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Abstract
Considering the increasing integration of renewable energies into the power grid, batteries are expected to play a key role in the challenge of compensating the stochastic and intermittent nature of these energy sources. Besides, the deployment of batteries can increase the benefits of a renewable power plant. One way to increase the profits with batteries studied in this paper is performing energy arbitrage. This strategy is based on storing energy at low electricity price moments and selling it when electricity price is high. In this paper, a hybrid renewable energy system consisting of wind and solar power with batteries is studied, and an optimization process is conducted in order to maximize the benefits regarding the day-ahead production scheduling of the plant. A multi-objective cost function is proposed, which, on the one hand, maximizes the obtained profit, and, on the other hand, reduces the loss of value of the battery. A particle swarm optimization algorithm is developed and fitted in order to solve this non-linear multi-objective function. With the aim of analyzing the importance of considering both the energy efficiency of the battery and its loss of value, two more simplified cost functions are proposed. Results show the importance of including the energy efficiency in the cost function to optimize. Besides, it is proven that the battery lifetime increases substantially by using the multi-objective cost function, whereas the profitability is similar to the one obtained in case the loss of value is not considered. Finally, due to the small difference in price among hours in the analyzed Iberian electricity market, it is observed that low profits can be provided to the plant by using batteries just for arbitrage purposes in the day-ahead market.
The authors would like to thank the scientific illustrator and designer Patricia Nagashiro for the illustration of
Fig. 1 Exponential trend of battery pack price.
Fig. 2 Graphical representation of hybrid renewable power plant.
RENEWABLE energy sources (RESs) have become key solutions to reduce greenhouse gas emissions and fossil fuel dependency on energy production [
Considering the production variability, hybrid combinations of these alternative sources can become complementary, and therefore improve the performance of the generation plant. As an example, a combination between wind and solar energy appears to be interesting for a hybrid renewable energy system (HRES) due to their greater development compared with less mature RESs [
Besides, in order to introduce a larger number of RESs into the power grid, the deployment of energy storage systems (ESSs) becomes a key point for the purpose of compensating the production intermittency, as well as for enhancing the profitability of renewable power plants [
Another fact that makes this technology attractive for its use is that the price of Li-ion batteries has dropped drastically in the last decade. This price drop is mainly attached to the development and rise in sales of electric cars, for which this technology is commonly applied. According to the last survey published by Bloomberg New Energy Finance (BNEF) [
The use of batteries brings multiple benefits to renewable plants, both in economic and technical aspects. A renewable plant can reduce deviations between firmed capacity and real production by using batteries, since batteries can provide the missing part when the HRES plant gives less power than expected. Likewise, when the plant produces more power than forecasted, the battery energy storage system (BESS) can store the energy surpluses. This fact, apart from being beneficial for the grid power management, also becomes economically beneficial for the plant, as penalties related to those differences are minimized. Moreover, an HRES is able to perform energy arbitrage by using an ESS, which consists in shifting energy from a certain moment to another. The aim of this strategy is to bid more energy when the price is higher, and to store energy in batteries when the price is lower, so that the benefits can be maximized [
Furthermore, the use of batteries gives the HRES the opportunity to provide ancillary service such as frequency control and secondary reserve. Therefore, HRES can participate not only in energy markets, but also in the ancillary service markets [
Several studies have previously optimized the production schedule of a power plant using an ESS for the day-ahead market. Nevertheless, most of them propose a single-objective optimization problem, which is usually linearized so that it can be solved with classical optimization methods [
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In this paper, to improve the profits of an HRES, a day-ahead market participation optimization is developed for a plant consisting of wind turbines, PV modules, and a Li-ion ESS. The main contribution of this paper is to propose a production scheduling optimization methodology, which maximizes the profits obtained from performing the energy arbitrage, and minimizes the loss of value of the BESS at the same time. The loss of value is calculated considering both the loss of life with the change of its state of health (SOH), and the effect of the price drop with time. Furthermore, in contrast to other similar studies, energy efficiency of the battery is included into the cost function, which has a significant effect on the result.
The aim of this study is to optimize the participation of a hybrid renewable power plant into an electricity market in order to maximize its profits by applying energy arbitrage with the use of a BESS. For the present work, the Iberian electricity market has been selected, and therefore, some insights about the procedure carried out in this market should be remarked.
The Iberian electricity market is a liberalized market, in which different traders offer and buy energies in different sequential markets, and their offers are cleared depending on the price they bid. The first of these sequential markets, and the one to be optimized in this paper is the day-ahead market [
The day-ahead market is the core market among all the existing markets, as it is the main mechanism to conduct the electricity transactions. The majority of the electricity to be produced in the following day is sold and purchased in this market. It is composed of a single session, in which traders make their offers for each of the 24-hour periods of the following day (day ). Traders send their offers to the Spanish Market Operator (MO), called OMIE, until 12 a.m. of day D, and after that, a complex algorithm clears the offers to decide which of them are accepted or refused.
An important point to consider is that, regardless of the price of each offer, there is going to be a common and unique price for each hourly period once the auction is finished. Therefore, renewable plants usually make their offers with a near-zero price in order to always be accepted. That is why all the energy offered by the plant is going to be considered as accepted in this study.
As for the price and production estimations used for this study, the following models are used.
In order to conduct the optimization, the developed algorithm needs to consider certain prices for each hourly period of the day. As the main aim of the study is to present the benefits of conducting a multi-objective optimization, the price estimations used are going to be taken from real data published by the Spanish System Operator for year 2018 [
In real-time operation, wind power plants need to use weather forecasts to calculate the energy expected to be produced in the following hours, since the production offers are made a few hours before the real production time [
Regarding the wind power estimation, the electricity produced by wind turbines is going to be calculated based on the P-V curves of the wind turbines. As for the calculation, the wind speed values taken from the nearest weather station to the considered HRES are extrapolated to the hub height with the following equation [
| (1) |
where and are the wind speeds at the heights and , respectively; and is the power law exponent. To calculate , the equation proposed by Counihan [
| (2) |
For the studied case, is taken as corresponding to a surface with few trees.
As for the solar power estimation, the energy produced with solar modules is calculated with (3):
| (3) |
where is the maximum power at a certain cell temperature and irradiance ; is the maximum power at standard test conditions (STCs); and is the maximum power point (MPP) power coefficient of the module.
As for the cell temperature, its relationship with the ambient temperature can be expressed as:
| (4) |
where is the temperature of the cell under nominal operating conditions (), and is the wind velocity. The value of is usually given by the manufacturer in the datasheet of the solar module.
It should be noted that, to estimate the power, some assumptions are made as follows.
1) All wind turbines are receiving the same wind speed, uniformly distributed along each wind turbine.
2) All solar modules are receiving the same irradiance, uniformly distributed along each solar module.
3) In both cases, generators are always working at their MPPs under the given conditions.
4) No losses are considered regarding the connections and transmission lines of the system.
Regarding the BESS, a simple equivalent circuit model (ECM) consisting of an ideal voltage source and a series resistance has been used to model the static response of the batteries. This simplified model is used to obtain the energetic efficiency curves.
The energetic efficiency can be defined as the relationship between voltage source power (internal power of the battery ) and the power in the terminals (external power ). Nevertheless, depending on the battery charging/discharging state, the equation changes as follows.
In charging case, the energetic efficiency is calculated as:
| (5) |
In discharging case, the energetic efficiency is calculated as:
| (6) |
where is the open circuit voltage; and is the series resistance.
In addition to modelling the energy efficiency, the SOH of the battery is also considered in this study. In many optimization studies, this parameter is not taken into account, but as it is going to be proved, it has an important effect on the final optimization result. The SOH refers to the current maximum capacity of the battery compared with its nominal capacity. The two main factors that affect the SOH are cycling (charging and discharging) and calendar aging. In this study, the SOH is calculated focusing on the cycling. The Wöhler method is selected to estimate SOH [
As explained before, the HRES plant is capable of performing energy arbitrage by using a storage system. Therefore, the optimization includes offering a certain quantity of energy each hour in order to make as many profits as possible based on generation forecasts and price estimations for day .
One of the benefits of the battery system incorporated to the hybrid plant is that wind turbines and solar panels can be expected to work at their MPPs regardless of the power schedule of the plant, as the batteries should be able to damp those differences.
Therefore, considering the forecasting production as the real production, wind and solar productions are constant values for the cost function, and the target is to optimize the battery deployment.
The proposed objective function is defined for a multi-objective optimization problem, as it covers two main aims. The first aim is to optimize the battery use in order to maximize the profit of the plant, and the second aim is to minimize the loss of value of the battery due to using it.
As for the second aim, two factors are taken into account to calculate the loss of value of the battery.
On one hand, the SOH of the battery is considered in terms of the loss of life each day. In order to calculate the loss of life of the battery, a fatigue model known as Wöhler method is selected [
| (7) |
| (8) |
where is the loss of life at a certain DOD range; is the number of ranges into which the depth of discharge is divided; is the number of cycles given at the
When reaches a value of 1, it means the battery has reached its end of life. Therefore, it is also possible to calculate the battery lifetime left by the following equation:
| (9) |
where is the lifetime years; and is the loss of life given in a complete year.
As for the number of fatigue cycles in a certain period, since the cycles are not cyclical and do not have constant amplitudes, determining the number of them requires a specific method. The method widely used for this purpose is known as the Rainflow cycle counting algorithm, which is used for extracting cycles from a complex load history, and organizing them depending on their mean values and amplitudes [
For the battery case, the parameter analyzed to determine the given number of cycles is the state of charge (SOC) of the battery during a certain period. A cycle describes the charging and discharging of the battery, and the cycles are classified depending on their DODs.
There exist some different types of Rainflow cycle counting algorithms, and the one chosen for this study is the three-point method for a nonperiodic load time history. This method is more efficient computationally than other methods, and it can be used in applications of real-time cycle counting [
On the other hand, apart from the SOH, the other parameters considered in this study for calculating the loss of value in the battery is the change of market price. As previously explained, the battery price has fallen drastically in the last decade, and the trends indicate that the price is going to keep decreasing.
As shown in
The exponential curve estimates the unit price () for the battery in energy terms can be calculated as:
| (10) |
where is the unit price of a certain day; and is the number of the days analyzed starting from January 1, 2018.
The curve has been obtained by fitting the data from 2017 until 2030, using the estimations of the latest New Energy Outlook [
Considering the SOH of the battery in terms of the and the , the loss of value of the battery from one day to another is defined as:
| (11) |
where is the rated energy of the battery at the beginning of its life; is the total cumulative loss of life after day D; and is the total cumulative loss of life at the end of day .
Finally, the global multi-objective cost function to maximize at day D is ( is always zero or negative):
| (12) |
where is the total energy given at each hour; and is the forecasting price for each hour.
As explained before, the energy given by the battery is affected by its energy efficiency, and the efficiency curves are different in charging and discharging cases. Therefore, is going to have one of the following expressions for each of the hours.
In charging and discharging cases, is given in (13) and (14), respectively.
| (13) |
| (14) |
where is the forecasting energy generation at each hour; and is energy at the battery at each hour. Energy efficiencies and are the ones defined in (5) and (6).
An important point to take into account is that, in order to extend the battery life, charging and discharging cycles should not overpass certain SOC limits. These limits correspond to the bounds of optimization variables, and they are expressed as:
| (15) |
| (16) |
where and are the minimum and maximum energies of the battery, respectively; and and are expressed in percentage, and for the studied case, the SOC range is taken between 20% and 80% [
The first constraints to be considered in the storage system are the ones related to the maximum charging and discharging power of the battery, namely and . Considering an hour as a time step, power constraints can be expressed as energy constraints with the following inequalities:
| (17) |
| (18) |
It should be noted that these maximum charging and discharging power values refer to the internal power given by the battery . Therefore, as energy efficiency drops with the higher power, the efficiencies of giving or receiving the maximum internal power are the minimum efficiency values.
Secondly, in order not to make the battery at its lowest level at the end of the day, a constraint linked to the SOC at the last hour () is established. The aim is to keep the SOC of the battery similar to the one at the beginning of the day, and in order not to create an equality constraint, two inequality constraints are modelled as:
| (19) |
| (20) |
where and are the minimum and maximum SOCs of the battery at the last hour, respectively. For the simulations, the values assigned are 55% and 65%, respectively.
Finally, in the studied case, it is considered that batteries can only be charged with the HRES plant and cannot get energy directly from the power grid. This implies that the maximum charging value of the battery in an hour is limited by the energy generated, which is expressed as:
| (21) |
where is the charging efficiency for each .
In order to obtain a solution which meets all the constraints, for each constraint that is not fulfilled, a penalty is applied to the cost function. In this way, the solutions without any constraint violation obtain a better fitness.
In order to solve the optimization problem, a particle swarm optimization (PSO) algorithm has been developed. This algorithm comes from the family of heuristic algorithms, which are widely used to solve complex multi-objective and non-linear problems [
To solve the optimization problem, the algorithm uses a set of particles. These particles are different possible solutions for the problem, and for this case, each of them is a vector with 24 components (energy of the battery at the end of each hour of the day). After creating the initial population of particles, the fitness of each of them is calculated, and the best global and local solutions are stored for the following iterations.
Depending on the fitness of each of the particles, the values of its components change with a certain speed (they move their positions). The particles which are far from the best solution move faster, and the ones which have a better fitness move slower.
The speed and position of each particle are defined as:
| (22) |
| (23) |
where is the inertia of the th particle at iteration ; is the th particle position at iteration ; is the local best position of the th particle at iteration ; is the global best position at iteration ; and are the uniform random values for the exploration and exploitation, respectively; and is the position update term.
As for the initial population of particles, i.e., the initial possible solutions for the optimization problem, more than one initialization method is used in order to assure that a profitable solution is found.
Firstly, the PSO algorithm is run with a completely random initial population in order to cover the solution domain and find the best solution. Nevertheless, it could happen that the PSO algorithm does not find a solution which fulfills all the constraints, or that the solution found is not profitable.
To solve this issue, the PSO algorithm is run a second time with a new initialization method. Here, the initial population is composed of random particles as well, but one of the particles corresponds to the solution obtained for a simplified cost function. This solution is calculated by an LP algorithm.
LP is a powerful optimization technique when the cost function and constraints of the problem are linear [
| (24) |
The solution obtained by both initialization methods is compared, and the solution with a better fitness is chosen as the result for the multi-objective optimization problem.
Nevertheless, as explained in the next section, applying energy efficiencies to the solution obtained with the simplified cost function, the profit could be less than those of others without the ESSs. Therefore, as a definitive way to assure that a profitable solution is always found, a third initialization method is used if needed. The third method is similar to the second one (LP particle + random particles), but a new particle is introduced into the initial population. This new particle keeps the battery SOC at its initial value during the complete day so that a non-negative profit is assured.
As explained before, in the present study, a grid-connected HRES consisting of wind turbines, solar modules, and Li-ion batteries is considered.
A graphical representation of the plant is shown in
The sizing of the power plant considered for the simulations is as follows: 50 MW of wind power, 30 MW of solar power, and 10 MW/50 MWh of battery. For conducting the simulations, WindPACT baseline 1.5 MW wind turbines [
Regarding the BESS, the data for the LiFeBATT X-2E 15 Ah 40166 Cell are used in order to parametrize the model as shown in
The resulting curves for different power values (maximum external power value is ) are calculated based on (5) and (6), and the result is shown in
Fig. 3 Efficiency curves for the studied BESS.
In order to get the same , the maximum internal power is different for charging and discharging cases. Besides, it should be pointed that is considered as constant during the simulation.
As for the battery Wöhler curve, the values used are taken from [
In order to analyze the effects of performing energy arbitrage in a representative period, the data of a complete year have been simulated. The data in 2018 are taken from the data published by the Spanish System Operator for price values [
Before analyzing the effects of the battery in the economic revenues, the parameters of the PSO have been fitted by an iterative method. In the case of the PSO, the inertia is considered as the main parameter affecting the final solution, so the rest of the parameters are fitted as constant, with the values in
As for the inertia, there exists a wide range of methods to calculate it [
Fig. 4 Profit obtained by different inertia calculation methods.
As it can be seen in
After fitting the parameters, simulations are conducted for the complete year. Each day is optimized and simulated consecutively, following the real-time schedules of the Iberian Electricity Market.
In order to analyze the effects of performing a multi-objective optimization, three different cost functions have been tested.
1) Multi-objective cost function is solved with PSO, namely PSOMO, as defined in (12).
2) Single-objective cost function is solved with PSO, not considering the loss of value of the battery, namely PSOSO. The function is:
| (25) |
3) Simplified objective function is solved with LP, not considering neither the loss of value of the battery, nor the energy efficiencies, as defined in (24).
As for the mean computation time, based on the parameters from
Fig. 5 Net profitability obtained for each day with different cost functions.
Fig. 6 Number of cycles for each DOD range with different cost functions.
It can be better understood that with neglecting energy efficiency, the profit obtained would be negative by analyzing a single day case.
Figures
Fig. 7 Curves of SOC obtained on Day 259 with different cost functions and forecasting price of day-ahead elecrticity market.
Fig. 8 Hourly wind and solar production and stored energy in the battery on Day 259 with different cost functions.
Another aspect shown in
Besides, it is also observed that the net profitability obtained with PSOSO is higher than with PSOMO in most cases as it can shown in
Fig. 9 Net profitability histograms with different cost functions.
This result is consistent considering that the PSOMO also tries to optimize the battery lifetime. Therefore, it is necessary to analyze both the net profitability and lifetime in a complete year to perform a complete comparison. The results are shown in
The results in a complete year show that performing the optimization with the multi-objective cost function, the battery lifetime is extended considerably, and in contrast, mean net profitability is similar to the one obtained with the single objective strategy. Besides, in both cases, the mean net profitability and lifetime are improved compared with the LP cost function result. Presumably, the real battery lifetime is less than the value obtained with these cost functions, since calendar aging is not included. Nevertheless, it is proven that the SOH associated to the cycling of the battery is significantly reduced with PSOMO method, while the mean net profitability is still better than in the LP case. Therefore, based on the multi-objective PSO strategy, global results are better than in the rest of the cases.
In this paper, a production scheduling optimization for the day-ahead market is conducted in an HRES plant with a BESS.
The main aim of this study is to analyze the importance of applying a multi-objective optimization to schedule the production. The multi-objective cost function optimizes both the net profitability of the plant and the loss of value of the battery, which are calculated with the number of cycles and the change of market price.
After simulating the data of a complete year, it can be seen that the global performance and profit of the plant are improved by implementing a PSO algorithm. In contrast, if the effects of the energy efficiency are neglected, the net profitability can be negative. Besides, it is proven that battery lifetime is substantially increased by using a multi-objective optimization, whereas the net profitability remains similar values.
Another conclusion is that the profitability is low by performing energy arbitrage uniquely in the day-ahead market. Benefits obtained from the arbitrage depend on price variation during the day, and in the Iberian Electricity Market, these differences are not substantial, nor are the benefits from it. Nevertheless, depending on price variations in each country, the profits could be significant.
Furthermore, it must be considered that production forecasts have been taken as ideal, and therefore there are no penalties for deviations in the production. Considering this aspect, the profits obtained with batteries could increase substantially, as batteries would be able to damp the differences between the forecasting and real production.
A last point to remark is that by participating in providing ancillary services with the ESS, the profits could increase considerably. This is a topic to be tackled in future works.
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