Electricity market clearing algorithms: A case study of the Bulgarian power system

ABSTRACT

This work presents a generic optimization framework (ANNEX model), including three alternative algorithms for the electricity market-clearing process in order to optimally determine the annual energy mix of a power system. The effectiveness of the ANNEX model has been tested on an illustrative case study of the Bulgarian power system to investigate the impacts of each market design on the system’s technical and economic aspects. The results highlight the influences of each market-clearing algorithm on the technology selection in the resulting electricity mix, as well as the effects on the system’s marginal price, capturing both the annual dynamics and the short-term challenges of critical days. The developed methodological framework can provide useful insights on the determination of the optimal electricity mixes, highlighting the system’s requirements to address the future market operating challenges of modern energy markets, subject to several technical, economic, and regulatory constraints.

KEYWORDS:

• Optimization
• mixed-integer linear programming
• economic dispatch
• block orders
• unit commitment
• electricity trading
• market clearing
• renewable energy sources
• system’s marginal price

Nomenclature

Sets	=
$a:$	=	Set of fossil fuel-fired and nuclear power generating units
$d:$	=	Set of demand bids
$dt:$	=	Set of dates
$h:$	=	Set of hydroelectric power generating units
$l:$	=	Set of capacity blocks of power units and interconnections (traders)
$m:$	=	Set of external interconnections (imports) of the studied power system
$r:$	=	Set of renewable energy sources
$t$:	=	Set of hourly time periods
$w:$	=	Set of dispatchable power units including fossil fuel-fired, biomass-fired, hydroelectric and nuclear power generating units
$x:$	=	Set of external interconnections (exports) of the studied power system
Parameters	=
$A_{r,t}:$	=	Availability factor of each power generating unit $r$ in each time period $t$ (p.u.)
$B{L}_{a,l,t}:$	=	Available capacity of each power unit $a$ in each block $l$ and time period $t$ (MW)
$B{L}_{m,l,t}:$	=	Available capacity of each external interconnection $m$ in each block $l$ and time period $t$ (MW)
$B{L}_{d,l,t}:$	=	Available capacity of each demand bid $d$ in each block $l$ and time period $t$ (MW)
$B{L}_{x,l,t}:$	=	Available capacity of each external interconnection $x$ in each block $l$ and time period $t$ (MW)
$C_{a,l,t}^{unit}:$	=	Energy supply cost of each unit $a$ in each capacity block $l$ and time period $t$ (€/MWh)
$C_{a,t}^{block}:$	=	Energy supply cost of the block order submitted by each unit $a$ in each time period $t$ (€/MWh)
$C_{h,t}^{hydro}:$	=	Energy supply cost of each unit $h$ in each time period $t$ (€/MWh)
$C_{m,l,t}^{imp}:$	=	Energy supply cost of each external interconnection $m$ in each capacity block $l$ and time period $t$ (€/MWh)
$C_{r,t}^{res}:$	=	Energy supply cost of each unit $r$ in each time period $t$ (€/MWh)
$C_{w,t}^{1up}:$	=	Primary-up reserve supply cost of each power generating unit $w$ in each time period $t$ (€/MW)
$C_{w,t}^{2dn}:$	=	Secondary-down reserve supply cost of each power generating unit $w$ in each time period $t$ (€/MW)
$C_{w,t}^{2up}:$	=	Secondary-up reserve supply cost of each power generating unit $w$ in each time period $t$ (€/MW)
$C_w^{sd}:$	=	Shut-down cost of each power generating unit $w$ (€)
$C_{d,l,t}^{dem}:$	=	Energy demand bid cost $d$ in each capacity block $l$ and time period $t$ (€/MWh)
$C_{x,l,t}^{exp}:$	=	Energy exports bid cost to each external interconnection $x$ in each capacity block $l$ and time period $t$ (€/MWh)
$D_t^{1up}:$	=	Primary-up reserve requirements in each time period $t$ (MW)
$D_t^{2dn}:$	=	Secondary-down reserve requirements in each time period $t$ (MW)
$D_t^{2up}:$	=	Secondary-up reserve requirements in each time period $t$ (MW)
$D_t^3:$	=	Tertiary reserve requirements in each time period $t$ (MW)
$E_{dt}^{hyd}:$	=	Daily hydroelectric power generation in each date $dt$ (MWh)
$I_{m,t}:$	=	Available capacity of each external interconnection $m$ in each time period $t$ (MW)
$I_{r,t}:$	=	Installed capacity of each power generating unit $r$ in each time period $t$ (MW)
$I_{x,t}:$	=	Available capacity of each external interconnection $x$ in each time period $t$ (MW)
$P_w^{max}:$	=	Technical maximum of each power unit $w$ (MW)
$P_w^{min}:$	=	Technical minimum of each power unit $w$ (MW)
$R{D}_w:$	=	Ramp-down limit of each power generating unit $w$ (MW/min)
$R{U}_w:$	=	Ramp-up limit of each power generating unit $w$ (MW/min)
$T_w^{dt}:$	=	Minimum downtime of each power generating unit $w$ (h)
$T_w^{ut}:$	=	Minimum uptime of each power generating unit $w$ (h)
$Z_w^{1up}:$	=	Primary-up reserve capability of each power generating unit $w$ (MW)
$Z_w^{2dn}:$	=	Secondary-down reserve capability of each power generating unit $w$ (MW)
$Z_w^{2up}:$	=	Secondary-up reserve capability of each power generating unit $w$ (MW)
$Z_w^{3ns}:$	=	Tertiary non-spinning reserve capability of each power generating unit $w$ (MW)
$Z_w^{3s}:$	=	Tertiary spinning reserve capability of each power generating unit $w$ (MW)
Positive variables	=
$b_{a,l,t}:$	=	Cleared energy supply of each power generating unit $a$ in each capacity block $l$ and time period $t$ (MWh)
$b_{m,l,t}:$	=	Cleared energy supply of each external interconnection $m$ in each capacity block $l$ and time period $t$ (MWh)
$b_{x,l,t}:$	=	Cleared energy consumption of each external interconnection $x$ in each capacity block $l$ and time period $t$ (MWh)
$e_{w,t}^{1up}:$	=	Cleared primary-up reserve provision of each power generating unit $w$ in each time period $t$ (MW)
$e_{w,t}^{2dn}:$	=	Cleared secondary-down reserve provision of each power generating unit $w$ in each time period $t$ (MW)
$e_{w,t}^{2up}:$	=	Cleared secondary-up reserve provision of each power generating unit $w$ in each time period $t$ (MW)
$e_{w,t}^{3ns}:$	=	Tertiary non-spinning reserve provision of each power generating unit $w$ in each time period $t$ (MW)
$e_{w,t}^{3s}:$	=	Tertiary spinning reserve provision of each power generating unit $w$ in each time period $t$ (MW)
$f_a:$	=	Cleared acceptance ratio of the submitted block order of each power generating unit $a$ ($0\le f_a\le 1)$
$p_{a,t}:$	=	Cleared energy supply of each power generating unit $a$ in each time period $t$ (MWh)
$p_{h,t}:$	=	Cleared energy supply of each power generating unit $h$ in each time period $t$ (MWh)
$p_{m,t}:$	=	Cleared energy supply of each external interconnection $m$ in each time period $t$ (MWh)
$p_{r,t}:$	=	Cleared energy supply of each power generating unit $r$ in each time period $t$ (MWh)
$p_{d,t}:$	=	Cleared energy consumption of each demand bid $d$ in each time period $t$ (MWh)
$p_{x,t}:$	=	Cleared energy consumption of each external interconnection $x$ in each time period $t$ (MWh)
Binary variables	=
$n_a:$	=	1, if block order submitted by each power generating unit $a$ is activated 0, otherwise
$g_{w,t}:$	=	1, if each power generating unit $w$ starts-up in each time period $t$ 0, otherwise
$j_{w,t}:$	=	1, if each power generating unit $w$ shuts-down in each time period $t$ 0, otherwise
$u_{w,t}:$	=	1, if each power generating unit $w$ operates in each time period $t$ 0, otherwise

Additional information

Funding

This work has been supported by the Horizon 2020 research project INTERRFACE: TSO-DSO-Consumer INTERFACE architecture to provide innovative grid services for an efficient power system, Greece [Project Grant Agreement No. 824330].