This paper proposes a hierarchical economic dispatch (HED) mechanism for computing distribution locational marginal prices (DLMPs). The HED mechanism involves three levels: 1) the top level is the national (regional) transmission network; 2) the middle level is the distribution network; and while 3) the lowest level reflects local embedded networks or microgrids. Each network operator communicates its generalized bid functions (GBFs) to the next higher level of the hierarchy. The GBFs approximate the true cost function of a network by a series of affine functions. The concept of Benders cuts are employed in simulating the GBFs. The ac optimal power flow (ACOPF) is convexified and then used for dispatching generators and calculating GBFs and DLMPs. The proposed convexification is based on the second order cone reformulation. A sequential optimization algorithm is developed to tighten the proposed second order cone relaxation of ACOPF. The properties of the sequential tightness algorithm are discussed and proved. The HED is implemented in the GAMS grid computing platform. The GBFs and DLMPs are calculated for the modified IEEE 342 node low voltage test system. The numerical results show the utility of the proposed HED and GBF in implementing DLMP.

In this article, the power fluctuation problem caused by adding renewable energy sources to microgrids (MGs) is addressed. These power fluctuations which can cause several adverse effects, including system instability, load shedding, and eventually blackouts are attenuated by designing a load frequency controller (LFC) to provide a constant and uniform frequency in different operation cases of MGs. This article designs a dynamic output feedback controller (DOFC) for LFC in MGs while considering the contraction observer for attack mitigation. We suggest a new formulation of the sufficient conditions for the DOFC design problem in the form of bilinear matrix inequalities (BMIs) and try to minimize the frequency deviation subject to load, solar, and wind energy changes. The proposed formulation effectively changes the problem to a new BMI model which can easily be divided into two problems, one is a convex optimization problem and the remained part is a quadratic matrix inequality problem which is linearized around the feasible solution of the linear matrix inequality part by a Taylor-like expansion. This leads to a more exact and less conservative solution as compared to the previous methods suggested in the literature. To illustrate the merits of the developed approach, numerical simulations on a sample ac–MG are carried out. Comparing norms of the frequency variations in the closed-loop system with multiple prominent methods in previous works, including ${{\bm{H}}_\infty },{\bm{\ \mu }}$ , fuzzy type-1, and intelligent-PI, shows that our proposed method reduces the two and infinity norms of frequency fluctuations by 84% and 80%, respectively compared to the traditional ${{\bm{H}}_\infty }$ method which is the best among the analyzed approaches. This further verifies the efficacy of the designed DOFC in our article.

In this paper, we propose a data-driven algorithm for probabilistic optimal power flow (POPF). In particular, we develop a nonparametric Bayesian framework based on Dirichlet process mixture model (DPMM) and variational Bayesian inference (VBI) to establish a probabilistic model for capturing the uncertainties involved with wind generation and load power in power systems. In the proposed setup, the number of components in the mixture model can be automatically and analytically obtained from the consistently updated data. Moreover, we develop an efficient quasi-Monte Carlo sampling method to draw samples from the obtained DPMM, then propose the dynamic data-driven POPF algorithm. Performance of uncertainty modeling framework on publicly available datasets is examined by extensive numerical simulations. Furthermore, the proposed POPF algorithm is verified on multiple IEEE benchmark power systems. Numerical results show the feasibility and superiority of the proposed DPMM-based POPF algorithm for better informed decision-making in power systems with high level of uncertainties.

Active power losses of distribution systems are higher than transmission ones, in which these losses affect the distribution operational costs directly. One of the efficient and effective methods for power losses reduction is distribution system reconfiguration (DSR). In this way, the network configuration is changed based on a specific power demand that has been already predicted by load forecasting techniques. The ohmic loss level in distribution system is affected by energy demand level, this is while an error in load forecasting can influence losses. Accordingly, including load uncertainty in DSR formulation is essential but this issue should not lead to change of the reconfiguration results significantly (i.e. the model should be robust). This paper presents a robust and efficient model for considering load uncertainty in network reconfiguration that is simple enough to implement in available commercial software packages and it is precise enough to find accurate solutions with low computational time. The analysis of results shows high efficiency and robustness of the proposed model for reconfiguration of distribution systems under demand uncertainty.

This paper proposes a stochastic bilevel program for strategic bidding of a hydropower producer. The price, quantity and ramp-rate bids are considered. The uncertainty of wind power generation, variation of inflows for the hydropower producer, and demand variability are modeled through the momentmatching scenario generation technique. Using discretization the stochastic bilevel program is reformulated as a stochastic mixedinteger linear program (MILP) with disjunctive constraints. We propose a modified Benders decomposition algorithm (MBDA), which fully exploits the disjunctive structure of reformatted MILP model. More importantly, the MBDA does not require optimal tuning of disjunctive parameters and it can be efficiently parallelized. Through an illustrative 5-node example, we identify possible strategies (specific to a hydropower producer) for maximizing profit, which in turn leads to market insights. We also use the IEEE 24-node, 118-node and 300-node case studies to show how our parallelized MBDA outperforms the standard Benders decomposition algorithm. The parallelized MBDA is also compared to the state-of-the-art CPLEX solver.