Hydropower Planning in Combination with Ba tt eries and Solar Energy

: Ba tt ery storage is an important factor for power systems made up of renewable energy sources. Technologies for ba tt ery storage are crucial to accelerating the transition from fossil fuels to renewable energy. Between responding to electricity demand and using renewable energy sources, ba tt ery storage devices will become increasingly important. The aim of this study is to examine how ba tt ery storage a ﬀ ects a power system consisting of solar and hydroelectric energy and to draw conclusions about whether energy storage recommends a power system. The method involves designing a model of eight real cascade hydropower power plants and solving an optimization problem. This power system model is based on existing hydroelectric power plants powered by solar energy and ba tt eries in the Turkish cities of Yozgat and Tokat. A case study with four different ba tt ery capacities in the system was carried out to assess the implications of energy storage in the power system. The stochastic nonlinear optimization problem was modeled for 72 h and solved with the MATLAB programming tool. The stochastic Quasi-Newton method performs very well in hybrid renewable problems arising from large-scale machine learning. When solar energy and ba tt eries were added to the system, the maximum installed wind power was found to be 2 MW and 3.6 MW, respectively. In terms of pro ﬁ t and hydropower planning, a medium-proportion battery was found to be the most suitable. Increased variability in hydropower generation results from the installation of an energy storage system.


Introduction
Electricity generation based on renewable energy in the future is an important piece of the puzzle for achieving the global goals adopted by the United Nations in 2015. Today, approximately 66% of the total amount of emitted greenhouse gases originates from energy production [1]. Adopted by all United Nations Member States in 2015, the 2030 Agenda for Sustainable Development provides a common blueprint for the well-being of people and the planet and consists 17 Sustainable Development Goals. One of these goals, goal number 7, means that everyone must have access to reliable, affordable, sustainable, and modern energy [2]. This goal can be basically interpreted as all electricity production that includes fossil fuels needs to be phased out by 2030. A challenge with the new renewable energy sources that are now being introduced is their inconsistent energy production [3]. Solar energy, which is the main new renewable energy source in Turkey, depends on the weather, which is one of the few parameters that society cannot affect [4]. This can lead to the electricity system becoming unstable, and good regulation possibilities are required to maintain the balance between production and consumption [5].
As of the end of February 2023, Turkey's installed power reached 104,136 MW, and its distribution according to sources is as follows: 30.3% hydraulic energy, 24.4% natural gas, 20.9% coal, 11% wind, 9.3% solar, 1.6% geothermal, and 2.5% in the form of other sources [6]. In addition, the nuclear energy being established will meet approximately 10% of the country's total electricity production [7]. If global emissions are to decrease, expanding the possibility of increased renewable electricity investments in the country will be of great interest. It is at this point that solar energy, a type of renewable energy, is explored in this study to see how it can be installed in an established hydropower system without jeopardizing its stability.
Hydropower is an important piece of the puzzle for future sustainable electricity supply. To continue to ensure that generation fully meets the consumption in the electricity grid, existing hydropower supported by new energy sources may need to be supplemented with energy storage to handle periods of over-and under-generation. The variability in solar and wind energy and electricity grids must also be taken into account.
Previous studies [8][9][10][11][12] show that most of the capacity of power systems is not used, especially when the power demand is not at its peak. With the installation of energy storage, energy can be stored when electricity production exceeds the demand [13][14][15].
In order to achieve a balanced electricity system [16], the operational planning of a hydropower plant is a central issue where the economic aspect of sustainability comes to the fore [17]. Hydropower operations should be planned according to the varying generation capacity of solar energy. Therefore, it is important to examine how short-term hydropower planning is affected when energy storage is included in the system. A welldesigned model of this scenario can then be adapted to changing conditions to be used as a basis as well as an object of study for reports on the design and function of future power systems.
The aim of this study is to plan and program the generation of an electric power system with eight hydroelectric power plants on the Cekerek River in a region around the province of Tokat in Turkey. The electricity system includes hydropower plants as well as batteries and solar panels. The study aims to draw conclusions about how batteries affect the planning of electricity generation. This includes optimizing electricity generation by planning and scheduling hydropower in which solar energy is integrated at different rates. Hydro and solar power generation in the region must meet local consumption without overloading the system.
The main question of the study is as follows: • How can the eight cascade hydropower plants in the province of Tokat be designed together with solar energy to provide a balance between production and consumption?
The main objectives of the study are as follows: • To create a reliable model for the planning of electricity generation from the eight cascade hydropower plants in Tokat, where solar energy is also installed. In the model, the output, input, and power flow of the existing hydropower plant and the power flow and loads of solar energy should be simulated.

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Optimizing electricity generation and the amount of solar energy that can be installed in the region to maintain the balance of the grid with minimal operation from hydropower.

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A review of current research on hydropower planning and scheduling when integrating batteries and solar power.
The remainder of this paper is arranged as follows: Section 2 describes the proposed renewable energy system and operating strategy, Section 3 gives a formulation of the system's objective function and limitations, and Section 4 presents the case study and optimal operating strategy. Section 5 presents simulation results, and Section 6 provides an intensive discussion on combining solar photovoltaic power plants and hydropower reservoirs with a virtual battery of great global potential. Finally, Section 7 covers the conclusions and directions for future work.

Materials and Methods
This section presents a background of hydropower modeling and operation planning, along with a background of solar and battery solutions in electrical systems.

Hydropower and Operational Planning
The basic principle of hydropower is to utilize the potential energy in watercourses' height differences. Hydropower reservoirs contain a limited amount of energy and should be used optimally. For this reason, it is essential to generate electricity with the highest possible efficiency and as much as possible during periods when electricity prices are high. A hydropower station with a control reservoir can be likened to a battery for the electrical system; storing water is storing energy. If requested by the system, it is possible to increase generation within minutes. In the operational planning of hydropower, the unit hourly equivalent (HE) is often used, which can be described both as a flow in cubic meters per second (m 3 /s) and as a volume in cubic meters (m 3 ). The HE unit is used in this study.
It can be said that hydropower plants have dynamic efficiency that is not fixed [18]. Efficiency is, among other things, a nonlinear function of the height and drop in the plant, which means that electricity generation also becomes a nonlinear function [19]. However, in simpler models (run-off-river), the height is assumed to have a relatively minor effect on production and it is therefore neglected. A linear optimization model requires that the efficiency be described as a linear function. Therefore, the function is approximated to a piecewise linear function. If electricity generation is to be maximized, the facility should be operated at maximum efficiency if possible [20].

Programming Models
Both deterministic [21,22] and stochastic [23][24][25] methods are used in various renewable resource modeling systems. In a deterministic model, all parameters are known from the beginning and only one scenario is analyzed. The advantage of a stochastic model is that several scenarios can be analyzed simultaneously based on a possible estimate with a standard deviation. This is to simulate reality when solar radiation and electricity prices are not known at the time of planning. One problem with a stochastic model is that it requires a large amount of computational capacity [24]. Another limitation is that it can be difficult to generate data and weigh different scenarios appropriately. In a deterministic model, possible uncertainties in the input data such as electricity price and solar radiation estimates are not taken into account, but they are modeled as parameters as if they were known beforehand. The objective function is the mathematical function to be optimized, somehow maximized [26], or minimized [27], and it is generally aimed at maximizing profit [28,29] when investing or finding the desired balance between risk and expected return. While optimizing the operation planning of a hydroelectric power plant, the objective function can be defined as maximizing the profit of the plant during the planning period.
In recent years, hybrid renewable energy systems have received considerable attention from academia. Many studies have been carried out on the joint operation of batteries and various renewable energy resources. Many researchers are analyzing this fact from different perspectives. Related research mainly focuses on three issues: complementary operation on different time scales, the optimization of system configuration, and the complementarity analysis of renewable energy sources. Daadaa et al. [30] determined the objective function and the best combinations of active turbines for each period to maximize the energy produced. The model could choose different combinations from one period to the next, but a limited number of starts was recommended because frequent starts cause maintenance costs and reduce the turbine's lifetime. In a study by Zhang et al. [31], two large cascade hydropower plants on the Lancang River in China with different renewable facilities and the solar and wind power plants surrounding them were chosen as the aim of the study. They used a stochastic model to optimize long-term solar-wind-hydro operation. Liu et al. [32] proposed an optimization model to determine the short-term operation of integrated PV-hydro systems, where solar power generation was estimated under different seasonal conditions and maximizing the power output of the hybrid renewable system was considered as the objective function. Durmaz and Bilgen [33] used an objective function for the most profitable, appropriate planning and design of each biomass supply chain network included in the model. Wang et al. [34] proposed a short-term multi-objective scheduling model of hydroelectric, PV, wind power, thermal power, and power plants, taking into account the extensive use of reservoirs. Zhu et al. [35] proposed a stochastic optimization model for a photovoltaic-hydro-wind hybrid system. It simulated the multiple uncertainties of load demand and renewable energy generation. Xu et al. [36] developed a stochastic programming model to determine the operating strategies of a wind-hydro hybrid system and a model to capture the evolution of wind energy forecast uncertainty. Abadie et al. [37] analyzed the optimal management of pumped hydro storage, taking into account uncertainties under stochastic hourly electricity prices.
However, renewable energy electricity generation in Turkey has been popular for the last 15 years, and investments continue. Turkey's goal is to provide 100% renewable generation while ensuring the stability and security of its grids; it must absorb renewable energy. Most previous studies on the joint operation of hydro-PV-battery hybrid systems only considered the electricity generation of the system but ignored the consumption requirements. In addition, technical and natural constraints of hydropower plants were rarely taken into account in these studies [38][39][40].
The operation of PV-hydro-battery systems is very difficult due to the complex hydraulic operating constraints, the intermittent nature of renewable resources, and the integrated consideration of multiple uncertainties [41]. Mathematically, this problem is stochastic because of its nonlinear and noncontinuous properties. Considering the above issues, this study presents a practical mode for PV power, battery, and hydropower. In the case study, a stochastic optimization model is established for the short-term operation of the PV-hydro-battery system. The main contribution of this study is the improvement in the joint operation of a PV-hydro-cell hybrid system, and a practical mode of coordination of PV panels, batteries, and hydropower plants is proposed, which takes into account technical and natural constraints. The optimum solution of the stochastic nonlinear programming model can be obtained efficiently with the help of the MATLAB program [42].
This study is based on multi-objective optimization to determine the optimal key parameters of the solar and cascade hydropower plant system combined with a battery energy storage system. Different methods such as Latin hypercube sampling [43], cross-sectional estimation methodology [44], the droop control method [45,46], Particle swarm optimization [47][48][49], gravitational search algorithm [50], genetic algorithm [49], ant colony optimization algorithms [49], cat swarm algorithm [51], Lagrange optimization [52], Firefly algorithm [48,49,53], and Monte Carlo method [54,55] are used in the literature to evaluate the effect of batteries of power systems. However, because of its rapid and good convergence to the solution, this study focused on multi-objective optimization based on a Quasi-Newton method.

The Amount of Stored Water
The price of electricity in the electricity market may change over time as supply and demand change, depending on the seasons. Therefore, these variations should be taken into account when planning the operation of hydroelectric power plants. There may be times when the price of electricity is very low and it is more profitable to produce no electricity and instead save water until the price rises again. In business planning, this means that it is not sufficient to maximize revenues during the operating period, but also, the estimated future electricity price must be included in the calculations. In the case of short-term planning, this can be achieved by specifying a value function for the water saved, where the value, which depends on how much electricity the water can produce, is estimated and at what price. Water stored in a reservoir can be reused in a downstream power station after it has been discharged from a power station. The construction of hydropower plants involves major interventions in the local environment around the watercourse. To minimize damage to nature and the surrounding environment, many hydropower stations are regulated with the minimum amount of flow allowed in the river channel. In the regulation, the amount of mental flow (natural life water) to be released into the stream bed is determined as at least 10% of the last 10-year average flow based on the hydroelectric project [56].

Travel Time of Water between Reservoirs
In reality, water that has left a power plant will not instantly appear at the next power plant downstream. When water is released from an upstream power station, it reaches the downstream reservoirs after a while. The time it takes for the water to reach the lower reservoir after the release process is called the transition time. It depends on a number of factors, including the travel time of the water and the amount of water, which means that its function is nonlinear. The run time can be approximated with a fixed mean value, as it can be assumed to have a relatively minor effect on the model's results. In most models, the time step is used in whole hours, and the running time is often measured more precisely than that, for example, in minutes.

Solar Power
Due to its favorable geographical position, Turkey has more solar energy potential compared to many countries [57,58]. According to the research conducted by the General Directorate of State Meteorology Affairs for the sunshine duration and radiation intensity data, the annual average sunshine duration of Turkey is 2640 h (7,2 h per day), the average sunshine duration is 2640 h, and the radiation intensity is 1311 kWh/m 2 -year (a total of 3.6 kWh/m 2 per day). The most important factors affecting the operating performance of PV panels are solar radiation and panel temperature [59][60][61]. The short-circuit current of solar cells tends to increase with a smooth increase in temperature [62]. In addition, photovoltaic panels become polluted over time depending on shading and environmental conditions and cause performance drops [63].

Batteries
The problem with variable solar power generation can be compensated for by installing energy storage next to the solar panels. The aim is to store the excess power obtained from solar energy that cannot be used at a certain time. When there is no sun at any other time, the stored energy must be able to be drawn.
There are several different methods of energy storage: mechanical, electrochemical, electromagnetic, and thermal. Energy storage can also be divided into large-scale and small-scale and short-term and long-term. Batteries are applied on a smaller scale of energy storage, and they are electrochemical in type and the most common storage device in distributed systems. Battery storage is already used in energy systems today. Suntrace GmbH and BayWa, together with B2Gold, have installed the world's largest off-grid solarbattery hybrid system for the mining industry at the Fekola gold mine in Mali [64]. "This project is a milestone in terms of battery and PV plant size for an off-grid project," said Martin Schlecht, CEO of Suntrace. The facility compensates for fluctuations in energy production with 15.4 MWh of battery storage and meets 75% of the gold mine's electricity demand.
The challenge with batteries is their high cost, as well as their components. Batteries contain a variety of chemicals that are toxic and harmful to the environment, including acids, lead, nickel, lithium, cadmium, mercury, and nickel metal hydride [65,66]. A lot of research has been carried out on batteries, and recently, the materials used in batteries have developed and expanded their usage areas. The discharge rate, depth of discharge, and the number of discharge cycles have been important parameters throughout the life of batteries in areas of use. The continued development of batteries has also shown that the cost of batteries has dropped by 97% since the first commercial lithium-ion battery [67].

Mathematical Model
In this section, firstly, the design of the model is explained, and then, how to formulate the optimization problem is explained. Methods for generating the relevant parameters and variables are explained along with a formulation of the optimization problem being solved.

Modeling the system
• Overview: The system is modeled as a nonlinear optimization problem (NLP) and solved using the MATLAB program. The model has an hourly resolution and the period modeled is 72 h (three days).

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Stochastic model: In the case study, a stochastic model is used where electricity prices, water flow, solar power generation, and electricity consumption are assumed to be known in advance. Uncertainties in these parameters are taken into account.

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Hydrological connection: Since the eight cascaded hydropower stations are all located in the same river, the operation of each power plant must be coordinated to use the available water as efficiently as possible. In part, coordination is about achieving the best efficiency in all power plants and at the same time minimizing the need for water wastage. When the upstream hydroelectric plant releases water, the water reaches the reservoir of the other plant after a delay, which risks overflowing and causing spillage in the case of large flows from the power plants in the river. The hydropower plants in the model are not independent, but connected by the river. How the level of a reservoir changes is explained as follows: This relationship is applied to each reservoir every hour during the planning period. All these quantities are measured in hourly equivalents (HEs), which are defined as a flow of 1 m 3 /s during one hour. Although 1HE = 3600 m 3 , in some cases, the HE is also considered as equivalent to a water flow in m 3 /s.

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Efficiency rates: Since this study models a fictitious system based on real cascade power plants in Tokat province and real efficiencies are not available for these plants, efficiencies are estimated based on real but anonymized power plants. In this study, since it is not possible to obtain the necessary facts for a more accurate model of the power plants, it is chosen to model all the power plants with two linear segments with a breakpoint at 80% of the maximum efficiency. The maximum flow through the various segments is as follows: This selection is based on the assumption that the best efficiency for a hydropower plant is approximately 80% of the maximum reduction. After the breakpoint, the marginal production equivalent is assumed to be 5% lower. Thus, the electricity production in a hydropower plant is approximated by a straight-line function from the zero point to the breaking level, which is 80% of the maximum efficiency. In stages above the breaking point, the production of the line is zoomed in from the breakpoint to the maximum stage at which maximum power is obtained. The slopes must therefore meet the following conditions: The power generated from a hydropower plant depends on the water inflow and the generation equivalent where is further constrained by the co-conditions in (5). The total generation from a hydropower plant i then becomes: In all previous conditions, which depend on the flow, , is now changed to ∑ , , Q to fit this new way of expressing the water flow. The hydropower plant's relationship between flow rate and output is modeled as two linear sections; see Figure 1.

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Travel time: The travel time is a complex function of, among other things, the amount of water flowing in the river, resulting in the nonlinearity of the term. The water passage in a hydropower station is assumed to be constant when a time step ends and the next step begins. But the journey of water from one hydropower plant to the next does not happen all at once. The travel time of water is approximated by an average value in this study, as it is assumed to have a relatively minor effect on the final result. Since time t is measured in full hours and run times are usually in the order of minutes, a method is needed to compensate for this. The weighted average of travel time between power plants can be expressed in hours and minutes as follows: Because the travel times between power facilities are long, some undesirable situations may arise in the simulations. Among other things, the inlet at the downstream plant will only consist of water flowing from the nearby field until the first water from the plant above reaches it. An extra term has been added so that the inlet is as large as the annual average water flow in the first minutes, as it is unlikely that the above plant will be completely closed at the time before the start of the simulation. The water that has flowed out of the reservoir is simply the sum of the drawdown and spillage during the time step: The data required to describe the water flow in the system as a model based on local flow, seepage, overflow, travel times, and the contents of the reservoirs at the initial time are described. Input, run times, and initial content are predetermined parameters. Efficiency and diffusion are optimization variables that can be controlled to find optimal operating plans.
• Solar power: In the selected area, basic criteria such as the solar energy potential of the region, local climate situation, land structure, network connection, usage status of the land, proximity to energy consumption areas, and accessibility are suitable. The Solar Power Plant Project with power of 2.65 MW, which will save the Zile Municipality from high electricity costs, provide additional income to the municipality, and which has been started to be installed on a 60-decare area located in Güvercinlik, which is in the municipality, is about to be completed. Solar power generation in the system is based on data on solar power generation in the central Anatolian solar electric field in Turkey. Most of the cities of Yozgat and Tokat receive an average of 2655 h of sunshine per year, and the average solar radiation level is 4.5 kWh/m 2 -day.

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Limitations: Neglecting the operating times of the system means that the water flow from an upstream hydropower plant reaches the downstream reservoir after a very short time. Another limitation is that the system is modeled as a node instead of a power grid; therefore, transmission losses and limitations are not taken into account. Other limitations to the system are the size of the reservoirs, how much water can be released from turbines or spillways, and how quickly it can switch between different discharges. However, these are rarely of any relevance to the model, as there are often stricter legal restrictions. Legal restrictions today include a water jurisdiction that determines how intervention in a watercourse can look and how it can be used. In the regulation, the amount of mental flow (natural life water) to be released into the stream bed is determined as at least 10% of the last ten-year average flow based on the hydroelectric project [56]. • The electrical system: The electricity network consists of nodes with connections between them. The maximum power in each line between two nodes can be approximated using the following equation: Assuming that sin = 1, the maximum transmittable power in a line is given by ≅ To calculate the length of the transmission lines, the approximate position of the nodes is assumed. Based on this, the length of the lines and the maximum amount of transferable power on the lines can be calculated with Equation (11). These limit the transferable power of the nodes in the following equation: In this study, since the distance between hydropower plants is approximately 3 km, the Pmax between nodes is neglected since there will be no problem of maximum transferable power to the line. For grid limitations in (10), X can be assumed to be 0.5 ohm/km, giving X = 1.5 ohm/km in three phases. In each node, all power is assumed to be active power. Together with the constraints on the power on the line from Equation (11), the node balances of the specific power system can limit the production in each node, since the consumption is fixed.

Energy Storage in Systems
When the total power produced exceeds the power requirement, it is possible to store the excess energy in batteries. When solar energy cannot produce enough power to meet the power demand, the energy stored in the batteries must first be used to fill the gap. Storage and delivery in batteries are limited by the storage capacity of the batteries according to: The model has been simplified, assuming that today, batteries can be charged and discharged to maximum capacity in a very short time. However, heat losses and efficiency are taken into account when charging and discharging batteries. The losses are modeled as efficiency during the respective charge and discharge. During discharge, it is calculated that the battery is discharged with a certain power, and the battery model is used to describe the battery characteristics under possible operating conditions such as temperature, voltage, and discharge rate. Li-ion batteries are frequently used in both high-power applications and portable low-power applications. The most important reason for this is the high-power density and high-efficiency charge/discharge characteristics of Li-ion batteries. Despite all their advantages, their low resistance to physical stresses makes it necessary to take additional security measures specific to applications. The power stored in a battery at a given hour is defined as:

The Optimization Problem
• Objective function: In the model, the objective function is defined as maximizing the profit of the power facility. The profit is based partly on the income from sold electricity during the planning period and partly on how the value of the water in the reservoirs and the energy stored in the batteries changes during the planning period. This is described by: • The amount of water stored in the reservoir: When planning the operation of hydropower plants, it must be taken into account that the price of electricity can vary. At certain times when the price of electricity is low, it may well be better not to produce any electricity at all and instead store that water in the power plant reservoir to be used at a later time, when the price of electricity is more favorable. The easiest thing is to decide in advance how much water will be left at the end of the planning period. The amount of stored water is calculated based on the difference between the volume of water in each reservoir at the end of the planning period and the volume at the beginning of the planning period. The value of water depends in part on how much electricity can be produced and at what electricity price it can be sold.
Another possibility would have been to use the value of the water at the end of the planning period rather than how the value of the water has changed. Because the planning period is short and the water flow is high in the river at certain times (in April and May) of the year, the value of the objective function is largely dependent on the time of year, while how the hydropower plant's generation is planned has relatively little influence.
In this study, it should be taken into account that since there are eight cascade hydropower plants, the water in a particular reservoir eventually flows into the reservoirs downstream and therefore can be used for electricity generation in other power plants.
The value of is positive, and at the end of the period, if the amount of water is higher than at the beginning, there is a gain, and if the amount of water decreases, there is a loss. The predicted future electricity price is the average electricity price for the period 2020-2023.

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Other terms: Cascade hydropower plants in the model are not independent but they are connected to each other by the river. How the water level of each reservoir changes is explained as follows: To achieve the balance of power in the system, the equation is defined: The total production in the system is described according to: The total consumption in the system is described according to the following equation: For further development of the model, the following variable limits are defined: 10%. ≤ (23)

Case Study
The case study consists of the electricity system around part of Tokat city. In this study, a case study was conducted on eight cascade hydropower plants which has vertical a Kaplan hydro turbine on Cekerek River, Cekerek-1, -2, -3, -4, -5, -6, -7, and -8, with associated reservoirs. The model also includes energy storage in the form of batteries and solar power generation. However, a load is modeled to create an isolated system. Figure 2 shows a schematic view of the system. The location of power stations is shown in Figure  3 by symbolizing red color.  The regulation of the water flow in all eight power plants on the river is carried out through the state waterworks. The model also includes eight regulating reservoirs, and it is assumed that 100% of the water flowing through these waterways must be used as soon as it arrives at the next power plant; the storage option is very limited. The electrical system of the model is assumed to consist of three nodes connected by a single line; see Figure  2. At node 1, there is the Cekerek-1 and Cekerek-2 hydropower plants. Node 2 has a fraction of the total consumption. At the third node, there is the Cekerek-5,6,7,8 hydropower plants. Node 3 has most of the consumption. The 154 kV regional network runs along the river which is located in Zile town (population 53,315), the largest district in the region (see Figure 3), close to node 2, which contains the Cekerek-3 and Cekerek-4 hydropower stations. It is assumed that most of the consumption in the network takes place here. The planning period is chosen as 72 h, and the time period is chosen based on the available data on hydro and solar power generation. The time resolution is defined as hourly. The node balance calculations are explained with the following equations: Consumption is split between three nodes, where the consumption at node 2 is assumed to be greater than at the other nodes because node 2 is adjacent to the significantly larger town of Zile. The relationship between the consumptions at the three nodes is described as follows: The scenario is developed with different amounts of installed solar energy distributed among the nodes in different ways. An area close to the second node of the model near the Yildizeli and Zile districts has been determined as a suitable area for solar panels. Therefore, two of the nodes for which solar generation is modeled are nodes 1 and 2, which are consumption nodes before solar generation is implemented, and these nodes are considered the most interesting to investigate because node 3 is more limited than nodes 1 and 2.
Four scenarios with the increasing capacity of battery energy storage are examined. To determine the impact of batteries on the profitability of the hydropower business, a first scenario modeled without any storage capacity is created to create a new alternative. The remaining scenarios are modeled with degrees of storage capacity classified as small share, medium, and high share, and the scenarios are summarized in Table 1. The installed power, reservoir volume, annual production, and water flow data for all power plants are based on real values. These data were obtained by interviewing the plant operator. The eight reservoirs in series on the Cekerek River have been simplified to form only one reservoir. According to the information received from the power plant operator, there is a distance of approximately 2 km between each power plant, and it takes approximately 1.5 h for the water to reach the power plant below. Cekerek-4 and Cekerek-6 power houses and reservoirs are shown in Figure 4. The river flow and thus the conditions of hydropower plants vary considerably throughout the year. The selected timeframes are week 14 in 2019. The 14th week reflects the annual average flow. This is to make the model more reliable as hydropower conditions vary throughout the year. Input data for reservoirs and power plants are summarized in Table 2. Data on the daily natural flow of water flow in the river are obtained from the state waterworks network, and the power plant operator and the flow is assumed to be constant over a 24 h period. These data are then converted into an input in cubic meters per second, that is, hourly equivalents. At the beginning of the planning period, the reservoir volume was accepted as half of the maximum volume of the relevant reservoir. The future electricity price is estimated at USD 34/MWh, calculated as the average value of hourly spot prices between 2019 and 2022. During the planning period, hourly electricity spot prices and data on spot prices were obtained from EPİAŞ [68]. The solar energy installed power in the system is determined as 2 MW. The electricity generated by the solar panels installed in the system is also converted to normal hourly production. It is assumed that the normal hourly consumption in the system is equal to the normal hourly production. Consumption in the system is based on actual data and the selected period in 2022. Data are rescaled to accommodate the system's normal hourly consumption while maintaining variability over the planning period. The battery storage capacity in the model is chosen to be a certain percentage of the total capacity of the solar panels in the case studies. A small battery percentage is considered 25% of the solar panels' capacity. A medium rate is determined as 50%, and a high rate as 75%. Battery storage is divided into three batteries, where batteries 1 and 2 account for 70% of the total storage capacity and battery 3 for the rest. These data are shown in Table 1. The batteries are lithium-ion batteries and have corresponding efficiency ratings for charging and discharging. These efficiencies are based on total losses of 2-10% for lithium-ion batteries [31]. The charging and discharging efficiencies of the batteries are determined as 90% and 91%, respectively.

Results
Figures 5-8 show solar generation, power stored in batteries, hydroelectric generation, and consumption in MWh for all scenarios. These results show that the hydroelectric operation planning is affected by the increasing installed storage power ratio. In the absence of any power storage, only hydropower operation looks decent with variations in solar generation and consumption in the system. Hydropower operation changes drastically when energy storage is added to the system. As the battery ratio of the system increases, hydropower operation becomes shorter and often more variable. This means that the discharge flow through the turbines in the facilities becomes more erratic and the water volume in each reservoir changes more over time. The simulation also shows that the total generated power in hydropower plants slightly increases with increasing installed energy storage. According to the optimization cycle, the generation of the hybrid system can be verified, especially by supervising the battery's state of charge. The efficient power generation and storage methodology proposed in this work was verified on the Matlab platform, and the generation under different conditions has been verified by using real solar irradiation data. Various case studies were investigated to verify the validity of the proposed algorithm and define the multi-source system behavior under varying battery storage conditions. The results show an 8.82% increase in hydropower generation and a 2.64% increase in solar PV generation (see Figure 6). The simulation results verify the validity of the proposed energy commitment scheme by adding battery energy storage.   Adding batteries to the system does not affect the volume of water spilled in hydroelectric power plants. The battery storage target function value Ε for each scenario is shown in Table 3. The table also demonstrates the percentage increase in profit per scenario compared to the scenario without battery share. Also, the table shows that profit does not increase significantly with increasing battery ratio, both when the energy stored in the batteries is included in the target function and excluded. From the no battery margin to the highest battery margin, the target function value increases from USD 160 K, to USD 163.1 K, corresponding to an increase of 1.9%. According to these results, it is seen that there is a positive relationship between the storage capacity in the system and the profit from the hydroelectric operation. Regular maintenance and operation expenses (presented in Table 3), such as battery replacements and system monitoring, can add to the lifetime cost of a battery storage system. According to the Electric Power Research Institute (EPRI) [69] and National Renewable Energy Laboratory (NREL) [70], for a battery storage system, most fixed operation and maintenance costs are in the range of USD 2/kW-year to USD 6/kW-year for largescale systems. Since even with the highest yearly cost of USD 6000/MW-year, the fixed operational and maintenance cost is <0.5% of the total installation cost of the storage system, for the sake of simplicity, the fixed maintenance cost is not included in this study.

Discussion
The results show that the highest profit is achieved with the largest battery capacity. But in reality, it is not certain that this is a desirable and reasonable way to plan operations. There may be legal restrictions on how much of the water in a river can be used in a given time period, or there may be security reasons that do not allow such action. Limits are included in the calculations in order to obtain a more realistic study by taking such situations into account. Therefore, the third scenario with an installed energy storage capacity of 3.6 MWh was considered the most suitable scenario for installation. Scenario 3 had a higher profit than Scenarios 1 and 2.
The hours when the batteries are charged are usually when the electricity price in the electricity market is high and there is no solar power generation, which means that hydropower plants can operate at a higher output than the relevant hour consumption requires. The time when the batteries are discharged is usually during low electricity hours, which discharges the batteries instead of producing in hydropower plants, allowing water to be stored in the reservoir for higher price hours. Thus, this means that the hydropower plant can be operated more economically, because the batteries create a power buffer, which gives hydropower the opportunity to operate during the hours when the electricity price is higher. Adding battery capacity to the system facilitates better matching of the generation and price of hydropower plants.
The increase in generation in hydropower plants with increasing installed power storage may be the reason for the increase in profits to some extent. The increased storage capacity also allows for a greater generation of hydropower. Excess energy is stored in batteries, and it is consumed when the price of electricity drops. This is because of the market model based on two actors: battery owners and hydropower owners. According to the market conditions, it allows hydropower owners to generate excess energy at high electricity prices, and the excess is sold to battery owners. Battery owners therefore buy electricity when it is expensive and sell it when it is cheap, which means they incur financial losses. This is not financially sustainable for battery owners. An alternative market model would be for hydroelectric owners to also own the batteries. In this case, the batteries would create a kind of extra energy storage in addition to the water stored in the reservoirs. The electricity discharged from the batteries is sold to the market. Energy storage in batteries will likely decrease, as the extra losses make batteries unnecessary and costly. The losses that occur during the charging and discharging of the batteries require the production to increase in parallel with the losses in order to ensure the power balance of the system. Since solar energy is considered as a parameter in the model, this generation should take place in hydropower plants. Thus, it is con-cluded that the profit obtained from hydropower plants also increases somewhat in parallel with the losses. If battery systems are not included in the objective function, the simulation shows that the objective function value is slightly lower in each scenario than when included.
The model should consider the entire chain of power plants in the river in order to plan the operation of hydropower plants in a real situation. The hydrological balance is adjusted in MATLAB, where travel times between stations are neglected, meaning that water from an upper station is assumed to come directly to the lower station. During the interview with the power plant operators, it was stated that the travel time between the power plants was close to 1.5 h. Also, the model is based on a node and therefore does not take into account the losses and limitations on the lines that will affect the operation of the batteries and the planning of electricity generation. This study does not have a limitation on the nodes, which depends on their geographical location and the nature of the electrical network. The results show the total generation of eight cascade power plants, but in reality, it matters where the power is generated and transmitted at a given moment. If there are more nodes, the batteries will primarily store excess energy from nearby solar panels.
The model consists of eight cascade hydropower plants in a 47 km section of the river. In fact, the travel time (t ) between the power plants should be taken into account, and the amount of water used for irrigation in some seasons should also be considered.
The location of solar panels has an impact on revenues. Among those with 2 MW, the most cost-effective deployment of solar panels is 2 MW evenly distributed between node 1 and node 2, or 1.25 MW on node 1 and 0.75 MW on node 2.
To obtain more reliable results, a sensitivity analysis of the model will be needed. The model can be tested in different seasons throughout the year with different input datasets to examine how parameter variations affect the results. In addition, the modeled solar power generation was considered an average for the Turkish cities of Yozgat and Tokat, meaning that large deviations were avoided. But using local solar data for each area could be used to model solar panels in different geographic areas. It is better to store solar panels and batteries in areas with smaller hydropower plants, such as the eastern and southern parts of Turkey.
Although batteries do not provide a significant increase in target function, there are other positive aspects of installing battery storage in networks with hydroelectric generation. Thanks to its fast reaction time, the batteries can act as both backup power and frequency control in the case of short-term power outages. This is an important step towards a greenhouse-gas-free electricity system and contributes to achieving Sustainable Energy for All, goal 7 of the global goals.

Conclusions and Future Studies
Hydropower plants have good opportunities to balance the intermittent nature of solar power shares in the power system. The results of the study show that batteries can be recommended for hydroelectric and solar energy systems because the optimization problem can be solved and the objective function value increases with increasing installed storage capacity.
The operation of hydropower generation via solar power and batteries can be optimized to maximize the profit generated by hydropower. The optimal amount of installed battery capacity is considered to be the medium rate according to Scenario 3. However, the objective function value does not increase significantly in a system with large hydropower generation. Thus, it can be concluded that batteries can be recommended for the electrical system and can be a contributing factor in the efforts to achieve a sustainable future.
The case study also shows that it is the limitations of the power grid that determine the maximum installable solar power, not the regulating ability of hydropower. On the other hand, it is difficult to draw definite conclusions about how much solar energy can be installed in the region based on the results.
It would be interesting to expand the electric grid model and increase its complexity in future research, not only to determine the place of solar and batteries in the grid. The study could be extended to include possible expansions in the electricity grid and determine how these will affect profits and the amount of installed solar and batteries. It is also interesting to look at how the results change when the electricity grid is modeled as an open system with the possibility of exporting and importing electricity. Also, future studies should deepen the power system model by taking into account node balances and power transmission constraints. With these limitations, it is also possible to investigate the impact of the placement of batteries and solar panels on the operation and profits of hydropower plants. Travel times between reservoirs should be considered in future models to provide a more realistic model and hence simulation results. It would also be interesting to simulate a hybrid system by adding a highly variable power source such as wind power to this existing system. In this way, it will be possible to investigate how batteries affect the operation and profitability of the hydropower plant in a system where energy production seems more variable.