Non-dominated sorting culture differential evolution algorithm for multi-objective optimal operation of Wind-Solar-Hydro complementary power generation system

1 Introduction

Due to extensive fossil fuel consumption, energy shortage, environmental pollution, and ecological environment deterioration ae becoming increasingly severe.As alternatives, renewable energy such as hydropower generation, wind power generation, and photovoltaic power [1, 2] are being researched.However, both wind power generation and photovoltaic power generation have strong randomness, volatility, and intermittency.Large-scale windsolar complementary power grid connection limits the security and stability of power systems [3, 4].Hydropower, as a large-scale power source with good regulation performance, can effectively suppress wind and photovoltaic power generation fluctuation, and improve the bearing capacity of power grids.Therefore, wind power, solar power, and hydropower have highly complementary potentials.

Scholars have extensively studied the joint operation of complementary power generation systems.Allan et al.[5] analyzed the temporal and regional characteristics of land and offshore water and wind in Brazil to compare the correlation and complementarity of wind power and hydropower in different regions.Florina et al.[6] useda combination of pumped-storage and wind fields to increase the profitability of wind fields and the reliability of grid power supply.Shang et al.[7] studied the optimal operation of the wind-storage-water complementary system and obtained maximum daily benefits.However, most of the current literature focusses on the foundation of complementary power generation models and the analysis of the complementary relationship between energy sources.The solution of the model still bears some deficiencies, resulting in slow convergence of calculation results and relatively poor spatial distribution.

In recent years, multi-objective evolutionary algorithm has developed rapidly.One of the most well-known algorithms is NSGA-Ⅱ [8].The NSGA-Ⅱ uses a nondominated sorting process, fast elite reserved strategy, and niche operators without parameters to overcome high computation complexity.The NSGA-Ⅱ algorithm retains the strategy and manually Shared radius defects.However, convergence and distribution performance still requires improvement when applied to solve complex practical multi-objective optimization problems.

In this study, a multi-objective optimization model of Wind-Solar-Hydro complementary power generation system is established.A non-dominated sorting culture differential evolution algorithm (NSCDE) is presented to solve this model efficiently.Considering the generation benefit and the stability of the power system, maximizing generated electricity and maximizing minimum output are chosen as two primary targets for the model.This paper focuses on the economic benefit of Wind-Solar-Hydro complementary power generation systems in Jinping.The case study results validate the effectiveness of the proposed model and method.

2 Wind-Solar-Hydro complementary power generation system model

2.1 Hydropower

Hydropower output is determined from the drop between upstream and downstream water level.The energy loss depends on the efficiency of the hydroelectric generator.The formula is given as [9]:

where, N is the power output of hydropower station, Q is the water flow rate passing through the turbine, H is the net water head of the power station, and Kh is the output coefficient.

2.2 Wind power

Wind power is mainly related to wind speed.It is also related to air density, fan efficiency and rotor radius.Its formula is given as [10]:

where, N is the power output of wind power units, ρ is the air density, A is the swept area by the turbine blades, Cp is the power coefficient, and v is the wind speed.

2.3 Solar power

Wind power is mainly related to light intensity, photoelectric conversion efficiency, and photovoltaic array area.Its formula is given as:

where, N is the power output of solar power units, HA is the total horizontal solar intensity, PAZ is the component installation capacity, ES is the irradiance under standard conditions, and Ks is the efficiency coefficient.

2.4 Objective function

The objectives of the complementary model are to reduce transmission volatility and increase power generation.Economic benefits are directly related to power generation, which is considered by almost every power station, and this paper is no exception.It is essential to guarantee power supply smoothness and improve supply quality.Thus, the two main aims of this paper are to: 1) maximize annual total amount of power generation; 2) maximize the minimum ten-day joint output of the whole scheduling period to increase the power generation guarantee rate of the system.This paper selects the annual schedule and uses a period of ten days as the time period to design an optimized scheduling scheme for wind power, solar power, and hydropower.The objective function can be written as:

where Nh,t, Nw,t, Nl,t are the hydropower output, wind power output, and solar power output, respectively, T is the total time period length, and the value is 36 periods of ten days.

2.5 Constraints

(1) Water volume balance constraints

(2) Water level constraints

(3) Reservoir discharge flow constraints

(4) Hydropower plant output constraints

(5) Wind speed constraints

(6) Solar power generation capacity constraints

where: Vt, Vt+1 are the first and last storage capacities during the t-th period.It and Qt are inflows and outflows of the reservoir during the t-th period, Zmin,t, Zmax,t are the upper and lower water levels during the t-th period.Qmin,t, and Qmax,t are the upper and lower discharge flow, respectively, during the t-th period.Nh,min, Nh,max are the upper and lower limits of the output, respectively.vmin and vmax are the upper and lower available wind speed, respectively.Nl,min, Nl,max are the upper and lower capacity of solar power generation, respectively.

3 Methodology

3.1 NSCDE

Grants elitism and diversity preservation strategy make NSGA-Ⅱ an ideal optimization algorithm to solve MOPs [11].However, NSGA-Ⅱ has potential for improvement when it comes to uniformity of solution set distribution and the convergence speed of reaching the optimal solution.Inspired by NSGA-Ⅱ, this paper proposes a multiobjective optimization algorithm named non-dominated sorting culture differential evolution algorithm to get a set of the non-dominated solutions of Jinping Wind-Solar-Hydro complementary power generation system model we established.

In the NSCDE, culture algorithm (CA) is introduced [12].CA is a technique that adds domain knowledge to improve the performance of evolutionary algorithms [13].Its main features include population space and belief space.Population space comprises a set of individuals, which will be updated according to some evolutionary algorithms [14].Belief space comprises different kinds of knowledge, which can be learned from the evolutionary process.In this paper, we define two knowledge structures and use NSGA-Ⅱ as the population space of CA.

There are two kinds of knowledge proposed in NSCDE: situational knowledge and normative knowledge.

(1) The set of optimal solutions obtained from the population space is called the archive set, and these constitute the situational knowledge.After each generation of updates is completed, all non-dominated individuals are selected for inclusion in situational knowledge.To prevent local optimum, an upper limit of the archive set is preset.When the number of individuals exceeds the upper limit, the archive set has a truncation step similar to SPEA2[15].The principle is to eliminate by distance to the k-th nearest data point.

(2) The evolutionary algorithm chosen in NSCDE is DE [16], and the normative knowledge comprises N sets of DE evolutionary algorithm parameters (F and CR).In order to reasonably select parameters and improve the algorithm optimization ability, NSCDE chooses to use the belief space to update parameters dynamically

In Fig.1, the main steps of NSCDE are described in detail.

Fig.1 The procedures of NSCDE

3.2 Function test

The obtained non-dominated solutions of the function tests are shown in Fig.2.a-e.The population size is set to 50, the polynomial mutation probability of 0.03 is carried out, and the maximal iteration number is 50 for ZDT1, ZDT2 and ZDT3, and 300 for ZDT4 and ZDT6.Besides, the external archive size is 50 for NSCDE.The crossover probability is set to 0.8.From the result of ZDT1 to ZDT6, it is evident that (1) The convergence speed of NSCDE is obviously faster than that of NSGA-Ⅱ in ZDT2, ZDT4, and ZDT6.(2) The distributivity of NSCDE is obviously betterthan that of NSGA-Ⅱ in ZDT1, ZDT2, and ZDT3.From the discussions above, we may safely draw the conclusion that NSCDE has better convergence and distributivity compared to NSGA-Ⅱ.

Fig.2 Pareto Front of test function by NSCDA and NSGA-Ⅱ

Fig.3 Wind speed and wind output process

Fig.4 Light intensity variation and solar output process

4 Case study: Jinping Wind-Solar-Hydro complementary power generation system

4.1 Overview

JinpingⅠhydropower station is located in southwest China.Its average annual runoff is 38.5 billion m3 and its surrounding wind and solar fields are suitable for joint power generation scheduling.In this study, historical runoff data, wind speed data, and light intensity data of a normal year (2000) were selected for analysis and calculation.In spring and winter, the wind speed is strong and the light intensity is weak, while in summer and autumn, the opposite is true.A significant complementary effect is formed by wind and light in the season.The wind speed data and light intensity data of the corresponding year were selected for analysis.The output of the calculation for the wind and solar fields for a period of 10 days is presented in Fig.3 and Fig.4.

4.2 Scheduling period and calculation period division

During the flood period from July to September, the reservoir operates at a flood control level of 1859 m, and water storage begins on October 1.This study is scheduled for one year.Each calculation period was 10 days.Three calculation periods were taken in each month, and the total number of calculation periods was 36.

4.3 Parameter settings

According to the optimization principle and process of the NSCDA algorithm, the program is written in Java to optimize the design.The selected population size is 50, the maximum number of iterations is 5000, the space of situational knowledge is 50, the crossover probability is 0.8, and the mutation probability is 0.03.Forty sets of Pareto optimal solutions are obtained by the NSCDA algorithm.

4.4 Results and discuss

In this work, the model of Jinping Wind-Solar-Hydro complementary power generation system is calculated using data for the year 2000.Under the condition of guaranteeing the maximum Wind-Solar-Hydro joint minimum output, the joint power generation benefit is also considered.Table 1 presents the optimization schemes for multi-objective scheduling of a Wind-Solar-Hydro complementary power generation system in Jinping.It can be seen from Table 1 that the minimum output is negatively correlated with the amount of joint power generation.An increase in one will inevitably lead to a decrease in the other.The data in Table 1 also verify the validity of the NSCDE in optimizing multiobjective model problems.

In order to further analyse the relationship between the various schemes, two extreme schemes were selected for comparison: Scheme 1 (Maximize power generation), Scheme 40 (Maximize minimum output).(1) When the multi-objective optimization model takes power generation as the main target, then Scheme 1 can be selected; (2) When the multi-objective optimization model takes the minimum output as the main target, then Scheme 40 can be selected.Therefore, an appropriate scheduling scheme should be selected based on the actual situation of the power station.

Table 1 Multi-objective optimization scheduling for Jinping Wind-Solar-Hydro complementary power generation system

Scheme Power generation (108 kW·h)Minimum output (MW)Scheme Power generation (108 kW·h)Minimum output (MW)1 211.253 700.367 21 211.19 751.516 2 211.251 702.312 22 211.187 753.427 3 211.25 704.649 23 211.184 755.098 4 211.248 706.816 24 211.179 756.842 5 211.247 710.597 25 211.178 759.247 6 211.244 712.438 26 211.173 762.693 7 211.242 715.112 27 211.164 765.908 8 211.24 716.934 28 211.159 767.957 9 211.237 720.072 29 211.152 771.202 10 211.233 721.833 30 211.15 773.403 11 211.23 724.668 31 211.144 777.043 12 211.23 726.928 32 211.143 779.705 13 211.228 729.025 33 211.136 781.648 14 211.224 731.322 34 211.132 785.004 15 211.22 735.081 35 211.128 787.297 16 211.216 737.357 36 211.12 789.773 17 211.213 739.998 37 211.119 791.533 18 211.203 743.691 38 211.106 794.76 19 211.199 745.449 39 211.102 796.93 20 211.196 748.052 40 211.096 800.392

Fig.5 and Fig.6 show the water level change and discharge process of hydropower station under two typical optimization schemes, respectively.

Fig.5 The variation process of the water level

Fig.6 The variation process of the discharge flow

Fig.7 shows the hydropower station output process of hydropower stations under two typical optimization schemes.

Fig.7 Output process of hydropower station

In scheme 1, to maintain high power generation, the reservoir water level is always kept at the highest of 1880 m during the non-flood period.In scheme 40, to maximize the minimum output, the non-flooding water level is decreased slightly.In a broad sense, some power generations are sacrificed to increase the stability of power system.

By comparing the output of wind power, solar power, and hydropower for one year, it is evident that solar power and wind power, wind power and hydropower can form a great complementary effect of energy sources.In summer and autumn, the hydropower is in flooding season, and the output of the hydropower station reaches its maximum.The wind speed is weak, while the solar radiation is strong.During this period, hydropower and solar power can make up for the wind power.In spring and winter, the hydropower is in the non-flooding season, and the output of the hydropower station is less than flooding season.The solar radiation is weak, but the wind speed is strong.During this period, wind power and solar power can make up for the hydropower.From the view of complementary energy sources, Wind-Solar-Hydro power can form a good complement, making up for the lack of hydropower generation in the region and increasing the output of guarantees.

5 Conclusion

Wind-Solar-Hydro complementary power generation system model is established with the objectives of maximizing power generation and maximizing the minimum ten-day joint output.To solve the model, a new algorithm named non-dominated sorting culture difference evolution algorithm (NSCDE) is proposed.The calculated results indicate that wind power, solar power, and hydropower have strong complementarity under natural conditions.It is also verified that the NSCDE can provide decision makers an optimized scheduling schemes set.The Wind-Solar-Hydro complementary power generation system model has additional reference values for other power stations than that studied here.

Acknowledgements

This work is supported by the National Key R&D Program of China (2016YFC0402209), the Major Research Plan of the National Natural Science Foundation of China (No.91647114) and special thanks are given to the anonymous reviewers and editors for their constructive comments.