In this study, a linearized and convergence-guaranteed optimal power flow (OPF) model with reactive power (Q ) and voltage magnitude (v) is proposed. Based on a linearized network model, a fully linearly-constrained OPF model is formulated with constraints on Q and v and limits on the apparent branch flow. Compared with the commonly used DC OPF method, the proposed method narrows the deviation from the AC OPF solution without requiring any additional information of the power grid. The locational marginal price (LMP) of the proposed method is closer to the AC OPF solution than the DC OPF method. The marginal price of the reactive power (Q-LMP) is provided, which offers the opportunity to price the reactive power. Case studies on several IEEE and Polish benchmark systems show that the proposed OPF method substantially enhances the performance of the prevalent DC OPF method. In addition, it is shown that if the accuracy of the linearized network model needs to be further improved, such as that during the iterative quasi-optimization process that reconstitutes the AC feasibility, a solution that is notably close to the optimum of the AC OPF model can be obtained by taking only one more iteration.

Linear power flow models are widely used in power systems to simplify the nonlinear power flow equations. The DC power flow model is one of the representatives. There are many other linear power flow models that improve the DC power flow model with the inclusion of Q and $v$ . However, existing linear models are derived based on empirical mathematical approximation without a general methodology guidance. In this paper, we found that the fundamental difference among different linear power flow models lies in the formulation of “independent variables”. Based on this finding, a general formulation of linear power flow models is proposed. The linearization error is theoretically analyzed. In particular, the case when $\theta$ and $v^k$ are regarded as independent variables is thoroughly investigated. Method for finding the linear power flow with the minimum error is presented. The formulation of the independent variables associated with the minimum linearization error is determined by the distribution of state variables $v$ and $\theta$ . It is shown that the linearization error when $v^2$ is regarded as an independent variable is normally smaller than that for v because of the special properties of the distribution of $v$ in power grids.

This paper proposes a data-driven approach for optimal power flow (OPF) based on the stacked extreme learning machine (SELM) framework. SELM has a fast training speed and does not require the time-consuming parameter tuning process compared with the deep learning algorithms. However, the direct application of SELM for OPF is not tractable due to the complicated relationship between the system operating status and the OPF solutions. To this end, a data-driven OPF regression framework is developed that decomposes the OPF model features into three stages. This not only reduces the learning complexity but also helps correct the learning bias. A sample pre-classification strategy based on active constraint identification is also developed to achieve enhanced feature attractions. Numerical results carried out on IEEE and Polish benchmark systems demonstrate that the proposed method outperforms other alternatives. It is also shown that the proposed method can be easily extended to address different test systems by adjusting only a few hyperparameters.

Probabilistic power flow (PPF) plays a critical role in power system analysis. However, the high computational burden makes it challenging for the practical implementation of PPF. This paper proposes a model-based deep learning approach to overcome the computational challenge. A deep neural network (DNN) is used to approximate the power flow calculation and is trained according to the physical power flow equations to improve its learning ability. The training process consists of several steps: 1) the branch flows are added into the objective function of the DNN as a penalty term, which improves the approximation accuracy of the DNN; 2) the gradients used in the back propagation process are simplified according to the physical characteristics of the transmission grid, which accelerates the training speed while maintaining effective guidance of the physical model; and 3) an improved initialization method for the DNN parameters is proposed to improve the convergence speed. The simulation results demonstrate the accuracy and efficiency of the proposed method in standard IEEE and utility benchmark systems.

The data-driven method with strong approximation capabilities and high computational efficiency provides a promising tool for optimal power flow (OPF) calculation with stochastic renewable energy. However, the topology change dramatically increases the learning difficulties and the demand for learning samples. In this work, we propose a physics-guided graph convolution neural network (GCNN) for OPF calculation with consideration of varying topologies, including the physics-guided graph convolution kernel, feature construction, and loss function formulation. Specifically, a physics-embedded graph convolution kernel is derived by aggregating the features from local neighborhoods utilizing the nodal OPF model formulation. An iterative feature construction method is also developed that encodes both the physical feature and practical constraints into the node vector. Finally, a correlative learning loss function to optimize the unbalanced power injection is developed. Extensive numerical results carried out on various IEEE test systems show that the prediction accuracy of OPF using the proposed method under varying topology changes can be improved by an average of 13.30% and up to 32.63% compared with state-of-the-art methods.

In this study, the authors introduce a new solution to the alternating current optimal power flow problem based on successive linear approximation of power flow equations. The polar coordination of the power flow equations is used to take advantage of the quasi‐linear P– θ relationship. A mathematical transformation for the crossing term of voltage magnitude is used, which guarantees the accuracy of the linear approximation when the quality of initial points regarding voltage magnitude is relatively low in the first few iterations. As a result, the accuracy of the proposed approximation becomes very high in very few iterations. Linearisation method for the quadratic apparent branch flow limits is provided. Methods to recover the AC feasibility from the obtained optimal power flow solution and correct possible constraint violations are introduced. The proposed method is tested in several IEEE and Polish benchmark systems. The difference in objective functions relative to MATPOWER benchmark results is generally <0.1% when the algorithm terminates.