amp; Guardianship Respect right to family autonomy Prevent inappropriate/unnecessary separation of juveniles &amp;

669 views • 8 slides
Encouraging HUB Participation Learning Objectives What is a Historically Underutilized

Encouraging HUB Participation Learning Objectives What is a Historically Underutilized

Lead the Way Encouraging HUB Participation Learning Objectives What is a Historically Underutilized Business? The Business Case for HUB participation Tools you can use to increase HUB participation What is a HUB? NC G.S. 143-128.4

210 views • 17 slides

More recommend