Energy balance

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What is energy balance and how is it modelled?


Summing up the amount of energy produced and subtracting the amount of energy consumed within a time period gives the energy balance. Since the electricity grid and district heat network lack significant storage mechanics, the balance has to be virtually zero over short periods. When considering the balance of a particular area (e.g. Helsinki), we can make the assumption that electricity can be imported and exported in international markets. The energy in the district heat network, however, has to be produced locally. This sets up the non-trivial problem of optimising production so that there are no significant deficits as well as minimising losses and maximising profits. This problem is solved (to some extent) by market forces in the real world.

In Opasnet, there are two different ways to calculate energy balance. Our most recent energy balance model uses linear programming tools to solve an optimum for the activity of a given set of production units in simulated instances created by the main model. The main model is responsible for the decision making aspects, while the energy balance optimisation only functions as an approximation of real world market mechanics. This version was used in Helsinki energy decision 2015.

The previous version was based on setting up a set of linear equations describing the inputs, outputs, and shares of different energy and plant processes. This approach is less flexible, because it does not use an optimising function and everything must be described as linear (or piecewise linear). However, this approach was successfully used in Energy balance in Kuopio and Energy balance in Suzhou.

This code is an example how the energy balance model is used in a city case. The data comes from Helsinki energy decision 2015.

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Energy balance with linear programming

The linear programming problem is set up as follows.

For each production unit: let xi be activity of the plant. Lets also have variables yj for deficits and excesses for each type of energy produced.

The objective function is the function we are optimising. Each production unit has a unit profit per activity denoted by ai which is determined by the amount of different input commodities (e.g. coal) per amount of different output commodities (i.e. electricity and heat) and their market prices. Also, lets say we want to make sure that district heat demand is always met when possible and have a large penalty factor for each unit of heat demand not met (1 M€ in the model). In addition, it must be noted that excess district heat becomes wasted so it counts as loss. Let these deficit and excess related losses be denoted by bj. The whole objective function then becomes: sum(xiai) + sum(yjbj).

The values of variables are constrained by equalities and inequalities: the sum of production of a commodity is equal to its demand minus deficit plus excess, activity is constrained by the maximum capacity and all variables are non-negative by definition. This can be efficiently solved by computers for each given instance. Production wind-up and wind-down is ignored, since time continuity is not considered. As a consequence fuel limits (e.g. diminishing hydropower capacity) are not modelled completely either.

Ovariables like EnergyNetworkOptim below are used in Helsinki energy decision 2015. Prices of fuels in heat production are used as direct inputs in the optimising.

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Fuel use and fuel shares in generic processes

There is an alternative way for calculating fuel use. It is based on the idea that for each heating type, there is a constant share of fuels used. For some heating types, this is generic and is shown on this page. For some others, the constant is case-specific and is determined on a case-specific page.

The table below contains connections of heating types and fuel usage in generic situations. There may be case-specific differences, which must be handled separately.

Fuel use in different heating types(-)
2OilHouseholdLight oil1
4Heating oilHouseholdLight oil1
6Other sourcesHouseholdOther sources1
7No energy sourceHouseholdOther sources1
8GeothermalGridElectricity0.3Geothermal does not sum up to 1 because more heat is produced than electricity consumed.
9Centrifuge, hydro-extractorGridElectricity0.3Not quite clear what this is but presumably a heat pump.
10Solar heater/ collectorGridElectricity0.1Use only; life-cycle impacts omitted.

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Old version with a set of linear equations

  • Energy balances are described as input = output on a coarse level (called classes) where the structure is the same or similar to the OECD energy balance tables. If possible, this is described on the Energy balance method level and it is shared by all cities.
  • On more detailed (variable level in the matrix), the fraction of each variable of the total class are described separately. Fractions are city specific and they are described on city level in a separate table.
  • Based on the fraction table, detailed equations with variables are created. The format will be fraction * class total = variable.
  • The last fraction has zero degrees of freedom when the class total is given. However, it must have a variable and thus a row in the fraction table. The result for that variable is an empty cell (which results in NA).
  • Unlike in the previous version, all variables are given either as values or equations, and the user interface is not used for BAU. In contrast, user interface or decision table may be used to derive values for alternative scenarios.
  • To make this work, the city-specific fraction data must be defined as ovariable (so that it can be changed with a decision table), and also the energy balance method must be described asa ovariable. How are we going to make the two interplay, as we may want to have several cities?
    • Define one city ovariable and evaluate energy balance with that. The ovariable has a generic name. Then, define a new city ovariable with the same name and re-evaluate the energy balance ovariable; this must be done so that the two cities are appended rather than replaced.
    • city ovariables are appended first into a large fraction table, and then that is used to create the large energy balance matrix. ←--#: . This is clearly better. (type: truth, paradigm: science view) --Jouni 17:09, 21 February 2013 (EET)
  • The city-specific ovariable may have Iter and other indices. A separate matrix is created and solved for each unique combination of indices. This makes it possible to have a very flexible approach.
  • We should check if the energy balance matrix (see Matti's Excel) has city-specific equations. If possible, energy transformations are described as generic equations on the energy balance method.
  • Structure of OECD Energy balance tables (data):
    • Fuel (given as observation columns in OECD table)
    • Activity (row in OECD table)
    • Description
  • Structure of the generic process table
    • Equation,
    • Col,
    • Result,
    • Description? ⇤--#: . This does not join up in a coherent way. (type: truth, paradigm: science view) --Jouni 17:09, 21 February 2013 (EET)
  • Columns for fraction table
    • Class
    • Item
    • Result (fraction)
    • Indices as needed
Example table for making matrices from text format equations. CHPcapacity describes which of the piecewise linear equations should be used. Policy is a decision option that alters the outcome. Dummy is only for compatibility but it is not used.
Equations(GWh /a)
1BiofuelCHP renewable = CHP peat1Biofuel policy contains half biofuels, half peat
2BAUCHP renewable = 89.241
3CHP peat + CHP renewable + CHP oil = CHP heat + CHP electricity1
4CHP peat = 90-98*CHP oil1
5CHP electricity = 0.689*CHP heat1
6CHP<1000H heat = 0.08*CHP heat1Small heat plants reflect the total heat need
7CHP>1000CHP heat + CHP electricity = 10001But production capacity of CHP may be overwhelmed, decoupling CHP heat and H heat.
8H biogas + H oil = H heat1
9H oil = 18.973*H biogas1
10Bought electricity + CHP electricity = Cons electricity1
11CHP heat + H heat = Cons heat1
12Cons electricity = 900-11001
13Cons heat = 900-10001
Example table to describe the details about nonlinear equations.
Nonlinearity parameters(GWh /a)
1Cons heatCHPcapacityResultCHP<1000CHP>10001080

This table is fetched if there are no nonlinearities. Therefore, there is no need to copy it to the case study page.
No nonlinearities(GWh /a)
This table is fetched if there are no modelled upstream variables that would affect the equations.
No modelled upstream variables(-)

Stored objects below used by Energy balance in Kuopio.

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How to give uncertain parameters?

  • In equations, the content is interpreted only inside solveMatrix. Therefore, the typical approach where all unique index combinations are run one at a time does not work.
  • There should be an update in parameter interpretation for terms with one entry only. It can no longer be based on as.numeric, if distributions (=text) is allowed.
    • If it starts with [a-z.] it is a variable name.
    • If it starts with [0-9<\\-] it is a parameter value.
  • Instead of params[[i]] and [[vars]] vectors, a data.frame will be created with Result as the params column.
  • The data.frame is then interpreted with N = N. If parameters are probabilistic, Iter column will appear.
  • When all parameters have been interpreted, check if Iter exists.
  • If Iter exists, make a for loop for all values of Iter.
    • Create a matrix from the parameters and solve.
    • Rbind the result to a data.frame with Iter.
  • Return the output.
  • Old code with an input table with columns Equation, Col, Result, Description: [1]

See also

Helsinki energy decision 2015
In English
Assessment Main page | Helsinki energy decision options 2015
Helsinki data Building stock in Helsinki | Helsinki energy production | Helsinki energy consumption | Energy use of buildings | Emission factors for burning processes | Prices of fuels in heat production | External cost
Models Building model | Energy balance | Health impact assessment | Economic impacts
Related assessments Climate change policies in Helsinki | Climate change policies and health in Kuopio | Climate change policies in Basel
In Finnish
Yhteenveto Helsingin energiapäätös 2015 | Helsingin energiapäätöksen vaihtoehdot 2015 | Helsingin energiapäätökseen liittyviä arvoja | Helsingin energiapäätös 2015.pptx
Urgenche research project 2011 - 2014: city-level climate change mitigation
Urgenche pages

Urgenche main page · Category:Urgenche · Urgenche project page (password-protected)

Relevant data
Building stock data in Urgenche‎ · Building regulations in Finland · Concentration-response to PM2.5 · Emission factors for burning processes · ERF of indoor dampness on respiratory health effects · ERF of several environmental pollutions · General criteria for land use · Indoor environment quality (IEQ) factors · Intake fractions of PM · Land use in Urgenche · Land use and boundary in Urgenche · Energy use of buildings

Relevant methods
Building model · Energy balance · Health impact assessment · Opasnet map · Help:Drawing graphs · OpasnetUtils‎ · Recommended R functions‎ · Using summary tables‎

City Kuopio
Climate change policies and health in Kuopio (assessment) · Climate change policies in Kuopio (plausible city-level climate policies) · Health impacts of energy consumption in Kuopio · Building stock in Kuopio · Cost curves for energy (prioritization of options) · Energy balance in Kuopio (energy data) · Energy consumption and GHG emissions in Kuopio by sector · Energy consumption classes (categorisation) · Energy consumption of heating of buildings in Kuopio · Energy transformations (energy production and use processes) · Fuels used by Haapaniemi energy plant · Greenhouse gas emissions in Kuopio · Haapaniemi energy plant in Kuopio · Land use in Kuopio · Building data availability in Kuopio · Password-protected pages: File:Heat use in Kuopio.csv · Kuopio housing

City Basel
Buildings in Basel (password-protected)

Energy balances
Energy balance in Basel · Energy balance in Kuopio · Energy balance in Stuttgart · Energy balance in Suzhou


Related files