The impact of policy measures on future power generation portfolio and infrastructure: a combined electricity and CCTS investment and dispatch model (ELCO)

Abstract

This paper presents a general electricity-CO$_{2}$ modeling framework that is able to simulate interactions of the energy-only market with different forms of national policy measures. We set up a two sector model where players can invest into various types of generation technologies including renewables, nuclear power and carbon capture, transport, and storage (CCTS). For a detailed representation of CCTS we also include industry players (iron and steel as well as cement), and CO$_{2}$ transport and CO$_{2}$ storage including the option for CO$_{2}$ enhanced oil recovery (CO$_{2}$-EOR). The players maximize their expected profits based on variable, fixed and investment costs as well as endogenous prices of electricity, CO$_{2}$ abatement cost and other incentives, subject to technical and environmental constraints. Demand is inelastic and represented via type hours. The model framework allows for regional disaggregation and features simplified electricity and CO$_{2}$ pipeline networks. It is balanced via a market clearing for the electricity as well as CO$_{2}$ market. The equilibrium solution is subject to constraints on CO$_{2}$ emissions and renewable generation share. We apply the model to a case study of the UK electricity market reform to illustrate the mechanisms and potential results attained from the model.

Appendix: Karush–Kuhn–Tucker conditions of the ELCO model

1.1 The electricity sector

$$\begin{aligned}&\begin{array}{l} \frac{\partial L^{T,N}}{\partial g_{h,n,t,a} }: \\ {\begin{array}{lll} {0\le \left( {\begin{array}{l} DF_a \cdot PD_a \cdot TD_h \cdot \left( {\begin{array}{l} -mu\_e_{h,n,a} \\ +EF\_EL_t \cdot \left( {1-CR\_G_t } \right) \cdot \left( {CPS_a +EUA_a } \right) \\ +VC\_G_{n,t,a} +INTC\_G_t \cdot g_{h,n,t,a} \\ -\lambda _a^{target\_CO2} \cdot \alpha _{t,a} \\ \end{array}} \right) \\ +TD_h \cdot \lambda _{n,t,a}^{emps} \cdot EF\_EL_t \cdot \left( {1-CR\_G_t } \right) +\lambda _{h,n,t,a}^{cap\_g} +\lambda _{h,a}^{curt\_el} \\ \end{array}} \right) } \\ \end{array} } \\ \end{array}\nonumber \\&\qquad \bot \, {g_{h,n,t,a} \ge 0}. \end{aligned}$$

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$$\begin{aligned} \begin{array}{lll} &{}&{}\frac{\partial L^{T,N}}{\partial g\_\hbox {cfd}_{h,n,t,aa,a} }: \\ &{}0\le &{} DF_a \cdot PD_a \cdot TD_h \cdot \left( {\begin{array}{lll} -SP_{t,aa} -\sum \limits _{aaa\in I\_USE_{t,aa,aaa} } {\alpha _{t,aaa} \cdot \lambda _{aaa}^{target\_co2} } \\ -\sum \limits _{\begin{array}{lll} aaa\in I\_USE\_EL_{t,aa,aaa} , \\ t\in T\_RES \\ \end{array}}\\ {\left[ {\left( {1-TARGET\_RE_{aaa} } \right) \cdot \lambda _{aaa}^{target\_RE} } \right] } \\ +\sum \limits _{\begin{array}{c} aaa\in I\_USE\_EL_{t,aa,aaa} , \\ t\notin T\_RES \end{array}}\\ {\left[ {TARGET\_RE_{aaa} \cdot \lambda _{aaa}^{target\_RE} } \right] } \\ +EF\_EL_t \cdot \left( {1-CR\_G_t } \right) \cdot \left( {CPS_a +EUA_a } \right) \\ +EF\_EL_t \cdot CR\_G_t \cdot mu\_co2_{h,n,a} \\ +VC\_G_{n,t,a} +INTC\_G_t \cdot g\_cfd_{h,n,t,aa,a} \\ \end{array}} \right) \\ &{}&{}+\,TD_h \cdot \sum \limits _{tt\in ONEFUEL_{tt,t} } {\lambda _{n,tt,a}^{emps} } \cdot EF\_EL_t \cdot \left( {1-CR\_G_t } \right) +\lambda _{h,n,t,aa,a}^{cap\_g\_cfd} +\lambda _{h,a}^{curt\_el} \\ &{}&{}+\,TD_h \cdot \lambda _{t,a}^{diff\_g} -TD_h \cdot DIFF\_G_t \cdot \left( {\lambda _{t,a+1}^{diff\_g} +\lambda _{t,a+2}^{diff\_g} } \right) \\ &{}&{} \quad \bot \hbox { }g\_cfd_{h,n,t,aa,a} \ge 0. \\ \end{array} \end{aligned}$$

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$$\begin{aligned} \begin{array}{l} {\begin{array}{ll} {\begin{array}{l} \frac{\partial L^{T,N}}{\partial inv\_g_{n,t,a} }: \\ 0\le \left[ {\begin{array}{l} \sum \limits _{aa\in I\_USE\_EL_{t,a,aa} } {PD_{aa} \cdot DF_{aa} \cdot \left( {FC\_G_{n,t,aa} +INVC\_G_{n,t,aa} } \right) } \\ -\sum \limits _h {TD_h \cdot AVAIL_{h,n,t} } \cdot EMPS_a \cdot \sum \limits _{\begin{array}{l} aa\in I\_USE\_EL_{t,a,aa} \\ tt\in ONEFUEL_{tt,t} \\ \end{array}} {\lambda _{n,tt,aa}^{emps} } \\ -\sum \limits _h {\sum \limits _{aa\in I\_USE\_EL_{t,a,aa} } {\left( {\textit{AVAIL}_{h,n,t} \cdot \lambda _{h,n,t,aa}^{cap\_g} } \right) } } \\ -\sum \limits _h {\sum \limits _{aa\in USE\_EL_{t,a,aa} } {\left( {\textit{AVAIL}_{h,n,t} \cdot \lambda _{h,n,t,a,aa}^{cap\_g\_cfd} } \right) } } \\ +\sum \limits _{aa\in I\_USE\_EL_{t,a,aa} } {\lambda _{n,t,aa}^{pot\_g} } \\ \end{array}} \right] \\ \end{array}}\\ \quad \bot \hbox { }inv\_g_{h,n,t,a} \ge 0 \\ \end{array} } \end{array} \end{aligned}$$

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$$\begin{aligned} \begin{array}{l} \frac{\partial L^{T,N}}{\partial \lambda _{n,t,a}^{emps} }: \\ 0\le \left( {\begin{array}{l} \sum \limits _h {TD_h \cdot AVAIL_{h,n,t} \cdot } \sum \limits _{\begin{array}{l} aa\in USE\_EL_{t,a,aa} , \\ (t,tt)\in ONE\_FUEL_{t,tt} \\ \end{array}} {inv\_g_{n,tt,aa} } \cdot EMPS_{aa} \\ -\sum \limits _h {TD_h \cdot \left[ {\begin{array}{l} \left[ {g_{h,n,t,a} \cdot \left( {EF\_EL_t \cdot \left( {1-CR\_G_t } \right) } \right) } \right] \\ +\sum \limits _{\begin{array}{l} aa\in USE\_EL_{t,a,aa} , \\ \left( {t,tt} \right) \in ONE\_FUEL_{t,tt} \\ \end{array}} \left[ g\_cfd_{h,n,tt,aa,a}\right. \\ \left. \cdot \left( {EF\_EL_{tt} \cdot \left( {1-CR\_G_{tt} } \right) } \right) \right] \\ \end{array}} \right] } \\ \end{array}} \right) \\ \qquad \bot \hbox { }\lambda _{n,t,a}^{emps} \ge 0 \\ \end{array} \end{aligned}$$

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$$\begin{aligned}&\tfrac{\partial L^{T,N}}{\partial \lambda _{h,n,t,a}^{cap\_g} }:\nonumber \\&0\le AVAIL_{h,n,t} \cdot \left( {INICAP\_G_{n,t,a} +\sum \limits _{aa\in USE\_EL_{t,a,aa} } {inv\_g_{n,t,aa} } } \right) \nonumber \\&\qquad -g_{h,n,t,a} \hbox { }\bot \hbox { }\lambda _{h,n,t,a}^{cap\_g} \ge 0 \end{aligned}$$

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$$\begin{aligned} \begin{array}{l} \frac{\partial L^{T,N}}{\partial \lambda _{h,n,t,aa,a}^{cap\_g\_cfd} }: \\ 0\le AVAIL_{h,n,t} \cdot inv\_g_{n,t,aa} -g\_cfd_{h,n,t,aa,a} \hbox { }\bot \hbox { }\lambda _{h,n,t,aa,a}^{cap\_g\_cfd} \ge 0 \\ \end{array} \end{aligned}$$

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$$\begin{aligned} \begin{array}{l} \frac{\partial L^{T,N}}{\partial \lambda _{n,t,a}^{pot\_g} }: \\ 0\le MAX\_INV_{n,t} -\sum \limits _{aa\in USE\_EL_{t,a,aa} } {inv\_g_{n,t,aa} } \hbox { }\bot \hbox { }\lambda _{n,t,a}^{pot\_g} \ge 0 \\ \end{array} \end{aligned}$$

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$$\begin{aligned}&\tfrac{\partial L^{T,N}}{\partial \lambda _{t,a}^{diff\_g} }: \nonumber \\&0\le \left( START\_G_t \cdot \frac{\sum \limits _{h,n} {AVAIL_{h,n,t} \cdot TD_h } }{\# of\hbox { }nodes}\right. \nonumber \\&\qquad +\left. \left[ {\sum \limits _{h,n,aa} {TD_h \cdot \left( {g\_cfd_{h,n,t,aa,a-1} +g\_cfd_{h,n,t,aa,a-2} } \right) } } \right] \right) \cdot DIFF\_G_t\nonumber \\&\qquad -\sum \limits _{h,n,aa} {TD_h \cdot g\_cfd_{h,n,t,aa,a} } \hbox { }\bot \hbox { }\lambda _{t,a}^{diff\_g} \ge 0 \end{aligned}$$

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1.1.1 Shared environmental constraints for the electricity sector

$$\begin{aligned} 0\le & {} PD_a \cdot \sum _{h,n,t} {TD_h \cdot \left[ {\left( {g_{h,n,t,a} +\sum _{aa\in USE\_EL_{t,a,aa} } {g\_cfd_{h,n,t,aa,a} } } \right) \cdot \alpha _{t,a} } \right] } \nonumber \\&\bot \hbox { }\lambda _a^{target\_co2} \ge 0. \end{aligned}$$

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$$\begin{aligned} 0\le & {} PD_a \cdot \sum \limits _{h,n} {TD_h \cdot } \left[ {\begin{array}{l} \sum \limits _{\begin{array}{c} aa\in USE\_EL_{t,a,aa} , \\ t\in T\_RES \end{array}} {g\_cfd_{h,n,t,aa,a} } +RES\_OLD_{h,n,a} \\ -RE\_TARGET_a \cdot \sum \limits _{h,n} {d_{h,n,a} } \\ \end{array}} \right] \nonumber \\&\bot \hbox { }\lambda _a^{target\_RE} \ge 0. \end{aligned}$$

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1.2 The electricity transportation utility

$$\begin{aligned}&\tfrac{\partial L^{TSO\_E}}{\partial el\_t}: \nonumber \\&0\le DF_a \cdot PD_a \cdot TD_h \cdot \left( {mu\_el_{h,n,a} -mu\_el_{h,nn,a} +VC\_EL\_T_{n,nn} } \right) \nonumber \\&\qquad +\,\lambda _{h,n,nn,a}^{cap\_el} \hbox { }\bot \hbox { }el\_t_{h,n,nn,a} \ge 0 \end{aligned}$$

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$$\begin{aligned}&\tfrac{\partial L^{TSO\_E}}{\partial inv\_el\_t}: \nonumber \\&0\le \sum \limits _{aa>a} {PD_{aa} \cdot \left( {DF_{aa} \cdot INVC\_EL\_T_{n,nn} } \right) } -ADJ\_EL_{n,nn} \nonumber \\&\qquad \cdot \sum \limits _h {\sum \limits _{aa>a} {\left( {\lambda _{h,n,nn,aa}^{cap\_el\_t} +\lambda _{h,nn,n,aa}^{cap\_el\_t} } \right) } } \hbox { }\bot \hbox { }inv\_el\_t_{h,n,nn,a} \ge 0 \end{aligned}$$

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$$\begin{aligned}&\tfrac{\partial L^{TSO\_E}}{\partial \lambda _{h,n,nn,a}^{cap\_el\_t} }: \nonumber \\&0\le INICAP\_EL\_T_{n,nn} +\sum \limits _{aa<a} \left( ADJ\_EL_{n,nn} \cdot inv\_el\_t_{n,nn,aa} \right. \nonumber \\&\qquad +\left. ADJ\_EL_{nn,n} \cdot inv\_el\_t_{nn,n,aa} \right) -el\_t_{h,n,nn,a} \nonumber \\&\qquad \bot \hbox { }\lambda _{h,n,nn,a}^{cap\_el\_t} \ge 0 \end{aligned}$$

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1.3 The industry sector

$$\begin{aligned}&\tfrac{\partial L^{I,N}}{\partial co2\_c_{h,n,i,a} }: \nonumber \\&0\le DF_a \cdot PD_a \cdot TD_h \cdot \left( {-EUA_a +mu\_co2_{h,n,a} +VC\_CO2_{n,i,a} } \right) \nonumber \\&\qquad +\,\lambda _{h,n,i,a}^{max\_ind} +{\lambda _{h,n,i,a}^{cap\_co2\_c}}\hbox { }^{\bot \hbox { }co2\_c_{h,n,i,a} \ge 0} \end{aligned}$$

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$$\begin{aligned} {\begin{array}{ll} {\begin{array}{l} \frac{\partial L^{I,N}}{\partial inv\_co2\_c_{n,i,a} }: \\ 0\le \left[ {\begin{array}{l} \sum \limits _{aa\in I\_USE\_CO2_{i,a,aa} } PD_{aa} \cdot DF_{aa}\\ \cdot \left( {FC\_CO2_{n,i,aa} +INVC\_CO2_{n,i,aa} } \right) \\ -\sum \limits _h {\sum \limits _{aa\in I\_USE\_CO2_{i,a,aa} } {\lambda _{h,n,i,aa}^{cap\_co2\_c} \cdot CR\_IND_i } } \\ +\,\lambda _{i,a}^{diff\_co2\_c} -\sum \limits _{aa>a} {\left( {\lambda _{i,aa}^{diff\_co2\_c} \cdot DIFF\_CO2_i } \right) } \\ \end{array}} \right] \\ \end{array}}&{} {\bot \hbox { }inv\_co2\_c_{n,i,a} \ge 0} \\ \end{array} } \end{aligned}$$

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$$\begin{aligned} \begin{array}{l} \tfrac{\partial L^{I,N}}{\partial \lambda _{h,n,i,a}^{max\_ind} }: \\ 0\le CO2\_IND_{h,n,i,a} \cdot CR\_IND_i -co2\_c_{h,n,i,a} \hbox { }\bot \hbox { }\lambda _{h,n,i,a}^{max\_ind} \ge 0 \\ \end{array} \end{aligned}$$

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$$\begin{aligned} \begin{array}{l} \frac{\partial L^{I,N}}{\partial \lambda _{h,n,i,a}^{cap\_co2\_c} }: \\ \sum \limits _{aa\in USE\_CO2_{i,a,aa} } {inv\_co2\_c_{n,i,aa} } \cdot CR\_IND_i -co2\_c_{h,n,i,a} \hbox { }\bot \hbox { }\lambda _{h,n,i,a}^{cap\_co2\_c} \ge 0 \\ \end{array} \end{aligned}$$

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$$\begin{aligned} \begin{array}{l} \frac{\partial L^{I,N}}{\partial \lambda _{i,a}^{diff\_co2\_c} }: \\ 0\le \left( {START\_CO2_i +\sum \limits _n {\sum \limits _{aa<a} {inv\_co2\_c_{n,i,aa} } } } \right) \cdot DIFF\_CO2_i\\ \qquad -\sum \limits _n {inv\_co2\_c_{n,i,a} } \hbox { }\bot \hbox { }\lambda _{i,a}^{diff\_co2\_c} \ge 0 \\ \end{array} \end{aligned}$$

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1.4 The CO$_{2}$ transportation utility

$$\begin{aligned} \begin{array}{l} \frac{\partial L^{TSO\_CO2}}{\partial co2\_t_{h,n,nn,a} }: \\ 0\le DF_a \cdot PD_a \cdot TD_h \cdot \left( {mu\_co2_{h,nn,a} -mu\_co2_{h,n,a} +VC\_CO2\_t_{n,nn} } \right) \\ \qquad +\,\lambda _{h,n,nn,a}^{cap\_co2\_t} \hbox { }\bot \hbox { }co2\_t_{h,n,nn,a} \ge 0 \\ \end{array} \end{aligned}$$

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$$\begin{aligned}&\tfrac{\partial L^{TSO\_E}}{\partial inv\_co2\_t}: \nonumber \\&0\le \sum \limits _{aa>a} {PD_{aa} \cdot \left( {DF_{aa} \cdot INVC\_CO2\_T_{n,nn} } \right) }\nonumber \\&\qquad -ADJ\_CO2_{n,nn} \cdot \sum \limits _h {\sum \limits _{aa>a} {\left( {\lambda _{h,n,nn,aa}^{cap\_co2\_t} +\lambda _{h,nn,n,aa}^{cap\_co2\_t} } \right) } }\nonumber \\&\qquad \bot \hbox { }inv\_co2\_t_{h,n,nn,a} \ge 0 \end{aligned}$$

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$$\begin{aligned}&\tfrac{\partial L^{TSO\_E}}{\partial \lambda _{h,n,nn,a}^{cap\_co2\_t} }: \nonumber \\&0\le INICAP\_CO2\_T_{n,nn} +\sum \limits _{aa<a} \left( ADJ\_CO2_{n,nn} \cdot inv\_co2\_t_{n,nn,aa}\right. \nonumber \\&\qquad \left. +ADJ\_CO2_{nn,n} \cdot inv\_co2\_t_{nn,n,aa} \right) -co2\_t_{h,n,nn,a} \hbox { }\bot \hbox { }\lambda _{h,n,nn,a}^{cap\_co2\_t} \ge 0\nonumber \\ \end{aligned}$$

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1.5 The CO$_{2}$ storage sector

$$\begin{aligned} {\begin{array}{ll} {\begin{array}{l} \frac{\partial L^{S,N}}{\partial co2\_s_{h,n,s,a} }: \\ 0\le \left[ {\begin{array}{l} DF_a \cdot PD_a \cdot TD_h \cdot \left( {\begin{array}{l} -EFF\_CO2\cdot OILPRICE_a \\ -mu\_co2_{h,n,a} +VC\_CO2_{n,s,a} \\ +INTC\_S_t \cdot co2\_s_{h,n,s,a} \\ \end{array}} \right) \\ +\sum \limits _{hh} {TD_{hh} } \cdot \left( {\sum \limits _{aa\ge a} {PD_{aa} \cdot \lambda _{n,s,aa}^{max\_stor} } } \right) +\lambda _{h,n,s,a}^{cap\_co2\_s} \\ \end{array}} \right] \hbox { } \\ \end{array}}\\ \qquad \bot \hbox { }co2\_s_{h,n,s,a} \ge 0 \\ \end{array} } \end{aligned}$$

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$$\begin{aligned} {\begin{array}{ll} {\begin{array}{l} \frac{\partial L^{S,N}}{\partial inv\_co2\_s_{n,s,a} }: \\ 0\le \left[ {\begin{array}{l} \sum \limits _{aa\in I\_USE\_CO2_{s,a,aa} } PD_{aa} \cdot DF_{aa}\\ \cdot \left( {FC\_CO2_{n,s,aa} +INVC\_CO2_{n,s,aa} } \right) \\ -\sum \limits _h {\sum \limits _{aa\in I\_USE\_CO2_{s,a,aa} } {\lambda _{h,n,s,aa}^{cap\_co2\_s} } } +\lambda _{s,a}^{diff\_co2\_s}\\ -\sum \limits _{aa>a} {\left( {\lambda _{s,aa}^{diff\_co2\_s} \cdot DIFF\_CO2_s } \right) } \\ \end{array}} \right] \\ \hbox { } \\ \end{array}}&{} {\bot \hbox { }inv\_co2\_s_{n,s,a} \ge 0} \\ \end{array} } \end{aligned}$$

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$$\begin{aligned} \begin{array}{l} \frac{\partial L^{S,N}}{\partial \lambda _{h,n,s,a}^{cap\_co2\_s} }: \\ 0\le \sum \limits _{aa\in USE\_CO2_{s,a,aa} } {inv\_co2\_s_{n,s,aa} } -co2\_s_{h,n,s,a} \hbox { }\bot \hbox { }\lambda _{h,n,s,a}^{cap\_co2\_s} \ge 0 \\ \end{array} \end{aligned}$$

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$$\begin{aligned} \begin{array}{l} \frac{\partial L^{S,N}}{\partial \lambda _{n,s,a}^{\max \_stor} }: \\ 0\le MAX\_STOR_{n,s} -\sum \limits _h {\left( {TD_h \cdot \sum \limits _{aa\le a} {PD_{aa} \cdot co2\_s_{h,n,s,aa} } } \right) } \hbox { }\bot \hbox { }\lambda _{n,s,a}^{\max \_stor} \ge 0 \\ \end{array} \end{aligned}$$

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$$\begin{aligned}&\tfrac{\partial L^{S,N}}{\partial \lambda _{s,a}^{diff\_co2\_s} }: \nonumber \\&0\le \left( {START\_CO2_s +\sum \limits _n {\sum \limits _{aa<a} {inv\_co2\_s_{n,s,aa} } } } \right) \cdot DIFF\_CO2_s\nonumber \\&\qquad -\sum \limits _n {inv\_co2\_s_{n,s,a} } \hbox { }\bot \hbox { }\lambda _{s,a}^{diff\_co2\_s} \ge 0 \end{aligned}$$

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1.6 Market clearing conditions across all sectors

$$\begin{aligned} 0= & {} \sum \limits _t {\left( {g_{h,n,t,a} +\sum \limits _{aa\in USE\_EL_{t,a,aa} } {g\_cfd_{h,n,t,aa,a} } } \right) } +\sum \limits _{nn} {el\_t_{h,nn,n,a} }\nonumber \\&-\sum \limits _{nn} {el\_t_{h,n,nn,a} } -\left( {D_{h,n,a} -RES\_OLD_{h,n,a} } \right) mu\_e_{h,n,a} \hbox { }(free)\quad \forall h,n,a \nonumber \\ \end{aligned}$$

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$$\begin{aligned}&\tfrac{\partial L^{T,N}}{\partial \lambda _{h,a}^{curt\_el} }: \nonumber \\&0\le \sum \limits _n {\left( {D_{h,n,a} -RES\_OLD_{h,n,a} } \right) }\nonumber \\&\qquad -\sum \limits _{n,t} {\left( {g_{h,n,t,a} +\sum \limits _{aa\in USE\_EL_{t,a,aa} } {g\_cfd_{h,n,t,aa,a} } } \right) } \hbox { }\bot \hbox { }\lambda _{h,a}^{curt\_el} \ge 0 \end{aligned}$$

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$$\begin{aligned} 0= & {} -\left( {\begin{array}{l} \sum \limits _t {\left( {\sum \limits _{aa\in USE\_EL_{t,a,aa} } {g\_cfd_{h,n,t,aa,a} } \cdot EF\_EL_t \cdot CR\_G_t } \right) } \\ +\sum \limits _i {co2\_c_{h,n,i,a} } \\ +\sum \limits _{nn} {co2\_t_{h,nn,n,a} } -\sum \limits _{nn} {co2\_t_{h,n,nn,a} } -\sum \limits _s {co2\_s_{h,n,s,a} } \\ \end{array}} \right) \nonumber \\&mu\_co2_{h,n,a} \hbox { }(free)\quad \forall h,n,a \end{aligned}$$

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