Uncertainty Tracing of Distributed Generations via Complex Affine Arithmetic Based Unbalanced Three-Phase Power Flow

Abstract

Variations of load demands and generations bring multiple uncertainties to power system operation. Under this situation, power flows become increasingly uncertain, especially when significant distributed generations (DGs), such as wind and solar, are integrated into power systems. In this paper, a Complex Affine arithmetic based unbalanced Three-phase Forward-Backward Sweep power flow model (CATFBS) is proposed to study the impacts of uncertainties in unbalanced three-phase distribution systems. An index of Relative Influence of Uncertain Variables on Outcomes (RIUVO) is proposed for quantifying the impacts of individual uncertain factors on power flows and bus voltages.The CATFBS method is tested on the modified IEEE 13-bus system and a modified 292-bus system. Numerical results show that the proposed method outperforms the Monte Carlo method for exploring the impacts of uncertainties on the operation of distribution systems. The proposed CATFBS method can be used by power system operators and planners to effectively monitor and control unbalanced distribution systems under various uncertainties.

Interval Energy Flow Analysis in Integrated Electrical and Natural-Gas Systems Considering Uncertainties

“…Affine mathematics is an improved form of interval mathematics, which can describe the interconnection between uncertain variables, thus making the calculation results of interval energy flow more precise [37]. A quantityx is represented as an affine form (25):…”

An Affine Arithmetic-Based Power Flow Algorithm Considering the Regional Control of Unscheduled Power Fluctuation

“…indicates the set of buses included in region k; Ω nei k represents the set of neighboring b ion k; NDGR is the number of DGRs in the distribution system; P adj k stands for the adjus ity of the DGR in region k; P dev i and P dev j are maximum unscheduled power fluctuations at b j, which are equal to the deviations in the corresponding interval models of uncertain sou ts of wind turbines and photovoltaic modules, as well as load demands of electric ve ing stations are considered as uncertain sources in this letter, and more details of their inte ls can be found in References [12,13]. For any control region, Equation (1) guarantees tha table capacity of the DGR in this region can cover the corresponding unscheduled po ation; Equation (2) shows that adding any neighboring bus to this region would lead to iciency of the DGR's adjustable capacity.…”

“…Outputs of wind turbines and photovoltaic modules, as well as load demands of electric vehicle charging stations are considered as uncertain sources in this letter, and more details of their interval models can be found in References [12,13]. For any control region, Equation (1) guarantees that the adjustable capacity of the DGR in this region can cover the corresponding unscheduled power fluctuation; Equation (2) shows that adding any neighboring bus to this region would lead to the insufficiency of the DGR's adjustable capacity.…”

Interval power flow analysis via multi-stage affine arithmetic for unbalanced distribution network

“…[27] and [28] generalize the forward-backward sweep method based on affine arithmetic (AA) to three phase unbalanced systems, and an index of relative influence of uncertain variables on outcomes is proposed in Ref. [28] for quantifying the impacts of individual uncertain factors on power flows and bus voltages. Compared to IA, AA could keep track of the linear correlation among different uncertain variables, thus reducing the solution conservatism.…”