As the rapid development of natural-gas fired units (NGUs), power systems begin to rely more on a natural gas system to supply the primary fuel. On the other hand, natural gas system contingency might cause the nonavailability of NGUs and inevitably jeopardize power system security. To address this issue, this paper studies security-constrained joint expansion planning problems for this combined energy system. We develop a computationally efficient mixed-integer linear programming (MILP) approach that simultaneously considers N-1 contingency in both natural gas system and electricity power system. To reduce the combinatorial search space of MILP models, an extension of a reduced disjunctive model is proposed to decrease the numbers of binary and continuous variables as well as constraints. The involving nonlinear terms in N-1 constraints are exactly linearized without sacrificing any optimality. Numerical results on two typical integrated energy systems demonstrate the necessity of extending N-1 criterion to the whole network of a combined energy system. Experimental results also show that compared with the conventional approach, our proposed MILP approach achieves a great computational performance improvement in solving security-constrained co-optimization expansion planning problems.

Compared with commonly-used point forecasting, probabilistic forecasting provides quantitative information on the uncertainty associated with wind power output. However, most studies focus on modelling only a fixed set of quantiles or intervals, which cannot provide the entire information of wind power distribution. In this paper, we propose a non-parametric and flexible method for probabilistic wind power forecasting. First, the distribution of wind power output is specified by spline quantile function, which avoids assuming a parametric form and also provides flexible shape for wind power density. Then, autoregressive recurrent neural network is used to build the non-linear mapping from input features to the parameters of quadratic spline quantile function. A novel loss function based on continuous ranked probability score (CRPS) is designed to train the forecasting model. We also derive the closed-form solution of the integral required in computing the CRPS-based loss function in order to improve the computational efficiency in training. The effectiveness of our proposed method has been validated with public real-world data from Global Energy Forecasting Competition 2014. Compared with some advanced benchmarks, our proposed approach outperforms them at least six percent in terms of CRPS, indicating that it can provide probabilistic wind power forecasting with high quality.

Using off-site predictors to capture spatio-temporal correlations among geographically distributed wind farms is seen as one solution to improve the forecast accuracy of wind power generation. However, in practice, wind farm operators are usually unwilling to share their private data with each other because of competitive reasons and security considerations. To address this issue, this paper presents how wind power probabilistic forecasting using off-site information could be achieved in a privacy-preserving and distributed fashion. Wind power probabilistic forecasts are created by means of multiple quantile regression. The original large-scale forecasting problem is first decomposed into a large number of small-scale subproblems. The subproblem can be computed locally on each farm. Then, the closed-form solution to the subproblem is derived exactly for achieving high computational efficiency. The proposed approach offers a flexible framework for using off-site information, but without having to exchange commercially sensitive data among all participants. It relies on the alternating direction method of multipliers algorithm to achieve the cooperation among all participants and finally converges to the optimal solution. Case studies with real-world data validate improvements in the forecast accuracy when considering spatio-temporal correlations. Distributed approaches also show higher computational efficiency than traditional centralized approaches.

To improve the frequency stability of power systems with a high penetration of converter-based generators, this paper proposes an Enhanced Frequency-Constrained Unit Commitment (E-FCUC) considering variable-droop-controlled Frequency Control (FC) from converter-based generators. Unlike previous studies emphasizing conventional and fix-droop converter-based generators participating in primary frequency response, the impact of converter-based generators with variable-droop FC schemes is investigated, modeled, and then incorporated into the UC problems. Firstly, the transfer function of variable-droop-controlled converter-based generators is modeled; then the available primary power reserves bounding provided by converter-based generators is derived. Secondly, the frequency dynamic of power systems considering joint frequency control from conventional generators and variable-droop-controlled converter-based generators is derived based on an analytical aggregated System Frequency Response (SFR) model. Since the nonlinear non-smooth nature of frequency dynamic function, the max-affine Piece Wise Linearization (PWL) method is used to fitting the dynamic frequency function. The fitting function is subsequently reformulated into mix-integer linearized constraints participating in UC studies. Case studies based on a modified IEEE 6 bus test system and a modified IEEE 118 bus test system are carried out to verify the effectiveness of the proposed E-FCUC through comparisons of results with existing empirical models.