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Osemosys: motivation for using it as part of the tools for the IEPPresentation by Dr. Schalk Kok

Principal Researcher, Advanced Mathematical Modelling,

Modelling and Digital Science, CSIR

[email protected]

30 March 2012

mailto:[email protected]

© CSIR 2009 www.csir.co.za

Overview: Presentation

• Numerical Optimization- Linear programming

• Gnu Linear Programming Kit (GLPK)• Osemosys• Scenario Planning

- Example• Limitations and benefits of Osemosys• Closure


Numerical optimization

• Formal mathematical technique to choose the “best” elements from a set of available alternatives- A measure is required to define “best”- Simplest techniques uses a single scalar value,

known as the objective function, cost function or merit function, to quantify which solution is better that another

• The objective can either be maximized (e.g. profit, performance) or minimized (e.g. cost, risk)

• Common practise to always minimize (maximization problems solved by minimizing the negative of the cost function)

- Usually subject to constraints (limits)



• Constraints should “oppose” the cost function i.e. a trade-off should exist between the cost function and the constraints

• Examples include- Design a minimum cost aeroplane subject to

performance constraints and strength constraints- Design a minimum cost skyscraper subject to

size constraints and strength constraints• The solution to an optimization problem is

described by the design variables, or decision variables x.

• The cost function and constraints have to expressed as functions of x.


• Minimize w.r.t. x f(x)such that g

i(x) ≤ 0 i=1,2,...p

and hj(x) = 0 j=1,2,...q

• x is the design variable vector [x1, x

2, … x

n]

• x can contain real numbers, integers, or binary variables

• f(x) is the cost function• g

i(x) is the i-th inequality constraint

• hj(x) is the j-th equality constraint



Linear programming

• If the cost function f(x) and all the constraints g(x) and h(x) are linear functions of x, the problem is known as a linear programming problem

• Linear programming algorithms are mature, and can handle many thousands design variables

• If the variables are real, the problem is convex and very efficient solution schemes exist (usually variations of the Simplex method developed by Dantzig in 1947)- Convexity guarantees a global optimum, unless

there is no feasible region


Gnu Linear Programming Kit

• Gnu Linear programming Kit (GLPK): Open source linear programming suite of programs- Consists of a mathematical programming

language Gnu Mathprog- And a solver glpsol

• A reference manual is available fromhttp://www.cs.unb.ca/~bremner/docs/glpk/gmpl.pdf

• Structured language to set up linear programming problems- Define variables, parameters, sets,

objectives and constraints- The solver computes the variables that

minimizes the objective, and satisfies all the constraints


• Parameters and sets defined for convenience (allows powerful manipulation)

• Sets are used to address the indices of multi-dimensional arrays (similar to vectors in 1D and matrices in 2D)

• Parameters are used to store known numerical values that are required to compute the cost function and constraints

Gnu Mathprog


Osemosys

• Open Source Energy Modelling System• Written in GNU Mathprog• Objective: discounted cost (consisting of

operating, capital, emissions penalty and salvage components)

• Constraints: Energy demand constraints, and energy balance constraints

• Variables: activities of various technologies, and investment in technologies, per year for the complete model period


Osemosys (cont.)

• Determine in which technologies to invest, and how to use the available capacity (residual and new), in order to satisfy all the specified demands (annual demand and peak demand)

• If there is multiple options available to generate the required energy demand, choose the technology with the lowest cost


• Scenario planning similar to engineering design under multiple load cases

- The design must be feasible if subjected to every load case e.g. design a vehicle that will experience paved road and off-road conditions

• Scenarios in energy planning - One difference from conventional engineering

design is that modifications are allowed to the design in the future

- Completely independent scenarios are however problematic since the solution for scenario A might be infeasible for scenario B

- Suggested solution: enforce similarity between the solutions of each scenario within a “decision window”

Scenarios and energy planning


Scenarios and energy planning

• Some existing energy planning software1 supports scenario planning via “stochastic programming”. - Cost function becomes expected cost, or

“Expected utility criterion with linearized risk aversion”

- Any model parameter can be uncertain, and is resolved (its value is revealed) at the resolution time

• Can alter Osemosys to add a scenario set, and add technology lead time and decision window constraints

1 R. Loulou, M Labriet, ETSAP-TIMES: the TIMES integrated assessment model Part I: Model structure,CMS (2008) 5:7-40.


Scenario planning example

• Consider 4 scenarios, with 3 technology options

Scenario DiscountRate

Growth Rate

EmissionsTax

1 4% 2% 12 4% 2% 1-103 6% 4% 14 6% 4% 1-10

Tech Cap cost

Fix op cost

Var op cost

Emit Lead time

Life

A 100 5 10 10 7 20

B 500 5 1 1 10 60

C 50 1 10 20 2 5


Demand curves• 4% growth over 20 years requires capacity

doubling


Cumulative capacity: Tech A

• Independentsolution

• Simultaneoussolution


Cumulative capacity: Tech B




Cumulative capacity: Tech C




• The increased cost of simultaneous planning is offset by the cost of realising too late that a different future is playing out- E.g. future 3 years 1 to 4, then switch to future 4

• Independent cost: 9388• Simultaneous cost: 8002

Cost of solutionsScenario Independent Simultaneous % increase

1 4320 4677 8.3 %

2 7567 7604 0.5 %

3 4249 4811 13.2 %

4 8175 8436 3.2 %


Osemosys benefits

• Open source:- Since Osemosys is open source, all equations

are transparent and any modifications can be made (as long as the problem remains linear).

- No license fees are required- Reduced risk of becoming a captured client- Improved chances of developing a larger group

of researchers using energy planning tools• Learning curve:

- The learning curve to use Osemosys proficiently is not as steep as with commercial software

- Allows faster development of features not supported by commercial products


Osemosys limitations

• Linear programming problems- Since Osemosys models are solved using GLPK,

the models are required to be linear. Hence the objective function (cost) and constraints are required to be linear functions of the variables

• Continuous problems- Linear programming problems using continuous

variables can be solved efficiently- Introduction of integer variables makes the

problem combinatorial in nature, requiring exhaustive search or heuristics

- Hence the capacity of all new technologies are modelled as continuous (including the electricity supply options)

• Technology learning rates- Not yet implemented in Osemosys


Summary

• Osemosys is an open source energy planning tool, that can be tailored to the specific problem at hand

Thank you

Documents

Osemosys: motivation for using it as part of the tools for ... · Osemosys: motivation for using it as ... -Simplest techniques uses a single scalar value, ... tool, that can be tailored