Decentralized Stochastic Optimal Power Flow in Radial Networks With Distributed Generation

Abstract

Abstract-This paper develops a power management scheme that jointly optimizes the real power consumption of programmable loads and reactive power outputs of photovoltaic (PV) inverters in distribution networks. The premise is to determine the optimal demand response schedule that accounts for the stochastic availability of solar power, as well as to control the reactive power generation or consumption of PV inverters adaptively to the real power injections of all PV units. These uncertain real power injections by PV units are modeled as random variables taking values from a finite number of possible scenarios. Through the use of second order cone relaxation of the power flow equations, a convex stochastic program is formulated. The objectives are to minimize the negative user utility, cost of power provision, and thermal losses, while constraining voltages to remain within specified levels. To find the global optimum point, a decentralized algorithm is developed via the alternating direction method of multipliers that results in closed-form updates per node and per scenario, rendering it suitable to implement in distribution networks with large number of scenarios. Numerical tests and comparisons with an alternative deterministic approach are provided for typical residential distribution networks that confirm the efficiency of the algorithm.

Stochastic battery energy storage scheduling considering cell degradation and distributed energy resources

“…We can see from Figure A,B that the variance of the distribution of sum power scenario and forecast power has nearly same tendency, ie, increasing from morning, reach the peak at noon and then decrease to zero at night. This is in consistent with the Beta model in Bazrafshan and Gatsis . Compared with the distributions in Figure A,B, smaller variance (less overall uncertainties) is detected if the DER correlations are not considered.…”

“…Note that the PV units in the distribution network usually have strong correlations. The overall uncertainties could not be caught by separately generating scenarios of each PV unit as in Bazrafshan and Gatsis . The underestimation of overall uncertainties of DERs causes the underestimation of potential voltage instability.…”

“…However, PV unit power in the distribution network has strong dependence, and this could not be considered by the method in Bazrafshan and Gatsis. 23 Up to now, there are a great deal of studies [24][25][26] that focus on the wind power scenario generation methods in the transmission network while less of them are employed in the distribution network. In our previous works, 27 we proposed a scenario generation method to capture the uncertainties and correlations for multiple renewable power plants.…”

“…Renewable power uncertainties and correlations can be represented accurately by renewable power scenarios. Studies in Bazrafshan and Gatsis generate photovoltaic (PV) unit power scenarios by assuming that each PV unit follows a Beta distribution. However, PV unit power in the distribution network has strong dependence, and this could not be considered by the method in Bazrafshan and Gatsis .…”

“…Studies in Bazrafshan and Gatsis generate photovoltaic (PV) unit power scenarios by assuming that each PV unit follows a Beta distribution. However, PV unit power in the distribution network has strong dependence, and this could not be considered by the method in Bazrafshan and Gatsis . Up to now, there are a great deal of studies that focus on the wind power scenario generation methods in the transmission network while less of them are employed in the distribution network.…”