Energy optimization means of hydropower [616617]

Energy optimization means of hydropower
plants
SĂRĂCUȚ -ARDELEAN ANDREI -FLORIN1

1 PhD-Student: [anonimizat], Engineering Sciences Doctoral School
E-mails: [anonimizat]
Abstract
Whatever the exact figures, world energy consumption, particularly electricity consumption, can
increase significantly during couple of decades. It i s not possible solely due to demographic pressure, but also
due to expansion of living standards within the less developed countries. Hydropower has reached high levels of
technical sophistication in power generation as compared with other renewable energy sources.
The paper discusses recent hydropower optimization research and development activities using
metaheuristic approach. The article discusses emerging attempts to promote the optimization of hydropower. It
provides a comprehensive analysis of recent attempts to extend the operating policies of hydraulic structures to
reach extraordinary degrees of versatility, a subject of many recent research projects using metaheuristic
algorithms. In addition, groundbreaking technologies for hydroelectric energy p roduction are also discussed with
the study based on reservoir operation and scheduling of flow and energy.
Keywords: hydraulic machines, variable speed, turbopump, energy .
1 Introduction
Electricity has become a very important need of life and controls the stable functioning of any society. It
can be generated through various resour ces e.g. renewable and non -renewable resources. Global status report on
renewable energy stated that recently most part of electricity is generated through renewable energy resources as
compared to previous years. In 2018 power sector had an increased powe r installation of 18 GW using
renewable resources (Hannah E. Murdock and André, 2019). Hydropower has gained most attention among all
other resources due to its large load handling capacity, minimum fluctuation of electric energy and minimum
adverse enviro nmental impacts as compared to fossil fuels (Feng et al., 2020b). Hydropower is the power
generated by head difference of flowing water. This head difference can be generated with reservoir or without
reservoir depending on the type of hydropower plant (Ka raeren, 2014).
It accounts a share of 15.8% of total electricity production worldwide as shown in Fig. 1. Hydropower
generation is currently facing few challenges e.g. environmental regulations, operational constraints, limited
equipment capabilities, flow uncertainties and regulatory constraints (Stoll et al., 2017; leten et al., 2010). All
these challenges limit the power generation capability of a reservoir. As construction of new reservoirs is an
expansive task, it is needed to properly manage the exist ing hydropower resources to obtain the maximum power
potential of the reservoir. Few studies have reported energy complementation through incorporating wind and
solar energy into the electric grid. Both wind and solar sources are unpredictable and unknown, meaning that
their performance varies with time because of their reliance on environmental conditions and cannot be entirely
reliable option of energy maximization (Ibanez et al., 2014).
Two most reported solution for power optimization are (i) reservoir operation optimization and (ii)
scheduling the water flow. Hydropower production maximized by optimizing the river annual flow and reservoir
operating conditions can be considered as reliable option in this regard. However, these factors contain many
uncer tainties e.g. unpredictable future demand, flow, climate conditions and economic factors. Utilization of
various models used at planning stage help in handling such uncertainties (Neelakantan, 2013). These models
help in optimizing reservoir size, water de mand and release scheduling while satisfying the constraints. Parallel
to these factors risk of cost management is also needed to be dealt by the plant manager (Fleten et al., 2010).
Scheduling the reservoir operation helps in minimizing the operational co st of plant and can be achieved by
traditional or modern techniques (Sharma, 2002).
Handling all such factors makes hydropower production process complex in nature. Sometimes it
becomes impossible to solve these complex problems using traditional technique s (Nkechi Neboh et al., 2015)
e.g. linear, nonlinear (NL) and dynamic programming (DP) (Yoo, 2009). Linear programming -based approaches
can provide the optimal global solution for problems where the objective function and constraints can be
represented lin early via decision variables (Feng et al., 2019c). Complex nature of hydropower planning,
nonlinear objective functions and limitations make linear programming unreliable to guarantee the precision of
optimal solution for power generation (Feng et al., 201 7c).
A nonlinear model describes more accurately the characteristics of hydroelectric power production, and
the impact of head shift can be properly considered, which is one of the key challenges associated with the short

term hydropower scheduling problem . However, it fails to address the question of infinite quadratic
programming within finite time (Catalão et al., 2010). Dynamic programming has no strict constraint on the
unsmooth and non -convex characteristics of the hydropower scheduling problem, which makes it highly
common in water resource fields (Feng et al., 2017b). The parallel DP algorithm takes advantage of the
distributed memory structure and aims to reduce the processing time and enhance the RAM need (Feng et al.,
2019c). In orthogonal discret e differential dynamic programming (ODDDP), orthogonal experiment architecture
is adopted to minimize the quest space in each step while building the corridor around the current trajectory, and
then the classical dynamic programming recursive equation is u sed to check for a better trajectory, slowly
increasing the consistency of the solution by iterative computation. However, owing to the extreme curse of
dimensionality, conventional discrete differential dynamic programming cannot produce optimization outc omes
within a reasonable period (Feng et al., 2017a).
Therefor solving complicated hydropower functional difficulties, the problem of dimensionality remains
the largest challenge to dynamic programming. It has been reported that DP variants can reduce the dimensions
to certain degrees but the computational obligation can always increase dramatically as the problem size
expanded (Feng et al., 2017b). So, dimensionality always remains biggest curse in solving high -dimensional
optimization problems of hydropow er (Li et al., 2014).
Therefore, a growing interest has been developed for doing research in developing novel approaches to
solve complex natured optimization problems e.g. artificial neural network (ANN) (Hammid et al., 2018), real
time optimization algor ithms (Cordova et al., 2014), heuristic, hyper heuristic (Kheiri, 2014) and metaheuristic
approaches (Tsoukalas and Makropoulos, 2015; Yang et al., 2015). Meta heuristic approach is gaining most
interest in this regard because of its minimum cost and time. It is a high level approach towards problem solving
which is independent of the nature of the problem (Kheiri, 2014). The benefit of metaheuristic approaches over
traditional methods is the extraneity to establish a unique initial condition, convexity, co ntinuity and
differentiability (Ehteram et al., 2019).
Meta heuristic algorithms are classified in many classes as shown in Fig. 2. Multiple reservoirs e.g.
cascade reservoir has better power generation capacity than single reservoir (XingLi Yin et al., 20 19). It can be
calculated as follows:
(1)

where, PO (t) is power generated in time t; Qi(t) is the water discharge at ith reservoir in time t; Hi(t) is
net head of water at ith reservoir in time t; n is th e number of reservoirs; and Ki is the coefficient of power
generation. Power generation is function of turbine discharge and net head. It is obvious that net head varies
largely with reservoir storage and power generation can also be calculated integrating storage variable into Eq.
(1).
The goal of planning the operation of a hydropower plant is to optimize the overall profit generated
from the selling of the electricity provided to the National Grid. It is the application’s objective function, which
is de termined by combining the monthly hydropower output with the corresponding electricity prices (Ho and
Ioannis Kim, 2014). It can be calculated by Eq. (2) as follows:

(2)

where B is the profit; E is the energy generated; P is the energy price; j is the time period. Various constraints
must be considered for a real time optimal solution of hydropower generation such as water head, turbine
discharge, reservoir level, water balance and storage capacity constraints. The validity of simulated results can
be verified by root mean square error (RMSE), Pearson correlation coefficient (r) or efficiency index (E). If
RMSE = 0, r2 = 1 and E = 1 then it shows reliable simulation, also r should be higher than E should be greater
than 0.7 for suitable model (Sorachampa et al., 2020).

Fig. 1. Worldwide Electricity Production -End of 2018 (Hannah E. Murdock and André, 2019).

2. Reservoir operation optimization

The optimization of water supply facilities needs to do not only with the physical facilities and their
operating features but also with the parameters under which t he network is run. A concern with the operation of
a reservoir can be considered as an issue with other constraints in policymaking. The reservoir management
program is a series of rules, also referred to as the operating protocol or the release scheme (Hı nçal et al., 2010).
Reservoir operation management (ROM) involves allocating water for the required usage depending on the type
of reservoir, optimizing the energy production; while minimizing the possibility of floods, cost of operation,
adverse environme ntal effects and water shortage (Wurbs, 1993).

Fig. 2. Categories of meta heuristic algorithms

A wise decision for water release operation is needed to be taken for a good ROM on monthly or yearly
basis. General flowchart for ROM is shown in Fig. 3. It shows that ROM needs to schedule the reservoir flow
and storage balance throughout year to optimize the power generation, flood mitigation and water supply. Unit
commitment (UC) is also important parameter for decision makers for optimal operation of reservoir system. UC
of hydropower is subject to data va riability: water inflows into reservoirs, electricity demand, run -of-river and
wind generation, and equipment failures. While this variation may be compensated for by stochastic simulations,
in reality it is more common to change plans depending on the mos t up-todate details, often several times a day
(Marchand et al., 2019).

Fig. 3. Schematic diagram of a hydro power plant (Geng Feng and Beer, 2015)
When reservoir inflows are predicted accurately using good optimization techniques, more balanced and
effective solutions can be achieved for a reservoir multipurpose system. Generatio n of hydropower can also be
enhanced and improved (Zhang et al., 2020a). The management of reservoir activities is widely researched, with
original research concentrating mainly on water volume limits and more recent experiments integrating ecology
and wat er quality parameters (Shaw et al., 2017). Many rule curves and regulation rules, such as normal
procedure regulation, hedging law, space law, pack rule, linear decision rule, neural network dependent rule, etc.,
are applied and investigated for efficient reservoir operation system (Tayebiyan et al., 2019). Hedging polic y has
gained most attention in this regard. Wang et al. in their study proposed a hedging model using nonlinear
programming (NLP) to determine the end of year storage that can be utilized during dry period in next year. This
hedging rule was found better i n performance than standard operating policy (SOP) (Jian Wang et al., 2019). To
make the power production reliable during all time period following equation (Eq. (3)) was used as objective
function:
(3)

where Lt and Lt+1 are current and future loss in storage; Qt and St are water flow and storage at end of
period, respectively. Water release policies (Tayebiyan et al., 2016) and hedging rule have also been optimized
by genetic algorithm (GA) (Chiamsathit et al., 2014; Tayebiy an and Mohammad, 2016). Researchers aim to
apply the most efficient procedure to achieve the maximum operation efficiency to maximize effective
performance with the lowest energy consumption.
Various approaches are used in this regard including artificial neural network (ANN) (Shaw et al., 2017;
Xu et al., 2020), dynamic programming (DP) (Li et al., 2014), dynamic optimization algorithm (DP) (Rooholla
kolbadi nezhad, 2016), stochastic dynamic programming (Wu et al., 2018), nonlinear programming (NLP)
(Jothi prakash and Arunkumar, 2013), Shuffled Complex Evolution (SCE) algorithm (Wu and Chen, 2013),
Genetic algorithm (Olukanni et al., 2018), Particle swarm optimization algorithm (PSO) (Lu et al., 2013).
Reservoirs can vary in function e.g. Reservoirs which ar e multipurpose. Numerous studies revealed that
integrating effective river inflow forecasting procedures with efficient management strategies can provide
reliable and sustainable approaches to enhance the economy of hydropower output for multi -purpose rese rvoir
structures (Olofintoye et al., 2016).
Large -scale hydropower and reservoir system’s activity is known as a traditional high -dimensional
nonlinear and multi -stage optimization problem, and solving such a broad problem is very complicated or even
impra ctical with current approaches. Therefore Feng et al. suggested some powerful dimensionality reduction
techniques to improve conventional methods’ computational performance (Feng et al., 2019b). Meta heuristic
algorithms have shown efficiencies for managin g operation policies of such reservoirs with energy maximization
as one of the objective functions. However, more development in meta heuristic techniques will help further to

solve real time reservoir operation problems. The metaheuristic approaches appli cation in reservoir operation
management and scheduling are discussed in further sections.

3. Evolutionary algorithms (EAs)

Recently there has been widespread use of evolutionary and meta -heuristic algorithms as search and
optimization methods in differen t problem areas. Evolutionary algorithms have been particularly applied widely
in hydropower sector for various optimal problems. Such as Grey wolf optimization (GWO) algorithm was
applied in reservoir study for data forecasting (Dehghani et al., 2019), Po wer generation scheduling was done by
adaptive chaotic differential evolution algorithm (ACDE) (Lu et al., 2010b), multi objective optimal scheduling
was done based on differential evolution with adaptive Cauchy mutation (MODE -ACM), short term
hydrothermal scheduling was reported using clonal selection algorithm (CSA) from the group of evolutionary
computation (Swain et al., 2011), reservoir operation was optimized by an evolutionary algorithm named Borg
MOEA (Al -Jawad and Tanyimboh, 2017; Zatarain Salazar et al., 2017) and accompanying progressive
optimality algorithm (APOA) (Ji et al., 2018), optimal operation of spillway was determined by the progressive
optimality algorithm (POA) (Liu et al., 2017), multi -stage progressive optimality algorithm (POA) in t he
optimization of energy storage operation chart (Jiang et al., 2018), currently pareto front (PF) – based multi –
objective evolutionary algorithms (MOEAs) are frequently used in hydropower optimization problems. MOEAs
have ability to solve multiple problem s simultaneously such as NSGAII, NSGA -III, multi -objective particle
swarm optimization algorithm based on decomposition (dMOPSO), Moth –flame Optimization Algorithm based
on R -domination (R -IMOMFO) etc. Zhang et al. (2020). Hence wide application of EAs in hydropower
optimization problems make them an important part of literature to solve optimization problems.

3.1. Genetic algorithm (GA)

Genetic algorithm relates to the probabilistic algorithm category. It is referred as stochastic optimization
techniques whereby candidate solutions are created to search the solution space. It is represented by a
chromosome using binary coding encoding various numbers, integers or any variable (Robin Wardlaw, 1999).
Advantage of GA over traditional optimization is its treat ment of more practical, dynamic, and highly nonlinear
problems. In this process, an initial population is created; each individual is coded to be numerically represented;
then each person in the population is given a fitness value which is a metric in rela tion to which each entity is
determined whether or not to survive in subsequent generations. Genetic operators, discovery, crossover, and
mutation perform the classification and placement of entities that will be rewarded to exist in subsequent
generations (Hınçal et al., 2010). A general flowchart of GA is shown in Fig. 4.

Fig. 4. Flowchart of genetic algorithm (GA)

Many studies have been found for optimization of hydropower by crossover and mutation operation in
the simple genetic algorithms and modified one. 3.1.1. Modified genetic algorithms As G As are versatile enough
to handle a large range of complex problems still it is anticipated that increasing complexity of problem causes
more cost in terms of the calculation time needed and premature convergence (Tospornsampan et al., 2005).
Alterations i n GA and hybridization has helped to overcome this problem. Yeng et al. proposed new
trigonometric selective operators in GA to advance its convergence speed for optimal operation of cascade
reservoir (Yang et al., 2013b). An improved adaptive genetic algo rithm (AGA) was capable of fitting negative
data by sine roulette selective operator. The algorithm provided good results for Qing River cascade hydropower
system during the scheduled period (Yang et al., 2013a). An increased hydropower generation was achi eved by
adding two simulation algorithms in genetic algorithm optimization model (GAOM) (Al -Aqeeli et al., 2016).
The added algorithms changed the population value of GA and provided the optimal solution for the single
reservoir. Optimized operation policy for a system of four reservoirs was also determined by using genetic
algorithm optimization model (GAOM) and increased hydropower generation was achieved. The optimized
policy was evaluated by a simulation model (SM) and R 2 value of 0.99 confirmed the pe rformance of GAOM in
hydropower optimization (Al -Aqeeli, 2016).
Maximization of hydropower production was achieved by Zhou et al. by combining the non -dominated
sorting genetic algorithm -II (NSGA -II) with a successive approximation for mega cascade reservo ir in China
(Zhou et al., 2018). The NSGA -II model has two major defects: one is that with the rise in iteration levels,
population variation may slowly decline and all entities will have the same or identical genes, resulting in the
premature convergence problem; another flaw is the execution time, using serial computing, shows an average
square growth as the number of people in the population grows (Feng et al., 2018a). Liu et al. proposed NSGA -II
framework -based lion pride algorithm (LPA) and tested for reservoir operation problem (Liu et al., 2020a). The
proposed algorithm performed well in diversity and convergence and showed 2 –4 times better run time than
NSGA -II for dual objective optimization problem. The new form, Self -Learning Genetic Algorithm (SL GA),
which is an updated version of the SOM -based Multi -Objective GA (SBMOGA), was introduced in a study for
optimization of multipurpose reservoir operation (Hakimi -Asiabar et al., 2010).
The algorithm used Self -Organizing Map (SOM) and Variable Neighborh ood Search (VNS), to add
memory to the GA and increase its local search precision.

3.2. State of the art evolutionary algorithms
Comprehensive learning par ticle swarm optimization (CLPSO) is a state -of-the-art algorithm that is
effective in exploration. Zhang et al. proposed an improved CLPSO (ECLPSO) to increase the efficiency of
CLPSO in exploitation and related the ECLPSO to the optimal activity of hydrop ower systems with multi –
reservoirs (Zhang et al., 2016). Two new approaches to address the various physical and organizational
limitations were introduced in CLPSO. Firstly, the limits on outflow and storage capacity were sufficiently
applied to accomplish an exchange -off between maintaining flexibility and promoting convergence. Second, the
penalty factor was dynamically modified to facilitate initial quest space exploration and slowly direct the quest
to focus on the suitable region.
Strawberry optimizati on algorithm also a state of the art algorithm based on bio -inspired framework
was developed to help the optimal release pattern of reservoir (Asvini and Amudha, 2017). Single and multiple
objective optimization problems were considered, and results showed highly reliable performance of the
algorithm. The kidney algorithm (KA) has been found to be an incredibly efficient state -of-the-art optimization
algorithm ideal for tackling a wide variety of engineering applications. Zhou et al. proposed an improved KA by
adding three strategies; (i) exploration and exploitation strategy (ii) adaptive strategy and (iii) the elitism
strategy, into the existing KA and optimized the energy production policy of cascade reservoir with 7.8%
increased energy production compare d to the standard operation policy (Zhou et al., 2020).

4. Conclusion and future works

Optimization models are commonly used to assist decision taking. In several cases, however, the
problems to be solved are complex, non -linear, little known and, most likely, marked by incredibly wide spaces
for solutions. This finds it virtually difficult to find a range of solutions that offer great exchange -offs between
conflicting goals, such as mitigating costs and optimi zing environmental results, exploiting an implicit
‘‘optimization’’ approached, as part of that the optimal result was found surrounded by the help of domain
expertise, experience and judgment, combined with the outcomes from one or more simulation models .
Evolutionary algorithms yet more metaheuristics offer the way by overcoming the aforementioned drawbacks,
when it should be closely related for applications of ecological modeling included as apart of it is widely
implemented non -formal optimization meth od discussed over, thus authorizing for computationally efficient
exploration of broad search spaces. Mostly researches have centered on the exploit of hydroelectric power

scheme for electricity supply through the application of different modeling strategi es giving consideration to
environmental effects.
This review provided a condensed analysis of various mathematical models developed for the process
of hydropower generation. It was noticed whether there several parameters, including turbine and penstock size,
quantity of turbines, turbine scheduling were not previously explored for optimum process of hydroelectric
power station and hence more research is needed to understand the impact of those parameters. It can also be
noted from previous research very few of these researches are accessible for optimal short -run activity of
hydroelectric power stations. Hence more research is needed in this regard. State of the art algorithms have high
potential to be used with modern programming skills and modifications that should be explored. Cost
optimization using modern metaheuristic techniques also need to be explored.

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