3 | Methodology & Tools
MARKAL 65 well defined data format. In order to keep the model and the data standardised, there
are tools that have been developed for modellers by a group of developers mandated by ETSAP, Energy Technology Systems Analysis Programme of the International En-ergy Agency (IEA). The most recent tools for MARKAL are ANSWER and VEDA user interfaces. Both user interfaces can be used with either MARKAL or TIMES models.
They serve as model generators: from a general framework, the modeller can construct a model that addresses a specific case with specific data describing an energetic situation.
For new models, MARKAL is being replaced by its successor TIMES,TheIntegrated Markal Efom System that integrates MARKAL with many EFOM features. Again, there are ANSWER and VEDA interfaces to TIMES models. VEDA (VErsatile Data Analyst) is a data management tool specifically designed for large models formulated in GAMS (General Algebraic Modeling System) high-level mathematical programming language. A high-level language is a programming language that is closer to human lan-guages and further from machine lanlan-guages. Mathematical Programming (MP) is the use of mathematical models, particularly optimising models, to assist in taking decisions.
Since a MARKAL model is an optimisation model, it can be formulated as follows:
minimiseP
i(ciXi) subject to
P
iajiXi≤bj
Xi ≥0
where the coefficients ci for the objective function, technical coefficients aji (investment costs, availability factors, load factors, yields and efficiencies, etc.) are known parameters as well as exogenous demands bj (useful demands). VariablesXi (activities of technolo-gies and energy agents), represent the solution vector of the problem. The objective function to be minimised is the global system cost with contributions from each technol-ogy, each extracted or imported energy agent, each operation and maintenance cost.
MARKAL is a dynamic multi-period model usually with 9 periods with 5 years step, so the contributions have to be reckoned for every year and discounted in time. The constraints are physical (energy conservation, Carnot cycle efficiency), technical (energy transformation is not even close to maximum theorical efficiency and technologies do not always run at maximum potential), operational (peak demands are different in winter and in summer, technologies need maintenance that reduces availability), environmental constraints (emissions such as global constraint onCO2, local constraints onSO2,N Ox) and even political constraints (such as abandon of the nuclear power).
Every additional active constraint increases the global cost of the energy system and shadow prices are interesting results associated with dual variables. Shadow price is the instantaneous change in the objective value of the optimal solution obtained by relaxing
a constraint, expressed in the units of that constraint. It is the marginal utility of relax-ing the constraint, or the marginal cost of strengthenrelax-ing the constraint, and can serve to measure the cost of a constraint.
The above formulation is in its deterministic version with assumption of perfect fore-cast where the evolution of all the parameters is predictable and known in advance. To compare it with stochastic formulation, let’s rewrite it in a following way:
minimise cT x subject to A x ≤ b
Figure 3.2: Schematic representation of a determinist problem. Evolution of all the parameters is known or supposed to be known in advance, so-called perfect forecast.
Then the corresponding stochastic formulation of the objective function can be ex-pressed as a sum of two parts:
1. the deterministic part where there is only one evolution while waiting for the com-plement of information (costs c1), and
2. the stochastic part with branches corresponding to scenarios of evolution once the uncertainty has been resolved and the future evolution of parameters becomes known (costsc2, probabilitiesps):
minimise
"
cT1 x1 + PS
s=1
(ps cT2 x2,s)
#
subject to A0 x1 ≤b0
A1 x1+A2 x2,s ≤ bs for all s = 1, ... , S where
x1 are decisions to be determined before the resolution of uncertainty
x2,s are decisions afterwards adapted to the circumstances that occur in scenario s c1 are the costs before the resolution of uncertainty
c2 are the corresponding costs after the resolution of uncertainty
ps are the probabilities of evolution of parameters associated with scenario s
In a typical MARKAL model, the energy forms (ENT) are organised as disjoint sets of energy carriers classed as follows (Fishbone et al., 1983):
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Figure 3.3: Schematic representation of a stochastic problem. In this example, uncertainty in evolution of one parameter will be waived in period 5. Until then, a common strategy (hedging) is adopted with cost c1. After that, scenarios represent possible evolutions with probabilityps
and costc2. Typically, there are either S=2 scenarios of evolution of a parameter (high, low) or S=3 scenarios (high, medium, low). The probabilitiespsof evolution are usually only estimates.
EN T = EN C ∪ ELC ∪ LT H (3.1)
where
EN T is the set of all energy carriers
LT H is the Low Temperature Heat (cannot be stored) ELC is the Electricity (cannot be stored)
EN C is the set of all user-defined energy carriers other thanLT H andELC User-introduced energy forms fall into one of the following disjoint sets:
EN C = EF S ∪ ESY ∪ EN U ∪ ERN ∪ EHC (3.2)
where
EF S is the set of all fossil energy carriers ESY is the set of all synthetic energy carriers EN U is the the nuclear energy
EN C is the set of all user-defined energy carriers other thanLT H andELC Fossil and synthetic energy carriers can be in solid, liquid or gaseous form. These classes are introduced for easy sums over transportation forms:
EF S ∪ ESY = SLD ∪ LIQ ∪ GAZ (3.3)
MARKAL technologies are organised in the following sets:
T CH = P RC ∪ CON ∪ DM D (3.4)
where
P RC is the set of all process technologies CON is the set of all conversion technologies DM D is the set of all demand devices
SRC DMD DM PRC
CON
Figure 3.4: Schematic diagram of sources, con-version and process technologies, demand de-vices and useful demand in MARKAL.
The difference between P RC and CON is that process technologies pro-duce stockable energy agents such as gaso-line or heating fuel, while conversion tech-nologies are producing non-storable en-ergy forms like electricity or low tem-perature heat. In order to remain com-patible with the MARKAL model struc-ture, we have introduced consumer’s be-haviour as a virtual process technol-ogy.
Conversion technologies are also defined as disjoint user-defined classes:
CON = F OS ∪ N U C ∪ REN ∪ ST G (3.5)
where
F OS is the set of all technologies converting fossil fuel
N U C is the set of all nuclear technologies producing electricity or heat REN is the set of all renewable conversion technologies
ST Gis the set of all storage technologies
In order to be able to take into account transmission costs from the point of production to the point of consumption, the conversion technologies set CON is further split into yet another set of classes, centralised technologies CEN for which transmission costs have to be taken into account, and decentralised conversion technologiesDCN may have a positive distribution cost but the transmission cost is zero. This reflects the situation where the technologies are situated close to load centres. An electricity technology may fall into any of the two classes; if it is member of the setCEN, then there are transmission costs and losses but there are no losses if it is member ofDCN (for example, if the place of consumption is close to the last transformer).
CON = CEN ∪ DCN (3.6)
Another split is following the energy form that results from the conversion. Con-version technologies may produce only electricity, or they can be heat plants producing only heat, or they can be coupled-production technologies, i.e. those producing both electricity and low-temperature heat for district heating grid.
CON = ELE ∪ CP D ∪ HP L (3.7)
There is one more split into classes following the load management. Baseload tech-nologies BAS are conversion technologies that cannot follow a load and are subject to special constraints in the model and production vector is generated for day-time only.
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