Forecasting CO₂ Prices in the EU ETS

Abstract

The paper focuses on the market dynamics of the EU Emissions Trading Scheme (EU ETS), the cap-and-trade system implemented to reduce CO₂ emissions from electricity and heat plus some industrial sectors in the EU. An overview of carbon market models is presented and an analysis based on a particular model is used to illustrate some of the main price drivers in the market. The model results indicate that it is crucial to capture short and long term fuel switching in electricity generation and electricity demand response in order to forecast EU Allowance (EUA) prices. In addition, the impact of other policy measures is significant, e.g., support to renewable energy and compensation for industries at risk of carbon leakage. The applied model, together with the available data and market characteristics, imply that the dynamics of emission reductions from the heating sector is poorly understood, including the combined impact of the ETS and other policy measures such as the renewable energy target.

The article was written while the authors worked for Econ Pöyry, now Pöyry Management Consulting Norway (www.poyry.com).

The article was written while the authors worked for Econ Pöyry, now Pöyry Management Consulting Norway (www.poyry.com).

A Appendix: Econ Pöyry’s Carbon Market Model

1.1 A.1 Overview

Econ Pöyry’s Carbon Market Model – a numerical model for the European carbon and power market – was used for the simulations presented above. This appendix documents the model.

Econ Pöyry’s Carbon Market Model is a partial equilibrium model that solves for the EU ETS allowance market and the European electricity market simultaneously. The model covers EU-27 countries plus Norway and Switzerland.¹¹ The model is a combination of a bottom-up and top-down model.

For the allowance market, the allowance price is found by equilibrating supply and demand of allowances in the EU ETS market for the whole trading period (e.g., 2008–2012). For the electricity market, the model determines for each country electricity prices throughout each year, electricity consumption, production and investments to meet the electricity demand, reservoir levels for hydropower capacity, and trade between the countries.

The model determines a long-run equilibrium in the sense that investments in new power generation capacity are determined endogenously. Optimising behaviour of producers and consumers is assumed within the confines of restrictions that describe the actual market conditions. The restrictions include excise taxes and regulatory mark-ups that describe government interventions. There is no uncertainty in the model.

The model solves for wholesale (spot market) prices and end user prices of all agents. There are no explicit forward markets or long term contracts in the model. We interpret the model to contain implicit contracts: Since we assume rational expectations and full certainty, spot market prices over the contract period will equal implicit contract prices.

The model is developed in the GAMS programming language [19].

1.2 A.2 Market for Carbon Allowances

For allowance market, the model captures the fundamental supply and demand functions in the EU ETS market as well as in the linked Kyoto project-based mechanisms. Allowance price is found by balancing supply and demand. Total supply of allowances is given by the amount of allowances allocated to the participants. Total demand for allowances is determined by activity level in the sectors that are subject to the EU ETS: energy (electricity and heat production), pulp and paper, metal, mineral and chemical industries, refineries and aviation. These are grouped into electricity, heat and other industries in the model. The gap between business as usual (BAU) emissions¹² and the cap given by the total amount of allowances determines the required abatements. Which abatements are actually carried out depends on the costs of reducing emissions in the different ETS sectors.

CO₂ emissions stem from power generation, heat generation and industrial activities in other sectors i:

$$ \begin{array}{llll} E & = \sum\limits_l \,{E_{{l,{\rm{El}}}}} \\& + \sum\limits_l \,{E_{{l,{\rm{Heat}}}}} \\& + \sum\limits_i \,\left( {\sum\limits_l \,E_{{l,i}}^{\rm{BAU}} - \sum\limits_j \,{A_{{i,j}}}} \right) \end{array} $$

(1)

Equation 1 defines CO₂ emissions from different sources. The first line (right hand side) specifies emissions (E _l,El) from power production in each country l. These stem from use of fossil fuels both in existing and new power plants. The power sector will be discussed in detail below (Sect. A.3).

The second line of Eq. 1 is emissions from heat generation. Heat demand is determined by temperatures and economic growth. Supply comes from combined heat and power (CHP) units and district heating units and is specified by capacities and costs in these units. The heat market is not modelled explicitly; instead, emissions from heat production (E _{l, Heat}) in each country are included exogenously.

The third line of Eq. 1 defines emissions from other industries i that are part of the EU ETS: metal industries, pulp and paper, minerals, chemical industries, refineries and aviation. Emissions from industries in the business as usual case depend on the activity level, which is in turn a function of global economic growth and domestic conditions. Some of them (iron and steel, aluminium, pulp and paper, and chemical industry) are also power intensive, and as such important for the outcome of power market. Others (e.g., minerals) are not power intensive. The starting point is that emissions are equal to the emissions in BAU case (E ^BAU). However, various abatement activities j can be carried out to reduce emissions. Whether and which abatements are carried out depends on the marginal abatement costs ϖ and the allowance price. Hence, A is an endogenous variable. The abatement potential in each industry is limited by a pool of potential activities:

$$ {A_{{i,j}}} \leq A_{{i,j}}^{{\rm max}} $$

(2)

Emissions from all the installations in the EU ETS – grouped into power, heat and other industries in the model – are matched with the cap. In other words, total emissions from these sectors must not exceed the total amount of allowances:

$$ E \leq \overline E + \widehat{E}$$

(3)

If the total emissions exceed the cap, a penalty ϑ must be paid on the excess emissions Ê (in addition to the allowances that must be purchased in the market).

Since the EU ETS is a system where allowances can be traded, it is the total cap that is relevant, not individual countries’ caps. Therefore, Eq. 3 applies to the whole EU ETS area, not to different countries and installations separately.

As a result of this optimization, the model finds one equilibrium price for allowances for the whole emission trading period (e.g., 2008–2012). Since allowances can in practice be borrowed from the next year during the period, it is the total emissions and the total amount of allowances during the entire period that determine the price. High emissions in one year cause many allowances to be used in that year, leaving fewer allowances available for the next year, thus implicitly raising the price of allowances in the future. This mechanism equalizes the price in all years. With perfect information and no uncertainty (as in the model), there is no fluctuation in allowance price.

1.3 A.3 Electricity Market

For electricity market, it is important whether demand occurs during day or night, or during winter or summer. Hence, the electricity market module has a considerably finer time resolution than the allowance market module. The basic time unit in the electricity market module is a week that is divided into five load periods (night, day shoulder, day, day peak and afternoon peak). However, the weeks can be aggregated into months or seasons. The weeks (or months) are further aggregated into years, as the seasonal variation plays a key role in electricity demand and supply. The model can be run for one year or for several consecutive years.

1.3.1 A.3.1 Demand for Electricity

There are up to five end users of electricity in each country: households, services, industry (not including process industry), process industry (including pulp and paper) and electric boilers. Not all end users are present in all countries (e.g., electric boilers are specific to Norway and Sweden only).

End users maximize utility functions W _l,e  = Σ _m W _m,l,e (D _m,l,e ) of electricity demand (D) of end user e of country l in every period m. The outcome is log-linear electricity demand functions that are written in levels as

$$ {D_{{m,l,e}}} = \left[ {{\alpha_{{m,l,e}}}{{({\xi_{{l,e}}})}^{{{\gamma_{{l,e}}}}}}{\pi^{{{\kappa_{{l,e}}}}}}} \right]P_{{m,l,e}}^{{{\beta_{{l,e}}}}} $$

(4)

Electricity demand is a function of the end user price of electricity (P), the oil price (π) and income level (ξ). The first part of Eq. 4, inside the square brackets, is a constant for our purposes. α is used to calibrate the model to actual price and consumption in the base month. It also includes an exogenous seasonal variation pattern, which is especially strong in Norway and Sweden, due to the large amount of electricity used for heating in these countries. In other countries, electricity demand for air condition contributes to the seasonal pattern. γ, κ and β are the income elasticity, oil price elasticity and electricity price elasticity, respectively.

Different price and income elasticities are assigned to each sector. The electricity price elasticity varies between −0.2 and −0.8. Electric boilers are assumed to have a fairly elastic demand, as they are able to change between electricity and oil on a short notice. Demand in process industries is price inelastic.

The price elasticity refers to end user price of electricity (P) that includes the spot price (p) of electricity, the distribution tariffs (τ ⁿ), the excise tax on electricity (τ ^e), the mark-up (τ ^o) to the supplier and VAT(τ ^m).

$$ {P_{{m,l,e}}} = ({\tilde{p}_{{m,l}}} + \tau_{{l,e}}^n + \tau_{{l,e}}^e + \tau_{{l,e}}^o)(1 + \tau_{{l,e}}^m) $$

(5)

Consumption during a period m is divided between the different load periods a according to given ratios. Accordingly, consumers respond only to an average price level of a period (e.g., month). The spot price p of a period m is an aggregate of spot prices over load periods¹³:

$$ {\tilde{p}_{{m,l}}} = {\Sigma_a}{\lambda_{{l,a}}}{p_{{m,l,a}}} $$

(6)

λ is the share of consumption assigned to each load period.

1.3.2 A.3.2 Supply of Electricity

The supply side is represented by producers with different technologies and capacities at their disposal. The supply curve (merit order curve) for each country is the sum of the marginal cost curves of producers in the country. The marginal cost curve is dynamic, since investments can expand production capacity.

The existing and potential power plants are grouped into categories (cost classes) according to technology (hydropower, thermal power incl. combined heat and power, nuclear power, wind power, etc.), fuel (coal, gas, oil, biomass, etc.) and plant efficiency. Altogether, there are more than 70 different production categories (k). Exogenous short run marginal costs (δ) and emission factors (η) are assigned to each production category k. The marginal costs reflect fuel cost, operating cost and emission cost.

Production X is determined endogenously (exceptions are discussed below). Producers maximise profits:

$$ {\Pi_{{m,a,l,k}}} = {p_{{m,a,l}}}\,\,{X_{{m,a,l,k}}} - {\delta_{{l,k}}}{X_{{m,a,l,k}}} $$

(7)

Profit, Π, is income less short-run costs. Each period and production category requires a separate profit decision in each country. The outcome of maximising profit in isolation is a zero–one decision: no production (X _m,a,l,k  = 0) if costs exceed the output price (δ _k,l  > p _m,a,k,l ), and maximum production (${X_{{m,a,l,k}}} = X_{{m,a,l,k}}^{{\rm max}}$) if the output price exceeds costs (p _m,a,k,l  > δ _k,l ). Since prices vary with time, a technology may be operated part of the time.

The next step is to constrain production during those periods where the price exceeds costs – in other words to determine $X_{{m,a,l,k}}^{{\rm max}}$. The basic constraint in the model is physical production capacity, but available production capacity is further constrained by requirements for reserve capacity, maintenance and seasonal variation. Also, the minimum production level may be higher than zero (for instance for nuclear power plants). Hence, the minimum and maximum production for each production category in each country, month and load period is restricted to:

$$ \forall m,a,l,k:X_{{m,a,l,k}}^{{\rm min}} \leq {X_{{m,a,l,k}}} \leq X_{{m,a,l,k}}^{{\rm max}} $$

(8)

Additionally, the whole power system of a country is subject to a reserve requirement, ε, that further limits available capacity:

$$ \forall m,a,l:\sum\limits_k \,{X_{{m,a,l,k}}} \leq \left( {1 - \varepsilon } \right)\sum\limits_k \,{\mu_a}X_{{m,a,l,k}}^{{\rm max}} $$

(9)

To understand the combined effects of the constraints of Eqs. 8 and 9, it is useful to note that the capacity requirement, Eq. 8 gives one constraint for every technology k, area l, month m and load period a; while the reserve requirement, Eq. 9 gives one constraint for every area l, month m and load period a.

1.3.2.1 Investments and refurbishments

The physical production capacity can be expanded by investing in new capacity and refurbishing existing, outdated capacity. Refurbishing prolongs the lifetime of an existing power plant and is a cheaper option than building a new power plant. Unit costs are defined for investments and refurbishments, ι and ς, respectively. The total volumes of investments ι and refurbishments J in each production category and country are limited:

$$ \forall k,l:{I_{{k,l}}} \leq I_{{k,l}}^{{\rm max}} $$

(10)

$$ \forall k,l:{J_{{k,l}}} \leq J_{{k,l}}^{{\rm max}} $$

(11)

Total capacity in each plant category in each country is therefore the sum of original installed capacity $(X_{{m,a,k,l}}^{{\rm max\,\,{\rm{Start}}}})$, investments and refurbishments:

$$ \forall\, m, a,k,l:X_{{m,a,k,l}}^{{\rm max\,\,{\rm{Start}}}} + {I_{{k,l}}} + {J_{{k,l}}} = X_{{m,a,k,l}}^{{\rm max}} $$

(12)

1.3.2.2 Hydropower

In addition to production capacity, hydropower production is further restricted by water inflow and reservoir capacity. Three different types of hydropower plants are modelled: plants with reservoirs, run-of-river and pumped storage.

The short term marginal costs of hydropower are very low and the constraints given by Eqs. 8 and 9 are quite lax. But the alternative cost of producing hydropower now is the price one can obtain in the future. Thus, hydropower production depends both on the short term marginal cost and on the value of the stored water, which equals the expected future price less the expected future cost. Reservoirs are used in order to optimise production over a year: water can be stored in the reservoirs for production in later periods. Because of the flexibility in the hydropower production, the total supply curve of a period is not fixed by assumption. The reservoir level R of a country l in a period m depends on the inflow θ and hydropower production level of the country in the period:

$$ \forall m,l:{R_{{\left( {m + 1} \right),l}}} \leq {R_{{m,l}}} + {\theta_{{m,l}}} - \sum\limits_a \,{X_{{m,a,l,{\rm{hydro}}}}} $$

(13)

There is one reservoir per country. Bottlenecks within a country are thus not modelled. There is a minimum requirement on reservoir capacity that generates the alternative cost of producing now:

$$ \forall m,l:R_{{m,l}}^{{min}} \leq {R_{{m,l}}} \leq R_{{m,l}}^{{\rm max}} $$

(14)

The minimum reservoir level is typically 15%, the maximum is 95% of total reservoir capacity. The reason is that it is unlikely that all the reservoirs in a country are empty (full) at the same time.

In contrast to plants with reservoirs, run-of-river plants cannot store water and, hence, transfer production from low-price to high-price periods. Instead, production must occur when the water is there. Production in these plants is exogenously determined and is assumed to follow a seasonal profile.

A third type of hydropower plant, pumped storage plants, can use the same water over and over again. The water is used for electricity production during high-price periods (e.g., day) and the water is pumped from lower reservoir to higher reservoir during low-price periods (e.g., night). Two additional constraints limit production in pumped storage plants. Firstly, production in pumped storage plant requires consumption of electricity, Q, and there is an energy loss φ related to that:

$$ \forall m,l:\phi \sum\limits_a \,{Q_{{m,a,l}}} = \sum\limits_a \,{X_{{m,a,{\rm{Pumped\,\,Storage}},l}}} $$

(15)

Secondly, the same equipment cannot be used for production and consumption at the same time:

$$ \forall m,l,a:{Q_{{m,a,l}}} + {X_{{m,a,{\rm{Pumped\ Storage}},l}}} \leq X_{{m,a,{\rm{Pumped\ Storage}},l}}^{{\rm max}} $$

(16)

In an electricity market with significant hydro production, the amount of precipitation is important. We assume that precipitation is “normal” throughout the year. Normal precipitation is defined as a situation with median historic precipitation. Since we assume full certainty, precipitation is known: everybody knows at the beginning of the year that precipitation is going to be normal (or wet or dry) throughout the whole year. Sensitivities are used to analyse the impact of dry or wet years.

1.3.2.3 Exogenous production

Production in some technologies is not determined by profit-maximising behaviour, that is, production does not depend on power prices. For instance, power production in combined heat and power (CHP) plants is in reality determined by heat demand; power is merely a by-product. Heat demand and production are assumed to follow a seasonal profile. They can vary with temperature, but are assumed price inelastic. Wind power can only be produced when there is enough wind, and given enough wind, marginal costs are negligible. Production in these power plants is therefore included exogenously in the model.

1.3.2.4 Emissions

CO₂ emissions stem from use of fossil fuels both in existing and new power plants. Emissions from electricity sector E _l,El depend on the production level and emission factor η _k in each plant category:

$$ {E_{{l,{\rm{El}}}}} = \sum\limits_{{m,a,k}} \,{\eta_k}{X_{{m,a,l,k}}} $$

(17)

1.3.3 A.3.3 Trade

Both trade between the model countries (i.e., the countries that are endogenous in the model) and with the surrounding countries is included. There is no trade within a country, i.e. a country is seen as an entity (except Denmark that is modelled as two regions).

Trade between the model countries occurs when prices, adjusted for costs related to transmission losses, differ between the countries. Trade occurs until the price differences are eliminated or until the transmission capacity is fully utilised.

Trade between the model countries is described by the variable T. T _m,a,l,s means exports from country l to country s. There is a transmission loss (σ ^t _l,s ) on this trade, to the effect that available imports in country s are reduced compared with the original exports. Available imports are T _m,a,l,s / (1 + σ ^t _l,s ).¹⁴

Imports U _m,a,l,c and exports V _m,a,l,c to outside countries c are either modelled as fixed, based on historical levels and assumptions about future development, or price-dependent. In the latter case, prices in the countries outside the model (π ⁱ for imports and π ^e for exports) are constant, i.e. not influenced by trade. Nevertheless, π ⁱ and π ^e reflect daily and seasonal variation.

Capacity constraints on transmission lines are in effect on both types of trade.

1.3.4 A.3.4 Electricity Market Equilibrium

The various parts of the market – consumption, production and trade – are tied together in the equations for electricity flow equilibrium. These equations say that demand in any period and any country equals supply:

$$ \begin{array}{llll} \forall m,a,l :\sum\limits_e {{\lambda_{{l,a}}}(1 + \sigma_l^d){D_{{m,l,e}}} + {Q_{{m,a,l}}} + \sum\limits_s {{T_{{m,a,l,s}}} + } \sum\limits_c {{V_{{m,a,l,c}}}} } \\ \leq \sum\limits_k {{X_{{m,a,l,k}}} + \sum\limits_k {{\Gamma_{{m,a,l,k}}} + \sum\limits_s {\frac{{{T_{{m,a,s,l}}}}}{{1 + \sigma_{{l,s}}^t}} + \sum\limits_c {{U_{{m,a,l,c}}}} } } }\end{array} $$

(18)

To start at the right hand side of the equation: available supply equals domestic endogenous production (X _m,a,l,k ) plus domestic exogenous production (Γ _m,a,l,k ); plus imports from other model countries after “melting” $\left( {\frac{{{T_{{m,a,s,l}}}}}{{1 + \sigma_{{l,s}}^t}}} \right)$; plus imports from non-model countries (U _m,a,l,s ). Demand can be no larger than this supply. Demand (LHS) consists of consumption demand of the load period (λ _l,a (1 + σ ^d _l )D _m,l,e ), including domestic transmission losses (δ ^d _l ); plus power use by pumped storage plants (Q _m,a,l ); plus exports to model countries (T _m,a,l,s ); plus exports to non-model countries (V _m,a,l,c ).

1.4 A.4 Solution for Power and Allowance Market

The solution to the model is found by maximizing utility (that is, the areas under the demand curves of Eq. 4) less private economic costs including short run marginal costs, taxes and tariffs, investment and refurbishment costs, abatement costs of CO₂ emissions and penalty for non-compliance, if emissions exceed the cap.¹⁵ The maximization is constrained by the various technical and economical constraints of the market, including distribution and transmission losses. In other words, the idea is to mimic private behaviour. This implies to maximise

$$ \begin{array}{llll} W = \sum\limits_{{m,a,l}} {\left\{ {\sum\limits_e {{W_{{m,l,e}}}({D_{{m,l,e}}}) - \sum\limits_k {{\delta_{{l,k}}}} {X_{{m,a,l,k}}} - \sum\limits_e {\left( {\tau_{{l,e}}^n + \tau_{{l,e}}^e + \tau_{{l,e}}^o} \right){D_{{m,l,e}}}} } } \right.} \hfill \cr - \sum\limits_e {\left( {{\tilde{p}_{{m,l}}} + \tau_{{l,e}}^n + \tau_{{l,e}}^e + \tau_{{l,e}}^o} \right)\tau_{{l,e}}^m{D_{{m,l,e}}}\hfill} \\ \left. { + \sum\limits_c {\pi_{{c,a}}^e} {V_{{m,c,l,a}}} - \sum\limits_c {\pi_{{c,a}}^i{U_{{m,c,l,a}}}} - \sum\limits_s {\tau_{{l,s}}^t} {T_{{m,a,l,s}}}} \right\} \hfill \cr - \sum\limits_{{k,l}} {{\iota_{{k,l}}}} {I_{{k,l}}} - \sum\limits_{{k,l}} {{\varsigma_{{k,l}}}{J_{{k,l}}}} \hfill \cr - \sum\limits_{{i,j}} {{\varpi_{{i,j}}}{A_{{i,j}}} - \vartheta \widehat{E}} \end{array} $$

(19)

The maximisation is carried out subject to the electricity market equilibrium condition (18) that ties the quantity variables together; the constraints on electricity production, Eqs. 8, 9, 10, 11, 12, 13, 14, 15 and 16; the capacity constraints on trade; the constraints related to CO₂ emissions and allowances, Eqs. 1, 2, 3 and 17; and formally even the equations that determine prices in terms of consumption, Eqs. 4, 5 and 6.

The maximisation of Eq. 19 determines all quantity variables of the system: consumption (D _m,l,e ), production (X _m,a,l,k ), investments I _k,l , refurbishments J _k,l and trade (T _m,a,l,s , U _m,c,l,a and V _m,c,l,a ), emissions (E) and abatements (A _i ) in different sectors and formally even the producer price (p _m,l ) and allowance price.

1.5 A.5 Parameters and Variables

Endogenous variables are written in Latin letters.

D is electricity consumption

X is electricity production

T is trade within the model countries (EU-27 plus Norway and Switzerland)

U is imports to the model region

V is exports out of the model region

Q is demand in pumped storage plants

R is reservoirs

I is investments

J is refurbishments

P is end user price

p is wholesale (spot market) price

E is CO2 emissions

Ê is the excess emissions

A is abatements (in EU ETS industries other than power and heat)

Parameters are written (mostly) in Greek letters.

α is the constant term that defines the starting point of the model (found by a combination of observed end-user prices and consumption). α also includes seasonal variation

ξ is income level (GDP for services, industry and electric boilers, and private income for households)

π is oil price

γ is income elasticity

β is electricity price elasticity

κ is oil price elasticity

τ n is distribution cost

τ e is excise tax on electricity

τ o is mark-up on spot price to different end-users

τ m is VAT

τ t is border tariff

δ is marginal production costs

η is emission factor (CO2 emissions per unit of output)

σ d is transmission losses within a country

σ t is transmission losses on international interconnectors

θ is total inflow to the reservoirs

ε is minimum reserve requirement

λ is the share of consumption assigned to each load period, Σ a λ l,a  = 1.0,

μ is the relative length of each load period, Σ a μ a  = 1.0

X max is maximum production

X min is minimum production

X maxStart is maximum production, based only on today’s installed capacity (i.e., without additional investments)

Γ is exogenous production

I max is investment potential

J max is refurbishment potential

ι is unit cost of investment

ς is unit cost of refurbishment

φ is efficiency factor of pumped storage

π e is price for exports to non-model countries (e.g., Russia)

π i is price for imports from non-model countries (e.g., Russia)

ϖ is abatement cost in the EU ETS industrial sectors (other than power and heat)

E BAU is CO2 emissions from industrial sectors in the business-as-usual case, before abatements,

E Heat is CO2 emissions from heat production

Ē is the total emission cap

ϑ is penalty if the emission cap is exceeded

A max is the maximum abatement potential in the industrial sectors

Indices are written as footscripts in lower case Latin letters.

m∈{1,…,13} is a 4-week period (“month”)

a∈{night, day shoulder, day, day peak and afternoon peak} is load period

e∈{households, services, process industry (including pulp and paper), other industry, electric boilers} is end-user category

k∈{hydro, nuclear, wind, CHP, coal condensing, CCGT, …} is production technology and cost category

i∈{iron and steel, aluminium, pulp and paper, chemical industry, mineral industry, refineries, aviation} is sector in allowance market (except electricity and heat)

j∈{1,…,25} is potential abatement activity

l,s∈ {EU-27, Norway, Switzerland} is country in the model region

c∈{Russia, …} is trade partner outside the non-model region