Hydropower Technological Innovations

#### **Chapter 3**

## Hydro Power Tower (HYPOT)

*George Mamulashvili*

#### **Abstract**

Humanity has used the power of falling water for centuries to produce electrical energy, but there have been no significant changes in technology. Marine Energy has received an explosive development. Traditional technologies are passive and have low efficiency. It is not possible to use the effect of falling water in the ocean. The chapter considers the technology, which allows to convert not only the kinetic energy of a moving horizontal flow, but also the potential energy of water hammer in a combination of pressure drop between layers of water that have different hydrodynamic characteristics. This is a high efficiency due to the use of the Pitot-Prandtl tube principle and Bernoulli's law and in combination with the effect of raising the water of the hydraulic ram. The calculations are based on computational fluid dynamics (CFD) methods. It is known that 94% of incoming solar energy is converted into underwater currents and only 6% - on the surface. Therefore, the proposed technology can be highly competitive in relation for example to Orbital Marine Power (OMP) project and another known offshore wind and wave power plants which convert only the kinetic energy of the surface air and sea currents.

**Keywords:** Marine Energy, Water hammer, Shock wave, Pulsating flow, Pitot tube

#### **1. Introduction**

The formulation of the project theme includes general information about the facility as a new source of renewable energy for the ocean.

This is an underwater gravitational energy technology, which is one of the most promising generating devices due to the significant potential of generating electrical energy, as it converts a large volumetric part (almost 94%) from all the potential solar energy captured by the oceans.

A hydroelectric power plant perceives the kinetic energy of currents and the potential energy accumulated by it due to water hammer and pressure drop between the layers. It artificially creates a rising whirlpool in the open sea. At the same time, the gift wave from the water hammer propagates through the two-phase hyperbolic project HYPOT and increases the pressure - in the positive direction, when falling in the negative direction. This occurs when there is a sharp change in the direction of the current in the neck of the tower. The destructive effect of this phenomenon is associated with the inability of the fluid to contract smoothed out by the hyperbolic curve.

The chapter presents the main assumptions and results of the calculation of the digital twin, as well as the design methods of the HYPOT project. **Figure 1** shows a general view of the hydroelectric power plant of the cyclone action.

The HYPOT project in the complex can convert the kinetic energy of tidal and bottom flows, as well as the potential energy of pressure drop at different salinity

**Figure 1.** *Underwater hydroelectric power plant of cyclone action.*

and water temperature. With the help of water hammer, the kinetic energy of the moving liquid is transferred into the potential energy of the resting liquid. However, such a transition is not instantaneous, but proceeds at a certain speed, depending on the properties of the liquid and the geometry of the pipeline. The HYPOT enclosure has a two-phase hyperbole geometry that reproduces the narrowing configuration in the center of the torus.

This is done by analyzing the vector of motion of the lifting flow for the maximum approximation to natural conditions. With the tower version, the tower creates the initial necessary pressure for the operation of pulse devices (on the principle of "water hammer"), so the project refers to a gravitational-pulse hydroelectric power plant, since the potential energy of water is the gravitational energy accumulated in it.

### **2. Theoretical prerequisites for calculation**

Calculations of the HYPOT prototype in the ANSYS software package clearly proved the effect of water hammer into the neck of the tower on the increase in flow [1–3]. **Figure 2** shows spatial scheme of HYPOT digital twin for calculation in ANSYS as opposed to simple OMP [4]. The diagrams in **Figures 3** and **4** show how the pressure vector increases as the current in the collector moves to the neck of the tower, where there is a sharp pressure drop of 26.5 times, and the jump in the value of the flow vector increases respectively to 87.54 m/s due to water hammer. The calculation is made with the assumption that the entire volume of the incoming water flow flows into the collector. In order to find the balance of the incoming water into the collector and bypass it, it will be necessary to further solve the problem of multipoint calculation of the hydroelectric power plant, including the maximum possible sphere of water surrounding the station, in order to understand the losses at the entrance to the collector. Since the station works in general with water hammer and the release of water through the upper nozzle, the assumption that the entire volume of water will fall into the collector has a small error due to strong centripetal and forward motion along the current upwards in a hyperbolic tower.

#### **Figure 3.**

*Pressure at the speed of 4.5 m/s and inlet water flow of 32,4 m3 /s.*

Hydraulic shock at HYPOT is a short-term, but sharp and strong increase in pressure in the collector with a sharp braking of the fluid flow moving through it from the outside. The phenomenon of water hammer [5] here is creative - it is with its help that an impulse is given to the water intake, which then obeys Bernoulli's law of communicating vessels rises up, throwing water from the nozzle of the tower under high pressure.

First of all, it is necessary to take into account the high speed of the water hammer process. Since the speed of movement of the boundaries of zones with different

**Figure 4.** *Volocity speeds at the water speed 4.5 m/s and the incoming water flow of 32.4 m3 /s.*

pressures at high rigidity of the body and neck is determined by the speed of propagation of elastic deformations in the liquid, i.e. the speed of sound, everything happens in a very short time.

As the size of the tower increases, the power of the water hammer increases significantly, and at the same pressure at the entrance to the tower, this growth is usually steeper than the linear dependence. Here we will consider the qualitative reasons for this behavior (quantitative results automatically follow from the calculations in the ANSYS program given in the following sections of this page).

However, with an increase in linear mass sizes (and, consequently, kinetic energies at the same rate) increase in proportion to the volume, i.e. the cube of their change, and the friction losses against the walls of the pipe are proportional to the contact area, that is, the square of the size change. Thus, the specific loss of energy per friction per unit mass of the liquid decreases, which means that with the same driving force (external pressure), the flow rate increases, and hence the pressure jump at the time of stopping.

It should be noted that the pressure jump during water hammer does not depend on the initial pressure that caused the liquid to move through the tower, but depends only on the speed obtained by it. This means that the acceleration of a liquid with a relatively high pressure in a short time can be replaced by a longer acceleration under the influence of lower pressure. However, it will not be possible to indefinitely reduce the acceleration pressure: first, in real conditions, the low pressure already at a not too high flow rate will all go to compensate for hydraulic friction; secondly, even for super fluidity, there is a limit to the maximum speed that the flow can reach at a given head at the entrance to the tower in accordance with Bernoulli's equation.

However, it is this circumstance that allows hydraulic rams to raise the fluid to a height many times higher than the difference in levels that leads them.

Finally, it should be noted that the vacuum, up to the almost complete absence of pressure with a strong water hammer, does not mean that at this stage the liquid leaves the entire tower pipe. This only means that the liquid ceases to put pressure on its walls. In reality, the void is formed only in the separation zone near the neck of the tower - in the same place where there was a water hammer with a sharp change in flow.

Where does the fluid accelerate?

First of all, it is necessary to find out where the acceleration of the liquid occurs in the tower or outside it? The continuity equation gives an unambiguous answer: inside the tower of the unchanged cross-section, the flow rate is also unchanged, which means that all the acceleration occurs in the tank in front of the tower! It is easy to imagine by observing the discharge of water from the bath - the "funnel" over the drain hole is due to the zone of acceleration of water, which is located in the volume of the bath itself, and in the drain pipe the water speed no longer changes. Therefore, the water hammer energy is due to the fact that the entire volume of water moves in the pipe at the same speed.

Involving fluid in motion outside the tower.

Involving the fluid filling the tower in the movement beyond it.

The paler color in the chart shows areas at a higher rate. Gradations are shown conditionally, the increase in speed is sharp.

Shock wave damping [6].

As the liquid accelerates before entering the tower when the fluid in the collector has stopped as the result of water hammer, the liquid that has already gained some speed near the manifold entrance is forced to stop. This stop causes an increase in pressure around the inlet to the tower, which is often interpreted as "shock wave exit from the pipe".

However, the pressure drop is large, and therefore the liquid moves faster. Then the pressure outside the tower drops rapidly, and the speed of movement of the liquid outward also increases rapidly.

Finally, it should be recalled that all the processes described here occur very quickly in microseconds!

Above we have considered the water hammer from the "traditional" mechanistic positions.

It should be noted that for a short time, water hammer puts the substance in extremely extreme conditions - the pressure can increase by hundreds or even thousands of atmospheres, which corresponds to conditions at a depth of tens of kilometers. But even if the pressure does not grow very much (by dozens of atmospheres, or even just by several atmospheres), the rate of pressure changes for each particle of matter that falls under the influence is very high - 1012 Pa/s or more. It is quite comparable, and even exceeds the rate of change in pressure during explosions. At the same time, the gas or plasma environment formed during explosions is very compressible - it "absorbs" the impact, and a little further from the epicenter the pressure rises much more smoothly. But during water hammer, due to the low compressibility of liquids and the high rigidity of the wall material, this ultra-fast pressure jump affects almost the entire volume involved in the water hammer. Such sharp jumps in pressure correspond to gigantic accelerations and inhibition of particles of matter when the shock wave front passes through them. True, they last nano- and picoseconds, so the total displacement of liquid particles is small and usually is, in accordance with its low compressibility, micrometers or nanometers. However, by the standards of atoms and molecules, these shifts are very large, and the resulting forces are also significant.

For example, Carré (1705) observed a curious phenomenon: a bullet fired into a wooden box filled with water exploded. A shock bullet, transmitting a large pulse to the water, generates a shock wave that tears the walls [6].

### **3. Analytical calculation**

The subject of these applied research and experimental developments planned for the project is, first of all, the determination of the forces of intermolecular interaction of water in the stream at different pressures and ambient temperatures and when using a cyclone amplifier. Ocean currents carry kinetic energy obtained from solar radiation, entering the collector, the current experiences a sharp drop in pressure on the rise into the neck of the tower and increases the speed due to water hammer, which closes the chain reaction of overcoming gravity and ejecting water through the nozzle of the tower.

Depending on this, the flow rate and volume are calculated to generate electrical energy in a two-phase hyperbolic housing by a spiral turbine, which ultimately

#### **Figure 5.**

*The calculation diagrams of the HYPOT's distribution of velocity and pressure at flow rates m/s in the collector: 1.8; 2.5; 3.2.*


*Hydro Power Tower (HYPOT) DOI: http://dx.doi.org/10.5772/intechopen.100107*

**Table 1.**

*Results of preliminary calculations of the tower for the HYPOT project.*

determines all energy production. Based on the effect of Italian physicist Giacomo Batista Venturi, Daniel Bernoulli Low, Henry Pitot tubes [7] and the Navier–Stokes equation for incompressible liquid, using ANSYS software for the hydropower tower calculation scheme. **Figure 5** shows the calculation diagrams of the HYPOT's distribution of velocity and pressure at flow rates m/s in the collector: 1.8; 2.5; 3.2.

Preliminary calculations of the tower at a depth of 30 meters showed the following results, which are summarized in **Table 1**.

#### **4. Testing the digital twin of the lower**

Based on the preliminary calculations given in Chapter 2, the international HYPOT project developed a prototype of a digital twin hydroelectric power plant for installation in the Strait of Messina off the coast of Sicily (Italy).

The international project included the results of the calculation of an underwater hydroelectric power plant with a tower height of 7.5 m. Below is **Figure 6** of the HYPOT's section of the power plant developed as part of the project.

As you can see from the diagrams above, the initial flow is not essential. for generated hydraulic energy. The main role is played by the pressure difference between

#### *Technological Innovations and Advances in Hydropower Engineering*

the layers and the configuration of the intake manifold, which provides conditions for the occurrence of water hammer and obtaining the strongest acceleration in the neck of the tower. In addition, various sections from round to elliptical were tested from view of the analysis of the hydraulic power of the plant and the results are summarized for the selection of tower sections **Figure 7**. These graphs, being a purely empirical document, should not be distributed in one form or another, in addition, they are valid not only for choosing the configuration of the tower section.

The diagram below in **Figure 8** shows the kinetic energy levels available in the tower. We can see that 41% of this energy is still present at the exit of this tower, the rest is spent on walking from the pass to the exit. This means that up to 41% of the total energy entering the tower can be used to convert into a vortex turbine (the results are deposited from ANSYS CFD). The red curve is something that would be desirable to implement with a turbine so that it can return the maximum energy obtained in both images.

**Figure 6.** *The HYPOT's section of the power plant.*

**Figure 7.** *Analysis of hydraulic power.*

*Hydro Power Tower (HYPOT) DOI: http://dx.doi.org/10.5772/intechopen.100107*

**Figure 8.** *Analysis of kinetic energy levels.*

**Figure 9.** *Prototype of the HYPOT model in 1:3 scale.*

The prototype of the HYPOT's model of scale 1:3 is designed to test the principle of operation of the entire system in the conditions of the mouth of the river flowing into the open sea, shown in **Figure 9**.

The subject of these studies is the problem of creating a new technology for the stream generation of powerful products for underwater hydroelectric power plants and hydrogen production services. The subject of the project is current scientific research (theoretical and experimental), as well as the development of an experimental technical and technological solution for the production of electrical energy in an artificial whirlpool with the possibility of obtaining hydrogen to replenish the peak load of the power plant and use oxygen waste to clean the polluted ocean.

Thus, the subject of the application reflects the research essence and nature of the work (subject and object).

#### *Technological Innovations and Advances in Hydropower Engineering*

**Figure 10.** *Industrial project of HYPOT.*

#### **Figure 11.**

*Industrial prototype of the HYPOT in the Cartesian coordinate system.*

In the following sections, the wording to the description of the subject of the proposed work, as well as the characteristics of the composition of the work and the scientific and technical results of the work on the proposed project, contain the planned innovative solution of various bases (sea suspensions on the pontoon and river installed on the bottom at the mouth of the rivers when they fall into the ocean), which determines the image and contributes to the creation of the future product, which in turn is the determining condition for the implementation of the Horizon 2020 Framework project. Similar innovative marine renewable energy technologies and their integration into the energy system of the European Union, call to the Building low-carbon, climate-resilient future based on unique Highperformance technologies [8].

The industrial prototype of the hydropower tower an as underwater hydroelectric power plant, including a collector with a protective grid, a generator on permanent magnets, a vortex turbine, a tower, a steering bar with the possibility of turning downstream shown in **Figure 10**.

#### *Hydro Power Tower (HYPOT) DOI: http://dx.doi.org/10.5772/intechopen.100107*

Initial assumptions for the calculation of the prototype: The consumption in the design of the HPT prototype is taken 2 m/s, and the water consumption is 18,000 kg/s. The diameter of the neck of the tower at Z = 3.5 m - 1400 mm, Z = 5.6-1600 mm, Z = 7.5-1800 mm.

Preliminary laboratory research work of a hydropower tower model showed that there is a correlation between the power emitted by the jet nozzle and the distance to the surface of the water. That is, the lower the underwater power plant is installed, the higher its power should be for the stability of the entire complex.

The main elements of the model of the underwater hydroelectric power plant of the HPP were made of composite materials and painted with water-resistant nitro paint, since the main condition was to test the high corrosion resistance of the station to ensure its long-term use under water.

The HYPOT in the Cartesian coordinate system shown in **Figure 11** is designed to test the principle of operation of the entire system and compare theoretical and experimental results.

#### **5. The subject of the research**

The subject of the research is the problem of creating a new technology for the stream generation of high-power products for underwater hydroelectric power plants and hydrogen production services. The subject of the project is topical scientific research (theoretical and experimental), as well as the development of an experimental technical and technological solution for the production of electrical energy in an artificial whirlpool with the possibility of obtaining hydrogen to replenish the peak load of the power plant and use oxygen waste to clean the polluted ocean.

It is planned to apply a fairly simple method of dissociation of water into hydrogen and oxygen and a device for its implementation, suitable for industrial use, which will reduce the energy intensity of the water dissociation process and ensure the possibility of separate production of gases.

To solve the problem and achieve the claimed technical result with a known method of dissociation of water for hydrogen and oxygen, including the effect of an electric field on water or water electrolyte through electrodes located at a distance from each other, and the removal of dissociation products, the effect on water or electrolyte of water by an electric field is carried out with a calculated resonant frequency on harmonics, in relation to which the frequency of natural oscillations of water molecules is multiple. And the dissociation products are removed separately from each even and odd electrode.

Of course, the project will use publicly available data from the experience of construction and operation of all known underwater hydropower projects.

The proposed design of an underwater hydroelectric power plant with a vertical turbine and a hyperbolic housing is very different from conventional wind turbines immersed in water.

Unlike the Orbital Marine Power [4], the "Sea Gen" [9] and another invention [10], HYPOT has a steering stabilizer that easily deploys the structure in the direction of the current, which does not require additional expensive equipment to track the direction of the tidal current, which significantly reduces the construction of an underwater hydroelectric power plant.

The steel structure of the hydroelectric power plant is firmly fixed on the seabed on stilts.

It is necessary to compare the cost of building the most powerful offshore wind turbine and a small HYPOT project. At the same time, the tower can grow as in height, that is, fall lower on a very stable concrete base and without problems scale the power at times. And there is no windmill. This is its limit with the scope of the wind wheel of several hundred meters. At the same time, the weight of the windmill is several tens of times greater.

Oh well, that's why we cover 94% of the solar radiation falling into the ocean and distributed in the currents. And we can bring the power of HYPOT to the required values. And marine windmills have their own limit, depending on the huge size, and perceive only 6% of the solar radiation reflected from the surface of the ocean and distributed in the atmosphere. And do not forget that the density of water is 800 times higher than the density of air, that is, the energy losses in the twigs are simply not comparable to HYPOT.

HYPOT perceives the potential energy of the water hammer, which accumulates as the liquid moves in the collector and almost completely stops it in front of the neck of the tower. When a water hammer occurs in milliseconds, the speed increases according to Bernoulli's law and water gushes into an area of low pressure. Therefore, the process of wave, that is, the incoming kinetic energy is quantized. That is, the process is subject to quantum mechanics, and not just put a windmill in the wind.

HYPOT will completely abandon the construction of dams on rivers. They are no longer needed. Mankind has been using the power of falling water for centuries to obtain electrical energy. Hydroelectric power plants have been operating for decades and affect the climate. Apparently, this is why most people deny a fundamentally new source of energy from water rising up. The conversion of potential energy into kinetic energy occurs into a rollback Gravitational energy is accumulated in water, which is used in soliton therefore the HYPOT has following advantages:


In marine conditions, the underwater power plant should operate mainly on the bottom, in the lower reaches, although its design allows it to work in a suspended pontoon state, but in any case, its design should be simple and easily replaceable, which maximizes the profitability of electricity generation and reduces production costs.

#### **6. Development**

On the basis of fundamental and applied interdisciplinary research, this project considers the development of methodological, engineering and technological foundations for the creation of a new generation of environmentally friendly and costeffective technologies and autonomous energy systems based on the use of kinetic and potential energy of bottom and surface currents resulting from changes in temperature and pressure at different depths of the World Ocean and continental rivers.

The project solves the problem of creating efficient energy technologies for autonomous decentralized power supply of offshore oil platforms, including on the Arctic shelf, using new generation underwater power plants and intelligent automated control systems.

The central problem requires consideration and solution of a number of subtasks:

Development of modern computational methods and calculation tools, digital design methods, materials and technologies for the creation of underwater hydroelectric power plants with vertical spiral blades of medium and high power with high hydrodynamic characteristics and structural strength for the conditions of real runoff of bottom and surface waters, as well as climatic conditions inherent in the northern territories.

Analysis, research and development of the theory of intelligent control of the underwater power grid of cyclone HPPs on the example of the use of a primary energy source with a "random" or "stable" nature of the arrival, its reliable forecasting for different time intervals and the development of software and technologies for its effective use.

#### **7. Findings**

The development of computers, in particular cluster technologies, allows the use of computational methods of hydrodynamics in the calculation of viscous currents in turbomachines. The introduction of numerical modeling in the process of development and research of the device allows you to reduce the cost of subsequent experimental refinement, and ideally abandon it.

This gives more freedom when solving problems of optimizing the geometry of the blade and other elements, external problems, without resorting to the formulation of the experiment.

To simulate the characteristics and calculation of spiral hydraulic turbines, methods of CFD analysis with large grids comparable in number of cells with calculations of

non-sequencer processes, as well as the need for calculations on several low-detectable points to obtain the maximum efficiency mode and increase the energy eclipse of air ducts through four-blade horizontal-axial acceleration using active control systems, new profiles and geo-optimization are proposed blade metrics.

Preliminary results of mathematical tests showed significant results from the possible introduction of such power plants, which can be seen from the attached graph of the dependence of the hydraulic power capacity of the power plant on water consumption.

To study the effect of water hammers on renewable energy, it is proposed to create a pulsed shock wave generator that reproduces shocks close to real ones, and studies their effect on fragments of carbon fiber blades of spiral turbogenerators. Experimental studies of the influence of these effects on the blades are proposed.

As part of the task of digital design of elements and structures of a hydroelectric power plant, it is proposed to develop a design model of a blade system operating in real natural and climatic conditions, conduct CFD analysis using a high-performance cluster and build a 3D model of the blade that has better hydrodynamic performance and less weight compared to analogues.

The solution to the problem of creating a methodology for digital design of the conditions of the Far North (working under the ice) is interdisciplinary and complex: both known proven and tested methods from various branches of science and technology will be thoroughly studied and applied.

Scientifically based technical and technological solutions obtained during the work will be used to improve energy efficiency, efficiency, reliability, safety and technology in the North Sea.

The result of this approach will be the search for solutions for maximum autonomy of power plants without maintenance for a long time, respectively, the proposed systems will be more focused on self-healing, diagnostics and reconfiguration.

Analysis of the problem of building decentralized energy systems based on renewable hydropower sources using the theory of intelligent control.

Analysis and research of modern theoretical and applied issues of calculation, modeling and design of hydro turbine gravitational hydroelectric power plants for their manufacture using a new automated production technology.

Analysis of existing systems of active regulation of fluid flow in marine energy applications.

The analysis of the modern CAD world is adapted for end-to-end digital design of marine gravitational energy sources.

As part of the study of the existing scientific base, a method for forecasting underwater marine and channel river hydropower resources in different time intervals will be developed in order to configure the proposed energy device with the development of an interdepartmental approach to solving project problems.

#### **Notes/acknowledgements/other statements**

I want to express my deep gratitude to my daughter Helen and friends who took part in the request for a project to study a new renewable energy source.

#### **Conflict of interest**

The authors state that there is no conflict of interest.

*Hydro Power Tower (HYPOT) DOI: http://dx.doi.org/10.5772/intechopen.100107*

### **Abbreviations and abbreviations**

HYPOT Hydropower Tower

#### **Author details**

George Mamulashvili Highest Attestation Commission of the Russian Federation, Moscow, Russia

\*Address all correspondence to: Gsmprado2018@gmail.com

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### **References**

[1] Petostatic tube. Copyright © 2021 Elsevier B.V. or its licensors or authors. ScienceDirect ® is a registered trademark of Elsevier B.V. [Internet] Available at: https://www.sciencedirect. com/topics/engineering/pitot-statictube/

[2] Generating renewable power from water hammer 2 pressure surges A. Robertsa,∗ , B. Thomasa,, P. Sewella,, E. Hoarea, 3 4 aDepartment of Design and Engineering, Bournemouth University, Poole, Dorset, BH12 5 5BB [Internet] is available at: http://eprints. bournemouth.ac.uk/30975/1/renewable-1-BT.pdf;

[3] Hydraulic Pump Analysis and Improvement Using Computational Fluid Dynamics (CFD) by Piyush B. Shende Dr. S. K. Choudhary, A. P. Ninawe, IJIRST – International Journal of Innovative Research in Science and Technology| Volume 2 | Issue 03 | August 2015 ISSN (online): 2349-6010 All rights reserved www.ijirst.org 109 [Internet] Available at: http://www.ijirst.org/ articles/IJIRSTV2I3043.pdf

[4] Orbital Marine Energy (Orkney Islands) plc. Orbital 02 2 MW Tidal turbine. EMEC Pier 5, Fall of War, Edei, Orkney Islands. A summary of the project [Internet] is available at: https:// marine.gov.scot/sites/default/files/ project\_information\_summary\_4.pd f/ SR2-2000 Draft Information Document for a Maritime License.

[5] Water Hammer 1st Edition Practical Solutions 0.0 star rating Write a review Authors: Bruce Sharp David Sharp Hardcover ISBN: 9780340645970 eBook ISBN: 9780080543673 Imprint: Butterworth-Heinemann Published Date: 1st December 1995 Page Count: 192ISBN 978−0-340-64597-0 Language English Published 1995 Copyright Copyright © 1995 Elsevier Ltd.

All rights reserved Butter Imprintworth-Hemann DOI Available at: https://www. elsevier.com/books/water-hammer/ 9780340645970

[6] Handbook of Shock Waves Front Matter Copyright PREFACE CONTRIBUTORS Volume Contents SBN 978-0-12-086430-0 Language English Published 2001 Copyright Copyright © 2001 Elsevier Inc. All rights reserved Imprint Academic Press. Available at: https://www.sciencedirect. com/book/9780120864300/ handbook-of-shock-waves#book-info

[7] Arlan Skortegaña AlmeidaVladimir Caramori Borges de Sousa. An alternative method for measuring velocities in open channel flows: evaluating the performance of a Pitot tube compared to an acoustic meter. Available at: https://www.scielo.br/j/ rbrh/a/TqFxzyvfnHQZMky9c6nRQsq/ ?lang=en#/

[8] Research and innovation of the European Green Deal (H2020-LC-2020). [Internet] Available at: https:// waterquality.danube-region.eu/ new-calls-are-available-at-euroaccess/.

[9] SeaGen-S 2MW - SIMEC Atlantis Energy [Internet] is available at: https://atlantisresourcesltd.com/wp/ wp-content/uploads/2016/08/SeaGen-Brochure.pdf;

[10] US7832979B2.Vortex hydraulic turbine. United States. Inventor: Metin Ilbay Yaras; Mohammad Golriz. Application US11/736,766 event. [Internet] Available at: https://patents. google.com/patent/US7832979B2/ en?oq=US+Patent+7832979

Section 3

## Hydropower Managment Development

#### **Chapter 4**

## Improved Memetic Algorithm for Economic Load Dispatch in a Large Hydropower Plant

*Ling Shang, Xiaofei Li, Haifeng Shi, Feng Kong and Ying Wang*

#### **Abstract**

This paper is intended to study the method of solving the economic load dispatch problem (ELDP) of hydropower plants via using memetic algorithm. Based on characteristics of economical operation of the hydropower plant, this paper proposes an improvement method of mutation operator and selection operator of memetic algorithm. Taking Three Gorges hydropower station in China as an example, the performance of memetic algorithm before and after improvement is tested separately. The test result shows that the average water consumption for simulation of the improved memetic algorithm is less than that for simulation of the standard memetic algorithm by 1.35%–16.19%. When the total load of the hydropower station is low (8GW-10GW), the water consumption for the improved memetic algorithm is less than that for the standard memetic algorithm by more than 10%. When the total load of the hydropower station is high (11GW-16GW), the water consumption for the improved memetic algorithm is less than that for the standard memetic algorithm by more than 1%. This shows that improvement of mutation operator and selection operator can improve the global and local optimization capacity of memetic algorithm a lot indeed. In addition, by comparing the optimization result of memetic algorithm with that of DP algorithm, it finds that the optimization result of improved memetic algorithm can reach the same precision of optimization result of DP algorithm. Therefore, using the improved memetic algorithm to solve the ELDP problem of large hydropower stations is practical and feasible. Since "curse of dimensionality" may occur frequently while using DP algorithm to solve the ELDP problem of large hydropower plants, as a new heuristic algorithm, memetic algorithm has obvious advantages in solving large-scale, complex, highly-dimensional and dynamic problems.

**Keywords:** economic load dispatch problem, Three Gorges hydropower station, memetic algorithm

#### **1. Introduction**

All the time, humans are inspired from the nature and discover many natural laws by observing and thinking natural phenomena. People have obtained abundant inspirations for solving various problems based on these natural laws and their own thoughts [1]. In 1975, Holland proposed a stochastic optimization algorithm by reference to the natural law of "survival of the fittest" in the biosphere and the algorithm was called genetic algorithm (GA) later [2]. Although the genetic algorithm has a strong global optimization capacity, it has many defects [3]. For example, the genetic algorithm searches the whole objective group but only converges to one optimal solution finally. To improve the addressing efficiency, the genetic algorithm does not search all populations and individuals, causing failure to explore the whole available space. Hence, diversity of populations is lost and finally GA cannot find out the real optimal solution correctly but can only find out the relatively optimal solution [4]. In 1989, Moscato proposed to combine global search based on population with local heuristic search based on individual, so as to prevent insufficient search scope of genetic algorithm and prematurity of the algorithm [5, 6]. This is the primary design concept of memetic algorithm (MA). At first, the memetic algorithm was regarded as improvement of genetic algorithm and therefore was called "hybrid genetic algorithm" [7, 8]. With continuous research, the memetic algorithm has been developed into a general evolutionary algorithm framework consisting of global search strategy and local search strategy [9, 10].

Within the framework, great improvement space exists in the memetic algorithm. For a specific problem, a memetic algorithm suitable for the problem can be constructed flexibly [11–13]. During construction of the memetic algorithm, on the basis that the global search strategy of genetic algorithm is reserved, the researcher generally proposes an improvement scheme of local zone search strategy based on the problem characteristics, so as to construct various memetic algorithms. For example, Yeh [14] developed a memetic algorithm by combining a genetic algorithm and the greedy heuristic using the pairwise exchange method and the insert method, to solve the flowshop scheduling problem. Boughaci et al. [15] proposed an improved memetic algorithm by using a stochastic local search (SLS) component combined with a specific crossover operator. The resulting algorithm is proved to be able to solve the optimal winner determination problem in combinatorial auctions. Zou [16] solved the traveling salesperson problem (TSP) by using an improved memetic algorithm. The algorithm applies multiple local search strategies and each search operator executes with a predefined probability to increase the diversity of the population, so as to ensure a higher search efficiency of the algorithm. Castro et al. [17] proposed a new memetic algorithm for solving the traveling salesperson problem (TSP) with hotel selection. Using tabu search algorithm and individual neighborhood information as the meta-heuristics search algorithm and genetic algorithm as the global search strategy may obtain several feasible schemes in one time. In fact, the memetic algorithm has achieved a very good application effect in solving the scheduling problem in material distributing and supply chain management [18–20].

In recent years, the memetic algorithm attracts more and more attention from researchers of other industries and the algorithm achieves considerable development with continuous efforts of many researchers [21–24]. Ammaruekarat and Meesad [25] proposed an improved multi-objective memetic algorithms (MOMAs) for solving the multi-objective decision problem. This paper proposes a new iterative search strategy—Chaos Search and uses it as the local search strategy of the memetic algorithm. Combining with Chaos theorem, the efficiency of solving the multi-objective decision problem will be improved a lot and good results are achieved. Özcan et al. [26] developed an Interleaved Constructive Memetic Algorithm (ICMA), and successfully applied ICMA for Timetabling problems with complicated and challenging structures. In addition, the memetic algorithm is also frequently applied to the neural network training algorithm. O'Hara and Bull [27] and Abbass [28] use the memetic algorithm to train the neutral network separately and believe that the effect of neuron network training with the memetic algorithm

#### *Improved Memetic Algorithm for Economic Load Dispatch in a Large Hydropower Plant DOI: http://dx.doi.org/10.5772/intechopen.100309*

is better than that with the traditional method. Bonfim and Yamakami [29] not only use the memetic algorithm to train the neural network system, but also use it for Parallel Machine Scheduling, both which have achieved good effects.

Economical operation of hydropower plants is a very complex multi-objective optimization difficulty [30, 31]. Using traditional methods such as equal increment and dynamic programming for solving the problem cannot achieve perfect results [32, 33]. Especially for large hydropower stations, "curse of dimensionality" may occur frequently while using the dynamic programming algorithm for unit load dispatch, causing that load dispatch cannot meet the requirement of real-time control or the load cannot be dispatched at some times [34]. Three Gorges hydropower station in China is the hydropower plant with the largest installed capacity in the world at present; 32 units of seven types are installed; the capacity of single unit is 700,000 kW; and the total installed capacity is up to 22,400,000 kW. Although the generating capacity per unit is the same, the output character of unit is quite different due to different manufacturer of the unit [35]. Thus, using the simplified generating efficiency function to describe the generating character of all units is improper. Similarly, expressing the generating efficiency as the linear function of head will cause a big difference between the calculation result and actual operation condition [36].

Taking Three Gorges hydropower station in China (the largest hydropower station in the world) as an example, this paper studies the modeling method of economical operation model of Three Gorges hydropower station and proposes a method of using memetic algorithm to solve load dispatch and real-time scheduling of generating unit of Three Gorges hydropower station. On this basis, this paper refers to the optimization idea of differential evolution algorithm, further optimizes the solving process of ELDP problem and improves the memetic algorithm. The structure of residual parts of this paper is as follows: introduce the economical operation model of hydropower plant at first, introduce dynamic programming suitable for solving of the model, describe the standard memetic algorithm and its improvement method, use the memetic algorithm for solving of economical operation model of hydropower plant, compare the performance of memetic algorithm with that of dynamic programming, and discuss the possibility of application of memetic algorithm to the ELDP problem of hydropower plant. At last, this paper gives conclusions and looks forward to the application prospect of memetic algorithm.

#### **2. Methodology**

#### **2.1 Formation of ELDP problem of hydropower plant**

The ELDP problem of hydropower plant means that when the required load of system (the daily load chart is given generally in short-term economical operation) is determined, the consumed power discharge of the whole hydropower plant shall be the minimum, so as to obtain the maximum economic benefit of the hydropower plant [37]. For the economical operation model of hydropower plant, the minimum power discharge is the objective. The objective function and constraint conditions of the ELDP problem of hydropower plant are as follows:

Objective function:

$$\min Q = \sum\_{i=1}^{n} q\_i(N\_i, H) \tag{1}$$

Load balancing constraint:

$$\min Q = \sum\_{i=1}^{n} q\_i(N\_i, H) \tag{2}$$

Constraint of operation condition zone of unit:

$$0 \le N\_i \le N H\_i, \text{and } N\_i \notin \left[ \underline{N\_{i,j}}, \overline{N\_{i,j}} \right], j \in \Omega\_i(H) \tag{3}$$

Where, *Q* is the total power discharge; *n* is the number of units; *qi* ð Þ∙ is the power discharge of unit *i* (m<sup>3</sup> /s); *Ni* is the output of unit *i* (MW); *H* is the average head of time periods (m); *Nd* is the required load of power grid (MW); *NHi* is the expected output of unit *i* (MW); ?*i*ð Þ *H* is the set of vibration zones of unit *i*; *Ni*,*<sup>j</sup>* and *Ni*,*<sup>j</sup>* are the upper and lower limits of vibration zone *j* of unit *i* at the given head *H* respectively (MW).

It should be noted that the unit of hydropower plant will break through the constraint of unit operation condition inevitably during operation and operate in the restricted operation zone or even in the forbidden operation zone. If the unit operates in the restricted operation zone for a long time, the flow passage components will be damaged; the output and efficiency will be reduced; and noise and strong vibration of unit will be caused. In severe cases, longitudinal cracks will occur on the dam, endangering safety of the hydropower station and surrounding areas. To meet actual demands, not only the restriction of expected output of unit but also the requirements of avoiding unit cavitation zone/vibration zone are considered in the constraint of unit operation condition zone in the above model. In the optimization algorithm design later in this paper, the study will apply the penalty function method to handle the output-flow relation curve of unit cavitation zone/vibration zone, so as to make the unit avoid the unsafe operation zone as far as possible during load dispatch.

#### **2.2 Solution approaches**

#### *2.2.1 Dynamic programming (DP): A review*

Dynamic programming method is a classic and mature optimization algorithm. It regards the ELDP problem of hydropower plant as a multi-stage decision problem and has no restrictions on that whether the unit model is the same. In addition, the number of operating units, combination of units, load and corresponding water consumption of each unit can be obtained as well as the globally optimal solution [38]. The dynamic programming algorithm is used to solve the ELDP problem of hydropower plant. Details of the variable definition, constraint handling and solving process are as follows:

#### *2.2.1.1 Stage variable and state variable*

The serial number *i* of generator unit is the stage variable while the cumulative output of *i* units (P*<sup>i</sup> <sup>t</sup>*¼<sup>1</sup>*Nt*) is the state variable.

The step size of sate discretization is *dN* and the cumulative output is subject to state discretization as per the following formula:

$$\text{Ns}\_{i\circ} = \left\{ \begin{array}{c} \min \left\{ \\ \end{array} \right\} \begin{array}{c} \min \left\{ \\ \end{array} \right\} \begin{array}{c} \text{N}Y\_{\ell}, \text{Nd} \\ \end{array} \right\}, \quad \text{when } i \neq n \tag{4}$$
 
$$\text{Nd}, \qquad \text{when } i = n$$

*Improved Memetic Algorithm for Economic Load Dispatch in a Large Hydropower Plant DOI: http://dx.doi.org/10.5772/intechopen.100309*

Where,

$$j = \mathbf{0} \sim \text{int}\left[\min\left\{\sum\_{t=1}^{i} NY\_{t}, ND\right\} / dN\right] + \mathbf{1}$$

*Nsi*,*<sup>j</sup>* is the state variable value at stage *i* and state *j*; *NYt* is the installed capacity of unit *t*; and int½ � ∙ is the Gauss rounding function.

#### *2.2.1.2 Constraint handling*

While using the penalty function to handle the output condition constraint of unit, consider that the objective function of penalty quantity at stage *I* ( *fi Ni* ð Þ , *H* ) is as follows:

$$f\_i(N\_i, H) = q\_i(N\_i, H) + \Delta q\_i + \Delta q p\_i \tag{5}$$

$$
\Delta q\_i = a\_1 \bullet \text{INF}, \Delta q p\_i = a\_2 \bullet \text{INF} \tag{6}
$$

Where,

$$a\_1 = \begin{cases} \mathbf{1} & N\_i \in \left[ \underline{N\_{i,j}}, \overline{N\_{i,j}} \right], \exists j \\ \mathbf{0} & N\_i \notin \left[ \underline{N\_{i,j}}, \overline{N\_{i,j}} \right], \forall j \end{cases} \tag{7}$$

$$a\_2 = \begin{cases} 1 & N\_i \in ( -\infty, 0) \cup (NH\_i, +\infty) \\ 0 & N\_i \in [0, NH\_i] \end{cases} \tag{8}$$

Where, Δ*qi* is the penalty term of constraint of operation condition zone and Δ*qpi* is the penalty term of constraint of output definition domain. *α*<sup>1</sup> and *α*<sup>2</sup> are the penalty coefficients and *INF* is the maximum.

#### *2.2.1.3 State transition and state traversal*

Using *Ni* as the decision variable, the state transition equation can be written as follows:

$$\sum\_{t=1}^{i} N\_t = \sum\_{t=1}^{i-1} N\_t + N\_i \tag{9}$$

Recurrence equation:

$$Q\_i^\*\left(\sum\_{t=1}^i N\_t\right) = \min\left\{ f\_i(N\_i, N) + Q\_{i-1}^\*\left(\sum\_{t=1}^{i-1} N\_t\right) \right\} \tag{10}$$

Where, *Q* <sup>∗</sup> *i* P*<sup>i</sup> <sup>t</sup>*¼<sup>1</sup>*Nt* � � is the optimal cumulative power discharge in the remaining period.

#### *2.2.2 Memetic algorithm*

Local search is the root cause that the memetic algorithm is better than the genetic algorithm. Through local search, the search depth of the algorithm for the solution space is increased a lot, further improving the solution quality. In this paper, the memetic algorithm using simplex optimization method for local search operation is called standard memetic algorithm. In the following, we will introduce how to use the memetic algorithm to solve the ELDP problem of hydropower plant and give emphasis on the improvement method of standard memetic algorithm for the ELDP problem of hydropower plant.

#### *2.2.2.1 Standard memetic algorithm (SMA)*

For the ELDP problem of hydropower station, the memetic algorithm applies integer encoding and establishes a corresponding relation between encoding and cumulative output value of unit. Details of encoding of memetic algorithm, initial population generation method, definition of fitness function and its main operators are as follows:

#### *2.2.2.1.1 Gene encoding*

The cumulative output of *i* units (P*<sup>i</sup> <sup>t</sup>*¼<sup>1</sup>*Nt*) is defined as genes. Based on Formula (4) for discrete units with discrete step length defined as *dN*<sup>0</sup> , the genes are encoded as *pk*,*<sup>i</sup>* <sup>¼</sup> <sup>0</sup> � min <sup>P</sup>*<sup>i</sup> <sup>t</sup>*¼<sup>1</sup>*NYt*, *Nd* n o*=dN*<sup>0</sup> h i <sup>þ</sup> 1 to represent the element sequence of *Nsi*,*<sup>j</sup>*.

The cumulative output of *i* units is decoded as *Nsi*,*pk*,*<sup>i</sup>* (*k* ¼ 1 � *Pop*, *i* ¼ 1 � *n*, *Pop* stands for population and *n* stands for number of units).

#### *2.2.2.1.2 Initial population generation*

The linear constrained elimination method is used to generate the genes in reverse order under the conditions of load balance and output domain constraints.

When the cumulative output of *i* units is known as P*<sup>i</sup> <sup>t</sup>*¼<sup>1</sup>*Nt*, then

$$p\_{k,i} = \text{int}\left[\sum\_{t=1}^{i} N\_t / dN'\right].$$

The state transition equation (9) can be re-written as:

$$\sum\_{t=1}^{i-1} N\_t = \sum\_{t=1}^{i} N\_t - N\_i \tag{11}$$

When the output feasible region constraint of unit *Ni* ∈ 0, *NYi* ½ � is integrated into Formula (11), then:

$$\sum\_{t=1}^{i-1} N\_t \in \left[ \sum\_{t=1}^i N\_t - NY\_i, \sum\_{t=1}^i N\_t \right] \tag{12}$$

As the output is bound to be smaller than the installed capacity, i.e. *Nt* ∈ 0, *NYt* ½ �, to integrate it into Formula (11):

$$\sum\_{t=1}^{i-1} N\_t \in \left[ \mathbf{0}, \sum\_{t=1}^{i-1} N Y\_t \right] \tag{13}$$

The common solution to Formulas (12) and (13) can satisfy the requirement for output domain, then:

*Improved Memetic Algorithm for Economic Load Dispatch in a Large Hydropower Plant DOI: http://dx.doi.org/10.5772/intechopen.100309*

$$\sum\_{t=1}^{i-1} N\_t \in \left[ \max \left\{ \sum\_{t=1}^i N\_t - N Y\_{i\cdot} 0 \right\}, \min \left\{ \sum\_{t=1}^i N\_{t\cdot} \sum\_{t=1}^{i-1} N Y\_{t\cdot} \right\} \right] \tag{14}$$

Making *Ntmp* <sup>¼</sup> max <sup>P</sup>*<sup>i</sup> <sup>t</sup>*¼<sup>1</sup>*Nt* � *NYi*, 0 n o, *Ntmp* <sup>¼</sup> min <sup>P</sup>*<sup>i</sup> <sup>t</sup>*¼<sup>1</sup>*Nt*, P*i*�<sup>1</sup> *<sup>t</sup>*¼<sup>1</sup>*NYt* n o, the generating approach for gene *pk*,*i*�<sup>1</sup> is expressed as:

$$p\_{k,i-1} = \operatorname{int}\left[\underline{\operatorname{Ntmp}}/d\mathcal{N}'\right] + \operatorname{int}\left[\operatorname{Rnd}\bullet\left(\operatorname{int}\left[\overline{\operatorname{Ntmp}}/d\mathcal{N}'\right] - \operatorname{int}\left[\underline{\operatorname{Ntmp}}/d\mathcal{N}'\right]\right)\right] \tag{15}$$

Where, *Rnd* indicates a random number evenly distributed in the internal [0,1].

Given load balance P*<sup>n</sup> <sup>i</sup>*¼<sup>1</sup>*Ni* <sup>¼</sup> *Nd*, the reverse recursion of Formulas (14) and (15) from the last gene is performed to obtain individuals that satisfy output domain and load balancing constraints.

#### *2.2.2.1.3 Fitness function*

According to the objective function, the fitness formula is constructed:

$$Fitness = \frac{INF}{\sum\_{i=1}^{n} f\_i \left(Ns\_{i, p\_{k,i}} - NS\_{i-1, p\_{k,i-1}}, H\right)}\tag{16}$$

#### *2.2.2.1.4 Crossover operator*

For *Pop* individuals initially generated, select two individuals as per the preset crossover probability for crossover operation and generate a new generation of group (two new individuals).

$$X\_1^{new} = \alpha\_1 \bullet X\_1 + (1 - \alpha\_1) \bullet X\_2 \tag{17}$$

$$X\_2^{new} = a\_2 \bullet X\_2 + (1 - a\_2) \bullet X\_1 \tag{18}$$

*X*<sup>1</sup> and *X*<sup>2</sup> are two parent individuals selected from the population at random; *Xnew* <sup>1</sup> and *Xnew* <sup>2</sup> are new offspring individuals generated by crossover operation; and *ω*<sup>1</sup> and *ω*<sup>2</sup> are parameters selected from [0,1] at random.

#### *2.2.2.1.5 Mutation operator*

Among new individuals generated by crossover operation, select several individuals as per a certain mutation probability and conduct mutation operation as per the mutation operator in the following formula:

$$V\_{i,j}' = \begin{cases} X\_{i\bar{j}} + \left(b\_{\sup} - X\_{i\bar{j}}\right) \left[r \bullet \left(1 - t\right)^2\right], \text{sign} = \mathbf{0} \\\\ X\_{i\bar{j}} - \left(X\_{i\bar{j}} - b\_{i\bar{n}\bar{f}}\right) \left[r \bullet \left(1 - t\right)^2\right], \text{sign} = \mathbf{1} \end{cases} \tag{19}$$

Where, *Xi*,*<sup>j</sup>* is the component *j* of selected mutation individual *Xi*; *V*<sup>0</sup> *<sup>i</sup>*,*<sup>j</sup>* is the individual after mutation; *sign* is 0 or 1 at random; *bsup* and *binf* are the upper and lower limits of parameters respectively; *r* is the random number from [0,1]; and *t* is the population evolution mark and *t* = *gc*/*G*max, where *gc* is the current evolution algebra of population while *G*max is the maximum evolution algebra of population.

#### *2.2.2.1.6 Selection operator*

Select *Pop* excellent individuals from the current population, make them have the chance to be selected to the next iteration process, and abandon individuals with low fitness. The probability of each individual to be selected is in direct proportion to its fitness and the selection probability is as shown in Formula (20):

$$p'\_i = \frac{\frac{1}{f\_i}}{\sum \frac{1}{f\_i}}\tag{20}$$

#### *2.2.2.1.7 Local search operation*

The simplex method is used for local search operation, namely, for the convex polyhedron consisting of *n* + 1 peaks (*X*1, *X*2, … , *Xn*, *Xn* + 1) in *n*-dimensional space, calculate function values of *n* + 1 peaks and confirm the worst peak *Xw*, secondary bad peak *Xs* and optimal peak *Xb* and the centroid *Xm* of all points other than the worst peak in the simplex:

$$X\_m = (X\_1 + X\_2 + \dots + X\_n + X\_{n+1} - X\_w)/n \tag{21}$$

Then, calculate the reflection point *Xr* passing *Xm* and *Xw*:

$$X\_r = X\_m + (X\_m - X\_w) \tag{22}$$

There are three possible conditions for the reflection point:


In all the above conditions, the new simplex must have a peak better than certain peak of the initial simplex; the simplex is subject to reflection, extension and compression through circulation; and the search process may converge to certain locally optimal solution or may be completed till meeting the termination condition.

#### *2.2.2.2 The improvement to SMA (improved MA, IMA)*

Differential Evolution Algorithm is also an effective technique to solve complex optimization problems, which is widely used in the fields of parameter optimization, neural network training, robot, energy and so on [39–42]. The Differential Evolution Algorithm in essence is a kind of greedy genetic algorithm based on real

#### *Improved Memetic Algorithm for Economic Load Dispatch in a Large Hydropower Plant DOI: http://dx.doi.org/10.5772/intechopen.100309*

number encoding with the idea of guaranteeing optimality, which solves the optimization problems through the cooperation and competition among individuals in the population [43]. In this paper, the optimization idea of Differential Evolution Algorithm is used for reference to improve the mutation operators and selection operators of Standard Memetic Algorithm (SMA). The improvement methods for the mutation operators and selection operators of SMA are as follows:

#### *2.2.2.2.1 Improvement to mutation operator*

In differential evolution, the mutation operation uses the linear combination of multiple individuals in the parent population to generate new individuals, of which the most standard mutation component is the difference vector of the parent individual. For any target individual *Xi* in the parent population, the mutation individual *Vi* is generated according to the formula (23):

$$V\_i = X\_{r\_1} + F(X\_{r\_2} - X\_{r\_3}), i = 1, 2, \cdots \\Pop \tag{23}$$

Where, {*Xr*<sup>1</sup> , *Xr*<sup>2</sup> , *Xr*<sup>3</sup> } are three different individuals randomly selected from the parent population, and *r*<sup>1</sup> ¼6 *r*<sup>2</sup> ¼6 *r*<sup>3</sup> ¼6 *i*, in which F is the zoom factor and the value range is [0,2], which is used to control the influence of the difference vector *Xr*<sup>2</sup> � *Xr*<sup>3</sup> ð Þ.

#### *2.2.2.2.2 Improvement to selection operator*

The "greedy" selection method [44] is adopted in the selection operation, and *Vi* is accepted by the population if and only if the fitness value of the new vector individual *Vi* is better than that of the target vector individual *Xi*. Otherwise, *Xi* will remain in the next generation population and continue to perform mutation and crossover operations as the target vector in the next iterative computation. For the minimization problem:

$$X\_i^{t+1} = \begin{cases} V\_i & f(V\_i) < f\left(X\_i^t\right) \\ X\_i^t & \text{Other} \end{cases} \tag{24}$$

The selection operation is the one-to-one competition between the parent individuals and the newly generated candidate individuals to select the superior and eliminate the inferior, so that the offspring individuals are always superior to or equal to the parent individuals and thus the population can always evolve towards the optimal solution.

#### *2.2.2.3 Workflow of memetic algorithm*

**Figure 1** shows the flow diagram of the Memetic Algorithm. The execution steps of the Memetic Algorithm are as follows: ① to determine the coding scheme of the problem and set the relevant parameters; ② to initialize the population; ③ to execute the crossover operator; ④ to use the local search algorithm to conduct neighborhood search for individuals, and update all individuals. ⑤ To execute the mutation operator to generate new individuals. ⑥ To use the local search algorithm to conduct neighborhood search for individuals again, and update all individuals. ⑦ To calculate the fitness value of all individuals in the population through the fitness function.⑧ To execute the selection operator for the population screening as per the natural law of "survival of the fittest" to abandon the individuals with poor fitness and retain the individuals with high fitness. ⑨ To determine whether the

*Technological Innovations and Advances in Hydropower Engineering*

**Figure 1.**

*Flow diagram of the memetic algorithm.*

termination conditions are met. To determine whether the optimization criteria or the termination conditions of the algorithm have been met; if met, terminate the operation, otherwise continue to execute step ③.

#### **3. Experiment, results and analysis**

#### **3.1 Experimental setup**

The Three Gorges Hydropower Station is equipped with 14 generating units on the left bank and 12 on the right bank. Currently, 26 units of the power plants on the left and right banks have been automatically put into the power grid operation. The configuration of these units in the Three Gorges Hydropower Station is shown in **Figure 2**. Those 26 units can be classified into 5 categories: # 1 - # 3 and # 7 - # 9 are VGS; # 4 - # 6 and # 10 - # 14 are ALSTOM I; # 15 - # 18 are ORIENTAL I; # 19 - # 22 are ALSTOM II; and # 23 - # 26 are HARBIN. The output curves of the five types of units differ greatly. The unit output curves are shown in **Figure 3**.

*Improved Memetic Algorithm for Economic Load Dispatch in a Large Hydropower Plant DOI: http://dx.doi.org/10.5772/intechopen.100309*

Under the operating condition that the head of Three Gorges Hydropower Station is at 108 m, the unit load distribution performance of Memetic Algorithm before and after the improvement are tested in this paper. The overall water consumption of the hydropower station is mainly analyzed in the circumstance that the power grid load is increased step by step from 8GW to 16GW and the load distribution is carried out as per the unit load distribution results by Memetic Algorithm. Whether the algorithm performance is good or bad is determined by analyzing the water consumption under a given load. And it is believed that the smaller the total water consumption, the better the algorithm load distribution results, and the better the algorithm performance. In this analysis, 26 units that are automatically put into the power grid operation are taken as the research object in this paper, and the result of the DP algorithm is used as the benchmark for comparison.

The population size of the Memetic Algorithm is set to be 100, then the crossover probability *Pc* = 0.6, the mutation probability *Pm* = 0.5, the penalty factor *λ* = 4000, and the maximum generation *G*max = 300. Considering that the Memetic Algorithm is a stochastic optimization algorithm, the solution has a certain degree of uncertainty. In order to eliminate the influence of the randomness of initial solution on the calculation results, two kinds of Memetic Algorithms before and after the improvement are used in this paper to respectively carry out 10 operations for each load level, from which the best results are selected as the final optimal solution, and the average value of the operation results is used as the final result for analysis.

#### **3.2 Results and analysis**

For the nine load levels of 8GW, 9GW, 10GW, 11GW, 12GW, 13GW, 14GW, 15GW and 16GW, the load distribution schemes of the Memetic Algorithm before improvement (SMA) and of the Improved SMA (ISMA) are used respectively to calculate the total water consumption of 26 generating units of the Three Gorges Hydropower Station, which is shown in **Figure 4**.

It can be seen from **Figure 4** that with the increase of the total load of the hydropower station, the total water consumption of the hydropower station is always on the rise no matter whether the load distribution scheme of the Standard Memetic Algorithm (SMA) or of the improved Memetic Algorithm (ISMA) is adopted. However, on the whole, the average water consumption in the improved Memetic Algorithm is always lower than that of the standard Memetic Algorithm, which shows that the improved Memetic Algorithm reduces the water consumption rate of power generation and improves the utilization efficiency to water resources. **Figure 5** shows the reduction of the water consumption of the Three Gorges Hydropower Plant by ISMA compared with that by SMA.

It can be seen from **Figure 5** that the average water consumption for simulation of the improved Memetic Algorithm is less than that for simulation of the standard Memetic Algorithm by 1.35%–16.19%. The improved Memetic Algorithm saves more than 10% of the water consumption compared with the standard Memetic Algorithm when the total load of the power station is relatively low (8GW-10GW)

**Figure 3.**

*Output curve graphs of the five types of units of the Three Gorges Hydropower Plant (head at 70–110 m, variation interval of water level at 5 m). (a) VGS. (b) ALSTOM I. (c) ORIENTAL. (d) ALSTOM II. (e) HAERBIN.*

and also saves more than 1% of water consumption when the total load of the power station is relatively high (11GW-16GW). This shows that the Memetic Algorithm which improves the mutation operation and the selection operation enhances the global and local optimization capacities of the Memetic Algorithm.

In order to further compare the performances of the two algorithms, the evolutionary processes of the two algorithms at the total load of the Three Gorges Hydropower Station of 8GW, 10 GW, 12GW and 14 GW are analyzed in this paper, which is shown in **Figure 6**. As shown in **Figure 6**, the optimal water consumption obtained by the Standard Memetic Algorithm stimulation decreases in smaller range with the increase of the evolution algebra; the optimal water consumption obtained by the improved Memetic Algorithm stimulation decreases obviously with the increase of the evolution algebra, which shows that the improved Memetic Algorithm can perform an effective global search at the early stage of evolution and make the individuals in the population move closer to the globally optimal solution quickly, compared to which the Standard Memetic Algorithm has a weak global searching ability.

*Improved Memetic Algorithm for Economic Load Dispatch in a Large Hydropower Plant DOI: http://dx.doi.org/10.5772/intechopen.100309*

#### **Figure 4.**

*Total water consumption of the Three Gorges Hydropower Station under the load distribution carried out respectively as per SMA and ISMA calculation schemes.*

**Figure 5.** *Analysis of performance improvement degree of ISMA compared with that of SMA.*

In this paper, the optimal simulation results of the two Memetic Algorithms are compared with the DP optimization results under the same load discrete interval. See **Figure 7** for the comparison results. As can be seen from **Figure 7**, the optimization result of the improved Memetic Algorithm is almost identical with the DP calculation accuracy, while the result of the Standard Memetic Algorithm stimulation is poorer, which shows that compared with the Standard Memetic Algorithm, the improved Memetic Algorithm can effectively search the globally optimal solution. The comparison results indicate that it is feasible to use the improved Memetic Algorithm to solve the problem of economic operation in a large hydropower station.

#### *Technological Innovations and Advances in Hydropower Engineering*

#### **Figure 6.**

*Evolutionary processes of SMA and ISMA. (a) At the load of 8GW. (b) At the load of 10GW. (c) At the load of 12GW. (d) At the load of 14GW.*

**Figure 7.**

*Diagram of comparison between the optimal simulation results of the two memetic algorithms and the optimization results of DP algorithm.*

#### **4. Conclusion and discussion**

Through the in-depth study of biology, scientists gradually find that individuals in the nature behave in a simple manner and with very limited ability, but when they work together, what they show is not a simple superposition of individual capabilities but very shocking and complex behavior characteristics. Inspired by

#### *Improved Memetic Algorithm for Economic Load Dispatch in a Large Hydropower Plant DOI: http://dx.doi.org/10.5772/intechopen.100309*

this, scientists are paying more and more attention to the study of swarm intelligence algorithm, which also includes the study of the Memetic Algorithm. The combination of excellent global searching ability and fast local searching ability can produce enormous energy, therefore, the Memetic Algorithm has been paid more and more attention and has been recognized by more scientists. With the continuous in-depth study, Memetic Algorithm has not only improved the genetic algorithm but also has developed into a loose framework of the optimization algorithm.

In order to solve the problem of economic operation in hydropower plant, a new Memetic Algorithm is presented in this paper. Through the combination with the local search strategy, the Memetic Algorithm not only inherits the global optimization capacity of genetic algorithm itself, but also greatly improves the local searching ability of the algorithm by locally adjusting the new individuals generated by evolution. The framework and operational process similar with that of the genetic algorithm are used in Memetic Algorithm, but the Memetic Algorithm has an additional local search optimization process after crossover and mutation. Memetic Algorithm fully absorbs the advantages of genetic algorithm and local search algorithm and adopts the operational process of genetic algorithm, but after each crossover and mutation, local search is carried out, where the bad population will be removed early by optimizing the population distribution, thus reducing the iterations and speeding up the rate of convergence of the algorithm.

Taking China Three Gorges Hydropower Station, the largest hydropower station in the world, as an example, this paper studies the method of using Memetic Algorithm to solve the problem of economic operation in hydropower plant. The experiment result shows that it is feasible to use the Memetic Algorithm to solve the problem of economic operation in a large hydropower station. The experiment result also shows that the Memetic Algorithm improved by the idea of differential evolution demonstrates a better load distribution performance when compared with that before improvement. When the total load of the hydropower station is relatively low (8GW-10GW), the water consumption for the improved Memetic Algorithm is less than that for the standard Memetic Algorithm by more than 10%. When the total load of the hydropower station is relatively high (11GW-16GW), the water consumption for the improved Memetic Algorithm is also less than that for the standard Memetic Algorithm by more than 1%. This shows that the improvement of mutation operation and selection operation can greatly enhance the global and local optimization capacity of Memetic Algorithm.

As an intelligent algorithm of high efficiency, Memetic Algorithm has obvious advantages in solving large-scale, complex, high-dimensional and dynamic problems. However, the Memetic Algorithm needs a lot of improvements, for example, how to choose global search operators and local search operators, how to determine the control parameters such as population size, crossover probability and mutation probability, etc. All of these problems need to be further improved. In the future research work, the emphasis will be focused on the following aspects for in-depth study: ① How to further optimize the Memetic Algorithm framework to make the algorithm more flexible. ② To carry out in-depth study for the key control parameters to find out the setting rules of the control parameters. ③ To apply the optimized Memetic Algorithm to a wider field.

#### **Acknowledgements**

This work was supported by the natural science foundation of Nanjing vocational college of information technology under grant No.YK20190401; High level introduction of talent research start-up fund of Nanjing vocational college of information technology under grant No.YK20200501.

*Technological Innovations and Advances in Hydropower Engineering*

### **Author details**

Ling Shang<sup>1</sup> \*, Xiaofei Li<sup>2</sup> , Haifeng Shi1 , Feng Kong<sup>1</sup> and Ying Wang1

1 Nanjing Vocational College of Information Technology, Nanjing, Jiangsu Province, China

2 Beijing Sany Architectural Design Research Co., Ltd, Hunan, China

\*Address all correspondence to: shangling@njcit.cn

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Improved Memetic Algorithm for Economic Load Dispatch in a Large Hydropower Plant DOI: http://dx.doi.org/10.5772/intechopen.100309*

#### **References**

[1] Grosan, C., Abraham, A. Hybrid Evolutionary Algorithms: Methodologies, Architectures, and Reviews. In: Abraham A., Grosan C., Ishibuchi H. (eds.) Hybrid Evolutionary Algorithms. Studies in Computational Intelligence, Springer, Berlin, Heidelberg. 2007, 75:1-17.

[2] Kumar, M., Husian, M., Upreti, N., Gupta, D. Genetic algorithm: Review and application. International Journal of Information Technology and Knowledge Management, 2010, 2(2): 451-454.

[3] Tan, K.C., Lee, T. H., Khor, E.F. Evolutionary algorithms for multiobjective optimization: Performance assessments and comparisons. Artificial Intelligence Review, 2002, 17 (4): 251-290.

[4] Sivaraj, R., Ravichandran, D. T. A review of selection methods in genetic algorithm. International Journal of Engineering Science and Technology, 2011, 3(5):3792-3797.

[5] Krasnogor, N. Memetic Algorithms. In: Rozenberg G., Bäck T., Kok J.N. (eds.) Handbook of Natural Computing. Springer, Berlin, Heidelberg, 2012, 905-935.

[6] Wang, Y., Hao, J.K., Glover, F., Lü, Z. A tabu search based memetic algorithm for the maximum diversity problem. Engineering Applications of Artificial Intelligence, 2014, 27:103-114.

[7] Arab, A., Alfi, A. An adaptive gradient descent-based local search in memetic algorithm applied to optimal controller design. Information Sciences, 2015, 299:117-142.

[8] Radcliffe, N.J., Surry, P.D. Formal memetic algorithms. In: Fogarty T.C. (eds.) Evolutionary Computing. AISB EC 1994. Lecture Notes in Computer

Science, 1994 (865). Springer, Berlin, Heidelberg.

[9] Garzafabre, M., Kandathil, S.M., Handl, J., Knowles, J., Lovell, S.C. Generating, maintaining, and exploiting diversity in a Memetic Algorithm for protein structure prediction. 2016, 24 (4):577-607.

[10] Hu, Z., Bao, Y., Xiong, T. Comprehensive learning particle swarm optimization based memetic algorithm for model selection in short-term load forecasting using support vector regression. Applied Soft Computing, 2014, 25:15-25.

[11] Pishvaee, M.S., Farahani, R.Z., Dullaert, W. A memetic algorithm for bi-objective integrated forward/reverse logistics network design. Computers and Operations Research, 2010, 37 (6): 1100-1112

[12] Pan, Q.K., Wang, L., Sang, H.Y., Li, J.Q., Liu, M. A high performing Memetic Algorithm for the Flowshop scheduling problem with blocking. IEEE Transactions on Automation Science and Engineering, 2013, 10 (3):741-756.

[13] Acilar, A.M., Arslan, A. A novel approach for designing adaptive fuzzy classifiers based on the combination of an artificial immune network and a memetic algorithm. Information Sciences, 2014, 264: 158-181.

[14] Yeh, W. C. A memetic algorithm for the N/2/Flowshop Alpha F plus Beta C-Max scheduling problem. International Journal of Advanced Manufacturing Technology, 2002, 20 (6):464-473.

[15] Boughaci, Dalila, Benhamou, Belaïd, Drias, Habiba. A memetic algorithm for the optimal winner determination problem. Soft Computing, 2009, 13 (8-9):905-917.

[16] Zou, P., Zhou, Z., Chen, G. L., Yao, X. A novel memetic algorithm with random multi-local-search: a case study of TSP. Proceedings of the 2004 Congress on Evolutionary Computation, 2004, 2:2335-2340.

[17] Castro, M., Sörensen, K., Vansteenwegen, P., Goos, P. A memetic algorithm for the travelling salesperson problem with hotel selection. Computers and Operations Research, 2013, 40 (7):1716-1728.

[18] Divsalar, A., Vansteenwegen, P., Sörensen, K., Cattrysse, D. A memetic algorithm for the orienteering problem with hotel selection. European Journal of Operational Research, 2014, 237(1): 29-49.

[19] Hasani, A., Khosrojerdi, A. Robust global supply chain network design under disruption and uncertainty considering resilience strategies: A parallel memetic algorithm for a real-life case study. Transportation Research Part E: Logistics and Transportation Review, 2016, 87: 20-52.

[20] Bitar, A., Dauzère-Pérès, S., Yugma, C., Roussel, R. A memetic algorithm to solve an unrelated parallel machine scheduling problem with auxiliary resources in semiconductor manufacturing. Journal of Scheduling, 2016, 19 (4):367-376

[21] Deng, J., Wang, L. A competitive memetic algorithm for multi-objective distributed permutation flow shop scheduling problem. Swarm and Evolutionary Computation, 2017, 32: 121-131.

[22] Nalepa, J., Kawulok, M. Adaptive memetic algorithm enhanced with data geometry analysis to select training data for SVMs. Neurocomputing, 2016, 185: 113-132.

[23] Xue, X., Wang, Y., Ren, A. Optimizing ontology alignment through Memetic Algorithm based on Partial Reference Alignment. Expert Systems with Applications, 2014, 41(7): 3213-3222.

[24] Nekkaa, M., Boughaci, D. A memetic algorithm with support vector machine for feature selection and classification. Memetic Computing, 2015, 7 (1):59-73

[25] Ammaruekarat, P., Meesad, P. A chaos search for multi-objective memetic algorithm. Proceedings of International Conference on Information and Electronics Engineering (ICIEE 2011). 2011, 6: 140-144.

[26] Özcan, E., Parkes, A. J., Alkan, A. The Interleaved Constructive Memetic Algorithm and its application to timetabling. Computers and Operations Research, 2012, 39(10): 2310-2322.

[27] O'Hara, T., Bull, L. A memetic accuracy-based neural learning classifier system. IEEE Congress on Evolutionary Computation, 2005, 3:2040-2045.

[28] Abbass, H. A. A Memetic Pareto Evolutionary approach to artificial neural networks. Australian Joint Conference on Artificial Intelligence, 2001 (AI):1-12.

[29] Bonfim, T.R., Yamakami, A. Neural network applied to the coevolution of the memetic algorithm for solving the makespan minimization problem in parallel machine scheduling. Brazilian Symposium on Neural Networks, 2003, 44 (6):197.

[30] Shang, Y, Lu, S., Gong, J., Liu, R., Li, X., Fan, Q. Improved genetic algorithm for economic load dispatch in hydropower plants and comprehensive performance comparison with dynamic programming method. Journal of Hydrology, 2017, 554(C): 306-316.

[31] Fang, N., Zhou, J., Zhang, R., Liu, Y., Zhang, Y. A hybrid of real coded

*Improved Memetic Algorithm for Economic Load Dispatch in a Large Hydropower Plant DOI: http://dx.doi.org/10.5772/intechopen.100309*

genetic algorithm and artificial fish swarm algorithm for short-term optimal hydrothermal scheduling. International Journal of Electrical Power and Energy Systems, 2014, 62 (11):617-629.

[32] Li, C. L., Zhou, J. Z., Ouyang, S., Ding, X. L., Chen, L. Improved decomposition–coordination and discrete differential dynamic programming for optimization of largescale hydropower system. Energy Conversion and Management. 2014, 84: 363–373.

[33] He, D., Wang, F. Mao, Z. A hybrid genetic algorithm approach based on differential evolution for economic dispatch with valve-point effect. International Journal of Electrical Power and Energy Systems. 2008, 30(1):31-39.

[34] Shang, Y., Lu, S, Ye, Y, Liu, R, Shang, L., Liu, C, Meng, X., Li, X., Fan, Q. China'energy-water nexus: Hydropower generation potential of joint operation of the Three Gorges and Qingjiang cascade reservoirs. Energy, 2018, 142:14-32.

[35] Li, X., Li, T., Wei, J., Wang, G., Yeh, W. Hydro unit commitment via mixed integer linear programming: A case study of the Three Gorges project, China. IEEE Transactions on Power Systems. 2014, 29(3):1232-1241.

[36] Séguin, S., Côté, P. Self-scheduling short-term unit commitment and loading problem. IEEE Transactions on Power Systems, 2016, 31(1):133-142.

[37] Suman, M., Rao, M Venu Gopala., Hanumaiah, A., Rajesh, K. Solution of economic load dispatch problem in power system using Lambda iteration and back propagation neural network methods. International Journal on Electrical Engineering and Informatics, 2016, 8(2):347-355.

[38] Liang, Z.X., Glover, J.D. A zoom feature for a dynamic programming

solution to economic dispatch including transmission losses. IEEE Transactions on Power Systems, 1992, 7 (2):544-550.

[39] Sun, J., Zhang, Q., Tsang, E. P.K. DE/EDA: A new evolutionary algorithm for global optimization. Information Sciences, 2005, 169(3-4):249-262.

[40] Wang, L., Zeng, Y., Chen, T. Back propagation neural network with adaptive differential evolution algorithm for time series forecasting. Expert Systems with Applications, 42 (2): 855-863.

[41] Yildiz, A. R. A new hybrid differential evolution algorithm for the selection of optimal machining parameters in milling operations. Applied Soft Computing, 13(3): 1561-1566.

[42] Abido, M.A. A novel multiobjective evolutionary algorithm for environmental/economic power dispatch. Electric Power Systems Research, 65(1):71-81.

[43] Das, S., Suganthan, P.N. Differential evolution: A survey of the state-of-theart. IEEE Transactions on Evolutionary Computation, 2011, 15 (1):4-31.

[44] Merz, P., Freisleben, B. Fitness landscapes, Memetic algorithms, and Greedy operators for graph bipartitioning. Evolutionary Computation, 2000, 8(1):61-91.

Section 4
