# Spinning Reserve Capacity Optimization of a Power System When Considering Wind Speed Correlation
## 1 Introduction  
Wind power, which is a green, clean, and renewable energy source, has developed dramatically. Unlike traditional power sources, wind energy in a power system has the following characteristics: (1) the intermittent and variable nature of wind speed causes the output power of wind farms to be stochastic; (2) as wind farms are commonly clustered in a region rich in wind resources, wind speeds and wind speed forecast errors of different wind farms are dependent. As wind power cannot be predicted with great accuracy, additional spinning reserve needs to be carried in order to guarantee the operational reliability [1]. Therefore, it is of great significance that new spinning reserve dispatch methods capable of taking account into probabilistic and correlated characteristics of wind power are developed. There have been many studies on the spinning reserve of power grids with large-scale wind power. [PERSON], et al. [2] and [PERSON], et al. [3] set up deterministic optimization modes for spinning reserve capacity, where the objective function is the minimum cost to buy spinning reserve. In [4], the system states are quickly selected by using the enumeration and simulation method, and a new method is used to assess the operating reserve risk of the wind power system. An optimization algorithm for the spin reserve is presented in [5] for the different demand of spin reserves under risk, using the control performance of the generator set. However, the relationship between the abundantlevels of spinning reserves and the reliability and economy of the power grid is not well considered. In [6], a model of the generation and optimal coordinating dispatch reserves is built, in which the constraint condition of the quantitative relation of the ratio between the system reserves and expected loss of load is considered. Taking both system economy and reliability into consideration, Literature [7] propose a conditional value-at-risk-based optimal spinning reserve model and incorporate it into the generation scheduling model in wind power integrated systems, in order to minimize total generation cost. Considering uncertainties in wind power and load forecasts, a multi-objective energy and spinning reserve scheduling method for a wind-thermal power system is investigated in a market environment [8]. [PERSON], et al. [9] establishes a mathematical optimization model for the minimum cost of conventional generators and spinning reserve, and then adopts a robust linear optimization to get the optimal reserve capacity with the wind uncertainty, so as to guarantee the feasibility of the optional solutions for all the realizations of the uncertain data. In [10], based on a robust optimization approach, an energy and reserve joint dispatch model in the real-time electricity markets is presented, considering wind power generation uncertainties as well as zonal reserve constraints under both normal and \(N\)-1 contingency conditions. However, the above references have not considered the influence of wind speed correlation on the spinning reserve capacity. [PERSON], et al. [11], [PERSON], et al. [12], and [PERSON] and [PERSON] [13] take into account the wind speed correlation to investigate optimal power flow, reliability assessment, and dynamic economic dispatch of power systems with integrated wind power, respectively. These studies have shown wind speed correlation should not be neglected when several wind farms are connected to the same power system. In this paper, a stochastic spinning reserve capacity optimization model is set up, taking account into the wind speed correlation and some uncertain factors. Compared with the prior works, the major contributions of this paper are summarized as:  
1. The wind speed correlation is considered. The Nataf transformation and Cholesky decomposition are applied to model the correlated wind speed;
2.