{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Comparative net energy analysis of renewable electricity and carbon capture and storage\n", "*Sgouridis, Carbajales-Dale, Csala, Chiesa, Bardi*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Use this Jupyter workbook to reproduce all results presented in the paper." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Paper GitHub folder](https://github.com/csaladenes/sustainable-energy-transitions/ccs) \n", "[Parent project GitHub repository](https://github.com/csaladenes/sustainable-energy-transitions) \n", "[This workbook for machine reading on GitHub](https://github.com/csaladenes/sustainable-energy-transitions/blob/master/ccs/eroei-ccs-workbook.ipynb) \n", "[This workbook for human reading on nbviewever](nbviewer.jupyter.org/github/csaladenes/sustainable-energy-transitions/blob/master/ccs/eroei-ccs-workbook.ipynb) \n", "[High-resolution plots folder](https://github.com/csaladenes/sustainable-energy-transitions/tree/master/ccs/plot)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
This is document has been created using Jupyter Notebook in the Anaconda distribution and it can be edited and run in active mode by clicking download in top right corner of this page. The code is partitioned into sections, called cells. When you are using this workbook in active mode, double-click on a cell to edit it and then run using Ctrl + Enter
. Hitting Shift + Enter
runs the code and steps into the next cell, while Alt + Enter
runs the code and adds a new, empty cell. If you are running this notebook on a presonal computer, you will need a machine with at least 1GB of memory (2GB recommended) and a processor of 1GHz."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Import dependencies"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Running on Python 3.6.6 |Anaconda, Inc.| (default, Jun 28 2018, 11:27:44) [MSC v.1900 64 bit (AMD64)]\n"
]
}
],
"source": [
"import pandas as pd, matplotlib.pyplot as plt, numpy as np\n",
"from matplotlib.colors import BoundaryNorm\n",
"from matplotlib.ticker import MaxNLocator\n",
"import matplotlib.patches as patches\n",
"import matplotlib.lines as lines\n",
"%matplotlib inline\n",
"import sys, string\n",
"from sympy import *\n",
"init_printing() \n",
"print('Running on Python',sys.version)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Fossil fuels part"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Equations"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This section reproduces all the equations presented in the paper (supplementary material). This is just for easier visual guidance and for quick checking."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAJsAAAAWCAYAAADXT+6KAAAABHNCSVQICAgIfAhkiAAABRtJREFUaIHt2mmsXVMUB/DfKxWUIsYKiRpaY6piKiWGEomhfcEX8weUDxJqqqCImKKJhCDRKCEiQVTNIiRUiHkIMaR41Dyr2fNaH9Y+3nnnnvfu4Nzbfrj/5Oa8s9fae/3vO+vu9d97H7roYgXiSSyv87mojv83WISjG4i3Ja7A6/gBf6EPt2NSG3ju3wCnqtEs105gYwzg+kJ727iuWtK2C/4RCTAc7i/4L8fl6boqtsUMTMUsXFcyRo8gfSFWwzN4Dr9hZ5yAYzET8yvk+doI/u1Cs1w7gekYhQWF9o5x3UpzDyTzf6/Edlqy9ZXYenBbsr+MCSU+B6JffPHJFfF8v0H/KtEs107hMXyHVXJtbeU6qnC/a7q+3GD/zP/VEtvj6bpRiW02Tkr99sEHJT5P4WbxzzizIp6vNOhfJZrl2gmsgwPwkCilGdrKtapkK3uIW6fru4X28bgMfwpN9+cI4z+RrlOGidtNttZwqJAuxXLYVq5FzZYF2wubDdPnWqGr8v7FmW19zE1/X12wnYPRuAkf1+G3JF3XqYhnvWQ7E+vW8cnjDTxQx6dZrp1Ab4r3ZKG9Y1x78JORVyHfD+M/F5eKRcIdqX0pTi+J8UXqs6v62D/5vlMBzwGsVSdeX51xi5/b64zXLNdOYHX8gnsL7a1wvRH3tUJiYhpwUZP+ZZ9fcUhJn02TvV/5SriIC5L/nRXwfKeeYxvQLNcqMRePlLQfITgdU2hvhet66v+A/0Nes2UzzZsN9s3854tfRY8on7MwBnerLUkbpOsvYpU5EnrE1gdDtUWrPFekXmuUa5XYTfl37sXfahOxFa4/iomlIeRnl1YfYl6v/SD21KYI8X88bsjZf0rXdbEmfh9h/GOwg1hgLKyAZyPJVrVma+UBbo9rsK/Y4L4H5+KPZD9IJMoYUSFgc3wqFmWfCk01Oo0xB29jJ7GyPxxP4+f/yXUzoam3FVtKWwgN3ivk01R8hVNSvCFYJKbR3RsMlvnvUWI7ONmeL7F9lmzTRxh7gvhn9AuxWgXP4oq2DH2q1WzNcp0kvvdV2EZsC30iRHmGc0WS53G40Mg9olrtnou7iSh3DGrgUyvgephI6qw6Tk/9n8E0kfgPipOhIRglStsA1mggUObfLwRnEaPFFLtM6LQ8zk6kPiyxZV/iW1FmT6qQZyP+VaJZrvAi5hXazjN0M/outUk+R5y+ZJhhMPnyuCHx2bgCrhfihQKHpRiXaztRTC4YLKPbCaG3FOePEOAWsZrM/N9Uvk/Wj0dFKewVq5YM14njqOPEycNCMfVviL1FGfkq9XuoMG6rPN8yWIY6hWa5ThSzyskF+99iTyzDZLUJubOh5W9yul9e8Jshqs3X/5NrFjM/w07Cw/gy17YlFhcHOUH9kjGAtQv+t45A7KjkU1OvE44UCfmtSM6v8SzOwthh+rSDZ7vQLNcjxWxeXKXPM6gL10g+xZcJlghtlGGh2gP23VLMWRVwJU59ZubuF+OMwrgPKj8X72IF4yAhO9bMtY0Tuih7e2ZH8eDzpWpftVrrI7Uz5JXJb3wFXMeI5Mv0+lqJ+9SC3xKRyF2sZBgrXs26XpSf/UQpXGBQe20iHmpvut9DSJGi1upL42xqcHX9rtqFRauYkmJmP4y91G6ary+Se6eKYnZRMfbES2JL6CNcLBZbecwWW0yfi9OaS9SePx8rhPkyQ/VyVTitEPN0tW/+TBN6vpHN+y666KKLLrrooosuVhL8C2Xe6LFIWKEJAAAAAElFTkSuQmCC\n",
"text/latex": [
"$$EROEI = \\frac{E_{out}}{E_{in}}$$"
],
"text/plain": [
" Eₒᵤₜ\n",
"EROEI = ────\n",
" Eᵢₙ "
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"var('EROEI E_out E_in');\n",
"eq_S1=Eq(EROEI,E_out/E_in)\n",
"eq_S1"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$$EROEI = \\frac{E_{out}}{E_{OM} + E_{cap} + E_{f}}$$"
],
"text/plain": [
" Eₒᵤₜ \n",
"EROEI = ──────────────────\n",
" E_OM + E_cap + E_f"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"var('E_cap E_f E_OM');\n",
"eq_S1i=Eq(EROEI,E_out/(E_cap+E_OM+E_f))\n",
"eq_S1i"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$$E_{in} = E_{cap} \\left(L s_{OM} + 1\\right) + E_{f}$$"
],
"text/plain": [
"Eᵢₙ = E_cap⋅(L⋅s_OM + 1) + E_f"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"var('L s_OM');\n",
"eq_S2i=Eq(E_in,E_cap*(1+L*s_OM)+E_f)\n",
"eq_S2i"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$$E_{out} = L P cf$$"
],
"text/plain": [
"Eₒᵤₜ = L⋅P⋅cf"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"var('P L cf');\n",
"eq_S2ii=Eq(E_out,P*cf*L)\n",
"eq_S2ii"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$$E_{out} = E_{el}$$"
],
"text/plain": [
"Eₒᵤₜ = Eₑₗ"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"var('E_el');\n",
"eq_S2iii=Eq(E_out,E_el)\n",
"eq_S2iii"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$$E_{th} = \\frac{L P cf}{\\eta}$$"
],
"text/plain": [
" L⋅P⋅cf\n",
"Eₜₕ = ──────\n",
" η "
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"e=Symbol('eta')\n",
"var('E_th');\n",
"eq_S2iv=Eq(E_th,P*cf*L/e)\n",
"eq_S2iv"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$$E_{f} = \\frac{E_{th}}{EROEI_{th}}$$"
],
"text/plain": [
" Eₜₕ \n",
"E_f = ───────\n",
" EROEIₜₕ"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"var('EROEI_th');\n",
"eq_S3i=Eq(E_f,E_th/EROEI_th)\n",
"eq_S3i"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"#define pretty variable substituion function\n",
"def sub(var,eq):\n",
" return [var,solve(eq,var)[0]]\n",
"#create multiple substituion method by chaining\n",
"def multisub(eq0,msub):\n",
" for i in range(len(msub)//2):\n",
" eq0=eq0.subs([sub(msub[i*2],msub[i*2+1])])\n",
" return eq0"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$$EROEI_{el} = \\frac{L P cf}{E_{cap} L s_{OM} + E_{cap} + \\frac{L P cf}{EROEI_{th} \\eta}}$$"
],
"text/plain": [
" L⋅P⋅cf \n",
"EROEIₑₗ = ────────────────────────────────\n",
" L⋅P⋅cf \n",
" E_cap⋅L⋅s_OM + E_cap + ─────────\n",
" EROEIₜₕ⋅η"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"var('EROEI_el');\n",
"eq_S3=Eq(EROEI_el,multisub(eq_S1,[E_out,eq_S2ii,E_in,eq_S2i,E_f,eq_S3i,E_th,eq_S2iv]).rhs)\n",
"eq_S3"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
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"text/latex": [
"$$EROEI_{CCS} = \\frac{E_{el} \\left(- \\operatorname{f_{op}}{\\left (CR \\right )} + 1\\right)}{E_{cap} \\left(f_{cap} + 1\\right) \\left(L s_{OM} + 1\\right) + E_{f}}$$"
],
"text/plain": [
" Eₑₗ⋅(-fₒₚ(CR) + 1) \n",
"EROEI_CCS = ────────────────────────────────────\n",
" E_cap⋅(f_cap + 1)⋅(L⋅s_OM + 1) + E_f"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"var('CR f_op EROEI_CCS f_cap');\n",
"eq_S4=Eq(EROEI_CCS,E_el*(1-f_op(CR))/(E_cap*(1+f_cap)*(1+L*s_OM)+E_f))\n",
"eq_S4"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/latex": [
"$$EROEI_{CCS} = \\frac{EROEI_{el} \\left(E_{cap} \\left(L s_{OM} + 1\\right) + E_{f}\\right) \\left(- \\operatorname{f_{op}}{\\left (CR \\right )} + 1\\right)}{E_{cap} \\left(f_{cap} + 1\\right) \\left(L s_{OM} + 1\\right) + E_{f}}$$"
],
"text/plain": [
" EROEIₑₗ⋅(E_cap⋅(L⋅s_OM + 1) + E_f)⋅(-fₒₚ(CR) + 1)\n",
"EROEI_CCS = ─────────────────────────────────────────────────\n",
" E_cap⋅(f_cap + 1)⋅(L⋅s_OM + 1) + E_f "
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"var('CR f_op EROEI_CCS f_cap');\n",
"eq_S5=Eq(EROEI_CCS,(1-f_op(CR))*(E_cap*(1+L*s_OM)+E_f)*EROEI_el/(E_cap*(1+f_cap)*(1+L*s_OM)+E_f))\n",
"eq_S5"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$$R = \\frac{E_{f}}{E_{cap} \\left(L s_{OM} + 1\\right)}$$"
],
"text/plain": [
" E_f \n",
"R = ──────────────────\n",
" E_cap⋅(L⋅s_OM + 1)"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"var('R');\n",
"eq_S6i=Eq(R,E_f/(E_cap*(1+L*s_OM)))\n",
"eq_S6i"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$$EROEI_{CCS} = \\frac{EROEI_{el} \\left(R + 1\\right) \\left(- \\operatorname{f_{op}}{\\left (CR \\right )} + 1\\right)}{R + f_{cap} + 1}$$"
],
"text/plain": [
" EROEIₑₗ⋅(R + 1)⋅(-fₒₚ(CR) + 1)\n",
"EROEI_CCS = ──────────────────────────────\n",
" R + f_cap + 1 "
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eq_S6=Eq(EROEI_CCS,(1-f_op(CR))*(R+1)*EROEI_el/(R+1+f_cap))\n",
"eq_S6"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have made a major simplifaction step from _Eq. S5_ to reach _Eq. S6_. Here we prove by symbolic evaluation of the subtituted expressions that we were correct."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/latex": [
"$$EROEI_{CCS} = - \\frac{EROEI_{el} \\left(E_{cap} \\left(L s_{OM} + 1\\right) + E_{f}\\right) \\left(\\operatorname{f_{op}}{\\left (CR \\right )} - 1\\right)}{E_{cap} \\left(f_{cap} + 1\\right) \\left(L s_{OM} + 1\\right) + E_{f}}$$"
],
"text/plain": [
" -EROEIₑₗ⋅(E_cap⋅(L⋅s_OM + 1) + E_f)⋅(fₒₚ(CR) - 1) \n",
"EROEI_CCS = ──────────────────────────────────────────────────\n",
" E_cap⋅(f_cap + 1)⋅(L⋅s_OM + 1) + E_f "
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eq_S5.simplify()"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/latex": [
"$$EROEI_{CCS} = - \\frac{EROEI_{el} \\left(E_{cap} \\left(L s_{OM} + 1\\right) + E_{f}\\right) \\left(\\operatorname{f_{op}}{\\left (CR \\right )} - 1\\right)}{E_{cap} \\left(f_{cap} + 1\\right) \\left(L s_{OM} + 1\\right) + E_{f}}$$"
],
"text/plain": [
" -EROEIₑₗ⋅(E_cap⋅(L⋅s_OM + 1) + E_f)⋅(fₒₚ(CR) - 1) \n",
"EROEI_CCS = ──────────────────────────────────────────────────\n",
" E_cap⋅(f_cap + 1)⋅(L⋅s_OM + 1) + E_f "
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eq_S6.subs(R,eq_S6i.rhs).simplify()"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#eq_S6 is correct!\n",
"eq_S6.subs(R,eq_S6i.rhs).simplify()==eq_S5.simplify()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Simulation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this part we show you how to reproduce the graphs presented in the paper, which form the basis of our results discussion and conclusions. There is a similar section for the _Renewables_ part. First, we illustrate a representative range for _CCS_ operational parameters for a number of fossil fuel plants. We then take note of the _min_ and _max_ ranges and plot the values alongside those obtained from the _Renewables_ part. The calculations are based on actual power plant data, stored in the _Excel_ file `plants.xlsx`, found in the project folder and presented in _Table S1_ in the supplementary material of the paper."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using the formula in Eq.4 and the plant values from the Table S1 (reproduced from `plants.xlsx`) calculate the $EROEI_{el}$ for all capacity factors $CF$s between 50 and 90. We then use these values as a proxy to create an a adjustment factor for the $EROEI_{el}$ due to the indirect effect of the change of the capacity factor. The same is true for the _operational versus capital energy investment ratio_, $R$. We therefore created capacity-factor adjusted values for $R$ as well."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to manipulate the _Excel_ file on the fly, we use a _python_ module called `xlwings`. This will open an _Excel_ application in the background. Be sure to either manually close it after you're done or run the cell just above the **Auxiliary plots** section."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"import xlwings as xw #will open a MS Excel application, let it run in the background\n",
"wb = xw.Book('plants.xlsx')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We define a function `eroei_r_getter` which takes as parameters the capacity factor $CF$ and the $EROEI_{fuel}$ for the two studies fossil fuels, _Coal_ and _Natural Gas_. Then, this function sets the correct $CF$ and $EROEI_{fuel}$ values in the _Excel_ workbook, which then recalculates the resulting $EROEI_{el}$ and $R$ values. Since we have 3 _IGCC Coal_, 2 _Pulverized Coal_ and 1 _NGCC Gas_ plant, we average over $EROEI_{el}$ and $R$ values within each group. The resulting _pandas dataframe_ is returned by the function, which now contains 3 columns `['IGCC','PC','NGCC']` and 2 rows `['EROEI_el','R']`."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"def eroei_r_getter(CF=100,EROEI_fuel_coal=58,EROEI_fuel_gas=87):\n",
" xw.Range('L7').value=CF/100.0 #hard-coded Excel workbook cell ID for capacity factor\n",
" xw.Range('M8').value=EROEI_fuel_coal #hard-coded Excel workbook cell ID for EROEI_fuel for Coal\n",
" xw.Range('O8').value=EROEI_fuel_gas #hard-coded Excel workbook cell ID for EROEI_fuel for Gas\n",
" wb.save() #write new values\n",
" df=pd.read_excel('plants.xlsx',usecols=range(10,24)).loc[[37,38]]\n",
" df=df[df.columns[1::2]]\n",
" df.columns=['IGCC 1','IGCC 3','IGCC 5','PC 9','PC 11','NGCC 13']\n",
" df.index=['EROEI_el','R']\n",
" df['IGCC']=(df['IGCC 1']+df['IGCC 3']+df['IGCC 5'])/3.0\n",
" df['PC']=(df['PC 9']+df['PC 11'])/2.0\n",
" df['NGCC']=df['NGCC 13']\n",
" return df[['IGCC','PC','NGCC']]"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
\n", " | IGCC | \n", "PC | \n", "NGCC | \n", "
---|---|---|---|
EROEI_el | \n", "12.0177 | \n", "14.0583 | \n", "31.9783 | \n", "
R | \n", "1.5745 | \n", "2.06751 | \n", "2.91996 | \n", "
\n", " | \n", " | \n", " | \n", " | \n", " | Fossil $EROEI_{fuel}$ | \n", "Fossil $EROEI_{el}$ | \n", "Fossil $EROEI_{CCS}$ | \n", "RE $EROEI_{el}$ min | \n", "$\\varphi$ min (%) | \n", "RE $EROEI_{el}$ max | \n", "$\\varphi$ max (%) | \n", "
---|---|---|---|---|---|---|---|---|---|---|---|
EROEI case | \n", "Fossil | \n", "Renewable | \n", "Storage | \n", "Case ID | \n", "\n", " | \n", " | \n", " | \n", " | \n", " | \n", " | \n", " |
high | \n", "NGCC Gas | \n", "Wind | \n", "Battery storage | \n", "1 | \n", "87.0 | \n", "31.0 | \n", "21.3 | \n", "21.3 | \n", "0.0 | \n", "40.0 | \n", "26.2 | \n", "
Hydrogen storage | \n", "2 | \n", "87.0 | \n", "31.0 | \n", "21.3 | \n", "21.3 | \n", "0.0 | \n", "32.2 | \n", "35.0 | \n", "|||
Battery + Curtailment | \n", "3 | \n", "87.0 | \n", "31.0 | \n", "21.3 | \n", "22.9 | \n", "0.0 | \n", "40.0 | \n", "22.3 | \n", "|||
Pumped hydro storage | \n", "4 | \n", "87.0 | \n", "31.0 | \n", "21.3 | \n", "21.3 | \n", "0.0 | \n", "23.5 | \n", "35.0 | \n", "|||
PV | \n", "Battery storage | \n", "5 | \n", "87.0 | \n", "31.0 | \n", "21.3 | \n", "21.3 | \n", "0.0 | \n", "30.0 | \n", "16.3 | \n", "||
Hydrogen storage | \n", "6 | \n", "87.0 | \n", "31.0 | \n", "21.3 | \n", "21.3 | \n", "0.0 | \n", "30.0 | \n", "29.9 | \n", "|||
Battery + Curtailment | \n", "7 | \n", "87.0 | \n", "31.0 | \n", "21.3 | \n", "22.9 | \n", "0.0 | \n", "30.0 | \n", "12.4 | \n", "|||
Pumped hydro storage | \n", "8 | \n", "87.0 | \n", "31.0 | \n", "21.3 | \n", "21.3 | \n", "0.0 | \n", "23.5 | \n", "35.0 | \n", "|||
Pulverized Coal | \n", "PV | \n", "Battery storage | \n", "9 | \n", "58.0 | \n", "13.5 | \n", "8.4 | \n", "9.0 | \n", "8.7 | \n", "11.6 | \n", "35.0 | \n", "|
Hydrogen storage | \n", "10 | \n", "58.0 | \n", "13.5 | \n", "8.4 | \n", "9.0 | \n", "8.7 | \n", "11.6 | \n", "35.0 | \n", "|||
Battery + Curtailment | \n", "11 | \n", "58.0 | \n", "13.5 | \n", "8.4 | \n", "9.0 | \n", "0.4 | \n", "12.9 | \n", "35.0 | \n", "|||
Pumped hydro storage | \n", "12 | \n", "58.0 | \n", "13.5 | \n", "8.4 | \n", "9.0 | \n", "30.8 | \n", "9.1 | \n", "35.0 | \n", "|||
IGCC Coal | \n", "PV | \n", "Battery storage | \n", "13 | \n", "58.0 | \n", "11.5 | \n", "8.0 | \n", "9.0 | \n", "14.2 | \n", "11.0 | \n", "35.0 | \n", "|
Hydrogen storage | \n", "14 | \n", "58.0 | \n", "11.5 | \n", "8.0 | \n", "9.0 | \n", "13.8 | \n", "11.1 | \n", "35.0 | \n", "|||
Battery + Curtailment | \n", "15 | \n", "58.0 | \n", "11.5 | \n", "8.0 | \n", "9.0 | \n", "5.2 | \n", "12.2 | \n", "35.0 | \n", "|||
mid | \n", "NGCC Gas | \n", "Wind | \n", "Battery storage | \n", "16 | \n", "53.5 | \n", "21.4 | \n", "15.6 | \n", "20.0 | \n", "16.5 | \n", "29.4 | \n", "35.0 | \n", "
Hydrogen storage | \n", "17 | \n", "53.5 | \n", "21.4 | \n", "15.6 | \n", "20.0 | \n", "24.8 | \n", "22.6 | \n", "35.0 | \n", "|||
Battery + Curtailment | \n", "18 | \n", "53.5 | \n", "21.4 | \n", "15.6 | \n", "20.0 | \n", "11.3 | \n", "33.8 | \n", "35.0 | \n", "|||
PV | \n", "Battery storage | \n", "19 | \n", "53.5 | \n", "21.4 | \n", "15.6 | \n", "15.6 | \n", "0.0 | \n", "29.4 | \n", "35.0 | \n", "||
Hydrogen storage | \n", "20 | \n", "53.5 | \n", "21.4 | \n", "15.6 | \n", "15.6 | \n", "0.0 | \n", "22.6 | \n", "35.0 | \n", "|||
Battery + Curtailment | \n", "21 | \n", "53.5 | \n", "21.4 | \n", "15.6 | \n", "16.8 | \n", "0.0 | \n", "30.0 | \n", "30.6 | \n", "|||
Pumped hydro storage | \n", "22 | \n", "53.5 | \n", "21.4 | \n", "15.6 | \n", "15.6 | \n", "0.0 | \n", "17.0 | \n", "35.0 | \n", "|||
Pulverized Coal | \n", "PV | \n", "Hydrogen storage | \n", "23 | \n", "40.5 | \n", "10.6 | \n", "6.8 | \n", "9.0 | \n", "31.0 | \n", "9.4 | \n", "35.0 | \n", "|
Battery + Curtailment | \n", "24 | \n", "40.5 | \n", "10.6 | \n", "6.8 | \n", "9.0 | \n", "25.4 | \n", "9.8 | \n", "35.0 | \n", "|||
IGCC Coal | \n", "PV | \n", "Hydrogen storage | \n", "25 | \n", "40.5 | \n", "9.2 | \n", "6.6 | \n", "9.0 | \n", "34.8 | \n", "9.0 | \n", "35.0 | \n", "|
Battery + Curtailment | \n", "26 | \n", "40.5 | \n", "9.2 | \n", "6.6 | \n", "9.0 | \n", "30.4 | \n", "9.4 | \n", "35.0 | \n", "