1. Introduction
To meet the ambitious goals of the Paris agreement [
1] to prevent, or at least minimize, climate change, there is a global need for sustainable energy supply. Part of this energy supply must be produced by renewable sources. Market-driven policies are increasingly focused on promoting the use of wind and solar generation [
2]. The production of energy and electricity from wind sources can be carried out both on the ground (onshore) and in wind farms installed in the ocean (offshore). Locations for the construction of offshore wind power plants (WPPs) are usually a few hundred kilometers away from the nearest coast, which requires long-distance cables in the ocean [
3]. Being quick to install, especially when compared to other energy sources, great efforts to develop onshore and offshore wind farms are being made [
4,
5].
Figure 1 shows a simplified scheme of offshore wind energy production.
Generally, wind power generation occurs in three phases, as follows:
Wind turbines: the blades turn a shaft inside the wind unit. Power energy is produced via a rotational generator (which uses the conversion of magnetic energy into electric);
Offshore substation: the transformer equipment transforms the power for distribution and delivery to the onshore substation and;
Lines and grid: power transmission and distribution to consumers.
Active and reactive power dispatch problems are common in the power production area, usually known as optimal power flow (OPF) [
6]. Generally, OPF problems have a large dimensional space, and due to their multi-modality, nonlinearity, and non-convexity characteristics, these problems are considered large-scale optimization problems [
7]. Solving an OPF consists of finding the more appropriate setups for the controller system (active power and voltages), transformers taps, shunt reactors, and capacitors values [
8]. This work addresses an OPF-like problem: A wind power generation problem. We propose an optimal dispatch WPP controller, in which appropriate parameter settings of the algorithm are obtained automatically over time so that its performance is optimized. Several methods and techniques for solving OPF problems have been proposed in the state-of-the-art literature. The advantages and disadvantages associated with the most used methods for solving OPF problems can be found in the works of [
6,
9,
10]. We summarize this information in
Table 1.
Specifically in wind energy production, it is possible to find recent related works in the literature. Kotur and Stefanov [
3] proposed an optimal power flow control in a system with offshore wind power plants. Using the IEEE 14-bus system test system, the Interior Point Method was applied to solve the OPF-like problem. The authors concluded that the proposed approach was more efficient than a standard system controller. A mathematical modeling of wind generation was proposed in [
4]. The general idea was to minimize costs of wind intermittency using Linear Programming techniques. Results showed that the applied methodology is suitable for quantifying the effects of the shape of the forecast error distribution and the coefficient costs of wind intermittency.
A wind farm control strategy was proposed to maximize the power reserve during de-loading operation while maintaining the total power delivered by the WPP at the point of common coupling (PCC) [
20]. The problem was solved by the AEOLUS SimWindFarm (SWF) Simulink toolbox [
21]. Sakipour and Abdi [
22] proposed a study based on wind power generation testing nine evolutionary algorithms, as Grey Wolf Optimizer (GWO), Artificial Bee Colony (ABC), GA, PSO, and among others. The goal was to find an efficient microgrid configuration using storage systems into a wind farm. Results showed that the GWO performed better, increasing the remaining expected life of batteries in the system.
Self-Adaptive Evolutionary Programming (SAEP) was proposed in [
23] to minimize the wind power generation costs. Obtained solutions validated the proposed methodology. Gwabavu and Raji [
24] presented a dynamical control system based on model predictive control applying Quadratic Programming to solve the OPF problem. The results showed that the proposed method can reduce grid-connected wind power fluctuations and limit system faults in power generation. Joseph et al. [
25] proposed the use of a PSO method to maximize the system loadability within stability margins. Results showed that PSO improved the load carrying capacity when compared to the controller system installed in the plant. Bai et al. [
26] applied the ABC algorithm to minimize the production costs on a WPP. A comparison of results between ABC, GA, and PSO was performed, and ABC showed better average results.
Seok and Chen [
27] proposed an intelligent wind power plant coalition formation model solved by mathematical programming to achieve profit growth. The authors concluded that the model is especially applicable to heterogeneous WPPs. According to Helmi et al. [
28], improving the efficiency of distribution networks is a challenging goal for both large networks and microgrids connected to the public grid. In this context, the Harris Hawks Optimization (HHO) was proposed to minimize power losses of three IEEE systems: 33-bus, 85-bus, and 295-bus. Results showed that HHO performed better than Cuckoo search algorithm (CSA) and PSO for minimizing the losses of systems tested. An optimal network configuration in an active distribution network reduces power loss, improves voltage profile as well as system efficiency and reliability [
29]. Thus, the Water Cycle algorithm (WCA) was proposed to reduce the losses of the IEEE 33-bus and IEEE 69-bus systems. WCA outperformed other optimization techniques such as CSA, Harmony Search Algorithm (HSA), and Fireworks Algorithm (FWA). Similar approaches to minimize system loss in wind power plants were proposed in Packiasudha et al. [
30] using the Cumulative Gravitational Search Algorithm (CGSA). The minimization of system losses in wind farms was also solved via deterministic algorithms as seen in the works of Huang et al. [
31] and Sakar et al. [
32].
Pham et al. [
33] proposed an optimization method, the Mean-Variance Mapping Optimization (MVMO), to solve the reactive optimal control to WPPs, taking into account the minimization of losses. MVMO was applied to solve the problem using the IEEE 41-bus system as test scenario (available in [
34]). Obtained results showed that a fine-tuned MVMO version generated adequate solutions for the OPF-like problem. It is important to say that the IEEE 41-bus system model considers that there is no uncertainty associated with the decision variable values. For dealing with uncertainty in the variables, more complex approaches, such as stochastic or robust optimization methods, are needed. In [
35,
36], stochastic and a robust approaches were proposed to minimize network losses.
In this work, we solve a dynamic OPF-like problem representing the reactive power dispatch in wind power plants. We propose an integration between the Canonical Differential Evolutionary Particle Swarm Optimization algorithm (C-DEEPSO) [
37] and irace [
38] as an automatic control system to provide the electric dispatch for WPPs. C-DEEPSO, a hybridization between the particle swarm algorithm and the differential evolution algorithm, was proposed in 2018. The algorithm takes advantage of swarm intelligence methods and the canonical genetic operators of evolutionary computation techniques. Since its proposal, C-DEEPSO has been successfully applied to diverse power systems problems. In general, power system problems such as OPF (optimal power flow) and SCOPF (security constrained optimal power flow) are hard problems to solve, having a high number of distinct optimization variables to optimize and various constraints to deal with. It is well-known that algorithms for solving these types of problems demand a careful design. Motivated by the performance superiority of C-DEEPSO and its variants when applied to such problems (see [
37,
39,
40,
41,
42,
43,
44]), C-DEEPSO presents good features and is a viable and competitive method for solving the OPF-like problem in WPP.
However, the C-DEEPSO performance is related to the choice of its main parameters: the weight mutation and the particle communication. Using the irace package as an internal C-DEEPSO mechanism to automatically fine-tune the parameters, we propose a framework capable of establishing an automated controller to carry out the daily electrical dispatch. In the experimental design, 24 h are discretized into 15 min intervals, totalizing 96 test scenarios. The proposed approach finds the best parameter setting yielding the optimal decision variables for each test scenario. Since the daily electrical dispatch problem is solved by breaking it down into 96 sub-problems in a recursive manner, the proposed approach can be seen as a dynamic way of tackling the OPF-like problem in WPP. To the best of our knowledge, this innovation has not yet been found in the state-of-the-art literature. More specifically, this paper presents the following contributions:
A new electric dispatch controller with automatic adjustment to solve OPF-like problems in WPP;
A novel framework to fine-tune the parameters of the C-DEEPSO algorithm. For this, the irace package is coupled to the internal mechanism of C-DEEPSO;
A new approach to compare stochastic algorithms is performed via an application of post hoc tests using the DSCtool in order to validate the statistical robustness of the results;
An in-depth performance assessment of C-DEEPSO + irace compared to two different algorithms, DEPPSO and MVMO, when solving the OPF-like problem applied to WPPs;
Obtained results indicate a competitive performance favoring C-DEEPSO in terms of efficiency and accuracy when applied to the OPF-like problem;
A projection analysis is conducted indicating reduction of the system energy losses around 2.35 MWh per day.
The rest of the paper is structured as follows.
Section 2 presents Materials and Methods: the reactive power optimization applied to WPPs; the C-DEEPSO algorithm and the optimal adjustment control are proposed.
Section 3 describes the experiments and results.
Section 4 carries out a discussion about the obtained results. Finally,
Section 5 includes an overall conclusion and future work.
3. Experiments and Results
The experimental part of this work is carried out under the observation of the daily electrical dispatch. Generally, when planning the electrical dispatch operation, the seasonality of the region in relation to the generating source must be taken into account. According to Arce et al. [
55], the main stages of dispatch operation planning, taking into account seasonality, are: long (several-year horizon), medium (one-year horizon), short-term (one-week horizon), daily (one day), and in real time. In this work, we have chosen to carry out a study under the bias of daily planning of electrical dispatch operation in a wind power plant (WPP). This approach is justified by the fact of having in hand data for only one day testing in IEEE 41 Bus-System. The main rationale behind our choice has been the possibility of a performance comparison among the proposed approach and the two state-of-the-art approaches, DEEPSO and MVMO.
The electrical dispatch in WPPs discussed in this work is dynamic in nature. To handle its dynamicity, we use an integration between C-DEEPSO and irace, which works like an optimized automatic controller. The WPP system has 18 generators (5 MW) that are connected to the transformers (100 MVA) and the grid (220 kV) through a submarine cable (110 kV—around 30 km length). The transformers provide OLTC service and operate T1 (% kV with 33 taps and 220 kV to PCC) and T2 with 13 taps. There is no equality in the distances between the generators and the WPP main collector. Wind turbine terminals need to be maintained between 0.92 and 0.97 kV (which corresponds 920–970 V). The nominal voltage value is 0.95 kV (950 V). The system also has a shunt reactor adjusted with ON/OFF control (500 ) to adequate the excessive charging of the submarine cable.
The goal is to provide optimized sets of all VAR sources to meet the actual reactive power requirement at PCC including: the individual reactive power of each wind turbine, OLTC adjustments, and shunt reactor ON/OFF positions. The controller calculates the optimal adjustment in intervals of 15 min, in a total of 96 intervals, for which the reactive electric dispatch must be solved. Simulation has been done to show the reactive power control problem, which is defined by progressive changes in the necessary reactive power (
). The experimental design contemplates over a period of one day (24 h discretized to in intervals of 15 min).
Figure 4 shows a typical WPP output.
A control strategy must be carried out to ensure system availability and to continuously meet reactive power (). Here, the adopted experimental design is used to show that C-DEEPSO is able to solve the OPF-like problem addressed, respecting the constraints. C-DEEPSO was runned 31 times in each one of the 96 intervals of power production. The computational simulation was done using an Intel i9 3.7 Ghz and 64 GB de RAM on Ubuntu 20.04.2.0 LTS Operating System computer. The code was implemented in Matlab using the MATPOWER package. The integration of R (4.1.1) and Matlab was done with a Python (3.7) script.
To validate our proposal, the performance of C-DEEPSO integrated with irace is compared to the performance of DEEPSO and MVMO algorithms. Since C-DEEPSO has been derived from DEEPSO, the comparison between those algorithms also aims to see if the improvements brought by C-DEEPSO are relevant. On the other hand, MVMO is the reference algorithm for this problem. DEEPSO and MVMO [
33] results have been extracted from [
34], where they were used in their best parameter configuration.
Figure 5 shows the result obtained by each tested algorithm: C-DEEPSO + irace, DEEPSO, and MVMO. The graph presents the range of all scenarios, emphasizing cases 14–31 in its expansion. C-DEEPSO shows the best result among the tested methods.
The irace package implements the iterated racing methodology [
38], a method for automatic configuration with steps: (1) sampling new configurations according to a particular distribution; (2) selecting the best configurations from the newly sampled ones by means of racing; and (3) updating the sampling distribution in order to bias the sampling towards the best configurations.
Table 4 shows the algorithms’ results in terms of average (AVR) and standard deviation (STD). The configurations of Mutation and Communication rates found by irace are also displayed. As can be seen in
Table 4, C-DEEPSO coupled to irace obtained, after the iterated racing process, a specific set of parameters for each test scenario.
Results from 31 runs of each algorithm show that C-DEEPSO has the lowest average in 100% of cases tested. To show the efficiency of C-DEEPSO, we carried out a more complete statistical analysis. We used a new tool to perform a post hoc Kolmogorov–Smirnov test to perform a hypothesis test about mean differences, the DSCTool [
56]. We compared the results of the algorithms in order to rank them for each of the problem instances using DSCTool. DSCTool is a statistical tool used to compare the performance of algorithms under different scenarios. We applied the DSCTool with the Kolmogorov–Smirnov test with 95% confidence to compare the results of C-DEEPSO against the MVMO and DEEPSO algorithms for all 96 instances of the WPP problem. The algorithms have been ranked as shown in
Table 4. (Aiming to allow reproducibility and extension of our results, an online publicly repository is made available at
https://github.com/jvcavancini/C-DEEPSO (accessed on 17 October 2021). It contains our proposed approach (C-DEEPSO + irace), the WPP model, and a.csv file containing the optimal decision variable values for each test scenario, corresponding to the median solution over the 31 runs.)
4. Discussion
We adopted an
(significance level) to conduct the inference statistical test. In each power production interval (in a total of 96), if the Kolmogorov–Smirnov test finds a significant difference between the mean of algorithms, the DSCtool provides the ranking among of algorithm performances.
Table 4 shows the signal of statistical test realized: (+) exists differences among the means of algorithms with confidence of 95%, and (=) null hypothesis of equality of means is rejected. In our analysis, 84 test cases (87% of them, respectively) show that there are differences among the algorithm means. However, in 12 out of 96 scenarios, or in 12.5% of the scenarios, the Kolmogorov–Smirnov test was unable to reject the null hypothesis.
Thus, we can say that C-DEEPSO + irace has results with greater robustness when compared to the others in 87% of cases. Observe that C-DEEPSO + irace shows a lower mean value and presents the maximum ranking in the Kolmogorov–Smirnov test, as shown in
Table 4 with symbol (+). In the remaining 12 scenarios, the null hypothesis cannot be rejected, showing that there is no statistical significance in the difference of the algorithm means when compared to DEEPSO (indicated by the symbol (=) symbol in
Table 4). To summarize, in 87.5% of the test cases, C-DEEPSO + irace is the most efficient algorithm when compared to DEEPSO. In 12.5% of the test cases, C-DEEPSO + irace and DEEPSO are tied in the first position. It is worthwhile to notice that, in all 96 scenarios, C-DEEPSO + irace shows a low average in comparison to MVMO (state-of-the-art algorithm). Therefore, we can say that MVMO is always classified in the third position for solving the OPF-like problem addressed in this work.
Therefore, we consider that C-DEEPSO + irace is an effective method to solve the electric dispatch problem performing an optimal control of the WPP. C-DEEPSO minimizes the transmission losses. Furthermore, it complies with PCC power requirements ensuring the adjustment of all correlated variables. Observe that DEEPSO and MVMO use a single set of optimal parameters considering the whole time scenario. The novelty of the proposed approach is to treat the OPF-like problem in WPP as having a dynamic optimal set of parameters. Integrating irace with C-DEEPSO, the optimal parameters have been adjusted for each of the 96 test cases. This dynamic parameter configuration is responsible for the optimized performance of the proposed approach. C-DEEPSO has proved to be efficient and competitive for solving the problem in a dynamic way. Our algorithm works as a joint electrical dispatch control that learns from the system’s input data at each measured time interval. irace identifies the best mutation and communication rates at each time interval, ensuring the robustness of the proposed system controller.
The total sum of losses is shown in
Table 4 for each algorithm. The proposed approach presents a cumulative daily average value of 38.01 MWh per day, while DEEPSO and MVMO present 38.80 MWh and 40.35 MWh, respectively. As shown, the decrease in daily cumulative value is approximately 3% compared to C-DEEPSO and 6% in relation to MVMO. The statistical tests indicate these values show significant improvements. Considering C-DEEPSO + irace and the reference algorithm, MVMO, there is a difference of 2.35 MWh per day, favoring the C-DEEPSO + irace. In a monthly projection, we would have a total loss of
MWh per day, supporting the C-DEEPSO + irace.
5. Conclusions
Recent works have shown that wind and solar power have become viable energy sources in developing countries to serve as a sustainable way to produce electricity. The electric dispatch problem in wind power plants can be expressed as an OPF-like problem, in which the goal is to minimize the cost losses of a WPPs. In this work, we used an integrated methodology to minimize reactive power losses in the transmission network in wind farms (OPF-like), coupling C-DEEPSO and irace package (in a fine-tuning methodology). The C-DEEPSO + irace incorporates a single-objective meta-heuristic, implementing some procedures of Swarm Intelligence and Evolutionary Computation. In the proposed approach, the daily dispatch (24 h) was discretized into 15 min intervals, totalizing 96 test scenarios. For each test scenario, irace finds the best parameter configuration for the mutation and communication rates and C-DEEPSO finds the optimal decision variables yielding the minimization of the power losses. The problem is solved in a recursive way and can be seen as an automatic controller for the problem. Using the IEEE 41-bus test system, the proposed algorithm was compared to two other algorithms: DEEPSO and MVMO. Both algorithms were at their best performance with the set of best parameters optimized by their proponents. The results indicated that the proposed C-DEEPSO + irace algorithm outperformed its competitors, being statistically superior when dealing with hard OPF-like problems in WPP.
Although being a very promising approach, the proposed methodology has some limitations that can be addressed in future works. The problem can be solved using long- or medium-term electrical dispatch planning. Different objective criteria such as the minimization of the overall costs can be applied for solving the problem. The irace can also be coupled with a multi-objective evolutionary algorithm for solving the OPF-like problem, taking into account the two or more objective functions simultaneously. Finally, the IEEE 41-bus system model considers that there is no uncertainty associated with the decision variable values; however, a robustness analysis is an important aspect to be analyzed.