Abstract
To ensure the safety and reliability of the distribution network and adapt to the uncertain development of renewable energy sources and loads, a two-stage distributionally robust optimization model is proposed for the active distribution network (ADN) optimization problem considering the uncertainties of the source and load in this paper. By establishing an ambiguity set to capture the uncertainties of the photovoltaic (PV) power, wind power and load, the piecewise-linear function and auxiliary parameters are introduced to help characterize the probability distribution of uncertain variables. The optimization goal of the model is to minimize the total expected cost under the worst-case distribution in the ambiguity set. The first-stage expected cost is obtained based on the predicted value of the uncertainty variable. The second-stage expected cost is based on the actual value of the uncertainty variable to solve the first-stage decision. The generalized linear decision rule approximates the two-stage optimization model, and the affine function is introduced to provide a closer approximation to the second-stage optimization model. Finally, the improved IEEE 33-node and IEEE 118-node systems are simulated and analyzed with deterministic methods, stochastic programming, and robust optimization methods to verify the feasibility and superiority of the proposed model and algorithm.
Highlights
As renewable energy, which is based on photovoltaic (PV) and wind turbine (WT) power, increasingly penetrates the distribution network [1, 2], its uncertainty and volatility bring great challenges to the optimal operation of the distribution network [3, 4]
This paper establishes an active distribution network (ADN) scheduling model that considers the uncertainties of the source and load based on a distributionally robust optimization method, and introduces an ambiguity set to capture the uncertainties of renewable energy outputs and load
The auxiliary variable u is introduced into the original ambiguity set F, which imposes a tighter upper bound on the piecewise linear function gk; this increases the flexibility of the linear decision rules, and helps to reduce the conservative degree of the optimization solution
Summary
As renewable energy, which is based on photovoltaic (PV) and wind turbine (WT) power, increasingly penetrates the distribution network [1, 2], its uncertainty and volatility bring great challenges to the optimal operation of the distribution network [3, 4]. Due to the improved modeling capabilities, the two-stage robust optimization method has become a popular decision-making tool for power system scheduling problems In practical problems, both risk and ambiguity should be considered when modeling an optimization problem under uncertainty. This paper establishes an ADN scheduling model that considers the uncertainties of the source and load based on a distributionally robust optimization method, and introduces an ambiguity set to capture the uncertainties of renewable energy outputs and load. It uses the generalized linear decision rule to approximate the two-stage model strictly to reduce the conservativeness of the optimal solution obtained by the robust optimization method. The simulations are performed on the improved IEEE 33-node and IEEE 118-node systems for comparison with the deterministic, stochastic programming, and robust optimization methods to verify the validity and superiority of the proposed model and method
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