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:
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
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 . $t \in \mathbb{T}$
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.