1. Introduction
Currently, the development of offshore wind power is rapid. With the gradual improvement in nearshore wind resources development, the development of deep-sea wind resources has become the next focus. Three issues arise during the construction and operation of deep-sea OWFs, which have attracted people’s attention. Firstly, because of the long transmission lines, there is significant energy loss along the transmission lines. Secondly, the capacitive effect of submarine cables is pronounced, leading to the risk of WT terminal voltages at both ends of the same feeder line exceeding the safe and stable range. Thirdly, when the voltage at the grid connection point suddenly drops, the WF should provide a certain reactive power compensation capability. Therefore, WTs need to retain a certain level of reactive power margin. Consequently, it is necessary to study optimization strategies for issues such as energy loss, voltage stability, and reactive power reserve within OWFs.
Based on the above considerations, Ref. [
1] analyzed the influence of on-load tap changer (OLTC) settings on the terminal voltage of WTs. However, the established reactive power optimization model did not optimize the WT terminal voltage, which could lead to the WT terminal voltage at the end of the feeder line exceeding the safe and stable range. Refs. [
2,
3,
4] established reactive power optimization models for WFs with the objective of minimizing active power network losses within a WF. These models, while maintaining stable grid connection voltages, reduced active power losses within the WF and improved the economic operation of the WF. Ref. [
5] addressed both active power losses and grid connection voltage stability, establishing a multi-timescale reactive power optimization model for WFs. This model effectively reduced active power losses by coordinating the reactive power compensation capabilities of discrete compensation equipment and WTs, thereby lowering the probability of grid connection voltage violations and enhancing the robustness of WF operation. Ref. [
6] focused on the voltage stability issue at the grid connection point of OWFs, establishing a multi-objective reactive power optimization model aiming to minimize reactive power compensation output and grid connection voltage deviation. However, this model did not consider WT terminal voltage instability. Ref. [
7] accurately predicted the reactive power output limits of each WT studied based on wind power forecast information and established a multi-timescale reactive power optimization model with active power losses, grid connection voltage deviation, and the stability margin as optimization objectives. This model reduced the adjustment frequency of discrete reactive power compensation equipment and improved voltage support capability. Ref. [
8] addressed the issue of insufficient reactive power reserve in WFs leading to cascade tripping faults in WTs. It established a reactive power optimization model with the objective of maximizing the reactive power margin, thereby enhancing the robustness of WF operation. Ref. [
9] established a reactive power optimization model with the grid connection voltage stability margin and active power losses as optimization objectives. This model improved grid connection voltage stability by coordinating the output of static var generators (SVGs) and WT reactive power while also reducing active power losses.
The existing literature on reactive power optimization in WFs typically focuses on optimization objectives such as grid connection voltage stability, reducing active power network losses, and enhancing reactive power margin, which improves the grid connection stability and economic operation of WFs. However, there are two main shortcomings. Firstly, the existing models in the literature primarily concentrate on grid connection voltage stability, overlooking the need to maintain voltage balance among individual WTs. Secondly, the optimization models established in the existing literature cannot adapt to real-time changes in operating conditions. Specifically, during significant fluctuations in grid conditions, there may be instances of WT terminal voltage instability or even disconnection of WTs. At such times, the optimization model should prioritize optimizing the voltage stability of WTs. Conversely, when a WF is operating stably, the optimization model should focus on efficiently reducing active power network losses and enhancing the reactive power margin.
In response to the aforementioned issues, this paper proposes an adaptive reactive power optimization model for OWFs, with the objectives of minimizing the sum of voltage deviations at WT terminals, minimizing active power network losses, and maximizing the reactive power margin. Recognizing that the priorities of these three sub-objectives vary under different operating conditions, and that fixed weighting coefficients cannot dynamically adjust the priorities of these sub-objectives in real-time scenarios, this paper innovatively adjusts the weights of the three sub-objectives in the adaptive reactive power optimization model for OWFs based on real-time operating conditions.
The reactive power optimization problem in WFs is typically highly nonlinear, often requiring the utilization of intelligent optimization algorithms for solutions. Among these, the PSO algorithm is favored for its fast search speed, wide search range, and fewer parameters, and it has thus been applied to solve reactive power optimization problems in WFs [
10,
11,
12,
13]. However, the PSO algorithm suffers from drawbacks such as easily falling into local optima and low convergence accuracy [
14,
15], leading researchers to propose various improved algorithms. Ref. [
16] proposed an Adaptive Discrete Binary Particle Swarm Optimization (ADBPSO) algorithm, which adjusts the inertia coefficient based on the fitness value of particles, thus accelerating the convergence speed. However, the algorithm suffers from the limitation of a small initial search range, making it prone to local optima. Ref. [
17] introduced a novel PSO algorithm that adjusts the acceleration factor of particles based on the number of iterations, effectively preventing particles from converging to local optima. Ref. [
18] addressed the slow search problem of PSO by introducing a constraint factor to control the inertia coefficient of particles’ velocity, thereby enhancing the search speed and convergence accuracy. However, the algorithm still encounters issues with falling into local optima. Ref. [
19] improved the PSO algorithm by incorporating the advantages of the Firefly Algorithm, resulting in faster convergence without enhancing convergence accuracy. Ref. [
20] linearly adjusted the inertia coefficient and acceleration factor of particles based on the number of iterations, improving the optimization speed and accuracy of the PSO algorithm. Nonetheless, the algorithm’s utilization of the random initialization method introduces significant randomness into the initial search range of particles, hence increasing the risk of falling into local optima.
The existing literature has predominantly focused on adjusting the inertia coefficient and acceleration factor of particles in the PSO algorithm to improve its performance. Although these adjustments have enhanced the algorithm’s search speed and convergence accuracy, there are still two main shortcomings. Firstly, because of the utilization of the random initialization method, the initial search range of particles is unstable, making it susceptible to falling into local optima during the solution process. Secondly, insufficient consideration is given to differences in particle fitness during the update process of particle velocity, which may result in the slower convergence of particles with inferior fitness, thereby affecting convergence accuracy. To address these issues, this paper proposes a UAPSO algorithm capable of global fast optimization. The algorithm initializes particle positions using a uniform initialization method and adaptively adjusts the inertia coefficient of particles based on both the fitness level and the number of iterations.
In summary, this paper presents the following innovations:
- (1)
An adaptive reactive power optimization model for OWFs is established, with the objectives of minimizing the sum of voltage deviations at WT terminals, minimizing active power network losses, and maximizing the reactive power margin. The weights of the three sub-objectives in the model are adaptively adjusted based on real-time operating conditions.
- (2)
An improved PSO algorithm is proposed. The improvements include the utilization of a uniform initialization method for particle positions and the adaptive adjustment of particle inertia coefficients based on the fitness of particles.