MVMO-Based Identification of Key Input Variables and Design of Decision Trees for Transient Stability Assessment in Power Systems With High Penetration Levels of Wind Power

Abstract

Unlike synchronous generators, wind turbines cannot directly respond to large disturbances, which may cause transient instability, due to their power electronic-based interface and maximum power control strategy. To effectively monitor the influence of wind turbines, this paper proposes an approach that combines decision trees (DTs), and a newly developed variant of the Mean-Variance Mapping Optimization (MVMO) algorithm, to simultaneously tackle the problem of selecting the key variables that properly reflect the transient stability performance of a system dominated by wind power, and designing the DTs for reliable online assessment of transient stability. The notion of key variables refers to the set of variables that are closely related to the modified power system transient stability performance as a consequence of the replacement of conventional power plants by wind generators. The selection of key variables is formulated as a non-linear optimization problem with weight factors as decision variables and is tackled by MVMO. A weight factor is assigned to each key variable candidate, and its value is considered to reflect the degree of influence of the key variable candidate on the splitting property and estimation accuracy of the DTs. The samples of the key variable candidates and the initialized weight factors are used to build the first group of DTs. Then, MVMO iteratively evolves the weight factors according to its special mapping function with minimizing DTs' estimation error. According to the final list of optimized weight factors, system operators can select a reduced set of variables with the largest weight factors as key variables, depending on the resulting accuracy of the DTs. Meanwhile, DTs built by using key variables are considered as the optimal performance trees for transient stability estimation. In this way, the selection of key variables and the development of DTs are made jointly and automatically, without the interference of the users of the DTs. Test results Wang et al. MVMO Based Transient Stability Assessment on the modified IEEE 9 bus system and a synthetic model of a real power system show that the proposed method can correctly identify the set of key variables related to wind turbine dynamics, as well as its ability to provide a reliable estimation of the transient stability margin.

Power-Angle Modulation Controller to Support Transient Stability of Power Systems Dominated by Power Electronic Interfaced Wind Generation

“…In particular, all the controllers in a universal manner are iteratively changed based on an optimization function implemented as a software in Python (version 3.4, Python Software Fundation, DE, USA). The objective of the optimization function is the maximization of the key performance indicator (KPI) defined in [27] as shown in (7), where ∆δ represents the angular difference of a SG with respect to the slack machine in the power system. KPI = 180 − ∆δ (7)…”

Transient Stability Performance of Power Systems with High Share of Wind Generators Equipped with Power-Angle Modulation Controllers or Fast Local Voltage Controllers

“…In existing literature of heuristic optimization, there are several types of algorithms that could be used for this purpose. Among these algorithms, the mean-variance mapping optimization algorithm is selected (MVMO) due to its outstanding performance in solving different types of computational expensive optimization problems [16], including several applications to optimization problems in the field of power systems [4,17]. The optimal tuning of MVMO and a comparison of its performance (to solve the optimal tuning of PAM) against the performance of other competitive algorithms is being investigated and will be presented in a future publication.…”

“…The initial solution vector x is normalized, i.e., each random value is transformed from the original min-max scale into the range 0-1. The normalized solution vector is fed into the block of fitness evaluation, which has two internal functions: one function is used to de-normalize elements of the solution vector (i.e., K w-PAM_i and T w-PAM_i ), whereas the other function is used substitute the values of K w-PAM_i and T w-PAM_i in the dynamic model of each WG with PAM, and to run the RMS time domain simulations needed to evaluate (3) and (4). A static penalty scheme is used to penalize the objective function value by adding a high value (e.g., 1 × 10 6 ) when (4) is not satisfied.…”

“…The parameters used for MVMO to solve this optimization problem are listed in Table 3. The selection of the parameters was based on a sensitivity analysis (i.e., evaluating a (3) and (4) to ascertain if there is improvement of fitness by changing the settings of MVMO). In Table 3, the values of the parameters "scaling factor" and "number of the mutated variables" allow one to dynamically change the shape of the mapping function, as an adaptive operator to tune the balance between exploration (global search) and exploitation (local search) of MVMO throughout the optimization search process.…”

“…These impacts are due to a change of the dynamics' properties of the power system, e.g., low and variable system inertia [2,3]. Transient stability (i.e., the ability of the synchronous generators of the system to keep synchronism after being subjected to large-size 2 of 17 disturbances) is one of the main stability concerns when increasing the share of renewable power generation, especially when the target is to reach levels close to or above 50% [4].…”