CHALLENGES IN HEAT NETWORK TOPOLOGY OPTIMIZATION

PAUL EGBERTS, CAN TÜMER, KELVIN LOH, RYVO OCTAVIANO

PROBLEM DEFINITION

Among other solutions (hydrogen admixing to the gas grid, decentralized heat pumps etc.), transition towards a sustainable heat supply requires many new heat networks in NL.

Currently, heat grids are designed through evaluation of manually drafted topologies.

During design, there can be many design goals and large uncertainties in many design aspects.

Infeasible to evaluate all possibilities.This leads to suboptimal grid designs!

https://www.thermogis.nl

Geothermal Power Estimates in The Netherlands

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GOAL

(Final) Goal : Methodology for assisted grid design optimizationFor a given set of actors (e.g. producers, consumers etc.), the method should;

generate topologies, optimized on relevant KPIs (e.g. CAPEX/OPEX, Revenues, Network fairness, etc.),handle design parameters stochastically (e.g. expansion of the grid/future actors, uncertainty on prices/demand/supply) and optimize the grid concept under uncertainty (robust optimization).

Potential Pipeline

Producer

Existing User

Potential User

Tee

Existing Pipeline

ATES

Where (How) to expand? Is the grid design “fair” for all actors?

Producer

Existing User

Potential User

Potential Pipeline Tee

Existing Pipeline Potential

Producer

Potential ATES

ATES

Producer

Existing User

Tee

Existing Pipeline

ATES

Existing User

Original

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INHOUSE HEAT NETWORK SIMULATOR

Solver for momentum and energy equations.System controller to drive the system (pumps/valves).Solver and pre/post-processing in MATLAB.Easy prototyping of new concepts (system controllers, optimizers etc).Model Creation: ESDL Web Editor (GIS based).Many component models (Geo. Well, ATES, Heat Pump, PV Panels etc.) with different levels of detail from respective TNO departments.Currently being tested by engineering companies.

Sources and Demand

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https://smartenergysystems.eu/wp-content/uploads/2019/04/Track12_Booij.pdfMore on ESDL in session 30.

EXAMPLE CASE 1

Objective function 𝐽𝐽: Total Cost of Ownership (TCO)

Variables 𝑢𝑢 = (𝑦𝑦,𝑑𝑑):8 binaries for pipelines 𝑦𝑦 = 𝑦𝑦1,𝑦𝑦2, … , 𝑦𝑦813 diameters 𝑑𝑑 = 𝑑𝑑1,𝑑𝑑2, … ,𝑑𝑑13

Constraints (not allowing disconnected networks)𝑦𝑦2 + 𝑦𝑦3 ≥ 1; 𝑦𝑦2 + 𝑦𝑦5 + 𝑦𝑦8 ≥ 1; etc…

Optimization problem:

𝐽𝐽 𝑢𝑢 = 𝑇𝑇𝑇𝑇𝑇𝑇(𝑢𝑢) = �

𝐸𝐸=𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑝𝑝𝑝𝑝𝑝𝑝𝑠𝑠𝑠𝑠𝑝𝑝𝑠𝑠𝑝𝑝𝑝𝑝𝑠𝑠

𝐸𝐸𝐶𝐶𝐶𝐶𝑝𝑝𝑠𝑠𝐶𝐶 + 𝐸𝐸𝑂𝑂𝑝𝑝𝑠𝑠𝐶𝐶

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d1

d11

y4, d2

y7, d8

d3

y3, d4 d5

y2, d13

d9

y6, d6

y5, d7

y4, d12

y8, d10

Producer Consumer Bend/Tee

Pipeline Potential Pipeline

Based on real case; 6 producers, 8 demand clusters

minu=(𝑦𝑦, 𝑑𝑑)𝑦𝑦𝑖𝑖 ∈ 0,1𝑑𝑑𝑖𝑖 ∈ [0,1]

𝐽𝐽(𝑢𝑢)

SOLUTION APPROACH

DAKOTA used as framework From Sandia National Laboratories ( http://dakota.sandia.gov )

Open source

Ships several optimizers

Parallelization features

Allows set up of iterative workflows such as Nested loops, Hybrid optimization,…

Optimization running on HPCOptimizers that can handle both integer and continuous variables

Pattern search methods

Branch and bound method

Genetic algorithms (used in this presentation)

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0 100 200 300 400 500 600 700 800 900 1000

Iteration

5

5.5

6

6.5

7

7.5

8

8.5

9

9.5

10J1

: TC

O [E

UR

]10 8 6.10e+08, It. 980

RESULTS CASE 1Using a genetic algorithm (SOGA)

Convergence can be improved using hybrid optimizationUse GA to globally explore the variable space followed by a local (gradient based) optimizer

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100 200 300 400 500 600 700 800 900 1000

Iteration

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Pum

p El

Cco

ns

10 4

Pump Costs

TCO0 100 200 300 400 500 600 700 800 900 1000

Iteration

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Pipe

Cap

ex

10 8

Pipe Costs

RESULTS CASE 1

Minimum TCO found after 980 iterations

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0.22 0.38 0.78

0.280.38

0.23

0.18 0.160.410.61

0.52

No Pipe line

Optimized design

Pipe line

Planned Pipe line (not part of optimization)

UNCERTAINTY

In previous example no uncertainty assumed (deterministic optimization)In practise large uncertainties may be presents concerning future

DemandsEnergy pricesHeat sources availabilitiesUrban and industrial developments

Future proof topology design needs to account for increasing uncertainty over timeExample case 2

Same base case as before but with uncertainty in demandAssume that uncertainty is captured in 10 equiprobable realizations

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A B C D E F I J

Demand cluster

0

50

100

150

200

250

300

350

Dema

nd [M

W]

01

02

03

04

05

06

07

08

09

10

Sequence of connected point isa single realization

DETERMINISTIC OPTIMIZATION PER REALIZATION

Objective function 𝐽𝐽 ( e.g. TCO) depends also on realization so 𝐽𝐽 = 𝐽𝐽 𝑢𝑢, 𝑟𝑟with 𝑢𝑢 = 𝑦𝑦,𝑑𝑑 topology design and 𝑟𝑟 ∈ {𝑟𝑟1, … , 𝑟𝑟10} a realization

10 Deterministic Optimization problems: minimize the objective functions 𝐽𝐽 𝑢𝑢, 𝑟𝑟1 , … , 𝐽𝐽 𝑢𝑢, 𝑟𝑟10

0 1000 2000

Iteration

4

6

8

10

J1: T

CO

[EU

R]

10 8 5.71e+08, It. 1848

0 1000 2000

Iteration

4

6

8

10

J1: T

CO

[EU

R]

10 8 5.26e+08, It. 1980

0 1000 2000

Iteration

4

6

8

10

J1: T

CO

[EU

R]

10 8 5.67e+08, It. 1854

0 1000 2000

Iteration

4

6

8

10

J1: T

CO

[EU

R]

10 8 6.46e+08, It. 1765

0 1000 2000

Iteration

4

6

8

10

J1: T

CO

[EU

R]

10 8 5.29e+08, It. 1902

0 1000 2000

Iteration

4

6

8

10

J1: T

CO

[EU

R]

10 8 5.26e+08, It. 1983

0 1000 2000

Iteration

4

6

8

10

J1: T

CO

[EU

R]

10 8 5.49e+08, It. 1929

0 1000 2000

Iteration

4

6

8

10

J1: T

CO

[EU

R]

10 8 4.93e+08, It. 1925

0 1000 2000

Iteration

4

6

8

10

J1: T

CO

[EU

R]

10 8 5.72e+08, It. 1995

0 1000 2000

Iteration

4

6

8

10

J1: T

CO

[EU

R]

10 8 4.24e+08, It. 1874

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OPTIMAL DESIGNS PER REALIZATION

.. y1 y2 y3 y4 y5 y6 y7 y8 TCO (x108 )

1 1 1 1 1 1 0 0 1 5.72 1 1 1 1 1 0 0 1 5.33 0 1 1 1 0 1 1 0 5.74 1 0 1 1 1 0 1 1 6.55 1 1 0 1 1 0 1 1 5.36 1 1 1 1 1 0 1 0 4.87 1 1 1 1 1 0 1 0 5.58 1 1 0 1 1 0 0 0 4.99 1 1 0 1 0 1 1 1 5.7

10 1 1 1 1 1 0 1 0 4.2

8 different topologies

High (occurrence)MediumLow

Rea

lizat

ions

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𝑦𝑦4𝑦𝑦3𝑦𝑦6

𝑦𝑦5𝑦𝑦7

𝑦𝑦8

𝑦𝑦1 𝑦𝑦2

d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 d12 d13

Pipeline diameter variable

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pipe

line

diam

eter

[m]

01

02

03

04

05

06

07

08

09

10

Pipelines

Diameters

OVERALL PERFORMANCE OF THE FOUND SOLUTIONS

How good do the solutions perform for all realizations? For each realization 𝑟𝑟𝑝𝑝 , 𝑖𝑖 = 1, … , 10, an optimal design 𝑢𝑢𝑝𝑝

𝑠𝑠𝑝𝑝𝑜𝑜 is calculatedPerformance measure is the expected objective function value

Performance of the 10 optimal designs:

Optimized design 𝑢𝑢6𝑠𝑠𝑝𝑝𝑜𝑜 for realization 6 performs best among the 10 designs

This is still a suboptimal solution => rigorous approach is Robust Optimization

�𝐽𝐽 𝑢𝑢 = 110∑𝑝𝑝=110 𝐽𝐽 𝑢𝑢, 𝑟𝑟𝑝𝑝 for design 𝑢𝑢

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�𝐽𝐽 (𝑢𝑢6𝑠𝑠𝑝𝑝𝑜𝑜) �𝐽𝐽

5.3

ROBUST OPTIMIZATION (RO)

Let uncertainty (demands, prices,…) be captured by realizations 𝑟𝑟1, 𝑟𝑟2, … , 𝑟𝑟𝑀𝑀

Robust optimization:

Robust optimization aims at finding a topology design that is “good” for all realizations

RO is CPU expensive: 𝑀𝑀 simulations to calculate ̅𝐽𝐽 𝑢𝑢Parallelization is essential

Optimization

Sampling

Simulation

𝑟𝑟𝑝𝑝 𝐽𝐽(𝑢𝑢𝑘𝑘, 𝑟𝑟𝑝𝑝)

𝑢𝑢𝑘𝑘 ̅𝐽𝐽(𝑢𝑢𝑘𝑘)

RO: nested loops

Given realizations 𝑟𝑟1, 𝑟𝑟2, … , 𝑟𝑟𝑀𝑀, find topology design 𝑢𝑢 that minimizes the expected value ̅𝐽𝐽 𝑢𝑢 = 1

𝑀𝑀∑𝑝𝑝=1𝑀𝑀 𝐽𝐽 𝑢𝑢, 𝑟𝑟𝑝𝑝

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ROBUST OPTIMIZATION

Minimum TCO found after 897 iterationsSolution:

100 200 300 400 500 600 700 800 900

Iteration

4

6

8

10

12

14

J1: T

CO

[EU

R]

10 8 4.81e+08, It. 897

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No Pipe line

Pipe line

Existing Pipe line (not part of optimization)

0.19 0.56 0.87

0.550.44

0.43 0.19

0.30

0.23

Optimized design

0.370.13

ADDED VALUE ROBUST OPTIMIZATION

Added value of RO through comparison with solutions from deterministic optimization

�𝐽𝐽Mean of blue dots

Robust Optimization

Added value:9% improvement �𝐽𝐽 evaluated at solutions from Deterministic Optimization

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5.34.8

Best solution from Deterministic Optimization

5.9

WRAP UP/CONCLUSIONS

First steps presented towards a framework/methodology for assisting heat network designingHeat network design => optimization problem with continuous and binary variablesAn optimization framework was setup to solve the mixed integer optimization problem allowing

use of several optimizer, hybrid optimization, multi-objective optimization, constraintsOptimization under uncertainty (Robust Optimization) was setup

Added value demonstrated

Next stepsNetwork fairness/ load balancing

Investigating solution approach using Quantum Algorithms (Dwave’s 2000Q system)Incremental network designCPU Efficiency

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BACKUP SLIDES

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HYBRID OPTIMIZATION

Hybrid: Use GA as global optimizer to explore the variable spaceUse gradient based optimizer as local optimizer

0 100 200 300 400 500 600 700 800 900 1000

Iteration

5

5.5

6

6.5

7

7.5

8

8.5

9

9.5

10

J1: T

CO

[EU

R]

10 8 6.10e+08, It. 980

700 750 800 850 900 950 1000

Iteration

5.9

6

6.1

6.2

6.3

6.4

6.5

6.6

6.7

J1: T

CO

[EU

R]

Gradient based optimizer;Only optimizing diameters

6.1

5.9

Further reduction of objective

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ROBUST OPTIMIZATION

Robust Optimization (RO): Deals with uncertainty in a rigorous way and aims at finding a design that is good for all realizations.

Framing the problemDesign vector: 𝑢𝑢 (consisting of binaries 𝑦𝑦 and diameters 𝑑𝑑)

Parameter vector: 𝑟𝑟 (the demands of users)

Objective function: 𝐽𝐽 = 𝐽𝐽(𝑢𝑢, 𝑟𝑟) (cost function e.g. TCO)

Input-output system: 𝑢𝑢, 𝑟𝑟 Heat Network SSimulator

𝐽𝐽(𝑢𝑢, 𝑟𝑟)

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REDUCING RISK

Besides minimizing expectation �𝐽𝐽 one may desire to reduce riskMeasures of risk: Standard deviation 𝐽𝐽𝜎𝜎Spread at downside only: Semi- standard deviation

100 200 300 400 500 600 700 800 900 1000

Iteration

5

6

7

8

9

10

Obj

. fun

c

10 8

Standard deviation

Expected valuemin { ̅𝐽𝐽 (𝑢𝑢) + 𝐽𝐽𝜎𝜎(𝑢𝑢)}

min { ̅𝐽𝐽 (𝑢𝑢)}

Spread as measure for risk

Reduced spread at the cost of

Expectation value

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