├── CHANGELOG.md ├── LICENSE ├── MODEL.pdf ├── MODEL.tex ├── README.md ├── ca ├── 2014-09-01_reserves_0.json ├── 2014-09-01_reserves_1.json ├── 2014-09-01_reserves_3.json ├── 2014-09-01_reserves_5.json ├── 2014-12-01_reserves_0.json ├── 2014-12-01_reserves_1.json ├── 2014-12-01_reserves_3.json ├── 2014-12-01_reserves_5.json ├── 2015-03-01_reserves_0.json ├── 2015-03-01_reserves_1.json ├── 2015-03-01_reserves_3.json ├── 2015-03-01_reserves_5.json ├── 2015-06-01_reserves_0.json ├── 2015-06-01_reserves_1.json ├── 2015-06-01_reserves_3.json ├── 2015-06-01_reserves_5.json ├── Scenario400_reserves_0.json ├── Scenario400_reserves_1.json ├── Scenario400_reserves_3.json └── Scenario400_reserves_5.json ├── ferc ├── 2015-01-01_hw.json ├── 2015-01-01_lw.json ├── 2015-02-01_hw.json ├── 2015-02-01_lw.json ├── 2015-03-01_hw.json ├── 2015-03-01_lw.json ├── 2015-04-01_hw.json ├── 2015-04-01_lw.json ├── 2015-05-01_hw.json ├── 2015-05-01_lw.json ├── 2015-06-01_hw.json ├── 2015-06-01_lw.json ├── 2015-07-01_hw.json ├── 2015-07-01_lw.json ├── 2015-08-01_hw.json ├── 2015-08-01_lw.json ├── 2015-09-01_hw.json ├── 2015-09-01_lw.json ├── 2015-10-01_hw.json ├── 2015-10-01_lw.json ├── 2015-11-02_hw.json ├── 2015-11-02_lw.json ├── 2015-12-01_hw.json └── 2015-12-01_lw.json ├── rts_gmlc ├── 2020-01-27.json ├── 2020-02-09.json ├── 2020-03-05.json ├── 2020-04-03.json ├── 2020-05-05.json ├── 2020-06-09.json ├── 2020-07-06.json ├── 2020-08-12.json ├── 2020-09-20.json ├── 2020-10-27.json ├── 2020-11-25.json └── 2020-12-23.json ├── uc_model.jl └── uc_model.py /CHANGELOG.md: -------------------------------------------------------------------------------- 1 | PGLib UC Benchmarks Change Log 2 | ============================== 3 | 4 | ### v19.08 5 | - Initial release 6 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | Data License: 2 | 3 | Creative Commons Attribution 4.0 International license 4 | http://creativecommons.org/licenses/by/4.0/ 5 | 6 | See data files for specific copyright holders and attribution details. 7 | 8 | 9 | Software License: 10 | 11 | MIT License 12 | Copyright (c) 2019 A Library of IEEE PES Power Grid Benchmarks 13 | 14 | Permission is hereby granted, free of charge, to any person obtaining a copy 15 | of this software and associated documentation files (the "Software"), to deal 16 | in the Software without restriction, including without limitation the rights 17 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 18 | copies of the Software, and to permit persons to whom the Software is 19 | furnished to do so, subject to the following conditions: 20 | 21 | The above copyright notice and this permission notice shall be included in all 22 | copies or substantial portions of the Software. 23 | 24 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 25 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 26 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 27 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 28 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 29 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 30 | SOFTWARE. 31 | 32 | -------------------------------------------------------------------------------- /MODEL.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/power-grid-lib/pglib-uc/cc3ccc1f82a27c66f5e0935fcee005a2fabd1594/MODEL.pdf -------------------------------------------------------------------------------- /MODEL.tex: -------------------------------------------------------------------------------- 1 | \documentclass{article} 2 | % 3 | \usepackage{fullpage} 4 | \usepackage{amsmath} 5 | \usepackage{amssymb} 6 | 7 | \usepackage{IEEEtrantools} 8 | \usepackage{filecontents} 9 | 10 | 11 | \newcommand{\cT}{{\mathcal T}} 12 | \newcommand{\cS}{{\mathcal S}} 13 | \newcommand{\cG}{{\mathcal G}} 14 | \newcommand{\cL}{{\mathcal L}} 15 | \newcommand{\cW}{{\mathcal W}} 16 | \newcommand{\bbR}{{\mathbb R}} 17 | \newcommand{\uP}{\underline{P}} 18 | \newcommand{\oP}{\overline{P}} 19 | 20 | \newcommand\mydescriptionopt{ 21 | \IEEEsetlabelwidth{$g \in \cG_{\textit{off}}^0$]} 22 | \IEEEusemathlabelsep 23 | } 24 | \begin{document} 25 | 26 | \section{Nomenclature} 27 | \subsection{Indices and Sets} 28 | \begin{IEEEdescription}[\mydescriptionopt] 29 | \item[$g \in \cG$] Set of thermal generators. 30 | \item[$g \in \cG_{\textit{on}}^0$] Set of thermal generators which are initially committed (on). 31 | \item[$g \in \cG_{\textit{off}}^0$] Set of thermal generators which are not initially committed (off). 32 | \item[$w \in \cW$] Set of renewable generators. 33 | \item[$t \in \cT$] Hourly time steps: $1, \ldots, T$, $T$ = {\tt time\_periods} 34 | \item[$l \in \cL_g$] Piecewise production cost intervals for thermal generator $g$: $1, \ldots, L_g$. 35 | \item[$s \in \cS_g$] Startup categories for thermal generator $g$, from hottest ($1$) to coldest ($S_g$): $1, \ldots, S_g$. 36 | \end{IEEEdescription} 37 | 38 | \subsection{System Parameters} 39 | \begin{IEEEdescription}[\mydescriptionopt] 40 | \item[$D(t)$] Load (demand) at time $t$ (MW), {\tt demand}. 41 | \item[$R(t)$] Spinning reserve at time $t$ (MW), {\tt reserves}. 42 | \end{IEEEdescription} 43 | 44 | \subsection{Thermal Generator Parameters} 45 | \begin{IEEEdescription}[\mydescriptionopt] 46 | \item[$CS_g^s$] Startup cost in category $s$ for generator $g$ (\$), {\tt startup['cost']}. 47 | \item[$CP_g^l$] Cost of operating at piecewise generation point $l$ for generator $g$ (MW), {\tt piecewise\_production['cost']}. 48 | \item[$DT_g$] Minimum down time for generator $g$ (h), {\tt time\_down\_minimum}. 49 | \item[$DT^0_g$] Number of time periods the unit has been off prior to the first time period for generator $g$, {\tt time\_down\_t0}. 50 | \item[$\oP_g$] Maximum power output for generator $g$ (MW), {\tt power\_output\_maximum}. 51 | \item[$\uP_g$] Minimum power output for generator $g$ (MW), {\tt power\_output\_minimum}. 52 | \item[$P_g^0$] Power output for generator $g$ (MW) in the time period prior to t=1, {\tt power\_output\_t0}. 53 | \item[$P_g^l$] Power level for piecewise generation point $l$ for generator $g$ (MW); $P^1_g = \uP_g$ and $P^{L_g}_g = \oP_g$, {\tt piecewise\_production['mw']}. 54 | \item[$RD_g$] Ramp-down rate for generator $g$ (MW/h), {\tt ramp\_down\_limit}. 55 | \item[$RU_g$] Ramp-up rate for generator $g$ (MW/h), {\tt ramp\_up\_limit}. 56 | \item[$SD_g$] Shutdown capability for generator $g$ (MW), {\tt ramp\_shutdown\_limit}. 57 | \item[$SU_g$] Startup capability for generator $g$ (MW), {\tt ramp\_startup\_limit} 58 | \item[$TS^s_g$] Time offline after which the startup category $s$ becomes active (h), {\tt startup['lag']}. 59 | \item[$UT_g$] Minimum up time for generator $g$ (h), {\tt time\_up\_minimum}. 60 | \item[$UT^0_g$] Number of time periods the unit has been on prior to the first time period for generator $g$, {\tt time\_up\_t0}. 61 | \item[$U_g^0$] Initial on/off status for generator $g$, $U_g^0=1$ for $g \in \cG_{\textit{on}}^0$, $U_g^0=0$ for $g \in \cG_{\textit{off}}^0$, {\tt unit\_on\_t0}. 62 | \item[$U_g$] Must-run status for generator $g$, {\tt must\_run}. 63 | \end{IEEEdescription} 64 | 65 | \subsection{Renewable Generator Parameters} 66 | \begin{IEEEdescription}[\mydescriptionopt] 67 | \item[$\oP_w(t)$] Maximum renewable generation available from renewable generator $w$ at time $t$ (MW), {\tt power\_output\_maximum}. 68 | \item[$\uP_w(t)$] Minimum renewable generation available from renewable generator $w$ at time $t$ (MW), {\tt power\_output\_minimum}. 69 | \end{IEEEdescription} 70 | 71 | 72 | \subsection{Variables} 73 | \begin{IEEEdescription}[\mydescriptionopt] 74 | \item[$c_g(t)$] Cost of power produced above minimum for thermal generator $g$ at time $t$ (MW), $\in \bbR$. 75 | \item[$p_g(t)$] Power above minimum for thermal generator $g$ at time $t$ (MW), $\geq 0$. 76 | \item[$p_w(t)$] Renewable generation used from renewable generator $w$ at time $t$ (MW), $\geq 0$. 77 | \item[$r_g(t)$] Spinning reserves provided by thermal generator $g$ at time $t$ (MW), $\geq 0$. 78 | \item[$u_g(t)$] Commitment status of thermal generator $g$ at time $t$, $\in \{0,1\}$. 79 | \item[$v_g(t)$] Startup status of thermal generator $g$ at time $t$, $\in \{0,1\}$. 80 | \item[$w_g(t)$] Shutdown status of thermal generator $g$ at time $t$, $\in \{0,1\}$. \ 81 | \item[$\delta^s_g(t)$] Startup in category $s$ for thermal generator $g$ at time $t$, $\in \{0,1\}$. 82 | \item[$\lambda_g^l(t)$] Fraction of power from piecewise generation point $l$ for generator $g$ at time $t$ (MW), $\in [0,1]$. 83 | \ 84 | \end{IEEEdescription} 85 | 86 | \section{Model Description} 87 | Below we describe the unit commitment model given by~\cite{morales2013tight}, with the piecewise production cost description from~\cite{sridhar2013locally}. 88 | The unit commitment problem can then be formulated as: 89 | {\allowdisplaybreaks 90 | \begin{align} 91 | & \text{min } \sum_{g \in \cG} \sum_{t \in \cT} \left( c_g(t) + CP_g^1 \, u_g(t) + \sum_{s = 1}^{S_g} \left( CS^s_g \delta^s(t) \right) \right) \label{eq:obj} %\tag{UC} %\\ 92 | %\text{subject to } & & \nonumber 93 | \end{align} 94 | subject to: 95 | \begin{align} 96 | & \sum_{g \in \cG} \left( p_g(t) + \uP_g u_g(t) \right) + \sum_{w\in\cW} p_w(t) = D(t) & \hspace{5cm} \forall t \in \cT \label{eq:UCDemand} \\ 97 | & \sum_{g \in \cG} r_g(t) \geq R(t) & \forall t \in \cT \label{eq:UCReserves} 98 | \end{align} 99 | \begin{align} 100 | & \sum_{t=1}^{\min\{UT_g - UT_g^0, T\}} (u_g(t) - 1) = 0 & \hspace{3cm} \forall g \in \cG_{\textit{on}}^0 \label{eq:initialUpRequirement} \\ 101 | & \sum_{t=1}^{\min\{DT_g - DT_g^0, T\}} u_g(t) = 0 & \forall g \in \cG_{\textit{off}}^0 \label{eq:initialDownRequirement} \\ 102 | & u_g(1) - U_g^0 = v_g(1) - w_g(1) & \forall g \in \cG \label{eq:LogicalInitial} \\ 103 | & \sum_{s=1}^{S_g-1} \sum_{t=\max\{1, TS^{s+1}_g - DT^0_g + 1\}}^{\min\{TS^{s+1}_g -1,T\}} \delta^s_g(t) = 0 & \forall g \in \cG \label{eq:STIInit}\\ 104 | & p_g(1) + r_g(1) - U_g^0(P_g^0-\uP_g) \leq RU_g & \forall g \in \cG \label{eq:RampUpInit} \\ 105 | & U_g^0(P_g^0-\uP_g) - p_g(1) \leq RD_g & \forall g \in \cG \label{eq:RampDownInit} \\ 106 | & U_g^0(P_g^0-\uP_g) \leq (\oP_g - \uP_g) U_g^0 - \max\{(\oP_g - SD_g),0\} w_g(1) & \forall g \in \cG \label{eq:MaxOutput2Init} 107 | \end{align} 108 | \begin{align} 109 | & u_g(t) \geq U_g & \hspace{1cm} \forall t \in \cT, \, \forall g \in \cG \label{eq:MustRun} \\ 110 | & u_g(t) - u_g(t-1) = v_g(t) - w_g(t) & \forall t \in \cT\setminus\{1\}, \, \forall g \in \cG \label{eq:Logical} \\ 111 | & \sum_{i= t-\min\{UT_g,T\} + 1}^t v_g(i) \leq u_g(t) & \forall t \in \{\min\{UT_g,T\} \ldots, T\}, \, \forall g \in \cG \label{eq:Startup} \\ 112 | & \sum_{i= t-\min\{DT_g,T\} + 1}^t w_g(i) \leq 1 - u_g(t) & \forall t \in \{\min\{DT_g, T\}, \ldots, T\}, \, \forall g \in \cG \label{eq:Shutdown} \\ 113 | & \delta^s_g(t) \leq \sum_{i = TS^s_g}^{TS^{s+1}_g-1} w_g(t-i) & \forall t \in \{TS^{s+1}_g,\ldots,T\},\,\forall s \in \cS_g\!\setminus\!\{S_g\},\, \forall g \in \cG \label{eq:STISelect} \\ 114 | & v_g(t) = \sum_{s = 1}^{S_g} \delta^s_g(t) & \forall t \in \cT,\, \forall g \in \cG \label{eq:STILink} 115 | \end{align} 116 | \begin{align} 117 | & p_g(t) + r_g(t) \leq (\oP_g - \uP_g) u_g(t) - \max\{(\oP_g - SU_g),0\} v_g(t) & \forall t \in \cT, \, \forall g \in \cG \label{eq:MaxOutput1} \\ 118 | & p_g(t) + r_g(t) \leq (\oP_g - \uP_g) u_g(t) - \max\{(\oP_g - SD_g),0\} w_g(t+1) & \forall t \in \cT\setminus \{T\}, \, \forall g \in \cG \label{eq:MaxOutput2} \\ 119 | & p_g(t) + r_g(t) - p_g(t-1) \leq RU_g & \forall t \in \cT\setminus\{1\}, \, \forall g \in \cG \label{eq:RampUp} \\ 120 | & p_g(t-1) - p_g(t) \leq RD_g & \forall t \in \cT\setminus\{1\}, \, \forall g \in \cG \label{eq:RampDown} 121 | \end{align} 122 | \begin{align} 123 | & p_g(t) = \sum_{l \in \cL_g} (P_g^l - P_g^1) \lambda_g^l(t) &\hspace{5cm} \forall t \in \cT, \, \forall g \in \cG \label{eq:PiecewiseParts} \\ 124 | & c_g(t) = \sum_{l \in \cL_g} (CP_g^l - CP_g^1) \lambda_g^l(t) & \forall t \in \cT, \, \forall g \in \cG \label{eq:PiecewisePartsCost} \\ 125 | & u_g(t) = \sum_{l \in \cL_g} \lambda_g^l(t) & \forall t \in \cT, \forall g \in \cG \label{eq:PiecewiseLimits} 126 | \end{align} 127 | \begin{align} 128 | & \uP_w(t) \leq p_w(t) \leq \oP_w(t) &\hspace{6cm} \forall t \in \cT, \, \forall w \in \cW \label{eq:WindLimit} 129 | \end{align} 130 | }% 131 | Note that in constraints~\eqref{eq:initialUpRequirement}, \eqref{eq:initialDownRequirement}, and \eqref{eq:STIInit}, we use the convention that empty sums are $0$. 132 | 133 | %% add the bibtex 134 | \begin{filecontents*}{MODEL.bib} 135 | @article{morales2013tight, 136 | title={Tight and compact {MILP} formulation for the thermal unit commitment problem}, 137 | author={Morales-Espa{\~n}a, G. and Latorre, J. M. and Ramos, A.}, 138 | journal={IEEE Transactions on Power Systems}, 139 | volume={28}, 140 | number={4}, 141 | pages={4897--4908}, 142 | year={2013}, 143 | publisher={IEEE} 144 | } 145 | @article{sridhar2013locally, 146 | title={Locally ideal formulations for piecewise linear functions with indicator variables}, 147 | author={Sridhar, Srikrishna and Linderoth, Jeff and Luedtke, James}, 148 | journal={Operations Research Letters}, 149 | volume={41}, 150 | number={6}, 151 | pages={627--632}, 152 | year={2013}, 153 | publisher={Elsevier} 154 | } 155 | \end{filecontents*} 156 | 157 | \bibliographystyle{acm} 158 | \bibliography{MODEL} 159 | 160 | \end{document} 161 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Power Grid Lib - Unit Commitment 2 | 3 | This benchmark library is curated and maintained by the [IEEE PES Task Force on Benchmarks for Validation of Emerging Power System Algorithms](https://power-grid-lib.github.io/) and is designed to evaluate a well established version of the the Unit Commitment problem. Specifically, these cases are designed for benchmarking algorithms that solve the following the Mixed-Integer Linear Program described in the formulation [PDF document](MODEL.pdf). 4 | 5 | A detailed description of this mathematical model is available [here](http://www.optimization-online.org/DB_FILE/2018/11/6930.pdf). All of the cases files are curated in a json-based data format. Open-source reference implementations are available in [EGRET](https://github.com/grid-parity-exchange/Egret) and [psst](https://github.com/kdheepak/psst). 6 | 7 | ## Problem Overview 8 | 9 | These cases are useful for benchmarking solution methods for a variant of the unit commitment problem common in the academic literature. The features of this model are: 10 | * A global load requirement with time series 11 | * An optional global spinning reserve requirement with time series 12 | * Thermal generators with technical parameters, including 13 | * Minimum and maximum power output 14 | * Hourly ramp-up and ramp-down rates 15 | * Start-up and shut-down ramp rates 16 | * Minimum run-times and off-times 17 | * Off time dependent start-up costs 18 | * Piecewise linear convex production costs 19 | * No-load costs 20 | * Optional renewable generators with time series for minimum and maximum production. 21 | 22 | ## Case File Overview 23 | 24 | This is divided into three sets of generators, each with varying load and reserve profiles. Please see the reference documents for more detail on the sources and motivations for these test cases. 25 | 26 | ### /ca/*.json 27 | Generator and load data curated from publicly available data from the California ISO. There are four different load profiles by date, and varying reserve requirements as a percentage of load: 0%, 1%, 3%, and 5%. A fifth load profile (Scenario400) includes a hypothetical 40% wind generation supply. When using this data, please cite [1]. 28 | 29 | ### /ferc/*.json 30 | Generator data based on the publicly available unit commitment test instance from the Federal Energy Regulatory Commission. Load, reserves, and wind data is curated from publicly available data from PJM. The 'lw' moniker denotes a wind profile scaled to be 2% of annual load; the 'hw' denotes a wind profile scaled to be 30% of annual load. When using this data, please cite [1],[2]. 31 | 32 | ### /rts_gmlc/*.json 33 | Generator, load, and reserve data is curated from the publicly available [RTS-GMLC test system](https://github.com/GridMod/RTS-GMLC). Hourly generator ramp-rates are divided by a factor of three to ensure all the technical features listed above are captured at an hourly time scale. When using this data, please cite [3]. 34 | 35 | #### References 36 | [1] Knueven, Bernard, James Ostrowski, and Jean-Paul Watson. ["On mixed integer programming formulations for the unit commitment problem."](http://www.optimization-online.org/DB_FILE/2018/11/6930.pdf) (2018). 37 | 38 | [2] Krall, Eric, Michael Higgins, and Richard P. O’Neill. ["RTO unit commitment test system."](https://www.ferc.gov/industries-data/electric/power-sales-and-markets/increasing-efficiency-through-improved-software-1) Federal Energy Regulatory Commission (2012). 39 | 40 | [3] Barrows, Clayton, Aaron Bloom, Ali Ehlen, Jussi Ikaheimo, Jennie Jorgenson, Dheepak Krishnamurthy, Jessica Lau et al. ["The IEEE Reliability Test System: A Proposed 2019 Update."](https://ieeexplore.ieee.org/document/8753693) IEEE Transactions on Power Systems (2019). 41 | 42 | 43 | ## Contributions 44 | 45 | All case files are provided under a [Creative Commons Attribution License](http://creativecommons.org/licenses/by/4.0/), which allows anyone to share or adapt these cases as long as they give appropriate credit to the original author, provide a link to the license, and indicate if changes were made. 46 | 47 | Community-based recommendations and contributions are welcome and encouraged in all PGLib repositories. Please feel free to submit comments and questions in the [issue tracker](https://github.com/power-grid-lib/pglib-uc/issues). Corrections and new network contributions are welcome via pull requests. All data contributions are subject to a quality assurance review by the repository curator(s). 48 | 49 | 50 | ## Citation Guidelines 51 | 52 | This repository is not static. Consequently, it is critically important to indicate the version number when referencing this repository in scholarly work. 53 | 54 | Users of this these cases are encouraged to cite the original source documents mentioned in this overview document. 55 | -------------------------------------------------------------------------------- /rts_gmlc/2020-03-05.json: -------------------------------------------------------------------------------- 1 | {"time_periods": 48, "demand": [3092.1, 3015.71, 2993.42, 3025.4, 3162.21, 3453.4, 3664.25, 3718.68, 3773.99, 3807.84, 3842.99, 3867.81, 3867.33, 3862.68, 3851.33, 3804.7, 3796.89, 3954.79, 4314.12, 4270.62, 4163.03, 3860.68, 3532.93, 3278.42, 3135.88, 3066.02, 3037.5, 3067.84, 3190.72, 3488.23, 3702.56, 3792.69, 3873.46, 3918.72, 3964.63, 3961.42, 3916.5, 3894.92, 3864.88, 3824.15, 3821.36, 3982.68, 4328.01, 4248.62, 4103.35, 3887.09, 3609.3, 3374.87], "reserves": [92.76299999999999, 90.4713, 89.8026, 90.762, 94.8663, 103.602, 109.9275, 111.56039999999999, 113.21969999999999, 114.2352, 115.28969999999998, 116.03429999999999, 116.01989999999999, 115.8804, 115.53989999999999, 114.14099999999999, 113.90669999999999, 118.6437, 129.4236, 128.1186, 124.89089999999999, 115.82039999999999, 105.9879, 98.3526, 94.0764, 91.9806, 91.125, 92.0352, 95.7216, 104.6469, 111.07679999999999, 113.7807, 116.2038, 117.56159999999998, 118.9389, 118.8426, 117.49499999999999, 116.8476, 115.9464, 114.72449999999999, 114.6408, 119.48039999999999, 129.8403, 127.45859999999999, 123.10050000000001, 116.6127, 108.279, 101.2461], "thermal_generators": {"307_CT_2": {"must_run": 0, "power_output_minimum": 22.0, "power_output_maximum": 55.0, "ramp_up_limit": 74.0, "ramp_down_limit": 74.0, "ramp_startup_limit": 22.0, "ramp_shutdown_limit": 22.0, "time_up_minimum": 3, "time_down_minimum": 3, "power_output_t0": 0.0, "unit_on_t0": 0, "time_down_t0": 168, "time_up_t0": 0, "startup": [{"lag": 3, "cost": 5665.23}], "piecewise_production": [{"mw": 22.0, 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5.4, 6.4, 6.4, 6.3, 5.6, 3.8, 1.6, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.0, 4.0, 5.5, 6.1, 6.4, 6.4, 5.6, 4.0, 1.6, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], "name": "118_RTPV_2"}, "314_PV_4": {"power_output_minimum": [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], "power_output_maximum": [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 26.0, 33.3, 36.4, 37.1, 36.7, 36.2, 34.8, 31.6, 20.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 25.6, 32.7, 35.6, 34.6, 34.5, 33.7, 31.5, 29.5, 18.2, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], "name": "314_PV_4"}, "319_PV_1": {"power_output_minimum": [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], "power_output_maximum": [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 105.3, 136.3, 143.4, 145.8, 144.5, 141.1, 134.8, 115.4, 67.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 103.8, 135.4, 144.1, 141.8, 132.2, 130.1, 122.3, 112.6, 63.4, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], "name": "319_PV_1"}}} -------------------------------------------------------------------------------- /uc_model.jl: -------------------------------------------------------------------------------- 1 | # Tested with Julia v1.1, JSON v0.21, JuMP v0.19, Cbc v0.6 2 | 3 | using JSON 4 | using JuMP 5 | 6 | 7 | println("loading data") 8 | 9 | ## Grab instance file from first command line argument 10 | data_file = ARGS[1] 11 | data = JSON.parsefile(data_file) 12 | 13 | 14 | println("model building") 15 | 16 | thermal_gens = keys(data["thermal_generators"]) 17 | renewable_gens = keys(data["renewable_generators"]) 18 | time_periods = 1:data["time_periods"] 19 | 20 | gen_startup_categories = Dict(g => 1:length(gen["startup"]) for (g,gen) in data["thermal_generators"]) 21 | gen_pwl_points = Dict(g => 1:length(gen["piecewise_production"]) for (g,gen) in data["thermal_generators"]) 22 | 23 | m = Model() 24 | 25 | @variable(m, cg[thermal_gens,time_periods]) 26 | @variable(m, pg[thermal_gens,time_periods] >= 0) 27 | @variable(m, pw[renewable_gens,time_periods] >= 0) 28 | @variable(m, rg[thermal_gens,time_periods] >= 0) 29 | @variable(m, ug[thermal_gens,time_periods], binary=true) 30 | @variable(m, vg[thermal_gens,time_periods], binary=true) 31 | @variable(m, wg[thermal_gens,time_periods], binary=true) 32 | @variable(m, delta_sg[g in thermal_gens,gen_startup_categories[g],time_periods], binary=true) 33 | @variable(m, 0 <= lambda_lg[g in thermal_gens,gen_pwl_points[g],time_periods] <= 1) 34 | 35 | 36 | @objective(m, Min, 37 | sum( 38 | sum( 39 | cg[g,t] + gen["piecewise_production"][1]["cost"]*ug[g,t] + 40 | sum( 41 | gen_startup["cost"]*delta_sg[g,i,t] 42 | for (i, gen_startup) in enumerate(gen["startup"])) 43 | for t in time_periods) 44 | for (g, gen) in data["thermal_generators"]) 45 | ) # (1) 46 | 47 | for (g, gen) in data["thermal_generators"] 48 | 49 | if gen["unit_on_t0"] == 1 50 | @constraint(m, sum( (ug[g,t]-1) for t in 1:min(data["time_periods"], gen["time_up_minimum"] - gen["time_up_t0"]) ) == 0) # (4) 51 | else 52 | @constraint(m, sum( ug[g,t] for t in 1:min(data["time_periods"], gen["time_down_minimum"] - gen["time_down_t0"]) ) == 0) # (5) 53 | end 54 | 55 | @constraint(m, ug[g,1] - gen["unit_on_t0"] == vg[g,1] - wg[g,1]) # (6) 56 | 57 | @constraint(m, 0 == 58 | sum( 59 | sum( 60 | delta_sg[g,i,t] 61 | for t in max(1, gen["startup"][i+1]["lag"] - gen["time_down_t0"] + 1):min(gen["startup"][i+1]["lag"]-1, data["time_periods"])) 62 | for (i,startup) in enumerate(gen["startup"][1:end-1])) 63 | ) # (7) 64 | 65 | @constraint(m, pg[g,1] + rg[g,1] - gen["unit_on_t0"]*(gen["power_output_t0"] - gen["power_output_minimum"]) <= gen["ramp_up_limit"]) # (8) 66 | @constraint(m, gen["unit_on_t0"]*(gen["power_output_t0"] - gen["power_output_minimum"]) - pg[g,1] <= gen["ramp_down_limit"]) # (9) 67 | @constraint(m, gen["unit_on_t0"]*(gen["power_output_t0"] - gen["power_output_minimum"]) <= gen["unit_on_t0"]*(gen["power_output_maximum"] - gen["power_output_minimum"]) - max(0, gen["power_output_maximum"] - gen["ramp_shutdown_limit"])*wg[g,1]) # (10) 68 | end 69 | 70 | for t in time_periods 71 | @constraint(m, 72 | sum( pg[g,t] + gen["power_output_minimum"]*ug[g,t] for (g, gen) in data["thermal_generators"] ) + 73 | sum( pw[g,t] for g in renewable_gens) 74 | == data["demand"][t] 75 | ) # (2) 76 | 77 | @constraint(m, sum(rg[g,t] for g in thermal_gens) >= data["reserves"][t]) # (3) 78 | 79 | for (g, gen) in data["thermal_generators"] 80 | 81 | @constraint(m, ug[g,t] >= gen["must_run"]) # (11) 82 | 83 | if t > 1 84 | @constraint(m, ug[g,t] - ug[g,t-1] == vg[g,t] - wg[g,t]) # (12) 85 | @constraint(m, pg[g,t] + rg[g,t] - pg[g,t-1] <= gen["ramp_up_limit"]) # (19) 86 | @constraint(m, pg[g,t-1] - pg[g,t] <= gen["ramp_down_limit"]) # (20) 87 | end 88 | 89 | 90 | if t >= gen["time_up_minimum"] || t == data["time_periods"] 91 | @constraint(m, sum( vg[g,t2] for t2 in (t-min(gen["time_up_minimum"],data["time_periods"])+1):t) <= ug[g,t]) # (13) 92 | end 93 | 94 | if t >= gen["time_down_minimum"] || t == data["time_periods"] 95 | @constraint(m, sum( wg[g,t2] for t2 in (t-min(gen["time_down_minimum"],data["time_periods"])+1):t) <= 1 - ug[g,t]) # (14) 96 | end 97 | 98 | for (si,startup) in enumerate(gen["startup"][1:end-1]) 99 | if t >= gen["startup"][si+1]["lag"] 100 | time_range = startup["lag"]:(gen["startup"][si+1]["lag"]-1) 101 | @constraint(m, delta_sg[g,si,t] <= sum(wg[g,t-i] for i in time_range)) # (15) 102 | end 103 | end 104 | 105 | @constraint(m, vg[g,t] == sum( delta_sg[g,i,t] for i in gen_startup_categories[g])) # (16) 106 | 107 | @constraint(m, pg[g,t] + rg[g,t] <= (gen["power_output_maximum"] - gen["power_output_minimum"])*ug[g,t] - max(0, (gen["power_output_maximum"] - gen["ramp_startup_limit"]))*vg[g,t]) # (17) 108 | 109 | if t < data["time_periods"] 110 | @constraint(m, pg[g,t] + rg[g,t] <= (gen["power_output_maximum"] - gen["power_output_minimum"])*ug[g,t] - max(0, (gen["power_output_maximum"] - gen["ramp_shutdown_limit"]))*wg[g,t+1]) # (18) 111 | end 112 | 113 | @constraint(m, pg[g,t] == sum((gen["piecewise_production"][l]["mw"] - gen["piecewise_production"][1]["mw"])*lambda_lg[g,l,t] for l in gen_pwl_points[g])) # (21) 114 | @constraint(m, cg[g,t] == sum((gen["piecewise_production"][l]["cost"] - gen["piecewise_production"][1]["cost"])*lambda_lg[g,l,t] for l in gen_pwl_points[g])) # (22) 115 | @constraint(m, ug[g,t] == sum(lambda_lg[g,l,t] for l in gen_pwl_points[g])) # (23) 116 | end 117 | 118 | for (rg, rgen) in data["renewable_generators"] 119 | @constraint(m, rgen["power_output_minimum"][t] <= pw[rg,t] <= rgen["power_output_maximum"][t]) # (24) 120 | end 121 | end 122 | 123 | 124 | println("optimization") 125 | 126 | using Cbc 127 | optimize!(m, with_optimizer(Cbc.Optimizer, logLevel=1)) 128 | -------------------------------------------------------------------------------- /uc_model.py: -------------------------------------------------------------------------------- 1 | from pyomo.environ import * 2 | import json 3 | import sys 4 | 5 | ## Grab instance file from first command line argument 6 | data_file = sys.argv[1] 7 | 8 | print('loading data') 9 | data = json.load(open(data_file, 'r')) 10 | 11 | thermal_gens = data['thermal_generators'] 12 | renewable_gens = data['renewable_generators'] 13 | 14 | time_periods = {t+1 : t for t in range(data['time_periods'])} 15 | 16 | gen_startup_categories = {g : list(range(0, len(gen['startup']))) for (g, gen) in thermal_gens.items()} 17 | gen_pwl_points = {g : list(range(0, len(gen['piecewise_production']))) for (g, gen) in thermal_gens.items()} 18 | 19 | print('building model') 20 | m = ConcreteModel() 21 | 22 | m.cg = Var(thermal_gens.keys(), time_periods.keys()) 23 | m.pg = Var(thermal_gens.keys(), time_periods.keys(), within=NonNegativeReals) 24 | m.rg = Var(thermal_gens.keys(), time_periods.keys(), within=NonNegativeReals) 25 | m.pw = Var(renewable_gens.keys(), time_periods.keys(), within=NonNegativeReals) 26 | m.ug = Var(thermal_gens.keys(), time_periods.keys(), within=Binary) 27 | m.vg = Var(thermal_gens.keys(), time_periods.keys(), within=Binary) 28 | m.wg = Var(thermal_gens.keys(), time_periods.keys(), within=Binary) 29 | 30 | m.dg = Var(((g,s,t) for g in thermal_gens for s in gen_startup_categories[g] for t in time_periods), within=Binary) ## 31 | m.lg = Var(((g,l,t) for g in thermal_gens for l in gen_pwl_points[g] for t in time_periods), within=UnitInterval) ## 32 | 33 | m.obj = Objective(expr=sum( 34 | sum( 35 | m.cg[g,t] + gen['piecewise_production'][0]['cost']*m.ug[g,t] 36 | + sum( gen_startup['cost']*m.dg[g,s,t] for (s, gen_startup) in enumerate(gen['startup'])) 37 | for t in time_periods) 38 | for g, gen in thermal_gens.items() ) 39 | ) #(1) 40 | 41 | m.demand = Constraint(time_periods.keys()) 42 | m.reserves = Constraint(time_periods.keys()) 43 | for t,t_idx in time_periods.items(): 44 | m.demand[t] = sum( m.pg[g,t]+gen['power_output_minimum']*m.ug[g,t] for (g, gen) in thermal_gens.items() ) + sum( m.pw[w,t] for w in renewable_gens ) == data['demand'][t_idx] #(2) 45 | m.reserves[t] = sum( m.rg[g,t] for g in thermal_gens ) >= data['reserves'][t_idx] #(3) 46 | 47 | m.uptimet0 = Constraint(thermal_gens.keys()) 48 | m.downtimet0 = Constraint(thermal_gens.keys()) 49 | m.logicalt0 = Constraint(thermal_gens.keys()) 50 | m.startupt0 = Constraint(thermal_gens.keys()) 51 | 52 | m.rampupt0 = Constraint(thermal_gens.keys()) 53 | m.rampdownt0 = Constraint(thermal_gens.keys()) 54 | m.shutdownt0 = Constraint(thermal_gens.keys()) 55 | 56 | for g, gen in thermal_gens.items(): 57 | if gen['unit_on_t0'] == 1: 58 | if gen['time_up_minimum'] - gen['time_up_t0'] >= 1: 59 | m.uptimet0[g] = sum( (m.ug[g,t] - 1) for t in range(1, min(gen['time_up_minimum'] - gen['time_up_t0'], data['time_periods'])+1)) == 0 #(4) 60 | elif gen['unit_on_t0'] == 0: 61 | if gen['time_down_minimum'] - gen['time_down_t0'] >= 1: 62 | m.downtimet0[g] = sum( m.ug[g,t] for t in range(1, min(gen['time_down_minimum'] - gen['time_down_t0'], data['time_periods'])+1)) == 0 #(5) 63 | else: 64 | raise Exception('Invalid unit_on_t0 for generator {}, unit_on_t0={}'.format(g, gen['unit_on_t0'])) 65 | 66 | m.logicalt0[g] = m.ug[g,1] - gen['unit_on_t0'] == m.vg[g,1] - m.wg[g,1] #(6) 67 | 68 | startup_expr = sum( 69 | sum( m.dg[g,s,t] 70 | for t in range( 71 | max(1,gen['startup'][s+1]['lag']-gen['time_down_t0']+1), 72 | min(gen['startup'][s+1]['lag']-1,data['time_periods'])+1 73 | ) 74 | ) 75 | for s,_ in enumerate(gen['startup'][:-1])) ## all but last 76 | if isinstance(startup_expr, int): 77 | pass 78 | else: 79 | m.startupt0[g] = startup_expr == 0 #(7) 80 | 81 | m.rampupt0[g] = m.pg[g,1] + m.rg[g,1] - gen['unit_on_t0']*(gen['power_output_t0']-gen['power_output_minimum']) <= gen['ramp_up_limit'] #(8) 82 | 83 | m.rampdownt0[g] = gen['unit_on_t0']*(gen['power_output_t0']-gen['power_output_minimum']) - m.pg[g,1] <= gen['ramp_down_limit'] #(9) 84 | 85 | 86 | shutdown_constr = gen['unit_on_t0']*(gen['power_output_t0']-gen['power_output_minimum']) <= gen['unit_on_t0']*(gen['power_output_maximum'] - gen['power_output_minimum']) - max((gen['power_output_maximum'] - gen['ramp_shutdown_limit']),0)*m.wg[g,1] #(10) 87 | 88 | if isinstance(shutdown_constr, bool): 89 | pass 90 | else: 91 | m.shutdownt0[g] = shutdown_constr 92 | 93 | m.mustrun = Constraint(thermal_gens.keys(), time_periods.keys()) 94 | m.logical = Constraint(thermal_gens.keys(), time_periods.keys()) 95 | m.uptime = Constraint(thermal_gens.keys(), time_periods.keys()) 96 | m.downtime = Constraint(thermal_gens.keys(), time_periods.keys()) 97 | m.startup_select = Constraint(thermal_gens.keys(), time_periods.keys()) 98 | m.gen_limit1 = Constraint(thermal_gens.keys(), time_periods.keys()) 99 | m.gen_limit2 = Constraint(thermal_gens.keys(), time_periods.keys()) 100 | m.ramp_up = Constraint(thermal_gens.keys(), time_periods.keys()) 101 | m.ramp_down = Constraint(thermal_gens.keys(), time_periods.keys()) 102 | m.power_select = Constraint(thermal_gens.keys(), time_periods.keys()) 103 | m.cost_select = Constraint(thermal_gens.keys(), time_periods.keys()) 104 | m.on_select = Constraint(thermal_gens.keys(), time_periods.keys()) 105 | 106 | for g, gen in thermal_gens.items(): 107 | for t in time_periods: 108 | m.mustrun[g,t] = m.ug[g,t] >= gen['must_run'] #(11) 109 | 110 | if t > 1: 111 | m.logical[g,t] = m.ug[g,t] - m.ug[g,t-1] == m.vg[g,t] - m.wg[g,t] #(12) 112 | 113 | UT = min(gen['time_up_minimum'],data['time_periods']) 114 | if t >= UT: 115 | m.uptime[g,t] = sum(m.vg[g,t] for t in range(t-UT+1, t+1)) <= m.ug[g,t] #(13) 116 | DT = min(gen['time_down_minimum'],data['time_periods']) 117 | if t >= DT: 118 | m.downtime[g,t] = sum(m.wg[g,t] for t in range(t-DT+1, t+1)) <= 1-m.ug[g,t] #(14) 119 | m.startup_select[g,t] = m.vg[g,t] == sum(m.dg[g,s,t] for s,_ in enumerate(gen['startup'])) #(16) 120 | 121 | m.gen_limit1[g,t] = m.pg[g,t]+m.rg[g,t] <= (gen['power_output_maximum'] - gen['power_output_minimum'])*m.ug[g,t] - max((gen['power_output_maximum'] - gen['ramp_startup_limit']),0)*m.vg[g,t] #(17) 122 | 123 | if t < len(time_periods): 124 | m.gen_limit2[g,t] = m.pg[g,t]+m.rg[g,t] <= (gen['power_output_maximum'] - gen['power_output_minimum'])*m.ug[g,t] - max((gen['power_output_maximum'] - gen['ramp_shutdown_limit']),0)*m.wg[g,t+1] #(18) 125 | 126 | if t > 1: 127 | m.ramp_up[g,t] = m.pg[g,t]+m.rg[g,t] - m.pg[g,t-1] <= gen['ramp_up_limit'] #(19) 128 | m.ramp_down[g,t] = m.pg[g,t-1] - m.pg[g,t] <= gen['ramp_down_limit'] #(20 129 | 130 | piece_mw1 = gen['piecewise_production'][0]['mw'] 131 | piece_cost1 = gen['piecewise_production'][0]['cost'] 132 | m.power_select[g,t] = m.pg[g,t] == sum( (piece['mw'] - piece_mw1)*m.lg[g,l,t] for l,piece in enumerate(gen['piecewise_production'])) #(21) 133 | m.cost_select[g,t] = m.cg[g,t] == sum( (piece['cost'] - piece_cost1)*m.lg[g,l,t] for l,piece in enumerate(gen['piecewise_production'])) #(22) 134 | m.on_select[g,t] = m.ug[g,t] == sum(m.lg[g,l,t] for l,_ in enumerate(gen['piecewise_production'])) #(23) 135 | 136 | m.startup_allowed = Constraint(m.dg_index) 137 | for g, gen in thermal_gens.items(): 138 | for s,_ in enumerate(gen['startup'][:-1]): ## all but last 139 | for t in time_periods: 140 | if t >= gen['startup'][s+1]['lag']: 141 | m.startup_allowed[g,s,t] = m.dg[g,s,t] <= sum(m.wg[g,t-i] for i in range(gen['startup'][s]['lag'], gen['startup'][s+1]['lag'])) #(15) 142 | 143 | for w, gen in renewable_gens.items(): 144 | for t, t_idx in time_periods.items(): 145 | m.pw[w,t].setlb(gen['power_output_minimum'][t_idx]) #(24) 146 | m.pw[w,t].setub(gen['power_output_maximum'][t_idx]) #(24) 147 | 148 | print("model setup complete") 149 | 150 | from pyomo.opt import SolverFactory 151 | cbc = SolverFactory('cbc') 152 | 153 | print("solving") 154 | cbc.solve(m, options={'ratioGap':0.01}, tee=True) 155 | --------------------------------------------------------------------------------