Chen Shen

Zhiwen Wang, Chen Shen, Yin Xu et al.

Microgrids are resources that can be used to restore critical loads after a natural disaster, enhancing resilience of a distribution network. To deal with the stochastic nature of intermittent energy resources, such as wind turbines (WTs) and photovoltaics (PVs), many methods rely on forecast information. However, some microgrids may not be equipped with power forecasting tools. To fill this gap, a risk-limiting strategy based on measurements is proposed. Gaussian mixture model (GMM) is used to represent a prior joint probability density function (PDF) of power outputs of WTs and PVs over multiple periods. As time rolls forward, the distribution of WT/PV generation is updated based the latest measurement data in a recursive manner. The updated distribution is used as an input for the risk-limiting load restoration problem, enabling an equivalent transformation of the original chance constrained problem into a mixed integer linear programming (MILP). Simulation cases on a distribution system with three microgrids demonstrate the effectiveness of the proposed method. Results also indicate that networked microgrids have better uncertainty management capabilities than stand-alone microgrids.

Mengshuo Jia, Chen Shen, Zhaojian Wang

Due to the uncertainty of distributed wind generations (DWGs), a better understanding of the probability distributions (PD) of their wind power forecast errors (WPFEs) can help market participants (MPs) who own DWGs perform better during trading. Under the premise of an accurate PD model, considering the correlation among DWGs and absorbing the new information carried by the latest data are two ways to maintain an accurate PD. These two ways both require the historical and latest wind power and forecast data of all DWGs. Each MP, however, only has access to the data of its own DWGs and may refuse to share these data with MPs belonging to other stakeholders. Besides, because of the endless generation of new data, the PD updating burden increases sharply. Therefore, we use the distributed strategy to deal with the data collection problem. In addition, we further apply the incremental learning strategy to reduce the updating burden. Finally, we propose a distributed incremental update scheme to make each MP continually acquire the latest conditional PD of its DWGs' WPFE. Specifically, we first use the Gaussian-mixture-model-based (GMM-based) joint PD to characterize the correlation among DWGs. Then, we propose a distributed modified incremental GMM algorithm to enable MPs to update the parameters of the joint PD in a distributed and incremental manner. After that, we further propose a distributed derivation algorithm to make MPs derive their conditional PD of WPFE from the joint one in a distributed way. Combining the two original algorithms, we finally achieve the complete distributed incremental update scheme, by which each MP can continually obtain its latest conditional PD of its DWGs' WPFE via neighborhood communication and local calculation with its own data. The effectiveness, correctness, and efficiency of the proposed scheme are verified using the dataset from the NREL.

Kaihua Xi, Hai Xiang Lin, Chen Shen et al.

A consensus-control-based multi-level control law named Multi-Level Power-Imbalance Allocation Control (MLPIAC) is presented for a large-scale power system partitioned into two or more areas. Centralized control is implemented in each area while distributed control is implemented at the coordination level of the areas. Besides restoring nominal frequency with a minimal control cost, MLPIAC can improve the transient performance of the system through an accelerated convergence of the control inputs without oscillations. At the coordination level of the control areas, because the number of the areas is smaller than that of nodes, MLPIAC is more effective to obtain the minimized control cost than the purely distributed control law. At the level of the control in each area, because the number of nodes is much smaller than the total number of nodes in the whole network, the overheads in the communications and the computations are reduced compared to the pure centralized control. The asymptotic stability of MLPIAC is proven using the Lyapunov method and the performance is evaluated through simulations.

Zhiwen Wang, Chen Shen, Feng Liu et al.

With the fast growth of wind power penetration, power systems need additional flexibility to cope with wind power ramping. Several electricity markets have established requirements for flexible ramping capacity (FRC) reserves. This paper addresses two crucial issues that have rarely been discussed in the literature: 1) how to characterize wind power ramping under different forecast values and 2) how to achieve a reasonable trade-off between operational risks and FRC costs. Regarding the first issue, this paper proposes a concept of conditional distributions of wind power ramping, which is empirically verified by using simulation and real-world data. For the second issue, this paper develops an adjustable chance-constrained approach to optimally allocate FRC reserves. Equivalent tractable forms of the original problem are devised to improve computational efficiency. Tests carried out on a modified IEEE 118-bus system demonstrate the effectiveness and efficiency of the proposed method.

Mengshuo Jia, Shaowei Huang, Zhiwen Wang et al.

Building the conditional probability distribution of wind power forecast errors benefits both wind farms (WFs) and independent system operators (ISOs). Establishing the joint probability distribution of wind power and the corresponding forecast data of spatially correlated WFs is the foundation for deriving the conditional probability distribution. Traditional parameter estimation methods for probability distributions require the collection of historical data of all WFs. However, in the context of multi-regional interconnected grids, neither regional ISOs nor WFs can collect the raw data of WFs in other regions due to privacy or competition considerations. Therefore, based on the Gaussian mixture model, this paper first proposes a privacy-preserving distributed expectation-maximization algorithm to estimate the parameters of the joint probability distribution. This algorithm consists of two original methods: (1) a privacy-preserving distributed summation algorithm and (2) a privacy-preserving distributed inner product algorithm. Then, we derive each WF's conditional probability distribution of forecast error from the joint one. By the proposed algorithms, WFs only need local calculations and privacy-preserving neighboring communications to achieve the whole parameter estimation. These algorithms are verified using the wind integration data set published by the NREL.