Data-based Distributionally Robust Stochastic OPF Package

The distributionally robust stochastic optimal power flow (OPF) package is developed at the Control, Optimization and Networks Laboratory, The University of Texas at Dallas. This framework uses MATLAB to solve a multi-stage stochastic OPF problem based on limited information about forecast error distributions, which explicitly combines multi-stage feedback policies with any forecasting method and historical forecast error data. The objective is to determine power scheduling policies for controllable devices in a power network to balance operational cost and conditional value-at-risk (CVaR) of device and network constraint violations. These decisions include both nominal power schedules and reserve policies, which specify planned reactions to forecast errors in order to accommodate fluctuating renewable energy sources (RESs). Instead of assuming the uncertainties across the networks follow prescribed probability distributions, we consider ambiguity sets of distributions centered around a finite training dataset. By utilizing the Wasserstein metric to quantify differences between the empirical data-based distribution and the real unknown data-generating distribution, we formulate a multi-stage distributionally robust OPF problem to compute control policies that are robust to both forecast errors and sampling errors inherent in the dataset. This package includes two sub-packages, especially designed for distribution networks and transmission systems, respectively.

Outline of README Documentation

• Requirements
• Package Organization
• Capabilities of framework
• Getting Started
• Useful Tips
• Useful Resources
• Acknowledgement
• Notes
• License

Requirements

• Operating System:
  • Windows:
    • The framework has been tested with Windows 7 and Windows 10.
  • macOS:
    • The framework has been tested with IOS 12.
• Software:
  • MATLAB:
    • This package has been tested with MATLAB R2017b and R2018a. The additional required tool boxes/solvers are:
      • CVX: Disciplined convex programming for MATLAB.
      • MATPOWER: A power system simulation and optimization tool for MATLAB
    • For more information on these packages, please visit CVX Research, and MATPOWER.

Package Organization

The folders of the repository are:

• DistributionNetworks
  • Data-based distributionally robust stochastic OPF sub-package for distribution networks, which includes one main script and two additional functions.
    1. the main script of this sub-package is main_distribution.m.
    2. network admittance generation function is form_admittance.m.
    3. SDP relaxation solver for optimal power flow is getVSDP.m.
    4. Note: make sure CVX is installed properly.
• TransmissionSystems
  • Data-based distributionally robust stochastic OPF sub-package for transmission systems, which includes one main script.
    1. the main script of this sub-package is main_transmission.m.
    2. Note: make sure MATPOWER and CVX are installed properly.
• CVX
  • Convex optimization modeling language for MATLAB.
• MATPOWER
  • A power system simulation and optimization package for MATLAB.

Capabilities of framework

Overvoltage problem for distribution networks

This sub-package provides a computationally-affordable chance-contrained AC OPF framework to solve an overvoltage problem for IEEE 37-node distribution network. The proposed distributionally robust stochastic OPF methodologies mitigate overvoltages by controlling set points for renewable energy resources and energy storage devices. The set points of controllable devices are repeatedly optimized over a finite planning horizon within a MPC feedback scheme. The risk conservativeness of the voltage magnitude constraints and the out-of-sample performance robustness to sampling errors are explicitly adjustable by two scalar parameters (e.g., weight factor and Wasserstein distance).

N-1 Security problem for transmission systems

This sub-package provides a computationally-affordable chance-contrained DC OPF framework to solve a N-1 security problem for IEEE 118-bus transmission system. The proposed distributionally robust stochastic OPF will determine scheduled power output adjustments and reserve policies of generators, which specify planned reactions to wind power forecast errors in order to accommodate fluctuating renewable energy sources. The risk conservativeness of the line flow constraints and the out-of-sample performance robustness to sampling errors are explicitly adjustable by two scalar parameters (e.g., weight factor and Wasserstein distance).

Getting Started

The framework works in principle for any forecast method. The user needs to import forecast error data into this framework, (e.g., solar power forecast scenarios for distribution networks and wind power forecast error scenarios for transmission networks). In order to run this framework, the forecast data should be organized in the following format:

For distribution networks

Two MATLAB data files .mat are required in this sub-package: solar power forecast scenarios dataset and electric power loads dataset. The solar power forecast scenarios dataset will be imported in main_distribution.m by the command

load('solar.mat')

• three matrices contained data for different usages.
• first matrix, PV_Real24 contains the nominal solar power forecast in kW, which defined in the dimension PV_Real24 (Timestep,1).
• second matrix, PV_Errors_MPC_S contains forecast error scenarios of solar power within finite time horizon in kW, which defined in the dimension PV_Errors_MPC_S (Timestep, Horizon, DRScenarios).
• third matrix, PV_MC contains scenarios of solar power output for Monte Carlo simulation in kW, which defined in the dimension PV_MC (Timestep, MCScenarios).
• Note that all three matrices represent aggregated power output of PV inverters one node, the framework will do the distribution over the feeder.

Electric power loads dataset will be imported in main_distribution.m by the commend

load('load.mat')

• two matrices contain active power and reactive power loads for every node.
• P_l contains the deterministic active power loads in kW, which defined in the dimension P_l (Nnode, Timestep).
• Q_l contains the deterministic reactive power loads in kvar, which defined in the dimension Q_l (Nnode, Timestep).

The Timestep indicates the number of total timesteps; DRScenarios is the number of total scenarios for distributionally robust optimization; MCScenarios is the number of total scenarios for Monte Carlo simulation; Horizon is the finite time horizon setting of model predictive control; Nnode indicates the number of nodes in the distribution network.

For transmission systems

One MATLAB data file .mat is required in this sub-package: wind power forecast error scenarios dataset, which will be imported in main_transmission.m by the command

load('wind.mat')

• three vectors contain wind power forecast error scenarios (in MW) for each individual wind farm.
• G_error_1 contains the wind power forecast error scenarios for wind farm #1 (at bus 1), which defined in the dimension G_error_1 (DRScenarios, 1).
• G_error_2 contains the wind power forecast error scenarios for wind farm #2 (at bus 9), which defined in the dimension G_error_2 (DRScenarios, 1).
• G_error_3 contains the wind power forecast error scenarios for wind farm #3 (at bus 26), which defined in the dimension G_error_3 (DRScenarios, 1).

The DRScenarios is the number of scenarios for distributionally robust optimization.

Useful Tips

1. We recommend the MOSEK solver for distributionally robust optimizatoin, and SDPT3 solver for SDP relaxation problem. Note that Implementing MOSEK solver may request CVX academic license, which you may possibly apply from CVX Research.

Useful Resources

Further details on the mathematical formulation and example numerical results can be found in the following papers.

1. Y. Guo, K. Baker, E. Dall'Anese, Z. Hu and T.H. Summers, "Data-based distribubtionally robust stochastic optimal power flow, Part I: Methodologies", IEEE Transactions on Power Systems, vol.34, no.2, pp.1483-1492, March 2019.
2. Y. Guo, K. Baker, E. Dall'Anese, Z. Hu and T.H. Summers, "Data-based distribubtionally robust stochastic optimal power flow, Part II: Case studies", IEEE Transactions on Power Systems, vol.34, no.2, pp.1493-1503, March 2019.
3. Y. Guo, K. Baker, E. Dall'Anese, Z. Hu and T.H. Summers, "Stochastic optimal power flow based on data-driven distributionally robust optimization", 2018 Annual American Control Conference (ACC), Milwaukee, WI, June 2018.

Notes

The following links provide an access to publicly available data of renewable energy resources (RESs).

• National solar radiation databased (NSRDB).
• Global Energy Forecasting Competition 2012. Note that the solar radiation data used in the papers above are different from the publicly available data, so the plots from this package using different forecase error data will differ from the figures presented in the above papers.

Acknowledgement

This material is based on work supported by the National Science Foundation (NSF) under grant CNS-1566127.

License

MIT License

Copyright (c) 2018, Yi Guo, Tyler Summers (PI), Control, Optimization and Networks Laboratory, Department of Mechanical Engineering, The University of Texas at Dallas, Richardson, TX, USA.

Emails: yi.guo2@utdallas.edu, tyler.summers@utdallas.edu.

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.