Stochastic Optimal Power Flow Research Articles

Two-Level Dynamic Stochastic Optimal Power Flow Control for Power Systems With Intermittent Renewable Generation

High penetration of intermittent renewable energy imposes new challenges to the operation and control of power systems. Power system security needs to be ensured dynamically as the system operating condition continuously changes. The dynamic stochastic optimal power flow (DSOPF) control algorithm using the Adaptive Critic Designs (ACDs) has shown promising dynamic power flow control capability and has been demonstrated in a small system. To further investigate the potential of the DSOPF control algorithm for large power systems, a 70-bus test power system with different generation resources, including large wind plants, is developed. A two-level DSOPF control scheme is proposed in this paper to scale up the DSOPF algorithm for this 70-bus system. The lower-level area DSOPF controllers control their own area power network. The top-level global DSOPF controller coordinates the area controllers by adjusting the inter-area tie-line flows. This two-level architecture distributes the control and computation burden to multiple area DSOPF controllers, and reduces the training difficulty for implementing the DSOPF control for a large power network. Simulation studies on the 70-bus power system with large wind variation are shown to demonstrate the effectiveness of the proposed two-level DSOPF control scheme.

A Stochastic Optimal Power Flow Problem With Stability Constraints—Part II: The Optimization Problem

Stochastic optimal power flow can provide the system operator with adequate strategies for controlling the power flow to maintain secure operation under stochastic parameter variations. One limitation of stochastic optimal power flow has been that only limits on line flows have been used as stability constraints. In many systems voltage stability and small-signal stability also play an important role in constraining the operation. In this paper we aim to extend the stochastic optimal power flow problem to include constraints for voltage stability as well as small-signal stability. This is done by approximating the voltage stability and small-signal stability constraint surfaces with second-order approximations in parameter space. Then we refine methods from mathematical finance to be able to estimate the probability of violating the constraints. In this, the second part of the paper, we look at how Cornish-Fisher expansion combined with a method of excluding sets that are counted twice, can be used to estimate the probability of violating the stability constraints. We then show in a numerical example how this leads to an efficient solution method for the stochastic optimal power flow problem.

A Stochastic Optimal Power Flow Problem With Stability Constraints—Part I: Approximating the Stability Boundary

Stochastic optimal power flow can provide the system operator with adequate strategies for controlling the power flow to maintain secure operation under stochastic parameter variations. One limitation of stochastic optimal power flow has been that only line flows have been used as security constraints. In many systems voltage stability and small-signal stability also play an important role in constraining the operation. In this paper we aim to extend the stochastic optimal power flow problem to include constraints for voltage stability as well as small-signal stability. This is done by approximating the voltage stability and small-signal stability constraint boundaries with second-order approximations in parameter space. Then we refine methods from mathematical finance to be able to estimate the probability of violating the constraints. In this first part of the paper, we derive second-order approximations of stability boundaries in parameter space. In the second part, the approximations will be used to solve a stochastic optimal power flow problem.

Wide-Area Measurement Based Dynamic Stochastic Optimal Power Flow Control for Smart Grids With High Variability and Uncertainty

To achieve a high penetration level of intermittent renewable energy, the operation and control of power systems need to account for the associated high variability and uncertainty. Power system stability and security need to be ensured dynamically as the system operating condition continuously changes. A wide-area measurement based dynamic stochastic optimal power flow (DSOPF) control algorithm using the adaptive critic designs (ACDs) is presented in this paper. The proposed DSOPF control replaces the traditional AGC and secondary voltage control, and provides a coordinated AC power flow control solution to the smart grid operation in an environment with high short-term uncertainty and variability. The ACD technique, specifically the dual heuristic dynamic programming (DHP), is used to provide nonlinear optimal control, where the control objective is explicitly formulated to incorporate power system economy, stability and security considerations. The proposed DSOPF controller dynamically drives the power system to its optimal operating point by continuously adjusting the steady-state set points sent by the traditional OPF algorithm. A 12-bus test power system is used to demonstrate the development and effectiveness of the proposed DSOPF controller.

An Implementation of the Stochastic OPF Problem

This paper presents an algorithm for solution of the stochastic optimal power flow (OPF) problem. The stochastic OPF problem minimizes the total cost of a base-case operating state plus the expected cost of recovery from contingencies such as line or generator outages. The algorithm presented is based on a cutting plane method that decomposes the OPF problem into smaller subproblems, which can be solved quickly and efficiently. The solutions of the individual subproblems are coordinated by the addition of linear constraints to a master problem. Typical results show a slight increase in the cost of the base-case operating state but a significant reduction in the expected cost of contingency recovery.

Stochastic optimal load flow using a combined quasi-Newton and conjugate gradient technique

This paper treats the problem of optimal power flow in electric power systems using a method which includes the effects of uncertain variables in formulating the problem for an all thermal electric power system. The method assumes that the system power demand is random and is normally distributed with zero mean and unit variance. The equality constraints associated with the formulation are the power flow equations in polar form utilizing the nodal admittance matrix approach. The non-linear programming technique of Powell's penalty function is used to allow the incorporation of inequality constraints in the formulation. The resulting stochastic optimal power flow problem reduces to one of solving a set of non-linear equations. Here we use a technique that combines the quasi-Newton method and the conjugate gradient method in what is referred to as the CONMIN algorithm. Computational implementation results involving four IEEE standard test networks are given to demonstrate the validity of this method.

Stochastic Optimal Load Flow Using Newton-Raphson Iterative Technique

ABSTRACT In this paper we consider the problem of stochastic optimal power flow for an all thermal electric power system. The formulation includes the effects of variables uncertainty modeled as stochastic and normally distributed. The system performance is represented by the load flow equations in polar form, reformulated to include the uncertainty aspect. Inequality constraints are handled using Powell's penalty function method. We employ a variational approach to derive the optimality conditions resulting in a set of nonlinear equations. Newton's method is employed, to actually implement the optimum strategy by solving the nonlinear set of optimality conditions iteratively. An application example involving the IEEE standard 14 bus system is presented and the stochastic solution is compared with a deterministic solution for the same system in order to demonstrate the applicability of the proposed method.