Journal of Engineering

Volume 2018, Article ID 6139086, 11 pages

https://doi.org/10.1155/2018/6139086

## Bidding Strategy of Virtual Power Plant with Energy Storage Power Station and Photovoltaic and Wind Power

School of Economics and Management, North China Electric Power University, Beijing 102206, China

Correspondence should be addressed to Zhongfu Tan; moc.621@gnijiebufgnohznat

Received 19 October 2017; Revised 27 January 2018; Accepted 8 February 2018; Published 1 April 2018

Academic Editor: Yuh-Shyan Hwang

Copyright © 2018 Zhongfu Tan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

For the virtual power plants containing energy storage power stations and photovoltaic and wind power, the output of PV and wind power is uncertain and virtual power plants must consider this uncertainty when they participate in the auction in the electricity market. In this context, this paper studies the bidding strategy of the virtual power plant with photovoltaic and wind power. Assuming that the upper and lower limits of the combined output of photovoltaic and wind power are stochastically variable, the fluctuation range of the day-ahead energy market and capacity price is stochastically variable. If the capacity of the storage station is large enough to stabilize the fluctuation of the output of the wind and photovoltaic power, virtual power plants can participate in the electricity market bidding. This paper constructs a robust optimization model of virtual power plant bidding strategy in the electricity market, which considers the cost of charge and discharge of energy storage power station and transmission congestion. The model proposed in this paper is solved by CPLEX; the example results show that the model is reasonable and the method is valid.

#### 1. Introduction

The randomness and fluctuation of the wind and photovoltaic power output restrain its grid connected capability [1, 2]. In 2016, China’s wind and photovoltaic power installed capacity was 182.15 GW, which ranked first in the world, but the amount of wind power curtailment electricity reached 20 TW·h. The average number of hours of wind power utilization was 1728 h, especially in the “Three-North” area of China, where the wind and solar energy resource is relatively abundant and the equivalent utilization time of wind power is only about 1445 h. In order to achieve large-scale wind power integration, the system needs to arrange reserve services for wind and photovoltaic power, mainly including conventional thermal power units, pumped storage power stations, and energy storage power stations. As the environmental pressure reduction and transmission capacities caused storage power station reserve services inapplicability, this will limit the energy storage station providing the reserve service for wind and photovoltaic power. This paper constructs a virtual power plant with energy storage power station and photovoltaic and wind power which bids in the electricity market, maximizes the benefit of virtual power plant, and promotes the grid-connected generation of photovoltaic and wind power.

In recent years, many scholars have carried out research on the influencing factors of new energy utilization. Nick et al. [3] and Al Kaabi et al. [4] proposed the concept of generating units-power grid-system load interaction, which can effectively reduce the operation cost of the system and promote the grid-connected generation of wind power. Wu et al. [5] used demand side management and storage technology and construct power dispatching model with wind power and energy storage; Georgilakis and Hatziargyriou [6] established a day-ahead market clearing model of wind power based on demand side management, which provided a reasonable operation mechanism for the marketization of wind power. Sadeghi-Barzani et al. [7] established two-stage demand response of stochastic programming model with the wind power to maximize the lower cost of the demand response and enhance grid-connected capacity of wind power. Zhipeng et al. [8] considered price demand response and security constraints, where the system scheduling cost minimization was objective function, and established real-time optimization scheduling model. Huajie et al. [9] proposed regional and provincial two-level optimization scheduling model by adjusting the conventional unit output and interprovincial electricity trade balance wind power output; results show that the model could enhance grid-connected capacity of wind power. Binato et al. [10] proposed a new calculation method to reduce the amount of wind power curtailment in the peak period of the grid. Xiaogang et al. [11] established a dual-objective scheduling model with wind power, based on the second-generation noninferior dominating sorting genetic algorithm. Muñoz-Delgado et al. [12] considered the thermal power, hydropower and wind power, electric and heating load balance, and transmission capacity constraints, with operation cost minimization of the system as the objective function, and set up wind power grid-connected analysis model. The above literatures focus on the multiobjective optimization of wind power system and the improvement of the scheduling model. But the actual situation of China’s large-scale wind power centralized access only using these techniques is not enough.

Robust optimization theory is a tool to solve the problem of uncertainty [13, 14]. Haffner et al. [15] introduced the uncertainty set to the large-scale photovoltaic power optimal scheduling systems to make up for the conservative optimization of the box set to partial conservative. Wen and Kumar [16] introduced the game model into the robust optimization problem of the power system and obtained an economic scheduling strategy with strong robustness to short-term uncertainty of wind power generation. Ruozhen et al. [17] introduced the dual theory into the multiperiod inventory robust optimization model; the convex programming problem could be easily solved, which could effectively restrain the influence of the uncertainty of demand distribution on the effectiveness of the strategy. Wen and David (2001) [18] adjusted the boundary of the uncertain set to control the conservativeness of the robust optimization model and realized the economic and security balance of the decision. Pandžić et al. [19] proposed a robust optimization method based on moment uncertain distribution to solve the problem of economic and environmental scheduling with wind power. Kirschen et al. [20] optimized the power flow calculation of distribution network with the strong duality theory; the robust optimization model was transformed into mixed-integer linear programming to compensate for the shortcomings of robust optimization conservatism. Haipeng et al. [21] transformed a two-layer deterministic optimization model into double-layer optimization method, which was optimized by interior point method and had good engineering practicality. Ling et al. [22] introduced the sorted truncation method to improve the efficiency of the solution. Feng et al. [23] proposed an improved robust model for the problem of uncertainty on the right side, which improved the efficiency of the solution. Qiang et al. [24] proposed the scheduling model of the wind power system based on the robust optimization framework, which solved the problem of the objective function deterioration.

In electricity market bidding, Chao et al. [25] proposed a competitive bidding mechanism of the power market with both the supply and demand sides. Peiyi and Xinyan [26] took minimization of purchase cost as the objective function and proposed a bidding method of electricity market based on genetic algorithm. Zheng et al. [27] proposed the formation price mechanism and bidding strategy of renewable energy power generation and analyzed the influence of renewable energy on the electricity market bidding. Jianxue et al. [28] established mixed bidding model of power market, which solved the difficulty of dealing with sub-time constraint and improved the feasibility of the market clearing result. Li et al. [29] analyzed the competition psychology of the power supply market participants with the game theory and established the bidding strategy under different conditions. Yixin et al. [30] analyzed the bidding method of the electricity market in the power supply side with the participation of the microgrid and determined the optimal bidding strategy of the microgrid operators in the alliance and nonalliance. Long et al. [31] analyzed the relationship between the pricing mechanism, the energy substitution, and the bidding strategy and obtained the optimal strategy of the integrated energy sales company to participate in the market bidding purchase. Carrión and Arroyo [32] proposed a transferable bid strategy based on the autoregressive integral moving average mode. Mashhour and Moghaddas-Tafreshi [33] established the profitability model of the electricity sales company under the deviation assessment mechanism and constructed the optimal purchase model of the interruptible load with the minimum cost of the evaluation. Raab et al. [34] introduced the multiagent technology into bidding and optimization scheduling of the virtual power plant, which increased the distributed power generation participating in the electric power transaction.

As a method to deal with the uncertain factors, robust optimization has been paid more attention in many fields such as natural science and engineering technology. On the above background, this paper takes the virtual power plant to maximize the economic benefits as the objective function and the virtual power plant output and market price as uncertainties and constructs the virtual power plant bidding strategy robust optimization model with energy storage station and photovoltaic and wind power.

#### 2. Unit Output Model

##### 2.1. Wind Power Output Model

Wind turbine power is subject to the wind speed, but if the wind speed is lower than the cut-in speed or higher than the cut-out speed, wind turbines cannot generate electricity; the relationship between wind turbines power and wind speed is as follows:where is the output of wind turbine at time ; is the rated power of wind turbine; are the cut-in speed and the cut-out speed of wind turbine; is the rated speed of wind turbine; is the speed of wind turbine at time .

##### 2.2. Photovoltaic Power Model

The output curve of photovoltaic power system generally satisfies the* Beta* distribution; the specific formula is as follows:where are the parameters of the* Beta *distribution; is the radiosity correlation coefficient; the parameters of Beta are calculated by formula (3) as follows:where is the mean and normal distribution of solar radiation; is the variance of solar radiation; the probability of solar radiation can be calculated by the following formula:where is the radiation intensity; are the upper and lower limits of solar radiation ; the formula for calculating the conversion of solar radiation into electrical energy is as follows:where is area of photoelectricity; is photoelectric conversion efficiency of photovoltaic array; is output efficiency of photoelectric inverter.

##### 2.3. Photovoltaic and Wind Power Combined Output Model

Both photovoltaic power and wind power generation outputs have volatility and randomness, and their output conditions are closely related to weather conditions. In this paper, the Clay-Copula function is used to simulate the joint probability distribution of wind and photovoltaic power output; the formula is as follows:where are the wind power and photovoltaic power output; are the probability distribution functions for wind and photovoltaic power output; is the connection parameter, for wind and photovoltaic power outputs are not consistent with linear or normal assumptions. Therefore, the Spearman correlation coefficient is introduced in this paper.

In order to convert the edge distribution into corresponding ranks, the uniform probability distribution function is generated by transforming the cumulative probability density function . obeys uniform distribution , for ; the formula is as follows:

Similarly, is transformed into uniform distribution , and are uniform distributions on , , and . The formula for connection parameter is as follows:

For a given wind and photovoltaic power plant output , the paper can construct the joint distribution function ; the formula of Spearman correlation coefficient is shown as follows:

##### 2.4. Energy Storage Power Output Model

Storage power station is charging at night and discharging at daytime, which can effectively reduce the load curve peak valley difference, improve the stability of the grid, and promote wind and photovoltaic power connected grid.where and are the upper and lower limits of capacity for energy storage power plants; is energy storage power plants capacity at time .

When the energy storage power station is in the discharging state,

When the energy storage power station is in the charging state,where and are the charging and discharging power of the energy storage station at time ; is energy storage station power capacity at time ; and are discharging and charging loss of energy storage power station; Figure 1 shows bidding process of electricity market.