The operating status of power systems is influenced by growing varieties of factors, resulting from the developing sizes and complexity of power systems. In this situation, the model-based methods need to be revisited. A data-driven method, as the novel alternative on the other hand, is proposed in this paper. It reveals the correlations between the factors and the system status through statistical properties of data. An augmented matrix as the data source is the key trick for this method and is formulated by two parts: 1) status data as the basic part; and 2) factor data as the augmented part. The random matrix theory is applied as the mathematical framework. The linear eigenvalue statistics, such as the mean spectral radius, are defined to study data correlations through large random matrices. Compared with model-based methods, the proposed method is inspired by a pure statistical approach without a prior knowledge of operation and interaction mechanism models for power systems and factors. In general, this method is direct in analysis, robust against bad data, universal to various factors, and applicable for real-time analysis. A case study based on the standard IEEE 118-bus system validates the proposed method.
Current researches on correlation analysis are mainly model-based methods, for which the mechanism models are essential preconditions. These mechanism models are established based on assumptions and simplifications, and used for specific power systems and factors. Lian studied the effect of dynamic load characteristics on the voltage stability and sensitivity in power systems, using the P--V and the Q--V curves @cite_4 . In Lian's method, the power system is equivalent to an decentralized system; dynamic loads are approximated as differential equations. These processes increase the complexion and inaccuracy of the analysis. Parinya proposed a stochastic stability index to investigate the small signal stability of power systems incorporating wind power @cite_3 . The status space equations and energy functions need to be rewritten when the grid changes, and the test system is too small in scale to convince.
@cite_4 @cite_3
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The voltage stability and the sensitivity of power grid are presented by introducing the P-V and the Q-V curves based on the dynamic load. Firstly, a power grid is exactly rewritten into a simple equivalent decentralized system by the power flow calculation. Next, the dynamic load is modeled in a higher order polynomial form identified from the data at a load-bus observed in Sweden. Then, the system and the load P-V and Q-V curves are constructed, and finally the reactive power is shown to be more sensitive to the voltage stability than the active one by the sensitivity analysis comparing with the case of data observed in Japan. The stochastic stability index (SSI) is proposed in this paper to investigate the small signal stability (SSS) of the power system incorporating wind power. The SSI is developed using the first integral energy function method based on Lyapunov's stability and the theory of stochastic stability. The model of induction generator wind turbine is modified and applied for the SSS study. This proposed method can investigate impact of stochastic wind power quantitatively while the general deterministic methods cannot.