{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "{index} single: AMPL \n", "\n", "{index} single: AMPL MP library\n", "\n", "{index} single: conic optimization; second order cones\n", "\n", "{index} single: solver; Mosek\n", "\n", "{index} single: solver; Ipopt\n", "\n", "{index} single: application; building insulation\n", "\n", "# Optimal Design of Multilayered Building Insulation" ] }, { "cell_type": "markdown", "metadata": { "id": "-1sFCsTgp8Mk" }, "source": [ "Thermal insulation is installed in buildings to reduce annual energy costs. However, the installation costs money, so the decision of how much insulation to install is a trade-off between the annualized capital costs of insulation and the annual operating costs for heating and air conditioning. This notebook shows the formulation and solution of an optimization problem using conic optimization." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [] }, "outputs": [], "source": [ "# install dependencies and select solver\n", "%pip install -q amplpy numpy pandas\n", "\n", "SOLVER_CONIC = \"mosek\" # ipopt, mosek, gurobi, knitro\n", "\n", "from amplpy import AMPL, ampl_notebook\n", "\n", "ampl = ampl_notebook(\n", " modules=[\"coin\", \"mosek\"], # modules to install\n", " license_uuid=\"default\", # license to use\n", ") # instantiate AMPL object and register notebook magics" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Please provide a valid license UUID. You can use a free https://ampl.com/ce license.\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "ba3e27e3e92545e493ee8756a270e9fe", "version_major": 2, "version_minor": 0 }, "text/plain": [ "VBox(children=(Output(), HBox(children=(Text(value='', description='License UUID:', style=TextStyle(descriptio…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.display import Markdown, HTML\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": { "id": "ivrv3B4GsJgb" }, "source": [ "## A Model for Multi-Layered Insulation\n", "\n", "Consider a wall or surface separating conditioned interior space in a building at temperature $T_i$ from the external environment at temperature $T_o$. Heat conduction through the wall is given by\n", "\n", "$$\\dot{Q} = UA (T_i - T_o),$$\n", "\n", "where $U$ is the overall heat transfer coefficient and and $A$ is the heat transfer area. For a wall constructed from $N$ layers of different insulating materials, the inverse of the overall heat transfer coefficient $U$ is given by a sum of serial thermal \"resistances\"\n", "\n", "$$\\frac{1}{U} = R_0 + \\sum_{n=1}^N R_n,$$\n", "\n", "where $R_0$ is the thermal resistance of the structural elements. The thermal resistance of the $n$-th insulating layer is equal to $R_n = \\frac{x_n}{k_n}$ for a material with thickness $x_n$ and a thermal conductivity $k_n$, so we can rewrite\n", "\n", "$$\\frac{1}{U} = R_0 + \\sum_{n=1}^N \\frac{x_n}{k_n}.$$\n", "\n", "The economic objective is to minimize the cost $C$, obtained as the combined annual energy operating expenses and capital cost of insulation. \n", "\n", "We assume the annual energy costs are proportional to overall heat transfer coefficient $U$ and let $\\alpha \\geq 0$ be the coefficient for the proportional relationship of the overall heat transfer coefficient $U$ to the annual energy costs. Furthermore, we assume the cost of installing a unit area of insulation in the $n$-th layer is given by the affine expression $a_n + b_n x_n$. The combined annualized costs are then\n", "\n", "$$C = \\alpha U + \\beta\\sum_{n=1}^N (a_n y_n + b_n x_n),$$\n", "\n", "where $\\beta$ is a discount factor for the equivalent annualized cost of insulation, and $y_n$ is a binary variable that indicates whether or not layer $n$ is included in the installation. The feasible values for $x_n$ are subject to constraints\n", "\n", "\\begin{align}\n", "x_n & \\leq Ty_n \\\\\n", "\\sum_{n=1}^N x_n & \\leq T\n", "\\end{align}\n", "\n", "where $T$ is an upper bound on insulation thickness.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analytic solution for $N=1$\n", "\n", "In the case of a single layer, i.e., $N=1$, we have a one-dimensional cost optimization problem of which we can obtain a close-form analytical solution directly. Indeed, the expression for the cost $C(x)$ as a function of the thickness $x$ reads\n", "\n", "\\begin{align}\n", "C(x) = \\frac{\\alpha k}{k R_0 + x} + \\beta(a + bx).\n", "\\end{align}\n", "\n", "For fixed parameters $k$, $R_0$, $\\beta$, $b$, we can calculate the optimum thickness $x^*$ as\n", "\n", "$$x^{*} = - k R_0 + \\sqrt{\\frac{\\alpha k}{\\beta b}}.$$\n", "\n", "A plot illustrates the trade-off between energy operating costs and capital insulation costs and the corresponding optimal solution $x^*$.\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "tags": [] }, "outputs": [], "source": [ "# application parameters\n", "alpha = 30 # \$ K / W annualized cost per sq meter per W/sq m/K\n", "beta = 0.05 # equivalent annual cost factor\n", "R0 = 2.0 # Watts/K/m**2\n", "T = 0.30 # maximum insulation thickness\n", "\n", "# material properties\n", "k = 0.030 # thermal conductivity as installed\n", "a = 5.0 # installation cost per square meter\n", "b = 150.0 # installed material cost per cubic meter" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The optimal cost is equal to 4.99615 per sq. meter\n", "The optimal thickness is 0.28641 meters\n", "\n" ] }, { "data": { "image/png": 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", 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