Power System Modelling and Simulation Using Collocation Methods

Abstract

Due to diminishing of natural resources and greenhouse effect, renewable energy is wildly used through the world. In South Australia (SA), the total wind power generation provides up to 40% of power supply to the consumer in 2019, and the rooftop solar PV generation installed capacity is steadily increase. Whereas, due to the uncertain and variability features of these renewable generation, their impact on power system planning and operation is significant and needs to be considered. This thesis introduces a novel power system planning tools based on the “so called” collocation method to handle uncertainties and variability. The proposed approach includes three major parts: power system uncertainties modelling; probabilistic power flow (PPF) computation; and guidelines for practical applications in power system planning. First part of the thesis presents methods for power system uncertainties modelling. As an example, uncertainties of SA power network are considered. They include system demand, PV generation, wind power generation, and operation of interconnectors to Victoria (VIC). Historical data is used to construct probabilistic models to represent uncertainties. For system demand, available data are directly used to construct a probabilistic model. Typical type of PV generation in SA is roof top which are evenly spread in each region. Variability patterns of PV generation are highly related to weather and seasons. In addition, those patterns are correlated with the system demand as well. Hence, in our study, the PV generation data are combined with the system demand data. In modelling wind power generation, wind speed data acquired from nearby weather stations are used. Mapping of wind speed data to corresponding wind power generation data is proposed by applying collocation method. Uncertainty in operation of the interconnectors between SA and VIC is accounted for by considering the tie-line as system demand. The second part of the thesis details the PPF computation by using collocation method. The traditional deterministic power flow (DPF) computation method does not consider the probabilistic nature of power system uncertainties, therefore, the calculation results from DPF computation may unrealistically assess the power system performance. Hence, it is imperative to change the DPF computation method to include the impact of those system uncertainties. The commonly used PPF simulation method, the Monte Carlo Simulation (MCS), can calculate accurate simulation results but with expense of high computational burden. To overcome this limitation, collocation method is used to improve the computational efficiency. In this thesis, two collocation methods are proposed to account for different circumstance of PPF analysis. Historical data of SA power system is used to evaluate the practicability and feasibility of those methods. First of those two proposed methods is Probabilistic Collocation Method (PCM) which is based on the orthogonal polynomials and the Gaussian quadrature integration. This mathematical method is based on multivariate interpolation on a regular grid. Its computational efficiency is highly affected by the system dimension. When a system with a small number of uncertainties is considered, the PCM computation is faster than the MCS. However, for high number of system uncertainties the computation time is large and comparable to the MCS method. To overcome this limitation, another collocation method is introduced to solve high dimension PPF analysis, named the Sparse Grid Interpolation (SGI). In this interpolation method only a small subset of regular grid collocation points is used. This approach vastly improves the computation efficiency when handling high dimension PPF computation. In the last part of thesis, the demonstration and guidelines for practical applications of collocation method in power system planning are presented. Comparing with the MCS method, the significant advancement in computation efficiency in solving PPF model of SA makes this method makes this method favourable for practicing engineers. In this part, not just the historical power system data of SA are used, but also the forecasted data. Objective is to predict the impact of varying and increasing demand and generation with uncertainties to the transmission network operation. Computational effectiveness and practicability of the proposed novel methodology is evaluated via comparison with the well-established MCS method.