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Multi-Period Optimal Power Flow for Active Distribution Systems with Spatially Distributed Computation

MATLAB 62.90% Julia 37.04% Python 0.06%

battery-storage ieee123 inverter-control multi-period-optimization optimal-power-flow photovoltaics spatial-decomposition branch-flow-model multi-period-optimal-power-flow active-power-distribution-system

multiperiod-distopf-benchmark's Introduction

Multi-Period Distributed Optimal Power Flow

Optimization for Balanced Three-Phase Power Distribution Networks with Renewables and Storage in MATLAB.

Naive Brute Force Multi-Period OPF. A spatially decomposed, temporally brute-forced MPOPF has been implemented.

Objectives currently covered:

Loss Minimization

Description of the Modelling of the Radial Power Distribution System

Description of State Variables

Variable Notation	Variable Description	Number of Variables	Nature of Constraint
$P^{t}_{ij}$	Real Power flowing in branch	$m$	Nonlinear
$Q^{t}_{ij}$	Reactive Power flowing in branch	$m$	Nonlinear
$l^{t}_{ij}$	Square of Magnitude of branch Current	$m$	Nonlinear
$v^{t}_{j}$	Square of Magnitude of node Voltage	$N$	Nonlinear
$B^{t}_{j}$	Battery State of Charge	$n_{B}$	Linear

Description of Control Variables

Variable Notation	Variable Description	Number of Variables	Nature of Constraint
$q^{t}_{D_j}$	Reactive Power of DER (via inverter)	$n_{D}$	Linear¹
$P^{t}_{c_j}$	Charging Power of Battery	$n_{B}$	Linear
$P^{t}_{d_j}$	Discharging Power of Battery	$n_{B}$	Linear
$q^{t}_{B_j}$	Reactive Power of Battery (via inverter)	$n_{B}$	Linear¹

Description of Independent Variables

Variable Notation	Variable Description	Number of Variables	Nature of Constraint
$P^{t}_{L_j}$	Real Power Demand	$N$	Linear
$Q^{t}_{L_j}$	Reactive Power Demand	$N$	Linear
$P^{t}_{D_j}$	Real Power of DER	$n_{D}$	Linear¹
$B^{0}_{j}$	Battery Initial State of Charge	$n_{B}$	Linear

Miscellaneous Notation

Variable Notation	Variable Description	Cardinality
$\mathbb{N}$	Set of all the nodes	$N$
$\mathbb{L}$	Set containing all the branches	$m$
$\mathbb{D}$	Set containing all the nodes containing DERs. $\mathbb{D} \subset \mathbb{N}$	$n_{D}$
$\mathbb{B}$	Set containing all the nodes containing Batteries. $\mathbb{B} \subset \mathbb{N}$	$n_{B}$
$\mathbb{T}$	Set containing all the time-periods	$T$
$j$	Denotes a node. $j \in \mathbb{N}$
$(i, j)$	Denotes a branch connecting nodes $i$ and $j$. $(i, j) \in \mathbb{L}$
$t$	Denotes a time-period². $t \in \mathbb{T}$

Notes

Current modelling. Future modelling will incorporate reactive power as a non-linear function wrt maximum apparent power and real power. ↩
Except when used as a superscript in denoting Battery SOC $B^{t}_j$, $t$ refers to the average value of the variable within the time-period $t$. For Battery SOC, $B^{t}_j$ refers to the value of SOC at the end of time-period $t$. ↩

Related: You may also check out the Greedy Single Time Period Sequential OPF Model repo here. Temporal decomposition will be applied there later, after algorithm development.

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dkmahto

multiperiod-distopf-benchmark's Issues

Add B0 value in the SCD plots too. It is mildly annoying to see a decreasing B plot instead of a 'hill'-like plot.

I'm assuming that the x-axes are decoupled anyway. Still it would be cool if they have a head-to-head correlation.

For example the very first purple bar should always match the last one in height, so we should be showing B0 as the first one, not B1.

Add SCD and Battery Energy into simulation result display

MAYBE sometimes DOPF sims are giving more optimal results compared to COPF (MAYBE).
If there is no modelling fault, then I should really check if DOPF is abusing battery energy more (pretty sure SCD is in check for both cases).

Add a Battery Activity/Contribution Metric which shows total abs(Pc)+abs(Pd) for all batteries

Because right now, with the hard terminal SOC constraint in place, whatever contribution batteries have (and they basically don't have any contribution before T = 10, but that's more likely due to a boring time-series), batteries will always give a net 'contribution' of around 0kW, because they need to ensure (about) the same horizon-total amount of charging and discharging in order to arrive at the same SOC as that at the beginning of the Multi Period.
This new metric will really give a much better perspective on the role of the batteries in the grid.

Make root folder selection more systematic, both for `main` and `checkForSCD`

Just realized that if after a simulation I run validate and then run checkForSCD iterations, they are saved wrt validateOPF's path instead of main's path, which is why I see battery scd plots in validateAgainstOpenDSS folder

Add an Optional Separate Plot for `objfunValue_allT vs macroitr`

Add PLoss and PSubsCost vs macroItr plots

Furcate `plot_simulations_results` into independent functions, including the furcation of boundary variable plotting (vs macroItr vs time) and output variable plotting (vs time)

It is mildly annoying to wait for all six boundary convergence plot to show up before I can see my change in output plots. Maybe I can also turn off their showing?

Add an Optional Plot for Demand, PV and Cost Array Forecast

Model battery charge violation as a hard constraint instead of a soft constraint.

In this issue, it was found that COPF and DOPF violate the battery terminal charge penalty (a soft constraint) differently, causing different objective function values between the two simulations. Maybe it is time we put a hard constraint on it closed this gap between the simulations.

Add `QSubs` to the printed result in `main` file

Currently only PSubs is printed out, which is unlike the OpenDSS validation script, which prints out both PSubs, QSubs for power borrowed from the substation.

Use only COPF Area Data to decide GED buses, and figure out a way to ensure DOPF areas use only those buses as their GEDs.

Right now, because of area-wise selection of GED Buses based on a desired DER_percent and Batt_percent, causing discrepancy in both number of GED buses chosen as well as (probably) causing a non-overlapping set of GED buses to be chosen between the two simulations.