Zhiwen Wang

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.

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.