sopflow.md

Stochastic security-constrained multi-period optimal power flow (SOPFLOW)

SOPFLOW solves a stochastic security-constrained multi-period optimal power flow problem. The problem is set up as a two-stage optimization problem where the first-stage (base-case) represents the normal operation of the grid (or the most likely forecast) and the second-stage comprises of $N_s$ scenarios of forecast deviation. Compactly, the problem can be set up in the following form:

$$\begin{aligned} \text{min}&~\sum_{s=0}^{N_s-1}\pi_s\sum_{c=0}^{N_c-1}\sum_{t=0}^{N_t-1}f(x_{s,c,t})& \\\ &\text{s.t.}& \\\ &~g(x_{s,c,t}) = 0, &s \in \{1,N_s-1\},c \in \{0,N_c-1\}, t \in \{0,N_t-1\}& \\\ &~h(x_{s,c,t}) \le 0, &s \in \{1,N_s-1\},c \in \{0,N_c-1\}, t \in \{0,N_t-1\}& \\\ x^- & \le x_{s,c,t} \le x^+, &s \in \{1,N_s-1\},c \in \{0,N_c-1\}, t \in \{0,N_t-1\}& \\\ -\Delta x_t & \le x_{s,c,t} - x_{s,c,t-\Delta{t}} \le \Delta x_t,&s \in \{1,N_s-1\},c \in \{0,N_c-1\}, t \in \{1,N_t-1\}&\\\ -\Delta x_c & \le x_{s,c,0} - x_{s,0,0} \le \Delta x_c,&s \in \{1,N_s-1\},c \in \{1,N_c-1\}& \\\ -\Delta x_s & \le x_{s,0,0} - x_{0,0,0} \le \Delta x_s,&s \in \{1,N_s-1\}& \end{aligned}$$

where $N_s$ is the number of scenarios, $N_c$ is the number of contingencies, $N_t$ is the number of periods and $\pi_s$ is the probability of the scenario. Each scenario can either be an optimal power flow (see OPFLOW) or security-constrained optimal power flow (see SCOPFLOW). Each security-constrained optimal power flow case can be single or multi-period. The last equation is the coupling between the 2nd stage forecast deviations and the base case. Depending on the mode, SOPFLOW can either be preventive (mode = 0) or corrective (mode = 1). In the preventive mode, generator real power output is fixed to the base-case values except for any renewable generation (wind, solar), and generators at reference bus(es).The corrective mode allows deviation of the PV and PQ generator real power from the base-case dispatch constrained by its 30-min. ramp rate capability.

Depending on the options chosen, SOPFLOW can be run in three modes:

1. Single-period no-contingency stochastic optimal power flow
2. Single-period multi-contingency stochastic optimal power flow
3. Multi-period multi-contingency stochastic optimal power flow

Dependency

To use this application, one must have ExaGO built with Ipopt. Even when using HiOp as the main solver, this application still uses Ipopt (to solve the base subproblem).

Usage

The SOPFLOW code is executed via

mpiexec -n <N> ./sopflow <options>

where <options> are the available command line options as given in the next section.

Options

The current version has several options available for SOPFLOW. These options can be set either through the options file options/sopflowoptions or via the command line.

Option Name	Description	Values (Default value)	Compatibility
-netfile	Name of network file in MATPOWER format	(case9mod.m)	4096 characters max.
-windgen	Name of wind scenario list file	(10_scenarios_9bus.csv)	4096 characters max. Uses a native format for describing scenarios. See 10_scenarios_9bus.csv
-ctgcfile	Name of contingency list file		4096 characters max. Uses a native format for describing contingencies.
-sopflow_Ns	Number of scenarios		With this option set, SOPFLOW will only pick up the first Ns scenarios in the scenario file. To select all scenarios, use Ns = -1
-sopflow_model	SOPFLOW model type	GENRAMP, GENRAMPC (GENRAMP)
-sopflow_solver	Optimization solver	(Ipopt), HiOp, or EMPAR	See the note below on solvers
-sopflow_mode	Mode of operation	0 or 1 (0)	See the note below on mode of operation
-sopflow_subproblem_solver	Optimization solver for the subproblem when using HiOp solver	Ipopt or HiOp (Ipopt)	See opflow page for description of solvers
-sopflow_subproblem_model	Model for the subproblem when using HiOp solver	(POWER_BALANCE_POLAR)	See opflow page for available models
-sopflow_tolerance	Optimization solver tolerance	(1e-6)	All solvers
-sopflow_enable_multicontingency	Each scenario has multiple contingencies	0 or 1 (0)
-sopflow_Nc	Number of contingencies		With this option set, SOPFLOW will only pick up the first Nc contingencies in the contingency file. To select all contingencies, use Nc = -1
-sopflow_flatten_contingencies	Flattens out the scenario-contingency structure	0 or 1 (0)	Only used when multi-contingency is enabled
-print_output	Print SOPFLOW solution to screen	0 or 1 (0)	All solvers
-save_output	Save SOPFLOW solution to file	0 or 1 (0)	All solvers. Saves solution for each scenario.

Scenarios

There are two types of uncertainties supported: Wind generation and load (currently not implemented). Scenarios are specified in a native format. See datafiles/case9/10scenarios_9bus.csv as an example of a scenario file that describes wind generation scenarios for the 9-bus case.

Solver

SOPFLOW supports solving the problem using Ipopt, HiOP, or EMPAR solvers. With Ipopt, SOPFLOW can be only run on one processor (N = 1) as Ipopt only supports single process execution. HiOp supports solving the problem in parallel using a primal-decomposition algorithm. EMPAR is a parallel solver, however it merely executes an embarassingly parallel solver, i.e., all the scenarios are solved independently via optimal power flow.

Mode

Set SOPFLOW to either run in preventive (0) or corrective (1) mode. In preventive mode, the base-case and scenario real-power dispatch is equal for the PV and PQ generators. Any power surplus/deficit is contributed by the swing generator only. In the corrective mode, the scenario real-power dispatch for all generators is allowed to deviate from the base-case limited by its 30-min ramping limit.