Juan Carlos Munoz Guerrero
Affine Arithmetic Based Methods for Transient and Voltage Stability Assessment of Power Systems with Intermittent Sources of Power
Intermittent power sources such as wind and solar are increasingly penetrating electrical grids, mainly motivated by global warming concerns and government policies. These intermittent and non-dispatchable sources of power affect the operation and control of the power system because of the uncertainties associated with their output power. Depending on the penetration level of intermittent sources of power, the electric grid may experience considerable changes in power flows and synchronizing torques associated with system stability, because of the variability of the power injections, among several other factors. Thus, adequate and efficient techniques are required to properly analyze the system stability under such uncertainties.
A variety of methods are available in the literature to perform power flow, transient, and voltage stability analyses considering uncertainties associated with electrical parameters. Some of these methods are computationally inefficient and require assumptions regarding the probability density functions (pdfs) of the uncertain variables that may be unrealistic in some cases. Thus, this thesis proposes computationally efficient Affine Arithmetic (AA)-based approaches for voltage and transient stability assessment of power systems, considering uncertainties associated with power injections due to intermittent sources of power. In the proposed AA-based methods, the estimation of the output power of the intermittent sources and their associated uncertainty are modeled as intervals, without any need for assumptions regarding pdfs. This is a more desirable characteristic when dealing with intermittent sources of power, since the pdfs of the output power depends on the planning horizon and prediction method, among several other factors. The proposed AA-based approaches take into account the correlations among variables, thus avoiding error explosions attributed to other self-validated techniques such as Interval Arithmetic (IA).
The AA-based voltage stability method proposed in the thesis, computes the hull of PV curves associated with the assumed uncertainties, and is tested using two study cases, first, a 5-bus test system is used to illustrate the proposed technique in detail, and thereafter a 2383-bus test system to demonstrate its practical application. The results are compared with those obtained using conventional Monte Carlo Simulations (MCS) to verify the accuracy and computational burden of the proposed AA-based method, and also with respect to a previously proposed technique to estimate parameter sensitivities in voltage stability assessment. On the other hand, the proposed AA-based transient stability assessment method solves the set of Differential-Algebraic Equations (DAEs) in affine form, using a trapezoidal integration approach which leads to the hull of the dynamic response of the system for large disturbances on the system. This approach is tested using a Single Machine Infinite Bus (SMIB) test system with simplified models, and a two-area test system with variable input powers from synchronous generators, and wind turbines based on Doubly Fed Induction Generators (DFIGs). In all study cases, MCS is used for comparison purposes.
The results obtained using the proposed AA-based methods for voltage and transient stability assessment depict a reasonably good accuracy at significantly lower computational costs when compared to those obtained using simulation based techniques. These AA-based methods can be used by system operators to efficiently estimate the system dynamic response and PV curves associated with the input-power uncertainties, and thus devise countermeasures in case of insecure operation.