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Article

A Multi-Objective Co-Design Optimization Framework for Grid-Connected Hybrid Battery Energy Storage Systems: Optimal Sizing and Selection of Technology

1
MOBI-EPOWERS Research Group, ETEC Department, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium
2
Flanders Make, Gaston Geenslaan 8, 3001 Heverlee, Belgium
3
Cea-Liten, Universités Grenoble Alpes, 38000 Grenoble, France
4
Department of Powertrains, TNO, 5700 AT Helmond, The Netherlands
5
Cegasa Energia S.L.U., 01015 Vitoria, Spain
*
Author to whom correspondence should be addressed.
Energies 2022, 15(15), 5355; https://doi.org/10.3390/en15155355
Submission received: 27 June 2022 / Revised: 14 July 2022 / Accepted: 21 July 2022 / Published: 24 July 2022

Abstract

:
This paper develops a multi-objective co-design optimization framework for the optimal sizing and selection of battery and power electronics in hybrid battery energy storage systems (HBESSs) connected to the grid. The co-design optimization approach is crucial for such a complex system with coupled subcomponents. To this end, a nondominated sorting genetic algorithm (NSGA-II) is used for optimal sizing and selection of technologies in the design of the HBESS, considering design parameters such as cost, efficiency, and lifetime. The interoperable framework is applied considering three first-life battery cells and one second-life battery cell for forming two independent battery packs as a hybrid battery unit and considers two power conversion architectures for interfacing the hybrid battery unit to the grid with different power stages and levels of modularity. Finally, the globally best HBESS system obtained as the output of the framework is made up of LTO first-life and LFP second-life cells and enables a total cost of ownership (TCO) reduction of 29.6% compared to the baseline.

1. Introduction

The European Green Deal is expected to have zero net emission of greenhouse gases by 2050, when economic growth will be decoupled from resource use. Besides, the grid-related global storage systems deployment was about 10 GWh in 2019 and is projected to increase 15 times to almost 160 GWh with the deployment of 31.2 GWh in the EU and 34.3 GWh in the USA by 2030 [1]. A study in [2] also indicates that 150 to 900 million electric vehicles are expected to be on the market in 2040 and that stationary storage may reach up to 1300 GWh at that time. These projections point toward the potentially significant market growth of Li-ion batteries and a view of action against climate change by decarbonizing. However, the cost reduction of a lithium-ion battery (LIB) pack is slower in the stationary storage sector than in electric vehicles. In 2017, the benchmark costs of Li-ion stationary storage systems were approximately 500 EUR/kWh for energy-designed systems, 800 EUR/kWh for power-designed systems, and 750 EUR/kWh for residential batteries [2]. By 2040, stationary storage system costs are anticipated to range from 165–240 EUR/kWh for the energy-focused grid-connected system, while power-focused and residential systems are expected to cost 280–410 EUR/kWh and 250–365 EUR/kWh, respectively [2,3].
It is also found that for a battery-based system with more than 90% efficiency and a lifetime of thousands of cycles, the system cost is expected to be below 150 EUR/kWh (for a 100 kW reference system) in 2030 [4].
The different types of battery energy storage system (BESS) technologies and their suitability to grid-relieving applications have been presented in several research works with respect to efficiency, power, energy density, response time, cost, and other performance indicators [5,6,7]. Despite recent price reductions in Li-ion cells, the battery is one of the primary cost drivers of BESSs [6].
The standard stationary energy storage systems that use a single type of battery pack technology are able to supply services to the grid; however, a trade-off must often be made between power and energy performances [8]. It is found that most types of BESS and power electronics (PE) interfaces either have significant energy or power needs [9,10,11,12]; sizing one type of battery pack to multiple use cases is challenging. For example, by connecting additional cells in series/parallel, a single battery pack technology can provide the power and energy demands. However, the cells cannot be connected arbitrarily because of the voltage and current limits imposed by the PE interfaces. These current and voltage constraints increase complexity in design and contribute to oversizing the battery pack, resulting in either a higher power-to-energy ratio or a higher energy-to-power ratio. It should be noted that in most commercial battery systems, a greater energy-to-power battery pack is preferred since more energy in the battery pack increases longevity while reducing the strain on the cells. However, because of oversizing, this method is not cost-effective.
In contrast to this single-pack approach, a hybrid battery unit uses at least two different types of cells, which enhances the sizing and design possibilities. For example, combining a high-energy (HE) pack and a high-power (HP) pack enables to cover more applications for an interoperable service portfolio. Such a strategy increases the flexibility in sizing and thus the possibility of the economy of scales, which may help reduce the TCO.
There are different types of LIB technologies on the market, including the increasingly large number of second-life modules coming from the electric vehicle (EV) sector [13]. The LIB cells are mainly identified by name as lithium cobalt oxide (LCO), lithium manganese oxide (LMO), lithium iron phosphate (LFP), lithium nickel cobalt aluminum oxide (NCA), lithium nickel manganese cobalt oxide (NMC), and lithium titanate oxide (LTO). They have distinct cell voltage, energy density, cycle life, and cost because of their internal structure and composition [14]. Four types of lithium-ion cells are considered in this paper to cope with the high power and high energy demand in grid services.
The design optimization of BESSs is usually carried out regarding sizing, grid integration, technical performance, and economic perspective. In ref. [15], a single type of battery energy storage system was created from sodium sulfur (NaS), lead acid (LA), and vanadium redox (VR) and its related power converters to maximize profit for an EV park owner, using linear programming to identify the ideal storage size. The objective function includes cycle life and cost. In ref. [16], authors optimized and evaluated the BESS size for wind and solar energy fluctuations using genetic algorithm (GA). Optimizing the BESS installation capacity helps reduce power outage costs, fuel costs, and committed power plant costs. According to ref. [17], BESSs have issues with investment costs and operating lifetimes; therefore, adequate BESS sizing is crucial for microgrid design and administration. This article proposed a problem structure and solution approach for calculating the optimal size of BESSs in a microgrid using the binary particle swarm optimization (BPSO) combined with a quadratic programming algorithm for two objectives—investment cost and operating cost. Furthermore, to solve other multi-objective problems, such as minimization of annual net profits, energy consumptive rate, annual energy exchanged with the grid, and battery degradation, the NSGA-II algorithm has been utilized in [18,19]. To deal with BESS sizing, other optimization algorithms such as ant colony, particle swarm, and simulated annealing have been reviewed for multi-objective problems with different constraints based on different applications [20]. Among the other used algorithms, the NSGA-II and its derivative algorithms are found to be the popular ones in multi-objective optimization problem solving [21].
However, a multi-objective genetic algorithm (MOGA) can be used for nonlinear, nonconvex, discrete, continuous, mixed-integer, and multiple objective optimization problems [20,22]. For certain rule-based energy management methods, previous research optimized HBESS size. However, many studies [23,24] have focused on developing control strategies for the BESS sizing to achieve certain economic objectives, such as maximizing profit and minimizing power loss or battery degradation. In contrast, a system-level optimization technique is realized through the design of integrated subcomponents of HBESS and advanced control strategies, as it is necessary to know not only the revenue to maximize but also the upfront cost of investments, taking into account potential replacements over the system time horizon. In terms of assessment, the total ownership cost model has been used in [25,26] for BESS.
At the time of writing, to the authors’ best knowledge, a generalized co-design optimization framework (COF) for a lithium-ion HBESS design in a grid application has not been developed yet. In this work, each battery pack is sized from cell to pack level along with the sizing of the power converter system (PCS) for interfacing the battery system to the grid. In this paper, the sizing of the battery pack is referred to as cell configuration of series-parallel to the battery pack rating in power and energy. The sizing of PCS is referred to the required rating and value for different PCS topologies.
The main contribution of this work is three-fold: (a) first, instead of a single type of battery pack technology, two distinct battery packs have been sized with the optimal combination of series-parallel cells out of four lithium-ion battery technologies for the HBESS design; (b) second, a novel and interoperable multi-objective optimization methodology with a co-design approach is developed for the optimal design, selection, and sizing of the HBESS subcomponents (battery and PCS) with respect to system-level techno-economic performance (i.e., cost, roundtrip efficiency, and lifetime); and (c) third, two different PCS architectures with modularity have been incorporated to interface the battery to the grid instead of a single PCS architecture.
This paper is organized as follows. The methodology for sizing and designing an optimal HBESS applicable for COF is introduced in Section 2. The detailed modeling required for the coupled HBESS simulation in the COF is described in Section 3. Besides, the processes for implementing the optimization routine of multi-objective COF are discussed in Section 4 to find the optimal storage system sizing and selection; a real-field grid service (i.e., UK grid service) power profile for enhanced frequency support is used in the framework to find the optimal sizing and selection of technology for HBESS from the selected four types of cells and two distinct PCSs. The optimization results and global best selection are presented in Section 5. Finally, the conclusions are outlined in Section 6.

2. System Description

This section presents the system considered for the framework shown in Figure 1. A synergic design goal with nominal power of 100 kW and nominal capacity of 100 kWh HBESS with two different PCS topologies (defined in an optimization routine, Section 4) is set in the COF to define its variables presented in Table 1. The COF is applied to the DC side of the system for an optimal hybridization of cell technologies for two independent battery packs, namely battery pack-1 and battery pack-2, and to the PE interface with two distinct architectures, PCS-1 and PCS-2.
The first architecture (PCS-1) is comprised of a DC/DC stage and a DC/AC stage as a single module to connect the grid with different battery modules for bidirectional charging and discharging functionalities, as highlighted in Figure 1. A modular PCS has been considered in the COF to find the optimal number of modules to be used for the HBESS.
In the second PCS architecture (PCS-2), the modular DC/DC stage is connected with the modular DC/AC stage through a single DC-link capacitor, as highlighted in Figure 1, which also enables bidirectional power flow between the hybrid BESS and the grid.
The optimal voltage rating of the DC-link capacitor and the number of modules of the DC/DC and DC/AC stages for PCS-2 will be the outcome of the COF for the designed system. The details of the PCS architecture specification and constraints defined for HBESS are presented in Section 4.
The battery pack is sized by optimizing the number of cells in series and parallel. In the battery storage unit, two independent battery packs are sized where one acts as a high-power pack and the other one acts as a high-energy pack, considering different cell technologies. To this extent, this paper will propose an optimized battery storage unit based on the combination of battery pack-1 (high-energy) and battery pack-2 (high-power) to obtain the optimum level of power and energy of the battery for the considered mission power profile.
The design simulation framework, the COF, is prepared with a MATLAB/Simulink® environment and incorporates design optimization-oriented battery models and PCS models coupled with an operational control plant, namely an energy management system (EMS) for optimal sizing and selection.

2.1. Connection Topology (TO) of the HBESS

The specific connection configuration of the BESS affects the system performances, such as efficiency and reliability [27]. Considering both conceivable PCS architectures and their characteristics, four different connection topologies have been incorporated into the COF for individual selection or all at once while sizing the HBESS. The configurations are mentioned as follows in the remainder of the paper:
TO-1: Both battery packs are connected to the grid using PCS-1, as shown in Figure 2.
TO-2: Both battery packs are connected to the grid using PCS-2, as shown in Figure 3.
TO-3: Battery pack-1 is connected to the grid using PCS-2, while battery pack-2 is connected using PCS-1, as shown in Figure 4.
TO-4: Battery pack-1 is connected to the grid using PCS-1, while battery pack-2 is connected using PCS-2, as shown in Figure 5.

2.2. Real-Field Grid Load Profile for Case Study

The HBESS is subjected to multiple service scenarios. The framework considers a real-field grid-related service power profile [28]. The power profile dynamics from the UK grid services in enhanced frequency support have been considered in the COF. The power-to-frequency characteristic enables the conversion of recorded frequency variations to the required output/input power on a second-by-second basis, as shown in Figure 6.

3. Modeling for COF

This section describes the simulation models of the batteries and PE interfaces incorporated in the COF for the optimal design and sizing of the HBESS.

3.1. Battery Model

The COF uses battery cell modeling and parametrization based on the experimental characterization of real-life battery dynamics. The cell model contains the experimental data of the three first-life prismatic format cells (namely, NMC 1st life, LTO 1st life, and LFP 1st life) and one second-life LFP pouch format cell (namely, LFP 2nd life).
The electric behavior of cells is modeled with an electro-thermal model. This model couples an electric equivalent circuit model and a thermal model. The constant RC equivalent circuit model is derived from the classical electric equivalent circuit (EEC) model of lithium-ion battery cells [29,30,31,32,33]. This model is made of a DC voltage source, which models the variation of open circuit voltage (OCV) as a function of the state of charge (SoC), in series with a variable resistor R 0 , which models the cell’s internal resistance. To better model the dynamic voltage behavior of the cell, extra RC parallel blocks are added in series, as shown in Figure 7. A τ i = R i C i value is defined for each RC block, depending on the dynamics of the current profiles applied to the model during the simulation of the HBESS. Each RC parallel block represents a different timescale response under current variation. Hence, the number of blocks is defined manually, as well as the τ i = R i C i values. Then, during the model parameters identification process, only R i values are fitted by the algorithm. It allows a faster identification process ( C i values are calculated from the equation τ i = R i C i ).
The model parameter dependencies are:
OCV depends on SoC and temperature, but temperature dependency is considered negligible for a medium-fidelity model over SoC dependency [33].
R 0 , R n , and C n parameters depend on cell SoC, cell temperature, cell C-rate (charge and discharge current), and cell SoH (state of health).
A simple cell electro-thermal model is used to estimate the cell temperature variation. It is based on three equations:
  • Joule losses: heat generation inside the cell:
    Q i n ( t ) = i = 0 i = n R i I c e l l 2 ( t )
  • The thermal exchange between the cell and its surrounding environment:
    Q o u t ( t ) = h · S d T ( t ) d t
  • Thermal energy transfer through the cell:
    T =   Q i n ( t ) Q o u t ( t ) m C p d t
    where Q ( t ) [W] is the thermal power; T [K] is the cell temperature, assumed homogeneous inside the cell; m [K] is the mass of the cell; C p [J·K−1·Kg−1] is the specific heat capacity of the cell; S [m2] is the exchange surface of the cell; h [W·m−2·K−1] is the heat transfer coefficient of the cell; and the m ,   C p , and S parameters’ values are measured experimentally. The h parameter value depends on the cooling and thermal architecture of the battery pack. Typical values are 1 to 10 for air (stationary or forced convection) and 10 to 1000 for water (stationary or forced convection).
The model parameters are identified by testing each selected cell with current pulses under several SoC, temperature, and current conditions and fitting the model behavior to the laboratory test data. The test results of OCV over SoC for the LIB cells are shown in Figure 8. The cell specifications that are used in this article are presented in Table 2.
The prepared parametrized battery model inputs are either power or current profiles and an ambient temperature profile, while outputs can be configured as module/pack voltages, powers, currents, temperatures, energy losses, and the SoC of the battery pack by changing the number of cells in series ( N s ) and number of cells in parallel ( N p ). In this paper, using these model outputs, the respective efficiency ( η ) of different LIB cell technologies have been estimated using Equation (4), where P b a t and P b a t . l o s s represent the output module power and losses, respectively. The absolute value is taken to cover both charging and discharging of the battery.
η b a t = | t = o t P b a t d t   | | t = 0 t P b a t d t | + | t = 0 t P b a t . l o s s d t |

Battery Lifetime Estimation Modeling

The lifetime of the system is more dependent on the battery packs than on the PE interfaces because a battery is more likely to hit its end of life, on average, than a power MOSFET is likely to fail. Thus, it is necessary to determine the lifetime of the BESS based on the full equivalent cycles (FEC) it is subjected to. The most common method of determining the FEC of the battery is through the cycle counting algorithm shown in Equation (5).
F E C = 1 2 ( t = 1 T E b a t ( t ) E b a t ( t 1 ) D o D ( m a x ) S b a t )
where E b a t is the cumulative charging and discharging energy over a period, T, and Sbat is the total energy content of the battery in kWh. The FEC is related to the SoH of the battery as a ratio of the battery’s current cycle life to the maximum cycle life taken from the literature [34,35] being conservative in terms of tested C-rate. The maximum cycle life considered for the batteries is shown in Table 2. By convention, the end of the first life of a battery is reached when the capacity of a battery degrades by more than 80%, while the second life of the battery ends below 60% capacity degradation. The LFP 2nd-life battery considered here is assumed to have a 90% SoH and its cycle life is calculated based on the datasheet of its kind.

3.2. PCS Model

The COF uses the low-fidelity (LoFi) model of the PCS rather than the high-fidelity (HiFi) model to ensure faster system-level optimization simulation [36]. To consider the lifetime of the PCSs in the optimization, the LoFi models are extended with a fast electro-thermal model and analytical reliability assessment. The absolute worst-case reliability scenario has been modeled with regard to the PE system.
Generally, the HiFi models are employed for the physics-of-failure-based assessment and detailed characteristics test (e.g., dv/dt, short-circuit analysis) of the optimized PCS [36]. In contrast, the LoFi model is used for optimizations where simulation speed is critical. LoFi models combine a lookup table (LuT) and efficiency map from experimental test data alongside basic functional equations.
In this paper, the LoFi models for both power electronics interfaces (DC/DC and DC/AC converters) are based on efficiency ( η ) maps that are obtained from the original equipment manufacturer as a function of the battery voltage, DC-link voltage, and load power demand for their respective power converter test. Equations (6)–(9) describe the LoFi power flow model for the PCS-1 AC/DC module, while Equations (10)–(12) describe the power flow model for the PCS-2 AC/DC module, and Equations (13)–(15) describe the power flow model for the PCS-2 DC/DC module/power stage. The equations for power losses of PCS-1 and PCS-2 architecture are shown in Equations (9) and (16), respectively. The generic thermal model for the power electronics modules is shown in the next section.
η P C S 1 = L u T ( V b a t ,   P b a t )
P b a t = | P g r i d     η P C S 1   ,             P g r i d < 0     P g r i d   η P C S 1   ,             P g r i d 0
I b a t = P b a t V b a t
P l o s s _ P C S 1 = | P b a t P g r i d |
η p c s 2 ( a c / d c ) = L u T ( V d c l i n k ,   P d c l i n k )
P d c l i n k = | P g r i d     η p c s 2 ( a c / d c )   ,             P g r i d < 0     P g r i d η p c s 2 ( a c / d c )   ,             P g r i d 0
I d c l i n k = P d c l i n k V d c l i n k
η p c s 2 ( d c / d c ) = L u T ( V d c l i n k ,   I d c l i n k , V b a t t )
P b a t = | P d c l i n k     η p c s 2 ( d c / d c )   ,             P d c l i n k < 0     P d c l i n k η p c s 2 ( d c / d c )   ,             P d c l i n k 0
I b a t = P b a t V b a t
P l o s s _ P C S 2 = | P b a t P d c l i n k | + | P d c l i n k P g r i d |
where η P C S 1 is the efficiency of PCS-1 architecture; P b a t   is the charging or discharging load power in the battery side; V b a t   is the battery voltage; P g r i d is the load request by the grid; I b a t is the battery current; P l o s s _ P C S 1 is the power loss of the PCS-1 architecture; η p c s 2 ( a c / d c ) is efficiency of the AC/DC module in PCS-2 architecture; P d c l i n k   is the internal power of the dc-link bus in the PCS-2 architecture; V d c l i n k is the dc-link voltage;   I d c l i n k is the dc-link current; η p c s 2 ( d c / d c ) is the efficiency of the DC/DC module of PCS-2; and P l o s s _ P C S 2 is the power loss of the PCS-2 architecture.

3.2.1. Electro-Thermal Modelling

Power semiconductors and their packaging are subject to several failure mechanisms, such as bond wire lifting and solder wear-out, and solder plate fatigue on the base plate and in the chip soldering. Among these, bond wire-related failures are the most prominent cause of power module failures [37]. These are caused by the repetitive thermo-mechanical stress induced by the temperature gradients between the components caused by the dissipated heat losses [38]. Therefore, the MOSFET junction temperature estimation is utilized to estimate the lifetime of the PCS. The thermal estimation equations are given in Equations (17)–(19) [39].
R t o t = γ Q + δ
      Δ T = P l o s s R t o t
T m a x = Δ T + T a m b
where R t o t is the total thermal resistance, and γ and Q are the coefficients to characterize the thermal resistance. The temperature difference ( Δ T ) is calculated by multiplying the generated power losses ( P l o s s ) in terms of heat and R t o t ; the maximum temperature ( T m a x ) of the electrical component can be derived by the summation of Δ T and the ambient temperature of the system ( T a m b ).

3.2.2. System-Level Lifetime Estimation Modelling

This subsection seeks to estimate the system mean time between failures (MTBF) to evaluate the potential reliability of the modular PCS. This will assist in directing and planning for reliability and related program efforts and identifying design features critical to reliability. The reliability prediction method used in this analysis is taken from MIL-HDBK-217F(N1/2) [40]. The mathematical model used in determining the converter reliability is known as the series model. This model is based on Equations (20) and (21), where R ( t ) is the overall reliability of the converter, t is the elapsed operation time (h), and λ is the constant failure rate.
R ( t ) = e λ t = e t M T B F  
λ = 1 / M T B F
The reliability calculation of the PCS only considers the power semiconductors (i.e., a discrete SiC MOSFET, 1200 V, 115 A, 16 mΩ, Gen 3), which are the most failure-prone devices in PCSs [41]. The quality of the parts for the converter has been selected as MIL specified quality, but with a lower π Q factor since they are sourced commercially. The reliability model includes the effects of environment stresses through the environmental factors, π E , which for this paper has been selected to represent the ground, fixed type of environment. Moreover, the temperature response is taken from the thermal analysis for the worst ambient temperature (45 °C). The maximum range is fixed based on the thermal response of the PCS for the worst mission profile. If the PCS lifetime satisfies during the worst condition, it is evident that the lifetime will be higher for normal conditions. In Equation (22), the lifetime calculation for a MOSFET is presented.
λ p = λ b · π T · π Q · π E · π A · π B where   π T = e E a k     ( 1 T j + 273 1 298 ) ;   k = 8.6173303     10 5 .
Please note that, the overall part failure rate, λ p , of the individual components depends on a combination of the base failure rate, λ b , and various stress modifiers including π T (temperature factor), π Q (quality factor), π A (application factor), π E (environment factor), and π B (acceleration voltage breakdown).
The base failure rate is expressed by a model relating to the influence of electrical and thermal stresses on the MOSFET switch. The base failure rate is subjected to a modifier based on the power rating utilized by the MOSFET ( π A ), on the category of environmental application such as whether the MOSFET is utilized in a marine or aerial or space, or ground ( π E ), on the maximum junction temperature, Tj, expressed during the load profile, as given by T m a x in Equation (19) ( π T ), the level of quality at which the manufacturing process of the MOSFET is accomplished ( π Q ), and the final influence on the stress modifier of the base failure rate is the breakdown voltage stress factor ( π B ).These are considered from [40,41] for MOSFET lifetime formulation. The six switches (n = 6) in a series association are used in the convert power stages to estimate the PCS system-level lifetime. The system-level lifetime formula is given in Equation (23).
R ( t ) = ( e λ t ) n

4. Framework Implementation

The COF is developed in a MATLAB/Simulink® modeling environment to describe the behavior of fully coupled HBESS. The framework is built in a modular approach shown in Figure 9 and consists of an input layer and a programming layer for the flexibility of the framework operation. The input layer asks for the input from the user for design specifications and constraints and database selection for intended system components and connection topology, followed by selection criterion. The programming layer interfaces the input data and the component model with a specific system model configuration for simulation (with a selected connected topology) to the final output with an iterative optimization routine and decision-making criterion. The optimization routine incorporates a co-design method with multi-objective features and an evolutionary optimizer that identifies the Pareto front or feasible solution that satisfies all the constraints and requirements of the HBESS design. This section details the development of the optimization framework for HBESS. The core tasks of the COF are summarized as follows:
Sizing battery packs with optimal cell configuration by respecting all the system subcomponents’ specifications and constraints.
Sizing the PCSs in terms of rating and number of modules in a connection topology.
Finding the global optimal solution for HBESS from the selected connection topology defined in Section 2.1.

4.1. Co-Design Optimization Problem Formulation

Oversizing a battery pack by adding extra cells in series or parallel to increase system life and roundtrip efficiency impacts the system investment cost as it bears a major part of the BESS cost. However, lowering the energy content can reduce the investment cost but increase the average C-rate while in operation. This increase in C-rate may have an effect on the roundtrip efficiency of the system, which in turn may have an effect on the operational cost. Additionally, since the service or use case power requests can be instantaneous or marathon in nature, the SoC of the battery can be influenced by overcharging or undercharging a battery pack, which can affect the battery life as well. Please note that battery pack sizing also requires us to respect the PCS voltage and current rating while in operation and PCS is expected to run for higher efficiency and lower stress. In a BESS, the EMS determines each battery pack’s state (SoC and temperature) and also controls the power flow via the PE interfaces, in function of the allowed battery C-rate. So, to size the HBESS optimally, a simultaneous (SIM) co-design method has been used that guarantees a system level optimization [42]. The SIM co-design optimization problem for HBESS can be formulated as Equation (24), with a sizing plant and control plant. The control plant ensures the power sharing between two battery packs in function of their C-rate and SoC to meet the use case power profile. The dynamics of power sharing are adopted from ref. [43].
m i n x ϵ ( d s , d c ) F ( x ) = [ f 1 ( x ) , f 2 ( x ) , f 3 ( x ) , f 4 ( x ) ] Subject   to   g i ( x ) 0 X = { x | g m ( x ) 0 , m = 1 , 2 , 3 , . M } S = { F ( x | x X ) }
where x represents the vector of design variables comprised of control plant variables ( d c ) and system variables ( d s ); g i ( x ) is the inequality constraints vector for control plant and system variables and m is the number of inequality constraints, X denotes the feasible decision space, and S is the criterion space. The objective functions are deemed to be either maximized or minimized; the ones to be maximized are reflected to be minimized. In addition, vector x contains the number of cells in series and parallel for each battery pack, the DC link voltage for PCS-2 architecture, two distinct PCS ratings, the capacity of the battery packs, their SoC, and their maximum C-rates. The problem is also formulated as a mixed-integer problem where the number of cells in the battery and the number of modules in the PCS are discrete numbers while other design variables are continuous.

4.2. Multi-Objective Function

In the framework, to assess the economic viability of the HBESS while sizing and selecting the technology, the IEC60300-3-3 [44] standard has been taken into consideration, which consists of six cost components: (1) concept and definition, (2) design and development, (3) manufacturing, (4) installation, (5) operation and maintenance, and (6) disposal. These components are aggregated into capital expenditure cost (CAPEX) as outcome of 1, 2, 3, 4, and operational and maintenance cost (OPEX) to evaluate the TCO. It should be noted that the disposal cost of the batteries is included in their CAPEX and not considered separately for this study.
The multi-objective functions used in the framework are prepared in a structure so that the combination of different batteries and PE configurations can be evaluated in the same fashion.
The system economic objective is considered with the TCO, which is the summation of the CAPEX and OPEX. The CAPEX is calculated using Equation (25). Only power electronics and battery costs have been considered in the CAPEX as they directly affect the system design optimization outcome. The TCO is set with 10 years of service life as in ref. [45] to consider the influence of the system operation for a standard stationary energy storage system lifetime.
C A P E X = ( C P E 1 × P m · P E 1 × N P E 1 + C P E 2 × P m · P E 2 × N P E 2 ) + ( C B A T 1 × E B A T 1 + C B A T 2 × E B A T 2 )
where C P E 1 and C P E 2 are the costs of PE interfaces for PCS-1 and PCS-2, respectively [EUR/kW]; P m · P E 1 ,     P m · P E 2 are the modules rated power of the PE interfaces [kW]; N P E 1 , N P E 2 are the numbers of modules of the PE interfaces;   C B A T 1 , C B A T 2 are battery pack-1 and pack-2 costs, respectively [EUR/kWh], and E B A T 1 , E B A T 2 are the capacities of the battery pack-1 and pack-2, respectively [kWh].
The OPEX is calculated using Equation (26). In the OPEX, the potential battery replacement cost during the 10 years of operation has been considered with an 8% annual reduction of battery price up to 2030. However, in this study, the residual value of the systems (mainly the first-life batteries) is not considered, but it could be utilized while estimating the levelized cost of the storage systems.
O P E X = y = 1 y = 10 y r s ( E tariff × E tot × η s y s + r c )  
f 1 = T C O = C A P E X + O P E X
where E t a r i f f is the energy tariff of EU-27 in 2019 and amounts to 0,13 EUR/kWh [46]; E t o t is the total energy request in [kWh]; η s y s is the complement of the η s y s ; and r c is the replacement cost in [EUR].
The efficiency of the HBESS is estimated based on the efficiency of the two independent battery packs and their connected PCSs. The average system roundtrip efficiency is calculated as in Equation (28).
f 2 = η s y s = ( η P E · B 1 · η B 1 + η P E · B 2 · η B 2 ) 2
where η P E · B 1 ,   η P E · B 2 are the efficiencies of the PE interfaces connected to battery pack-1 and pack-2, respectively; η B 1 , η B 2 are the efficiencies of battery pack-1 and pack-2, respectively.
The lifetime of each battery and PCS has been estimated using Equations (29) and (30), as discussed in Section 3. In this task, 365 days have been considered for operation within one year. The objective is to maximize the lifetime of both the battery packs ( f 3 ) and the PCS interfaces ( f 4 ).
f 3 = B a t l i f e t i m e   = c y c l e l i f e / ( c y c l e × o p e r a t i n g   d a y s )
f 4 = R ( t ) = ( e λ t ) 6

4.3. Variables and Constraints

The constraints define conditions for variables for the designing system components that must be met. Table 3 and Table 4 present/summarize the explicit constraint/variables for PCS-1 and PCS-2 architecture for the HBESS, where the battery packs will be sized to satisfy an application with nominal power of 100 kW and nominal capacity of 100 kWh with an upper margin of 15%. Any power electronics interface must respect the constraints of the energy storage system as mentioned in Table 2, especially its C-rate and its SoC, which is capped at 80% since the batteries are always assumed to operate in the constant current mode.

4.4. Optimizer Selection

The optimization of the HBESS is a complex and nonconvex problem. Therefore, to keep the flexibility in decision-making without giving complete control to the algorithm to decide the final result, NSGA-II is considered in the task as NSGA-II uses a Pareto-front hierarchy and adopts an elitism mechanism to retain the best solutions generated during the search [47]. According to the study [48] carried out in a similar kind of problem-solving, NSGA-II gives more accurate results but is slightly slower than other multi-objective optimizers such as PSO. Since the COF is not developed for a real-time operation, it does not require a fast response, and priority is given to accuracy. Besides, by nature, GA performs an efficient and parallelizable search. Moreover, a similar characteristics system optimization problem has also been performed with the adopted algorithm [49,50] for its capacity to evolve solutions with multi-objective functions with discrete and continuous design variables. The NSGA-II algorithm, integer crossover, and mutation operator for a mixed-integer problem are well described and adapted from [51]. For iterative optimization run the optimizer is set with the following settings in this work for each possible combination in the connection topology:
Population size: 100
Crossover: simulated binary
Mutation: Gaussian distribution
Number of generations: 25
Stall generation limit: 50

4.5. Selection Criterion

When a number of Pareto optimal solutions are found after one successful complete iterative optimization routine, then to find the best solution among all feasible solutions, a composite function in Equation (31) is applied with different weighting factors for each objective based on their importance in the final HBESS solution. The weighted sum of the various objective functions is given by:
O w s ( x ) = i = 1 k w i f i ( x )
where w i [ 0 , 1 ] are the weight factors assigned to each objective and f i ( x ) is normalized to [0,1], resulting in a dimensionless number. In this paper, the solution selection criterion is set as in Equation (32) for the global optimal HBESS design with sizing and selection:
S = 0.6 · f 1 ( x ) + 0.1 · f 2 ( x ) + 0.2 · f 3 ( x ) + 0.1 · f 4 ( x )
where the system cost has a 60% weight; system efficiency has a 10% weight since the efficiency of system components is addressed before in the limitations; and battery lifetime has a higher percentage than PCS as battery replacement costs are higher.

5. Optimization Results

In this part, the results of the co-design optimization are presented for HBESS. The COF can be applied to each combination of battery packs and PE interfaces, totaling 16 combinations as indicated in Table 5.
The framework is capable of selecting any defined connection topology selection (Section 2.1) toward the global optimal HBESS sizing and selection. In the framework, the selection of batteries for HBESS combinations is based on the categorization of cell characteristics, particularly C-rate. LTO and NMC cells are regarded for HP applications because of their high C-rate and low energy capacity, while LFP (1st- and 2nd-life) cells are chosen for energy-centric applications because of their large energy capacity and relatively low C-rate restrictions. Despite the fact that the LFP 2nd-life battery has a limited energy capacity, it has been classified as an energy-focused application to increase its remaining usable lifetime by restricting the C-rate.
For each combination within the selected connection topology, the NSGA(II) algorithm finds the Pareto fonts that size the design components toward lower cost and higher efficiency and lifetime. Then, the programming layer stores these fronts in the database for further post-processing and reiterates another combination within the same selected connection topology. The Pareto fronts produced from the framework for connection topology-1 (Figure 2) are illustrated in Figure 10. Then applying the defined selection criteria, for example, here in Equation (32), the best HBESS solutions and their sizes are generated in terms of the defined objective functions and stored in the COF result database as per the combinational name such as C1, C2, C3, and C4 for the connection topology, TO-1. The best combinational HBESS solutions obtained from the framework result database for the TO-1 are presented in Table 6. Please note that a similar approach is followed if different topologies are selected in the framework at once.
To find the global optimal solution the same selection criteria is applied to the saved best optimal solution set by normalizing the multi-objective functions of the solution set. The normalized values for C1, C2, C3, and C4 are illustrated in Figure 11. The framework then finds the lowest value in the normalized solution set. The lowest value in the connection topology-1 indicates that solution C3, consisting in the use of LTO and second-life battery technologies, is the global optimum solution among the four possible hybridizations considered in the framework. It should be noted that different selection criteria with different weights can lead to different best/global optimum solutions; also, since in the used selection criteria the system cost carries the highest share of the weights, the system components’ cost will have an influence toward the best optimal solution.
However, a baseline comparison is carried out to assess the optimality of the obtained solution from the framework in terms of TCO and system efficiency for TO-1. For the baseline, each battery pack is sized with a nominal power of 50 kW as an equally balanced system to reach the previously mentioned system target of 100 kW/100 kWh. In the baseline, the sizing of the battery pack is first made based on the voltage operation defined by the PCS-1 (Table 3) and then on the maximum power and energy required for the designed system. The results of the sizing of each battery pack for the baseline comparison are presented in Table 7.
The baseline comparison in terms of TCO and system roundtrip efficiency with the obtained optimized solution is illustrated in Figure 12. Please note that during the assessment of TCO and system efficiency, the sizing from baseline and COF is evaluated under similar conditions by using the framework simulation models and power-sharing principle and by respecting all the PCS-1 constraints. The optimal sizing from the COF for C1, C2, C3, and C4 reduces the TCO by 29.3%, 12.3%, 29.6%, and 16.2%, respectively, compared to the baseline solutions; also, the system round trip efficiency is improved by 4.2%, 4.4%, 4.7%, and 5% against the baseline sizing for B1, B2, B3, and B4, respectively, which confirms the relevance of the co-design optimization framework.

6. Conclusions

This paper presents the development of a holistic and flexible framework for sizing and selecting the significant components of an HBESS by simulating such coupled and nonlinear systems iteratively. The framework supports several LIB cell technologies. In this study, four different types of cells are used to construct hybrid battery packs and their solutions are evaluated on a techno-economic scale. In addition, the framework provides four distinct HBESS-to-grid topologies and two unique PE architectures, which enable the flexibility of incorporating the commercial single-stage bidirectional PCS or bidirectional two-stage converter with a common DC link, or both, while sizing the coupled HBESS within the discussed variables and constraints for bi-directional grid service power profile. Besides, the NSGA-II algorithm and multi-objective selection criteria adopted in the framework help to reach the globally best solution based on any selected connection topology and achieve lower system cost, improved system efficiency, and longer lifetime. The obtained result from the framework for the frequency service power profile shows that it can reduce the TCO by 29.3% for an HBESS made up of LTO and LFP cell chemistries; 12.3% for the solution comprised of NMC and LFP cells; 29.6% for LTO and LFP 2nd-life cells; and 16.2% for NMC and LFP 2nd-life cells.
All in all, such a framework has high relevance in the design and techno-economic analysis of HBESSs, as these come with a large number of (iterative) simulations. Thus, the presented co-design optimization framework for automated simulation and optimization forms the basis for optimally sizing and selecting the HBESS subcomponents for grid applications.

Author Contributions

Methodology, M.M.H., S.C., T.G. and O.H.; software, M.M.H.; resources, B.B., T.M. and I.C.; writing—original draft preparation, M.M.H.; writing—review and editing, B.B., T.M., I.C., S.C., T.G. and O.H.; supervision, T.G. and O.H. All authors have read and agreed to the published version of the manuscript.

Funding

This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 963527 (iSTORMY).Energies 15 05355 i001

Data Availability Statement

Not applicable.

Acknowledgments

The authors would like to acknowledge the iSTORMY consortiums for providing their valuable inputs. Authors also acknowledge the Flanders Make for their support to the MOBI-EPOWERS research group.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Principle schematic of the considered HBESS.
Figure 1. Principle schematic of the considered HBESS.
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Figure 2. PE configuration 1: only PCS-1 is used.
Figure 2. PE configuration 1: only PCS-1 is used.
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Figure 3. PE configuration 2: only PCS-2 is used.
Figure 3. PE configuration 2: only PCS-2 is used.
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Figure 4. PE configuration 3: PCS-2 for battery pack-1 and PCS-1 for battery pack-2.
Figure 4. PE configuration 3: PCS-2 for battery pack-1 and PCS-1 for battery pack-2.
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Figure 5. PE configuration 4: PCS-1 for battery pack-1 and PCS-2 for battery pack-2.
Figure 5. PE configuration 4: PCS-1 for battery pack-1 and PCS-2 for battery pack-2.
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Figure 6. Eight-hour UK grid service profile to be used in the COF.
Figure 6. Eight-hour UK grid service profile to be used in the COF.
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Figure 7. Equivalent circuits model of battery cells.
Figure 7. Equivalent circuits model of battery cells.
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Figure 8. OCV identification result for the selected Li-ion cells in the COF.
Figure 8. OCV identification result for the selected Li-ion cells in the COF.
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Figure 9. Methodology of COF for sizing and selection of technology toward optimal HBESS design.
Figure 9. Methodology of COF for sizing and selection of technology toward optimal HBESS design.
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Figure 10. Pareto-optimal HBESS solutions found by the COF for TO-1.
Figure 10. Pareto-optimal HBESS solutions found by the COF for TO-1.
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Figure 11. Normalized values of selection criterion applied to saved best optimal Pareto fronts.
Figure 11. Normalized values of selection criterion applied to saved best optimal Pareto fronts.
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Figure 12. Comparison of the obtained optimal sizing from COF and baseline for HBESS solutions.
Figure 12. Comparison of the obtained optimal sizing from COF and baseline for HBESS solutions.
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Table 1. Notations used to define the size of HBESS.
Table 1. Notations used to define the size of HBESS.
NotationsDescriptions
N s × N p Number of cells in series and parallel for each battery pack configuration
V N o m Nominal voltage for each battery pack
E b p Battery pack energy
P m p e 1 Power rating of PCS-1 module
N m p e 1 Number of PCS-1 module
P m A C / D C p e 2 Power rating of PCS-2 AC/DC module
P m D C / D C p e 1 Power rating of PCS-2 DC/DC module
V d c l i n k p e 1 DC-link voltage for PCS-2 module
N m A C / D C p e 1 Number of PCS-2 AC/DC modules
N m D C / D C p e 1 Number of PCS-2 DC/DC modules
Table 2. Selected cell specifications to be used in the COF.
Table 2. Selected cell specifications to be used in the COF.
TechnologyNMC 1st LifeLTO 1st LifeLFP 1st LifeLFP 2nd Life
Nominal capacity [Ah]512028020
Nominal voltage [V]3.652.33.23.3
Max/min voltage [V]4.2–2.52.7–1.53.65–2.53.8–1.6
FormatPrismaticPrismaticPrismaticPouch
Mass [g]9255505220496
Parametrized C-rate−2C to +2C−2C to +2C−1C to +1C−2C to +2C
Lifecycle at 80% DOD for 25 °C142914,00045304000
Cost [EUR/kWh]200500260180
Table 3. Specifications and constraints for PCS- 1.
Table 3. Specifications and constraints for PCS- 1.
Constraints/VariablesDescription
i d x b a t [ 1 , 2 n ] N variants of battery types
i d x A C D C [ 1 , 2 , 3 n ] N variants of DC/AC module combinations
100 B a t t v o l t a g e 200 Battery voltage range
PE stage efficiency ≥ 98% ∗ 98%Power electronics efficiency input to output, half to full power
Specifications for PCS-1: Max. current rating per module is 200 A; Power rating per module is 25 kW.
Table 4. Specifications and constraints for PCS-2.
Table 4. Specifications and constraints for PCS-2.
Constraints/VariablesDescription
i d x b a t [ 1 , 2 n ] N variants of battery types
i d x D C D C [ 1 , 2 , 3 n ] N variants of DC/DC converter combinations
i d x A C D C [ 1 , 2 , 3 n ] N variants of DC/AC converter modularity
700   V V D C l i n k 800   V DC-Link voltage range
300 B a t t v o l t a g e 400 Battery voltage range
PE stage efficiency ≥ 98% ∗ 98%Power electronics efficiency input to output, half to full power
Specifications for PCS-2: power rating per module (DC/AC) is 33 kVA; power rating per module (DC/DC) is 15 kW–20 kW; max. current per module (DC/DC) is 50 A.
Table 5. Combination among the cells and PCS configurations for global optimum selection and sizing of HBESS technology.
Table 5. Combination among the cells and PCS configurations for global optimum selection and sizing of HBESS technology.
TO-1TO-2TO-3TO-4
LTOPCS-1LTOPCS-2LTOPCS-2LTOPCS-1
LFPPCS-1LFPPCS-2LFPPCS-1LFPPCS-2
C1C5C9C13
NMCPCS-1NMCPCS-2NMCPCS-2NMCPCS-1
LFPPCS-1LFPPCS-2LFPPCS-1LFPPCS-2
C2C6C10C14
LTOPCS-1LTOPCS-2LTOPCS-2LTOPCS-1
2ndlifePCS-12nd lifePCS-22nd lifePCS-12nd lifePCS-2
C3C7C11C15
NMCPCS-1NMCPCS-2NMCPCS-2NMCPCS-1
2nd lifePCS-12nd lifePCS-22nd lifePCS-12nd lifePCS-2
C4C8C12C16
Table 6. Optimal hybrid system configuration solutions with the topology, TO-1.
Table 6. Optimal hybrid system configuration solutions with the topology, TO-1.
HBESS   S o l n Cell Tech. N s × N p V N o m   ( V ) E b p ( k W h ) P m p e 1 ( k V A ) N m p e 1
C1LTO72s15p16248.6252
LFP60s1p19253.762
C2NMC42s6p15345.9252
LFP60s1p19253.762
C3LTO69s8p158.725.392251
2nd life56s22p174.976.953
C4NMC42s6p15345.9253
2nd life56s18p18455.21
Table 7. Baseline HBESS configurations.
Table 7. Baseline HBESS configurations.
Baseline   HBESS   S o l n Cell Tech. N s × N p V N o m   ( V ) E b p ( k W h )
B1LTO72s17p165.656.304
LFP53s1p169.647.488
B2NMC42s6p169.251.77
LFP60s1p172.848.384
B3LTO72s15p165.656.3
2nd life56s15p178.249.896
B4NMC42s6p169.251.77
2nd life56s18p181.550.82
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Hasan, M.M.; Berseneff, B.; Meulenbroeks, T.; Cantero, I.; Chakraborty, S.; Geury, T.; Hegazy, O. A Multi-Objective Co-Design Optimization Framework for Grid-Connected Hybrid Battery Energy Storage Systems: Optimal Sizing and Selection of Technology. Energies 2022, 15, 5355. https://doi.org/10.3390/en15155355

AMA Style

Hasan MM, Berseneff B, Meulenbroeks T, Cantero I, Chakraborty S, Geury T, Hegazy O. A Multi-Objective Co-Design Optimization Framework for Grid-Connected Hybrid Battery Energy Storage Systems: Optimal Sizing and Selection of Technology. Energies. 2022; 15(15):5355. https://doi.org/10.3390/en15155355

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Hasan, Md. Mahamudul, Boris Berseneff, Tim Meulenbroeks, Igor Cantero, Sajib Chakraborty, Thomas Geury, and Omar Hegazy. 2022. "A Multi-Objective Co-Design Optimization Framework for Grid-Connected Hybrid Battery Energy Storage Systems: Optimal Sizing and Selection of Technology" Energies 15, no. 15: 5355. https://doi.org/10.3390/en15155355

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