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Building Control and Automation
Energy Hubs Part 2: Advanced Topics
Friday 12 April 2019
Dr. L. Andrew Bollinger [email protected]
Urban Energy Systems Laboratory, Empa
Contents
2
1. Review of the last lecture
2. Advanced energy hub model formulations • Increasing model accuracy • Representing networks • Improving computational efficiency • Multi-objective optimization • Multi-stage optimization • Dealing with uncertainty
3. Applying energy hub modelling to real cases
Review: Energy hub modelling
Suurstoffi Areal, Risch-Rotkreuz, Switzerland (image source: ZugEstates.ch, Suurstoffi.ch)
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For a given urban area/district/community…
Problem
In order to minimize costs and/or emissions, maximize autonomy, etc?
How should a distributed energy system for the site be optimally designed and operated…
4
Suurstoffi Areal, Risch-Rotkreuz, Switzerland (image source: ZugEstates.ch, Suurstoffi.ch)
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How should a distributed energy system for the site be optimally designed and operated…
Given complexities such as: • Time-varying resource availability • Multi-energy demand patterns • Technical & economic constraints • Regulatory/policy environment • Uncertainties regarding fuel prices, energy
demand, policy, etc. • Possibilities for electricity market participation
For a given urban area/district/community…
In order to minimize costs and/or emissions, maximize autonomy, etc?
Why optimization?
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6
What is an energy hub?
Grid
Gas
PV
Boiler
Electricity
Heat
Inverter
Heat pump
Hot water tank IN
PUTS
OU
TPU
TS
A system to convert between and store multiple energy streams
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7
What is an energy hub model?
Grid
Gas
PV
Boiler
Electricity
Heat
Inverter
Heat pump
Hot water tank IN
PUTS
OU
TPU
TS
A mathematical representation of an energy hub that enables optimization
What do we want to optimize?
The set of processes (energy & technological pathways) by which we transform energy inputs into outputs.
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8
What is an energy hub model?
Igrid(t)
IPV(t)
Igas(t)
Lelec(t)
Lheat(t)
Pelec(t)
PHP(t)
Pboiler(t)
Qheat(t)
Grid
Gas
PV
Boiler
Electricity
Heat
Inverter
Heat pump
Hot water tank IN
PUTS
OU
TPU
TS
A mathematical representation of an energy hub that enables optimization
Variable
Constant
Variables: Elements for which you want to identify an optimal value Constants: Elements for which you already know the value
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Energy hub formulation – typical equations
Objective function
Load balance constraint
Storage continuity constraint
Capacity constraints
Storage charge/discharge constraints
Part-load constraints
Sum of energy outputs from technologies must be sufficient to provide for demand at the given timestep
Storage inputs and outputs determine the state of charge at the next timestep.
Conversion technologies cannot produce more than their capacities. Storages must not be filled more than their capacities.
Storages can only be charged/discharged at a maximum rate.
Conversion technologies cannot produce below a given power level.
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Simulation versus Optimization
Simulation
Descriptive and aim to emulate actual energy system performance, and aid understanding. Can be developed in software programs like TRNSYS, EnergyPlus, etc. – used to simulate various types of energy systems in conjunction with energy demand modelling.
Optimization
Prescriptive and aim to provide outputs that indicate how to maximize system performance, thereby aiding decision making. Can reveal relationships, solutions, and pathways that were not obvious or initially considered.
Energy hub modeling
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Optimization Methods
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So what can we model with this approach?
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Optimize operational variables - Conversions between different forms of energy - Storage dispatching (short-term and seasonal) - Grid interaction (peak shaving, grid services) Optimize technology selection and technology capacities - Storage and conversion selection and sizing - Initial and capacity-based costs - Energy prices & carbon factors
Represent single system bridging demand and supply - Local generation (considering renewables availability) - Time-varying loads & supply
Represent and optimize networks - Optimise the network configuration - Optimise the network type
What are the limitations of this approach?
‒ Mixed-integer linear programming (MILP) approach requires maintaining linearity of constraints
‒ Linear technology models
‒ Model size scales exponentially with the number of integer variables
‒ Critical to develop models that limit the number of integer variables by minimising
‒ Time intervals ‒ Distinct consumption/generation nodes
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Advanced energy hub modelling formulations
To avoid “garbage models”, we need to augment the basic energy hub concept.
Research has moved past the basic energy hub problem, and has extended it with: More accurate technical representations Representation of uncertainty Multiple performance criteria Representation of networks
Com
putational burden
We need additional methods to improve computational efficiency
Building on the basic energy hub concept
15
Garbage in = Garbage out
Advanced energy hub model formulations
1. Increasing model accuracy 2. Representing networks 3. Improving computational efficiency 4. Multi-objective optimization 5. Multi-stage optimization 6. Dealing with uncertainty
16
1. Increasing model accuracy
What’s the problem? Basic energy hub formulations neglect to include a number of important technical/economic properties and constraints of conversion & storage technologies. What can we do? Add further variables and constraints that more accurately represent technology operation. Specifically: 1. Minimum part load constraint 2. Maximum activations constraint 3. Minimum run time constraint 4. Ramping constraint 5. Nonlinear conversion efficiencies
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1.1 Minimum part load constraint
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Problem: Often, conversion technologies are not capable of operating below a certain minimum load level. Solution: Add an equation restricting the minimum output of the device
1.1 Minimum part load constraint
19 19
PHeatPump
PBoiler
PBoiler + PHeatPump = Lheat
PHeatPump ≤ PmaxHeatPump
PHeatPump ≥ PminHeatPump
Capacity constraint
Minimum part-load constraint
Problem: Often, conversion technologies are not capable of operating below a certain minimum load level. Solution: Add an equation restricting the minimum output of the device
Doesn’t allow for zero load! (i.e. your device is always forced to be operating)
Introduce binary variable bm which at each time step sets the device as on or off.
To formulate these constraints, we use big M method, where M is any sufficiently large number.
)(min tPP mm ≤
Basic minimum part-load constraint
Modified constraint formulation
If bm(t) = 0, then If bm(t) = 1, then
1.1 Minimum part load constraint
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When the technology is operating, output must be <= Pmin
When the technology is not operating, output must = 0
Binding constraint
Binding constraint
= 0 if state remains the same
= 1 if state changes
( -1 if shutdown) (+1 if start-up)
Now Previous timestep
Problem: Frequent start ups and shut downs of certain technologies can be damaging, so you sometimes need to limit the number of start ups and shut downs that are allowed in a given time period. Solution: Add 2 binary variables: • δon/off = status change in technology operation • δi,t,CHP = current status of technology operation
1.2 Maximum activations constraint
21
Maximum 4 startup/shutdowns allowed over a 24-hour time horizon
Constraint:
No Violation:
Hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 State (δi,t,chp) 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 0 0 0 Transition (δon/off) 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0
Hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 State (δi,t,chp) 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 Transition (δon/off) 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0
Violation:
1.2 Maximum activations constraint – Example (CHP unit)
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1.3 Minimum run time constraint
Problem: Some equipment must run continuously for a minimum amount of time, due to the nature of the process, mechanical concerns or need to maintain a reasonable efficiency. • e.g.: CHP plants and heat pumps have poor efficiency for some time after starting. Solution: • Formulate the model such that a given device must operate for a minimum
run time of tm timesteps. • Create a variable z(t) that tells you the nature of change in the device’s
operation between timesteps.
if a=0.5 and b=1:
z(t) = 0; still off z(t) = -1; start-up z(t) = -0.5; still on z(t) = 0.5; shutdown 23
Operation previous timestep
Operation this timestep
1.3 Minimum run time constraint
(a) Constraint maintained
(b) Constraint violated
t = 1 2 3 4 5 6 7 8
P z -4 -3 -3.5 0 -1 -0.25 0.25 0.251 -1 -4 -1 -1 -1 -0.5 0 0 0
1 -0.5 0 -2 -0.5 -0.5 -0.5 -0.25 0 0
1 -0.5 0 0 -2 -0.5 -0.5 -0.5 -0.25 0
0 0.5 0 0 0 2 0.5 0.5 0.5 0.25
t = 1 2 3 4 5 6 7 8
P z 0 -4 -3 0.5 -1 -0.5 0.25 0.250 0 0 0 0 0 0 0 0 0
1 -1 0 -4 -1 -1 -1 -0.5 0 0
1 -0.5 0 0 -2 -0.5 -0.5 -0.5 -0.25 0
0 0.5 0 0 0 2 0.5 0.5 0.5 0.25
Constraint:
R. Evins, K. Orehounig, V. Dorer and J. Carmeliet (2014). New formulations of the ‘energy hub’ model to address operational constraints. Energy, 73, 387–398. 24
Problem: Some conversion technologies are limited in how quickly they can ramp up or down their energy output. Solution: Add a set of constraints that control the difference in energy production levels between two consecutive time intervals.
Maximum allowable amount of ramping up
Maximum allowable amount of ramping down
1.4 Ramping constraint
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Power output this timestep
Power output previous timestep
Power output previous timestep
Power output this timestep
1.5 Nonlinear conversion efficiencies
Problem: Many technologies have efficiencies that depend nonlinearly on the power output.
Solution: Linearization of the efficiency curve: 1. Define the number/ranges of segments/steps into which to divide the original curve. 2. Define a virtual “bin” for each load segment, and add a binary variable for each bin. 3. Add a constraint that says that only one bin can be active at a time. 4. Add power output constraints for each bin & set the efficiency according to the bin.
Possibilities for stepwise linearization of conversion efficiency
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Why is this a problem?
1.5 Stepwise linearization of conversion efficiencies Example: Microturbine part load curve
L1 L2 L3 L4
ηL1
ηL2 ηL3
ηL4
Binary variables: yL(t) Bins: L = {L1, L2, L3, L4}
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“knapsack” constraint Power output constraints
Efficiency changes nonlinearly with percent load
Summary - increasing model accuracy
• Minimum part load constraint
• Maximum activations constraint
• Minimum run time constraint
• Ramping constraint
• Nonlinear conversion efficiencies
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General solution: It’s all about creating clever constraints that force your technologies to behave the way they’re supposed to
General problem: This tends to create a lot of new binary variables
2. Representing networks
What’s the problem? Basic energy hub formulations aggregate all components/buildings into a single “node”, thus neglecting the influence of networks. • Networks constrain how we can move energy between buildings What can we do? Model the system as being composed of multiple hubs with network elements (links) connecting them.
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Why is it important to consider networks?
- Nodes: Sites of energy generation/consumption (e.g. buildings or groups of buildings) - Links: Flow of energy between the nodes (e.g. electricity, heat)
Representing networks – multi-hub system
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Represent your system as a set of nodes connected by links
Each node is an energy hub in itself
The full system is represented as a multi-hub network
Objective function
Load balance constraint
Storage continuity constraint
Capacity constraints
Storage charge/discharge constraints
Part-load constraints
Sum of energy outputs from technologies must be sufficient to provide for demand at the given timestep
Storage inputs and outputs determine the state of charge at the next timestep.
Conversion technologies cannot produce more than their capacities. Storages must not be filled more than their capacities.
Storages can only be charged/discharged at a maximum rate.
Conversion technologies cannot produce below a given power level.
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Energy hub model formulation – typical constraints
Modified load balance constraint:
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Energy flowing into the node
(from node i to j)
Energy flowing out of the node
(from node j to i)
Equation to account for network losses:
Representing networks
Variable: Binary variable for each possible link indicating the installation of that link
Optimizing network layout
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Constraint: If a link is installed, then energy can be transferred via that link
Optimization problem decides which of the possible links it is optimal to install
Modelling district heating networks
Network layout
List of possible connections and network layout constraints
Investment costs related to distances
Represented by binaries
0
20
40
60
80
100
120
140
160
180
0
500
1000
1500
2000
2500
3000
0 50 100 150 200 250
Heat
loss
(W/m
)
Cost
(EUR
/m)
Capacity (kW)
Pipe size cost
Heat losses
Operation
Pipe size correlated to the maxium heat transfer
Heat losses correlated to the distance
High temperature DH network
Sour
ce: A
rup
B. Morvaj, R. Evins, J. Carmeliet (2016) Optimising urban energy systems: simultaneous system sizing, operation and district heating network layout, Energy
34
Modelling electricity distribution networks
Requires solving of power flow equations (which are nonlinear):
3 possible methods:
Linearised AC power flow
Energy hub (design +
operation)Genetic Algorithm (design)
Energy hub (operation)
Non-linear power flow
Genetic Algorithm (design)
Non-linear power flow
Energy hub (operation)
Linearised AC power flow
(a) Bi-level method (b) Linearised (c) Combined method
B. Morvaj, R. Evins, J. Carmeliet (2016) Optimisation framework for distributed energy systems with integrated electrical grid constraints, Applied Energy 35
Exercise
Thermal pipe
Building 1
Building 2
• Small neighborhood with 2 buildings
• There is a 2-way thermal pipe connecting buildings 1&2
• Excess heat energy from building 1 can feed into building 2, and vice versa
• You want to represent this as a multi-hub system
• What is the heat balance equation for building 1?
3. Improving computational efficiency
What’s the problem? Complex energy hub model formulations – especially with many discrete variables – become very difficult to solve using conventional MILP solvers. • MILP model size scales exponentially with the number of integer variables What can we do? Develop models that limit the number of integer variables by minimizing the number of: (1) time intervals, (2) distinct consumption/generation nodes Specifically: 1. Temporal discretization 2. Temporal decomposition 3. Spatial clustering 4. Bi-level optimization
37
Why?
3.1 Temporal discretization • What time period are we interested in optimizing? • Into how many discrete time periods to we divide the
overall time period? • Every minute, hour, day, week? • Every day in the year, or just “representative” days? • How do we choose days which are sufficiently
representative?
The fewer discrete time periods you have, the simpler/quicker your optimization problem will be.
38
Rolling horizon approach: • Rather than considering the whole time horizon, solve the problem for successive
planning intervals, each representing a small part of the horizon. • Reduces the size of the problem per interval, breaking down one large problem into
easily solved sub-problems.
3.2 Temporal decomposition
(a) Interval length Lint characterizes the length of one sub-problem (b) Step size Lstep is the number of periods before rolling to another planning interval (c) overlap Loverlap is the number of periods from the past interval reconsidered in the present interval (d) number of planning intervals n describes the number of sub-problems to be solved
J. Marquant, R. Evins and J. Carmeliet (2015). Reducing Computation Time with a Rolling Horizon Approach Applied to a MILP Formulation of Multiple Urban Energy Hub System. Procedia Computer Science, 51: 2137–2146
39
• Divides the problem into multiple overlapping intervals, through which the solver iterates.
• Disadvantage: Causes problems for seasonal storage scheduling.
3.3 Spatial clustering & multi-scale systems
Interactions
How can the interactions between these scales be coordinated to improve overall energy performance?
• Where should energy be produced/stored and in what quantities?
• How should transactions be coordinated?
Source: Marquant, 2014
40
Computationally expensive
3.3 Spatial clustering
Because: Modelling a 6 building system as 6 nodes is as computationally expensive as modelling a 36 building system clustered into 6 nodes. How to define clusters? ‒ Distance based? Or also consider load
magnitudes & patterns ‒ Which clustering algorithm? K-means
method? K-medoids method? Other method?
Disadvantage: Lose any ability to optimize within clusters.
Instead of representing each building individually, we aggregate buildings into clusters.
41
3.3 Spatial clustering Example – Case study Baden Nord
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• Which supply technologies should optimally be installed per cluster?
• How should these clusters be linked with one another?
Marquant et al. (2018). A new combined clustering method to analyse the potential of district heating networks at large-scale. Energy, 156, 73-83.
3.3 Spatial clustering for optimizing DES in large urban areas
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Identifying optimal energy hub designs and district heating network layouts in a large urban area
Level of discretisationCost function:o Installation costso £ per kW / kWh / m2
Design constraints:o Maximum capacitieso PV+ST < roof area
Demand profilesSolar availabilityPlant efficienciesCarbon factorsStorage lossesOperational constraints:o Fuel cell only on/offo CHP min load 50%o HP min load 10%
Genetic Algorithm
Energy Hub
Evaluation
Inputs
Initialise
Crossover & Mutation
Selection
Capacities Emissions
Optimised population
Variables:Plant, storage and renewables capacities
Mixed Integer Linear Programme:Ax = bCx ≤ d
lb ≤ x ≤ ub
Emissions
Costs
Variables:Operational schedules
3.4 Bi-level optimization
44
• Use GA or other metaheuristic for optimizing system design; use MILP to optimize system operation
• Allows for solving complex problems more quickly (and deal with some nonlinearities), but optimality is not assured.
3.4 Bi-level optimization
45
Example – Case study Empa campus
Results – Pareto front
4. Multi-objective optimization
What’s the problem? Often you don’t have a clear single objective, so you need to balance amongst different objectives in optimization. What can we do? Multi-objective optimization, either by: 1. assigning weights to different objectives and optimizing against the sum
of the weighted objectives, or 2. optimizing against a single objective and iteratively constraining the
values of one or more other variables.
46
Epsilon constraint method
What are possible objectives of an energy hub model?
F 1(x
)
F2(x)F2(x)≤εmaxF2(x)≤ε2F2(x)≤ε3
. . .
. . .F2(x)≤εmin
Optimal solutions by minimising F1 and satisfying constrainted F2 objective function
minimize {F1(x), F2(x)}
becomes
minimize {F1(x)} subject to the constraint that F2 (x) ≤ εa ∀a ∈ [ 1,…,n]
Multi-objective optimization – Epsilon constraint method
47
Each solution corresponds to a different value for ɛ
e.g. costs e.g. CO2 emissions
Iteratively set ɛ to different values and solve your optimization problem for each value of ɛ
Multi-objective optimization – Pareto front
48
• Each solution corresponds to a different optimal system configuration. • Instead of 1 optimal solution, you have a set of optimal solutions (Pareto front) • Allows you to see the trade-offs between different objectives
Multi-objective optimization – Pareto front
Emissions (kg CO2-eq)
Life
-cyc
le c
osts
(CH
F)
Cost-minimizing solution
Emissions-minimizing solution
Intermediate solutions (different ɛ values)
“pareto front”
5. Multi-stage optimization
What’s the problem? Sometimes we don’t want to identify a single optimal design solution, but rather an optimal sequence of technology investments over time. What can we do? Multi-stage optimization: Identify the optimal set of technologies to be installed in each of multiple stages (time periods)
49
Stage 1 (2020-2050)
1 decision point, 1 optimal set of technologies
Stage 1 (2020-2030)
Stage 2 (2030-2040) Stage n
n decision points, n optimal sets of technologies
…
Standard approach:
Multi-stage approach:
Decision point: Which technologies to install?
technology set
technology set 1 technology set 2 technology set 3
5. Multi-stage optimization
What’s the problem? Sometimes we don’t want to identify a single optimal design solution, but rather an optimal sequence of technology investments over time. What can we do? Multi-stage optimization: Identify the optimal set of technologies to be installed in each stage
50
Stage 1 (2020-2050)
1 decision point, 1 optimal set of technologies
Stage 1 (2020-2030)
Stage 2 (2030-2040) Stage n
n decision points, n optimal sets of technologies
…
Standard approach:
Multi-stage approach:
Decision point: Which technologies to install?
technology set
technology set 1 technology set 2 technology set 3
Example results from a multi-stage case study
Stage
6. Dealing with uncertainty
What’s the problem? Sometimes, the values of your input parameters are uncertain, and it is unclear how this uncertainty may affect outcome of your optimization. What can we do? Vary the values of input parameters and: (1) evaluate the effects of these variations, and/or (2) optimize to account for this uncertainty. Specifically: 1. Uncertainty analysis 2. Global sensitivity analysis 3. Stochastic optimization 4. Robust optimization
51
Which inputs might have some associated uncertainty?
6.1 Uncertainty analysis
How does the output of the model vary given uncertain input parameters?
Computational model
Computational model
μσ
Probability of exceedance
Mean/std.deviation
Does uncertainty matter? How does it change the optimal technical configuration?
Deterministic modelling
Monte Carlo simulations
52
6.2 Global sensitivity analysis
Computational model
Calculated using “Sobol indices” ‒ Quantify to what degree variation of the different input parameters influences the results ‒ First-order Sobol index, Si : contribution of parameter i only ‒ Total-order Sobol index, STi : contribution of parameter i with parameter interactions
What are the most important input parameters driving the variation of the output?
Which input uncertainties drive uncertainties in the results?
53
6.3 Stochastic & robust optimization
How can we make better design decisions under uncertainty?
1. Stochastic optimization: • Identifies the probabilistically best solution • Requires probabilistic descriptions of uncertainty
2. Robust optimization: • Particularly useful when probabilistic descriptions of uncertainty are not available • Uses interval uncertainty sets: e.g. Gas price: 𝑂𝑂𝑂𝑂𝑔𝑔𝑔𝑔𝑔𝑔 ∈ [𝑂𝑂𝑂𝑂𝑔𝑔𝑔𝑔𝑔𝑔
𝑚𝑚𝑚𝑚𝑚𝑚, 𝑂𝑂𝑂𝑂𝑔𝑔𝑔𝑔𝑔𝑔𝑚𝑚𝑔𝑔𝑚𝑚]
• Seeks solutions that are optimal for the worst-case realizations of uncertain parameters
54
Advanced energy hub model formulations
1. Increasing model accuracy 2. Representing networks 3. Improving computational efficiency 4. Multi-objective optimization 5. Multi-stage optimization 6. Dealing with uncertainty
55
Application case – Brig-Glis
Case study Main industry partner Size of site (buildings) Type of site1 Municipal authority 10-20 Existing2 Local utility 10-20 Greenfield3 Local utility 600 Existing4 Engineering consultancy 1000+ Existing
Validation projects with industry partners
57
1. City of Zurich • Energy strategy for a mixed-use industrial neighborhood
2. St. Galler Stadtwerke • Energy concept for a greenfield commercial campus
3. Regionalwerke Baden • Redevelopment of the energy system for a city district 4. Lauber Iwisa • Energy master planning for an alpine municipality (Brig-Glis)
1 2 3 4Network optimization thermal thermalSpatial clustering density-basedTemporal decomposition typical days typical days typical daysMulti-stage optimization 3-stageUncertainty handling scenarios scenarios scenarios
MethodologyCase study
Validation projects with industry partners
1. City of Zurich • Energy strategy for a mixed-use industrial neighborhood
2. St. Galler Stadtwerke • Energy concept for a greenfield commercial campus
3. Regionalwerke Baden • Redevelopment of the energy system for a city district 4. Lauber Iwisa • Energy master planning for an alpine municipality (Brig-Glis)
Energy hub analysis Brig-Glis
Background: • 2008: the first energy master plan for the municipality was developed. • 2018: the municipality requested an update of its energy master plan based
on the Swiss Energy Strategy 2050, which was to review the last 10 years while also giving an updated outlook for 2035 and 2050.
Goal of the study: • To understand how different combinations of energy technologies could best
contribute to meeting the new targets.
Energy inputs
Energy demands
Optimal energy supply system
Energy hub analysis Brig-Glis
Energy inputs
Energy demands
Optimal energy supply system
Energy hub analysis Brig-Glis
Energy hub analysis Brig-Glis Energy inputs
Energy supply technology options
Energy demands
Energy hub analysis Brig-Glis Energy inputs
Energy supply technology options
Energy demands
give
n
optimize
given
Energy hub analysis Brig-Glis Methodology – Multi-objective optimization
Emissions (kg CO2-eq)
Life
-cyc
le c
osts
(CH
F)
Cost-minimizing solution
Emissions-minimizing solution
Intermediate solutions
“pareto front”
Energy hub analysis Brig-Glis Results – scenario 2017
Cost-minimizing solution
Emissions-minimizing solution
Energy hub analysis Brig-Glis Results – Cost-minimizing solution
kWh
Energy hub analysis Brig-Glis Results – Emissions-minimizing solution
kWh
Energy hub analysis Brig-Glis Results – Technology capacities
1 2 3 4 5
6
7
8
kWh/
h Cost-minimizing
solution CO2-minimizing
solution
Energy hub analysis Brig-Glis Results – Technology capacities
1 2 3 4 5
6
7
8
kWh
Energy hub analysis Brig-Glis Results – Cost breakdown
1 2 3 4 5
6
7
8
Energy hub analysis Brig-Glis Comparison 2017-2035-2050
Hour of the year
Hour of the year
Heat
ing
dem
and
(kW
h)
Cool
ing
dem
and
(kW
h)
Energy hub analysis Brig-Glis Comparison 2017-2035-2050
scenario 2017 scenario 2035 scenario 2050
Energy hub analysis Brig-Glis Comparison 2017-2035-2050
2017 2050
kWh/
h
kWh/
h
More information «Energy Hubs - ein Beitrag zur Energiewende» Aqua + Gas, 2019. https://www.aquaetgas.ch/energie/effizienz/20190228_ag3_energy-hubs-ein-beitrag-zur-energiewende/
