From 72955c25512a3b2d29f5f57bf7b3d63dff7717b8 Mon Sep 17 00:00:00 2001 From: LIU ZHANWEI <50036800+Zhanwei-Liu@users.noreply.github.com> Date: Sat, 15 Jul 2023 16:40:50 +0800 Subject: [PATCH] Update Mathematical_notations.rst update `variables` mathematical notations --- doc/source/Mathematical_notations.rst | 131 +++++++++++++++++++------- 1 file changed, 97 insertions(+), 34 deletions(-) diff --git a/doc/source/Mathematical_notations.rst b/doc/source/Mathematical_notations.rst index 542c038..18f964d 100644 --- a/doc/source/Mathematical_notations.rst +++ b/doc/source/Mathematical_notations.rst @@ -146,58 +146,121 @@ Variable List - System-wide investment cost of transmission lines. - ``USD`` - * - :math:`\text{gen}_{h,m,y,z,te}` - - Generating capacity of the :math:`te`-th technology, in the :math:`z`-th zone, in the :math:`y`-th year, for the :math:`m` time period, and in the :math:`h`-th hour. - - ``MWh`` - - * - :math:`\text{cap}^\text{existing}_{y,z,te}` - - Existing installed capacity of the :math:`te`-th technology, in the :math:`z`-th zone, and in the :math:`y`-th year. - - ``MW`` + * - :math:`\rm{cost}^{\rm{annualfuel}}_{\it{y}}` + - Fuel cost of technologies in the modelled year:math:`y` (the present value of modelled year :math:`y`). + - ``USD`` - * - :math:`\text{cap}^\text{newtech}_{y,z,te}` - - Newly-built installed capacity of the :math:`te`-th technology, in the :math:`z`-th zone, and in the :math:`y`-th year. - - ``MW`` + * - :math:`\rm{cost}^{\rm{fuel}}_{\it{y}}` + - Fuel cost of technologies accumulated from modelled year :math:`y` to a non-modelled year before the immediate next modelled year (the present value of modelled year :math:`y`). + - ``USD`` - * - :math:`\text{cap}^\text{newline}_{y,z_s,z_o}` - - Newly-built transmission line capacity from the :math:`z_s`-th zone to the :math:`z_o`-th zone, and in the :math:`y`-th year. - - ``MW`` + * - :math:`\rm{gen}_{\it{h,m,y,z,e}}` + - Power generation of technology :math:`e` in zone :math:`z` in hour :math:`h` in month :math:`m` of year :math:`y`. + - ``MWh`` - * - :math:`\text{cap}^\text{remaining}_{y,z,te}` - - Remaining capacity of the :math:`te`-th technology, in the :math:`z`-th zone, and in the :math:`y`-th year. - - ``MW`` + * - :math:`\rm{charge}_{\it{h,m,y,z,e}}` + - Charging electricity of storage technology :math:`e` in zone :math:`z` in hour :math:`h` in month :math:`m` of year :math:`y`. + - ``MWh`` - * - :math:`\text{carbon}^\text{tech}_{y,te}` - - Carbon emission of the :math:`te`-th technology for all zones, and in the :math:`y`-th year - - ``tonnes`` + * - :math:`\rm{export}_{{\it{h,m,y,z}}_{\rm{from}},{\it{z}}_{\rm{to}}}` + - Electric energy exported from zone :math:`z_{\rm{from}}` to zone :math:`z_{\rm{to}}` in hour :math:`h` in month :math:`m` of year :math:`y`. + - ``MWh`` - * - :math:`\text{slack}_{h,y,z}` - - Unserved demand in the :math:`z`-th zone, in the :math:`y`-th year, and in the :math:`h`-th hour. + * - :math:`\rm{import}_{{\it{h,m,y,z}}_{\rm{from}},{\it{z}}_{\rm{to}}}` + - Electric energy imported from zone :math:`z_{\rm{from}}` to zone :math:`z_{\rm{to}}` in hour :math:`h` in month :math:`m` of year :math:`y`. - ``MWh`` - * - :math:`\text{trans}^\text{import}_{h,y,z1,z}` - - Generation output imported from the :math:`z1`-th zone to the :math:`z`-th zone, in the :math:`y`-th year, and in the :math:`h`-th hour. + * - :math:`\rm{storage}_{\it{h,m,y,z,e}}^{\rm{energy}}` + - Energy storage level of storage technology :math:`e` in hour :math:`h` in month :math:`m` of year :math:`y` in zone :math:`z`. - ``MWh`` - * - :math:`\text{cap}^\text{retire}_{y,z,te}` - - Retiring capacity of the :math:`te`-th technology, in the :math:`z`-th zone, and in the :math:`y`-th year. + * - :math:`\rm{storage}_{\it{s,h,m,y}}^{\rm{reservoir}}` + - Reservoir storage corresponding to hydropower station :math:`s` in hour :math:`h` in month :math:`m` of year :math:`y`. + - `:math:`\text{m}^\text{3}`` + + * - :math:`\rm{power}_{\it{h,m,y,z,e}}` + - Overall power output of technology :math:`e` in zone :math:`z` in hour :math:`h` in month :math:`m` of year :math:`y`. - ``MW`` - * - :math:`\text{storage}^\text{level}_{y,z,te}` - - Storage level of the :math:`te`-th technology, in the :math:`z`-th zone, and in the :math:`y`-th year. + * - :math:`\rm{power}_{\it{h,m,y,z,e}}^{\it{c}}` + - Charging power of storage technology :math:`e` in zone :math:`z` in hour :math:`h` in month :math:`m` of year :math:`y`. - ``MW`` - * - :math:`\text{consumption}_{h,y,z,te}` - - Cost of fuel consumption of the :math:`te`-th technology, in the :math:`z`-th zone, in the :math:`y`-th year, and in the :math:`h`-th hour. - - ``USD`` + * - :math:`\rm{power}_{\it{h,m,y,z,e}}^{\rm{up}}` + - Increment in power output of technology :math:`e` in zone :math:`z` from hour :math:`h`-1 to hour :math:`h` in month :math:`m` of year :math:`y`. + - ``MW`` + + * - :math:`\rm{power}_{\it{h,m,y,z,e}}^{\rm{down}}` + - Decrement in power output of technology :math:`e` in zone :math:`z` from hour :math:`h`-1 to hour :math:`h` in month :math:`m` of year :math:`y`. + - ``MW`` - * - :math:`\text{gen}^\text{up}_{h,y,z,te}` - - Output of change upward of the :math:`te`-th technology, in the :math:`z`-th zone, in the :math:`y`-th year, and in the :math:`h`-th hour. + * - :math:`\rm{power}_{\it{s,h,m,y}}^{\rm{hydro}}` + - Power output of hydropower station :math:`s` in hour :math:`h` in month :math:`m` of year :math:`y`. - ``MW`` - * - :math:`\text{gen}^\text{down}_{h,y,z,te}` - - Output of change downward of the :math:`te`-th technology, in the :math:`z`-th zone, in the :math:`y`-th year, and in the :math:`h`-th hour. + * - :math:`\rm{cap}_{\it{y,z,e}}^{\rm{existingtech}}` + - Existing installed capacity of technology :math:`e` in year :math:`y` in zone :math:`z`. - ``MW`` + * - :math:`\rm{cap}_{{\it{y,z}}_{\rm{from}},{\it{z}}_{\rm{to}}}^{\rm{existingline}}` + - Existing transmission capacity in year :math:`y` from zone :math:`z_{\rm{from}}` to zone :math:`z_{\rm{to}}`. + - ``MW`` + + * - :math:`\rm{cap}_{\it{y,z,e}}^{invtech}` + - Installed capacity of newly built technology :math:`e` in year :math:`y` in zone :math:`z`. + - ``MW`` + * - :math:`\rm{cap}_{{\it{y,z}}_{\rm{from}},{\it{z}}_{\rm{to}}}^{\rm{invline}}` + - Capacity of newly built transmission lines from zone :math:`z_{\rm{from}}` to zone :math:`z_{\rm{to}}` in year :math:`y` + - ``MW`` + + * - :math:`\rm{cap}_{\it{y,z,e}}^{\rm{remaining}}` + - Remaining installed capacity of technology :math:`e` in year :math:`y` in zone :math:`z` + - ``MW`` + + * - :math:`\rm{carbon}_{\it{y,e}}^{\rm{tech}}` + - Carbon dioxide equivalent emissions of technology :math:`e` in year :math:`y` + - ``tonne`` + + * - :math:`\rm{carbon}_{\it y}` + - Carbon dioxide equivalent emissions of the entire energy system in year :math:`y` + - ``tonne`` + + * - :math:`\rm{inflow}_{\it{s,h,m,y}}^{\rm{total}}` + - Total inflow of reservoir corresponding to hydropower station :math:`s` in hour :math:`h` in month :math:`m` of year :math:`y` + - `:math:`\text{m}^\text{3}/\text{s}`` + + * - :math:`\rm{outflow}_{\it{s,h,m,y}}^{\rm{total}}` + - Total outflow of reservoir corresponding to hydropower station :math:`s` in hour :math:`h` in month :math:`m` of year :math:`y` + - ``:math:`\text{m}^\text{3}/\text{s}``` + + * - :math:`\rm{outflow}_{\it{s,h,m,y}}^{\rm{gen}}` + - Generation outflow of reservoir corresponding to hydropower station :math:`s` in hour :math:`h` in month :math:`m` of year :math:`y` + - ``:math:`\text{m}^\text{3}/\text{s}``` + + * - :math:`\rm{outflow}_{\it{s,h,m,y}}^{\rm{withdraw}}` + - Water withdrawal of reservoir corresponding to hydropower station :math:`s` in hour :math:`h` in month :math:`m` of year :math:`y` + - ``:math:`\text{m}^\text{3}/\text{s}``` + + * - :math:`\rm{outflow}_{\it{s,h,m,y}}^{\rm{spillage}}` + - Spillage outflow of reservoir corresponding to hydropower station :math:`s` in hour :math:`h` in month :math:`m` of year :math:`y` + - ``:math:`\text{m}^\text{3}/\text{s}``` + + * - :math:`\rm{head}_{\it{s,h,m,y}}^{\rm{net}}` + - Net water head of hydropower station :math:`s` in hour :math:`h` in month :math:`m` of year :math:`y` + - ``m`` + + * - :math:`\rm{head}_{\it{s,h,m,y}}^{\rm{loss}}` + - Water head loss of hydropower station :math:`s` in hour :math:`h` in month :math:`m` of year :math:`y` + - ``m`` + + * - :math:`z_{\it{s,h,m,y}}^{\rm{forebay}}` + - Forebay water level of reservoir corresponding to hydropower station :math:`s` in hour :math:`h` in month :math:`m` of year :math:`y` + - ``m`` + + * - :math:`z_{\it{s,h,m,y}}^{\rm{tailrace}}` + - Tailrace water level of reservoir corresponding to hydropower station :math:`s` in hour :math:`h` in month :math:`m` of year :math:`y` + - ``m`` + Parameter List --------------