OPTIMAL SIZING AND OPERATION OF HYBRID POWER SYSTEMS CONSIDERING THE BATTERY CAPACITY DEGRADATION LIMITATIONS Musa Terkes
1. INTRODUCTION Integrating battery energy storage systems (BESS) is critical to fulfill intermittent renewable energy generation profiles and prevent excessive renewable penetration so that the supply-demand balance performs as desired. Evaluating the potential for integration, especially in hybrid power systems (HPS), in sustainable zero-carbon-based development plans offers many benefits. If the appropriate incentives are provided for higher battery investment costs, cost of energy (COE) Qi et al. (2022) , Zieba Falama et al. (2022), carbon emissions Jacobus et al. (2011), and grid dependency Üçtuğ and Azapagic (2018) can be reduced, and load coverage and self-consumption rates can be increased Liu et al. (2020). Appropriate determination of battery degradation
characteristics and extra costs due to degradation for optimal sizing of HPSs
is essential for many stakeholders to partner in reliable investments Bordin et al. (2017) , Jung et al. (2020).
Accordingly, the demand profile and the desired C-rate are the main factors
determining the battery degradation characteristics. In addition, other reasons
are anode plating thickness/particle size, state of health (SOH), and the shape
of the capacity decay curve Kucinskis et al. (2022). Overall, state of
charge (SOC) and operating time are highly influential parameters for calendar
aging. At the same time, the number of cycles and depth of discharge (DOD) are
highly significant parameters for cycling aging. At lower DODs, a lower C-rate
increases the number of cycles until the BESS replacements. In comparison, at
higher DODs, the effect of possible C-rate on the cycle gradually decreases De
La Torre et al. (2019). Obtaining proper
information on SOC, power state, and battery efficiency and considering battery
current-voltage characteristics under various operating conditions verifies the
high estimation of SOC during discharge while eliminating SOC underestimation
during charging at each time step (Shabani et al., 2021). Determining the optimal
average SOC for each day and the optimal DOD for each cycle guarantees reliable
planning of grid operating costs Fallahifar and Kalantar (2023). Moreover, determining
the optimum operating conditions for rated capacity and current rate minimizes
the annual BESS cost by reducing calendar and cycling aging Dulout
et al. (2017). However, the
economics of degradation effects versus cost should not be neglected. Higher
C-rates may be needed to provide additional grid revenues Sarker et al. (2017) On the other hand, the impact of calendar degradation on
battery aging is less than the cycling effect. In parallel with the energy
variation in supply and demand, C-rates and operational choices in DOD deeply
affect planning and optimization objectives Qiu
et al. (2022). The inability of most
electrochemical models to accurately predict lithium-ion battery behavior,
especially at rates higher than 2 C, is one of the main problems limiting their
use Li et al. (2019) In contrast to the C-rate, at optimum BESS capacity and
DOD, self-consumption and feed-in rate can be maximized while maintaining BESS
health by synchronizing generation and consumption Tsioumas et al. (2021), Wang et al. (2020). Especially in hybrid plants
considering hydrogen production, lowering the DOD will positively impact BESS
health but will slow down hydrogen production and reduce system efficiency Tebibel et al. (2015) Finally, many studies have comprehensively evaluated the
impacts of DOD and C-rate in terms of calendar and cycling aging. However, no
study evaluates the effects of operational operations (DOD 2. MATERIALS AND METHODS 2.1. HPS Model The HPS model in Figure 1 determines the optimal DOD Three parameters are used to model PV in HPS configuration: PV array output power, cell temperature, and panel efficiency at nominal test conditions. The relevant parameters are calculated in Equations (1), Equation (2), and Equation (3) respectively Terkes et al. (2023). (1) (2)
(3) Figure 1
HOMER Pro considers a two-tank model depending on three different parameters: chemically bound energy for the batteries and available energy for energy conversion. The total energy the two tanks can store in the relevant tank model determines the maximum storage capacity. In contrast, the ratio of the available energy size to the composite size of both tanks provides the capacity rate. The rate constant indicates the bidirectional energy conversion rate from bound to available energy. Based on these three parameters, the tank's maximum charging and discharging power is calculated from Equations (4) and Equation (5). If the discharge efficiency is considered, Equation (5) is revised as Equation (6). In addition to the maximum limits determining the input and output energy range, two different limits are set on the maximum charging power. The first one is related to the charging power corresponding to the maximum charging rate and is calculated by Equation (7). The second one is associated with the maximum charging current and is determined by Equation (8). For the three limitations related to charging power and efficiency, the calculation of the maximum charging power is based on the minimum in Equation (9). After determining the charging and discharging power at each time step, the bound and available energy are calculated in Equations (10) and Equation (11). Moreover, depending on the maximum capacity and voltage of the storage, the number of cycles until the replacement, and the DOD, the lifetime energy throughput of the battery pack is determined in Equation (12) Terkes and Demirci (2023).
(4)
(5)
(6)
(7)
(8) (9) (10) (11)
(12) In addition to the battery model, four sub-aging curves must be determined. The first sub-model uses the functional approach, i.e., the output power calculated in Equation (13), considering the losses related to the battery's internal resistance. The functional expression is known as capacity decay and growth series resistance. Considering the circuit behavior, the output power decreases with the square of the current flowing through the circuit. Suppose the derivative of the output power concerning the circuit current is equal to zero. In that case, the maximum current limitation corresponding to the maximum output power is found in Equation (14) Terkes and Demirci (2023).
(13) (14) Another sub-aging model involves characterizing the
temperature as the bulk thermal capacity. The energy dissipated in the active
series resistor is either converted into heat or increases the bulk temperature
in the storage bank. The heat transferred to or removed from the environment is
calculated according to the convection equation (q=hΔt), while the thermal
energy ultimately lost is determined by Equation (15). Considering the
energy balance in Equation (16), the differential
solution in Equation (17) is used to calculate
the rate of change in the battery's internal temperature. Depending on the
available temperature of the battery pack, HOMER Pro effectively adjusts the
SOC
(15) (16)
(17) The relative capacity about temperature represents another
sub-curve, and the corresponding curve is fitted to Equation
(18) based on the
parameters d (18) The last sub-aging models address how to calculate calendar and cycling aging. The increasing degradation rates at each time step, whether in use or idle, is known as calendar aging and depends only on temperature, as in Equation (19). In contrast, in the case of cycling aging, which refers to cycle fatigue, the cycle count curve, which will vary depending on the DOD, is determined by Equation (20). When the Rain flow Counting algorithm adjusts the SOC-dependent time series for discrete cycles about DOD, the cumulative cycling degradation is calculated by Equation (21) , Terkes and Demirci (2023).
(19) (20) (21) In contrast to BESS, the converters used in this study operate in two modes: inverter and rectifier. The inverter and rectifier output power and converter efficiency are calculated in Equations (22), Equation (23), and Equation (24) Terkes et al. (2023). 2.2. Material The technical and economic inputs and assumptions
considered in the optimization are summarized in Table 1 2.3. Scenarios This study evaluates the impact of DOD Table 1
Table 2
2.4. Objective Functions and Decision Criteria Minimizing the net present cost (NPC) is the objective for determining optimal HPS configurations. Simultaneously with the NPC, a lower levelized cost of energy (LCOE) is also desirable. The capital recovery factor (CRF) used for the calculations required for NPC and LCOE is determined by Equation (25). The difference between revenues and expenses at the end of each year, discounted to the present and summed over the years, is used to calculate the NPC with Equation (26), while the LCOE related to the CRF and NPC is determined with Equation (27). Another financial parameter, operating cost, is considered in Equation (28) Terkes and Demirci (2023).
(25)
(26)
(27)
(28) On the path to carbon neutrality and the economic objective, it is desired to increase the renewable share (RF) in meeting the electricity demand and thus reduce the carbon emissions from the electricity purchased from the grid. Therefore, the total carbon emission is calculated by Equation (30) considering the emission factor in the grid mix while determining the RF in Equation (29) , Terkes et al. (2023).
(29)
(30) Other essential parameters of concern for BESS are battery wear cost and autonomy. The storage wear cost in $/kWh, which represents the energy cycle cost, is calculated in Equation (31). In contrast, the autonomy, defined as the size of the storage bank about the electrical load, is evaluated in Equation (32) Terkes and Demirci (2023).
(31)
(32) 3. OPTIMIZATION RESULTS 3.1. Scenario A Optimal C-rate and DOD On the contrary, with increasing C-rate at lower DOD On the other hand, charge-discharge rates above 1 C-rate
do not change the feasibility of HPS much, while lower DOD Figure
2
3.2. Scenarios B, C, D, and E For the 20% EOL limit, a C-rate of 1 C and a DOD Figure 3
Another motivation is comparing the impact on HPS
feasibility of increasing DOD Figure 4
On the other hand, considering the optimal DOD Figure 5
The cases where cycling and calendar degradation dominate
the BESS replacement are indicated by coloring in the table. As the EOL limit
increases, the interval of years of replacement shortens by one year for 80%
DOD On the other hand, the BESS aging performance is analyzed
in Figure 5 for different EOL limits considering the
C-rate and DOD Figure 6
Therefore, for higher DOD Moreover, an in-depth analysis of the BESS aging
performance by year, depending on the EOL limits and considering the C-rate and
DOD Increasing C-rates for an EOL limit of 20%: cycling
degradation rises up to 2.76% during the first BESS replacement and up to 3.06%
at the project horizon; total equivalent cycles increase by 191.59 (32.63%) and
211.65 cycles (39.17%). If the EOL limit is increased by 30%, the respective
degradation rates rise to 4.55% and 4.76%, and the total number of equivalent
cycles increases by 11.68 (1.26%) and 5.34 cycles (0.67%). In-depth on a
year-by-year basis, as the EOL limit increases for the optimal 1 C-rate and 80%
DOD In addition to degradation parameters, throughput, and
BESS wear cost are also valuable for BESS performance. For increasing C-rates,
regardless of DOD 4. CONCLUSION This study optimizes the sizing of HPSs using a shared
BESS for prosumers in a common bus distribution network by considering BESS
operation with a minimum cost objective. DOD
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