Control strategy and corresponding parameters have significant impacts on the overall technical and economic characteristics of composite energy storage systems (CESS). A better control strategy and optimized control parameters can be used to improve the economic and technical characteristics of CESS, and determine the maximum power and stored energy capacity of CESS. A novel coordinated control strategy is proposed considering the coordination of various energy storage systems in CESS. To describe the degree of coordination, a new index, i.e. state of charge coordinated response margin of supercapacitor energy storage system, is presented. Based on the proposed control strategy and index, an optimization model was formulated to minimize the total equivalent cost in a given period for two purposes. The one is to obtain optimal control parameters of an existing CESS, and the other is to obtain the integrated optimal results of control parameters, maximum power and stored energy capacity for CESS in a given period. Case studies indicate that the developed index, control strategy and optimization model can be extensively applied to optimize the economic and technical characteristics of CESS. In addition, impacts of control parameters are discussed in detail.
1. Introduction
Up to now, among all the energy storage options available in practical engineering, no single type of energy storage can fulfill all the desirable features of an ideal storage device. Energy storage devices are generally divided into energytype storage and powertype storage. The energytype storage, such as lithiumion battery (LB), provides high energy capacity, low selfdischarge and relatively low cost, but suffers from short cycle life which has a great relationship with its charging and discharging process. In contrast, the powertype storage, such as supercapacitor (SC), has superior cycle efficiency, a long cycle life, and capability of dealing with high power charging or discharging, but it has small energy capacity, high selfdischarge rate and relatively high cost. A promising way is to exploit different types of energy storages in a composite manner, realizing the advantages of each cell while hiding their weaknesses. For example, composite energy storage system (CESS) using in practical engineering is composed of multiple different energy storages and their matching power conversion system (PCS), i.e. a plurality of energy storage systems (ESS). In order to maximize the strengths of various energy storages and to improve the overall performance, control strategy and optimization of CESS has become a research hotspot.
Control strategy, namely how to combine various ESSs of CESS, has been researched mainly in the fundamental problem, i.e. power allocation, and protection of power limit, overcharge and overdischarge. For the power allocation within CESS considering the complementary characteristics of various ESSs, the rule based method
[1
,
2]
, fuzzy control method
[3]
, wavelet analysis method
[4
,
5]
, lowpass/highpass filtering method
[6

14]
are used to exploit the advantages of various ESSs. Among these methods, the lowpass / highpass filtering method is most commonly used, and filter time constant can be used to quantify the distribution of power command to each ESS. For protection of CESS, the output power of each ESS is individually adjusted according to the respective circumstances of over charge, over discharge and over power limit, using the direct adjustment methods
[5
,
8]
or indirect adjustment methods such as fuzzy logic control etc.
[3
,
6]
to protect the components of CESS. In the intensive study, namely the coordination control of various ESSs, only the literature
[12]
discusses overcharge and over discharge protection control scheme when the SOC of two ESSs are in the different states, and only the literature
[15]
describes that the powertype storage remains full charge to satisfy the pulse load in microgrid, and only the literatures
[1]
and
[6]
propose that the SOC of powertype storage should be maintained at its intermediate value to maintain a certain power adjustment capability all the time.
Optimization of CESS can be divided into performance optimization for the existing CESS with fixed maximum power and fixed energy storage capacity, configuration optimization of maximum power and stored energy capacity for ESSs in CESS, and so on. With regard to performance optimization of CESS, charge allocation, charge replacement and charge migration (i.e. storage efficiency or energy loss) are optimized in
[16

18]
which belong to internal optimization for module units in CESS, and the effects of the lifetime influencing factor or quantization lifetime of energytype storage are analyzed in
[3
,
10

12]
and
[19]
. Prolonging the service life of energytype storage has an important impact on the overall performance of CESS because the service life of energy type storage is usually much smaller than powertype storage. As indirect approaches to analyze the lifetime impact of energytype storage, it shows that depth of discharge and current ripple of energytype storage can be reduced by filter control of CESS through simulation in
[11]
and
[12]
, and a method to minimize the output current fluctuation of energytype storage in CESS is proposed in
[19]
. And the quantified improvement of LB lifetime effected by control strategy of CESS is directly analyzed in
[3]
and
[10]
based on the lifetime quantization model of energytype storage. With regard to configuration optimization of CESS, the minimal configurations of maximum power and stored energy capacity of various ESSs with the requirement of renewable energy power output to be met are discussed in
[5]
and
[20]
, and stored energy capacities of CESS are optimized with the optimization objective such as annualized life cycle cost in
[2]
, onetime investment and operation costs in
[21]
considering lifetime quantification of all energy storage arrays. In addition, the parameters in control strategy of CESS have a certain impact on control effect, however, the filter time constant has only been considered on optimization configuration in
[2]
, and the effect on lifetime of LB, stored energy capacity of SCESS has only been analyzed in
[10]
when the filter time constant changes.
In order to maximize the advantages and complementary nature of various energy storage, the measures i.e. overall adjustment ability optimization and limitprotect coordination control are newly increase on the basis of filtering power allocation. A control strategy including coordination between two types of ESS and overall performance optimization is proposed for CESS. The core of proposed strategy is to optimize the overall adjustment ability, accordingly the SOC coordinated response margin of SCESS is proposed to reflect the state coordination between two types of ESS. Meanwhile, combining lifetime quantification model and economic factor of various energy storages and their matching PCS, the technical economic optimization model of CESS is established with the objectives to meet the technical requirement of application and to minimize total loss equivalent cost of CESS. The technical economic characteristics of the existing CESS are elevated after the optimization of two main control parameters i.e. filter time constant and proposed margin index. In addition, the integrated optimization of control parameters, maximum power and stored energy capacity of ESSs have been accomplished, and the impacts of control parameters variation on required energy storage capacity, loss equivalent cost of various ESSs are analyzed in detail.
The paper is organized as follows: Section 2 illustrates the contents and process of full text. The mathematical model and lifetime quantification model of CESS are given in Section 3. The proposed coordinated control strategy of CESS and a new index are discussed in Section 4. The models of operation optimization and integrated optimization are established in Section 5. The case studies of proposed strategy, operation optimization and integrated optimization are given in Section 6. The impact of main control parameters is discussed in Section 7. Conclusion of the paper is given in Section 8.
2. Models of ESS
 2.1 Mathematical model
The ESS can be charged and discharged as required, i.e. the direction and magnitude of energy exchange between the ESS and external grid is controllable. If the direction from the ESS is defined as the positive direction, then a positive value of power output indicates discharging process of the ESS, while a negative value indicates the charging process. As shown in
[2
,
4
,
5]
and
[22]
, the power output limits and SOC of ESS considering the effect of selfdischarge rate and chargedischarge efficiency are computed as (1)(4). This is the base model of ESSs available for both LBESS and SCESS.
 2.2 Lifetime quantification models
As integral parts of CESS, various PCSs are usually uninterrupted work, and their power electronic devices have a limited lifetime. Without taking into account the failure, lifetime loss coefficient of each PCS is approximately the ratio of running time and corresponding lifetime time. The coefficient is computed as (5).
In the CESS with LBESS and SCESS, lifetime quantization models of energy storages include lifetime quantization models of both LB and SC. The chargedischarge cycles of SC are more than one million times
[9
,
10]
, which are much larger than that of LB. Therefore, an approximate calculation model is used for lifetime quantization of SC, and a detailed calculation model is used for lifetime quantization of LB. The lifetime loss coefficient of SC is approximately the ratio of run cycles and its total cycles, which is computed as (6).
The lifetime of LB is mainly considered from degradation failure that degradation of certain performance index increases gradually with time in service, and life is end when the index reaches a failure threshold. The lifetime of LB is typically defined as cycle life or calendar life corresponding with the degenerative process from the nominal energy capacity to its 80%
[23

26]
. Capacity degradation algorithm of LB suitable for practical applications and irregular chargedischarge application in particular is proposed in
[23]
, as a function of the equivalent throughput cycles, the average SOC, the SOC normalized deviation and the operating temperature. The algorithm validated by experiments and actual operation has repeatedly been cited or applied directly in
[18
,
24

29]
. According to the algorithm, the increment of LB capacity degradation in the time interval τ is computed as (7).
where,
where
T_{ref}
=25℃,
T_{a,ref}
=
T_{ref}
+273,
T_{a,LB}
=
T_{LB}
+273,
K_{T}
= 0.0693,
K_{co}
= 3.66e5,
K_{ex}
= 0.717,
K_{SOC}
= 0.916. The last four coefficients as given in
[23]
are typical values, which are used as empirical constants of a particular LB. And these coefficients can be amended in accordance with the lifetime data for different LB.
The capacity degradation of LB for M time intervals is then given by (8).
The degradation
D_{LB}
of LB capacity as described in formula (8) changes from 0 (when LB is new) to 1 (when the capacity of LB degenerates to 0). And
D_{LB}
=0.2 means that the actual capacity of LB degenerates to 80% of its nominal capacity. So the lifetime loss coefficient of LB is computed as (9).
3. Coordinated Control and New Index of CESS
 3.1 Coordinated control strategy
A coordinated control strategy of CESS based on chargedischarge state of LBESS is proposed in order to improve the overall performance. In this strategy, power commands are allocated by the highpass filter. Then SOC of SCESS is adjusted based on the chargedischarge state of LBESS with the purpose of overall adjustment ability optimization. And the protection coordination between two ESSs is implemented for overcharge protection, overdischarge protection and maximum power limit. The control block diagram and control flow chart of the strategy are given as
Fig. 1
.
Coordinated control strategy of CESS
When allocating power in CESS, the highfrequency fluctuation power of
P_{CESS}
is separated by a highpass filter and absorbed by SCESS, and the remaining power is absorbed by LBESS. The power allocations are computed as follows.
When optimizing the overall adjustment ability, the usage of state coordinating between two ESSs is demanded. The stored energy of SCESS is maintained at a lower level when LBESS is discharging, and maintained at a higher level when LBESS is charging. In order to make SOC of SCESS to achieve the different control objectives set by the chargedischarge states of LBESS as far as possible, the time constant
T_{f}
should be repeatedly adjusted within the permissible range [
T_{fmin}
,
T_{fmax}
] in steps of
ΔT_{f}
, where
T_{fmax}
=
T_{f0}
+
T_{flim}
, and
T_{fmin}
= max(0,
T_{f0}

T_{flim}
).
When protection coordination is in progress, there is a need for coordination between two ESSs of CESS. The output power of ESSs should be adjusted due to overcharge protection, overdischarge protection and maximum power limit, at the same time the adjusted part of output power could be undertook by the other ESS within its allowable range.
 3.2 Coordinated response margin of SCESS
Fig. 2
illustrates the principle of overall adjustment ability optimization as the core part of the proposed strategy, where SOC of SCESS is dynamically adjusted according to chargedischarge status of LBESS. It shows that charging margin is reserved in SCESS when LBESS is discharging, and discharging margin is reserved in SCESS when LBESS is charging. Then there will be an enhanced response capability for instantaneous power changes, an optimization of charge and discharge process for LBESS, and an improvement of overall performance for CESS. Hence, a new index named as SOC coordinated response margin of SCESS is proposed and denoted by
ΔS_{co,SC}
, which is numerically equal to (
S_{max,SC}
–
S_{LBd,SC}
) or (
S_{LBc,SC}

S_{min,SC}
). And there is a relation described as
S_{max,SC}

S_{LBd,SC}
=
S_{LBc,SC}

S_{min,SC}
because the charging margin is equal to the discharge margin due to their interlinked principle.
Coordinated control diagram of overall adjustment ability optimization
4. Optimization Model of CESS
 4.1 Objective function
Technical characteristic of CESS can be considered consistent when PCESS is met by output powers of the internal ESSs all the time. Economic characteristic of CESS can be reflected by total acquisition cost or total loss equivalent cost, where the former represents only disposable investment cost and the latter considering as a comprehensive evaluation from the aspect of life cycle represents total lifetime loss quantization of CESS in a specific time. Meanwhile, the objective to minimize total loss equivalent cost within a certain time is used for operation optimization and integrated optimization of CESS based on consideration of comparability. In summary, a mathematical model of CESS technical economic optimization is proposed as follow.
where,
As shown in (12), the maximum power of an ESS is commonly limited by PCS, while its stored energy capacity is commonly affected by the number of seriesparallel modules in energy storage. PCS used in the actual project is usually complete equipment, and is different required for different ESSs, e.g. singlestage PCS and dualstage PCS used in LBESS and SCESS respectively.
 4.2 Operation optimization
Operation optimization is to optimize the main parameters of the proposed control strategy in an existing CESS wherein all ESSs have an assured maximum power and stored energy capacity, using optimization model shown as (12). The minimum of total loss equivalent cost within a certain time can be obtained for CESS while satisfying the same power requirement. The parameters to be optimized are the proposed strategy’s main control parameters
T_{f}
and
ΔS_{co,SC}
. Constraint conditions of operation optimization are provided as follows.

2) SOC operating ranges of ESSs

2) Output power limits of ESSs

3) SOC coordinated response margin range of SCESS
 4.3 Integrated optimization
Integrated optimization is to optimize the main parameters of the proposed control strategy, together with the required maximum power and required energy capacity of all ESSs in CESS, using optimization model shown as (12). The minimum of total loss equivalent cost within a certain time can be obtained for CESS while satisfying the same power requirement. The parameters to be optimized are the proposed strategy’s main control parameters
T_{f}
,
ΔS_{co,SC}
, the ESSs’ required maximum power
P_{r,LB}
,
P_{r,SC}
and required energy storage capacity
E_{r,LB}
,
E_{r,SC}
. In addition to (13) ~ (17), constraint conditions of integrated optimization include maximum power range of ESSs shown as follows.
In the engineering applications, PCS of ESS generally uses standard equipment package, which make the maximum power of ESSs to be one of the few optional specification values, such as 50kW, 100kW, 200kW, 250kW, 300kW, 400kW, 500kW, etc. The stored energy capacity of ESS is mainly affected by the number of seriesparallel modules in energy storage, and can be considered as approximate continuous change when the module number is increased or decreased.
Meanwhile, the maximum power and stored energy capacity of ESSs are considered in the integrated optimization, so the acquisition cost of CESS as an assistant index of technical economic comparison for integrated optimization will be affected directly [30]. The acquisition cost of CESS comprising of LBESS and SCESS is computed as (20).
where,

Cacq,LB=Cunit,LBEr,LB+CPCS,LB

Cacq,SC=Cunit,SCEr,SC+CPCS,SC
5. Case Studies
The parameters in the simulation are set as
ΔT_{f}
=1,
T_{flim}
=10, F=10,000$. The output power command of CESS, which is the operation curve of ESS taking as the system main power supply in an island independent microgrid, is shown in
Fig. 3
. The main parameters of LBESS and SCESS are provided in
Table 1
, where the matching PCSs typically have a lifetime of 10 years, and their acquisition costs are shown in
Table 2
.
The power command of CESS
Main parameter settings of two ESSs
Main parameter settings of two ESSs
Acquisition cost of the matching PCS for two ESSs
Acquisition cost of the matching PCS for two ESSs
 5.1 Technical economic comparison between base strategy and proposed strategy
Taking into account overall adjustment ability optimization, which is the core of proposed coordinated control strategy and the main improvement different from other CESS control strategies
[1

14]
, a contrast strategy without this optimization is set and named base strategy. The filter time constant
T_{f}
is set as 30 in the base strategy and proposed strategy, and the margin indicator
ΔS_{co,SC}
is set as 0.35 in the proposed strategy, i.e. SOC control objective of SCESS is set as the average value of its maximum and minimum. When the power command shown in
Fig. 3
is met in two strategies respectively, the power output curve and SOC curve of ESSs are given in
Fig. 4
.
Output power and SOC of two ESSs using two strategies
As seen in
Fig. 4
, the SOC of SCESS is closed to its limit for a long time in the absence of an orderly control, resulting in a significant decrease in their ability to participate in the system power regulation. By contrast, state adjustment of SCESS using the proposed strategy keeps its SOC in a reasonable range all the time through coordination between two ESSs, and thereby always maintaining a certain ability to regulate power.
The lifetime loss and equivalent cost of ESSs using the base strategy and the proposed strategy are given in
Table 3
. Compared with base strategy, the lifetime loss of LB arrays within the simulation time using proposed strategy is decreased significantly by 4.62%, and the decrease in equivalent cost of LBESS is 4.47%. At the same time, there is a slight increase in the lifetime loss of SC array as well as the equivalent cost of SCESS. And the total equivalent cost of CESS lifetime loss is significantly reduced by 4.13%.
Lifetime loss and equivalent cost of ESSs using two strategies
Lifetime loss and equivalent cost of ESSs using two strategies
In summary, the technical economic characteristics of CESS when using the proposed strategy is significantly better than using the base strategy through the coordination and cooperation between two ESSs.
 5.2 Improvement in technical economic characteristics after operation optimization
The results of operation optimization based on the proposed strategy are provided in
Table 4
, where the results are from the solution of optimization model shown in (12) using particle swarm optimization algorithm.
Operation optimization result of CESS using proposed strategy
Operation optimization result of CESS using proposed strategy
Compared with the nonoptimization control parameters of the proposed strategy, the total equivalent cost of CESS lifetime loss as shown in
Tables 3
and
Table 4
is significantly decreased by 3.59% after optimizing. Specifically, the lifetime loss of LBESS and SCESS are both significantly decreased by 3.42 % and 13.47 % respectively, and the equivalent cost of LBESS and SCESS are both significantly decreased by 3.30% and 7.05% respectively.
Consequently, operation optimization of the existing CESS can significantly enhance its overall technical economic characteristics by optimizing filter time constant and margin index.
 5.3 Improvement of technical economic characteristics after integrated optimization
In the integrated optimization of CESS, the parameters of ESSs are shown as
Table 1
and
Table 2
except the maximum power and stored energy capacity. Then the optimization model given in formula (12) is solved using particle swarm optimization algorithm based on the proposed strategy, and the optimal result of integrated optimization is provided in
Table 5
. Moreover, the results of operation optimization and integrated optimization are put together to facilitate comparative analysis. The gray parts of
Table 5
show that the maximum power, stored energy capacity and acquisition cost of two ESSs are all fixed values in operation optimization.
Operation optimization result and integrated optimization result of CESS using proposed strategy
Operation optimization result and integrated optimization result of CESS using proposed strategy
In
Table 5
, it shows that,

1) The parameters to be optimized of operation optimization areTfandΔSco,SC, the proposed strategy’s main control parameters. And their optimal values are 15 and 0.52 respectively. At the same time, the parameters to be optimized of integrated optimization are the required maximum powerPr,LB,Pr,SC, the required energy storage capacityEr,LB,Er,SC, the proposed strategy’s main control parametersTf,ΔSco,SC. And their optimal values are 500, 300, 761.80, 3.12, 23 and 0.53 respectively.

2) Comparing with the lifetime loss and homologous equivalent cost of ESSs after operation optimization, there are many benefits for the integrated optimization of CESS. For example, the lifetime loss of LB is significantly reduced by 10.90%, the equivalent cost of LBESS is substantially decreased by 31.01%, the equivalent cost is significantly decreased by 12.87% while lifetime loss of SC is amplified more than three times, and that total lifetime loss equivalent cost of CESS is substantially decreased by 29.65%.

3) From the further analysis combined with acquisition cost of ESSs, through the integrated optimization of CESS, there is not only a sharp fall in the total lifetime loss equivalent cost of CESS because of the substantial decrease in maximum power and stored energy capacity of ESSs, but also a decrease of 1.2729 million dollars in theCequ,CESS, i.e. a reduction up to 52.82%.
The previous analysis has shown that, comparing with the optimal result of operation optimization for the existing CESS, the integrated optimization of CESS can not only significantly reduce the total lifetime loss equivalent cost of CESS in a certain time, but also decrease its acquisition cost by more than half. So the technical economic characteristics has increased substantially both in initial investment cost and life cycle cost after the integrated optimization.
6. Impact Analysis of Control Parameters
Setting
T_{f}
as a fixed value, an optimal result of CESS integrated optimization can be computed by optimization model shown in (12). When
T_{f}
is set as different fixed values, the different optimal results can be obtained by reoptimization, and the variation trends of optimal results with change of
T_{f}
will be obtained. The variation trends of optimal results with the set value of
ΔS_{co,SC}
change can get in the same way. The variation range of
T_{f}
is set as {11, 12,…, 30} according to the results of integrated optimization in Table V, and the variation range of
ΔS_{co,SC}
is set as {0.05, 0.10, …, 0.65} according to its range constraint. In the light of the analysis of the optimal result, the influence of two control parameters presents certain regularity.
 6.1 Impact analysis ofTf
As shown in
Fig. 5
, the minimal
C_{equ,CESS}
decreases firstly and then increases as the constant
T_{f}
is increased.
Curve of optimal C_{equ,CESS} with changes in T_{f}
For LBESS in CESS, the minimum of
C_{equ,LB}
is decreased firstly and then increased slightly with increase of
T_{f}
as illustrated in
Fig. 6
. As Tf increaseing, the lifetime loss of LB is reduced gradually, and the required energy capacity is reduced firstly and then increased slightly. The slight increase of required energy capacity is normal, because in order to get a better smoothness the power output of LBESS needs to increase when
T_{f}
is larger than certain threshold.
Curves of relevant data for LBESS with changes in T_{f}
For SCESS in CESS, the minimum of
C_{equ,LB}
is increased constantly as illustrated in
Fig. 7
. As
T_{f}
increasing, the required energy capacity of SCESS is increased constantly, and the lifetime loss of SC is reduced gradually.
Curves of relevant data for SCESS with changes in T_{f}
In conclusion, the detailed effects of different control parameter on CESS and ESSs inside are got. For example, when
T_{f}
increases, the frequency domain range of highfrequency fluctuation of
P_{CESS}
born by SCESS becomes larger and the power output of SCESS is increased, and this will lead to a continuous increase in the required energy storage capacity of SCESS and a gradual rise in the lifetime loss equivalent cost of SCESS. At the same time, the output power of LBESS will become smoother, and the lifetime loss and corresponding equivalent cost will decrease gradually. The change tendency of lifetime loss equivalent cost in two ESSs is just opposite, but the total cost
C_{equ,CESS}
is decreased firstly and then increased, and the turning point is the optimal point.
 6.2 Impact analysis ofΔSco,SC
When the parameters except
T_{f}
as fixed value is optimizing, the optimal
ΔS_{co,SC}
corresponding to different
T_{f}
is within the compass of 0.50~0.53 as illustrated in
Fig. 8
, while the value range of
ΔS_{co,SC}
is 0~0.7.
Curve of optimal ΔS_{co,SC} with changes in T_{f}
The results of integrated optimization with different values of
ΔS_{co,SC}
in its permissible range
Figs. 9
and
Fig. 10
. As
ΔS_{co,SC}
increasing, the optimal values of
T_{f}
increase firstly and then decrease. Meanwhile, for LBESS,
E_{r,LB}
and
C_{equ,LB}
both decrease firstly and then increase, and for SCESS,
E_{r,SC}
decrease firstly and then increase while
C_{equ,LB}
increase firstly and then decrease, and for CESS, the total cost
C_{equ,CESS}
is decreased firstly and then increased, and the turning point is the optimal point.
Optimal results of parameters with changes in ΔS_{co,SC}
Optimal results with changes in ΔS_{co,SC}
7. Conclusion
A novel entirety control strategy of CESS is presented in this paper based on the power allocation method. Compared with no regard to the overall adjustment ability optimization, the proposed strategy can always maintain a certain ability in SCESS to regulate power output, and obviously improve the overall technical economic characteristics of CESS.
The proposed overall adjustment ability optimization which dynamically adjusts SOC of SCESS according to the chargedischarge state of LBESS can quantify coordination between two ESSs by the margin index. The optimization case study of two main control parameters shows that the technical economic characteristics of the existing CESS have improved significantly by operation optimization.
The impact of control parameters should be considered in integrated optimization of CESS where maximum power and stored energy capacity of various ESSs is optimized. Case study of integrated optimization shows that the total loss equivalent cost, required maximum power, required energy storage capacity and onetime investment are all substantially decreased. Furthermore, the impact analysis of margin index and filter time constant show that only when the filter time constant and margin index are all moderate size, the technical economic characteristics of CESS can be optimal.
The characteristics of ESS used in practical application have been fully considered in this paper, such as the impact of selfdischarge rate and chargedischarge efficiency in mathematical model, lifetime quantification of all energy storages and their matching PCS, the characteristics of PCS which is usually complete equipment and different for different ESS, and so on. Therefore the researches here are more reasonable and have more reference value. The coordinated control strategy and technical economic optimization method will be used in practical engineering as the follow work, and a further research and discussion will be done soon.
Nomenclature LB Lithiumion battery SC Supercapacitor CESS Composite energy storage system PCS Power conversion system ESS Energy storage system LBESS Lithiumion battery energy storage system SCESS Supercapacitor energy storage system SOC State of charge T Running time of system △T_{com} Time step of computation P_{out,ESS} Output power of ESS P_{cmax,ESS} Maximum charging power of ESS P_{dmax,ESS} Maximum discharging power of ESS P_{clim,ESS(n)} Charging power limit of ESS in the current period P_{dlim,ESS(n)} Discharging power limit of ESS in the current period P_{r,ESS} Rated power of ESS E_{r,ESS} Rated capacity of ESS S_{max,ESS} Maximum SOC of ESS S_{min,ESS} Minimum SOC of ESS E_{ESS(n)} Stored electric energy of ESS at the current moment E_{ESS(n1)} Stored electric energy of ESS at the previous moment S_{ESS(n)} SOC of ESS at the current moment S_{ESS(n1)} SOC of ESS at the previous moment σ_{ESS} Selfdischarge rate of ESS η_{c,ESS} Charging efficiency of ESS η_{d,ESS} Discharging efficiency of ESS T_{life,PCS} Lifetime of PCS L_{loss,PCS} Lifetime loss coefficient of PCS N_{cycle,SC} Charge and discharge cycles of SC N_{total,SC} Total charge and discharge cycles of SC L_{loss,SC} Lifetime loss coefficient of SC τ Certain time interval ΔD_{LB} Degenerate increment of LB capacity D_{1} Intermediate variable of ΔD_{LB} D_{2} Intermediate variable of ΔD_{LB} S_{avg,LB} SOC average value of LB S_{dev,LB} SOC normalized deviation of LB N_{LB} Equivalent throughput cycle of LB T_{ref} Reference temperature in degrees centigrade T_{LB} Operation temperature of LB in degrees centigrade T_{a,ref} Absolute temperature of T_{ref} T_{a,LB} Absolute temperature of T_{LB} τ_{life,LB} Calendar lifetime estimate of LB end of 80% initial capacity K_{T}, K_{co}, K_{ex}, K_{SOC} Empirical constant of specific LB D_{LB} Degradation of LB capacity △D_{LB}(m) Degenerate increment of LB capacity in time interval m D_{LB}(m1) Degradation of LB capacity for m1 time intervals D_{LB}(M) Degradation of LB capacity for M time intervals L_{loss,LB} Lifetime loss coefficient of LB P_{CESS} Power command of CESS P_{out,LB} Output power of LBESS P_{out,SC} Output power of SCESS T_{f} Filter time constant T_{f0} Initial value of Tf in power allocation △T_{f} Adjustment step of T_{f} T_{flim} Adjustment width of T_{f} T_{fmin} Minimum of T_{f} Adjustment T_{fmax} Maximum of T_{f} Adjustment S_{SC} SOC of SCESS S_{min,SC} Minimum SOC of SCESS S_{max,SC} Minimum SOC of SCESS S_{LBd,SC} SOC control objective of SCESS when LBESS discharges S_{LBc,SC} SOC control objective of SCESS when LBESS charges △S_{co,SC} SOC coordinated response margin of SCESS C_{equ,CESS} Loss equivalent cost of CESS C_{equ,LB} Loss equivalent cost of LBESS C_{equ,SC} Loss equivalent cost of SCESS C_{unit,LB} Unit energy capacity cost of LBESS C_{PCS,LB} Acquisition cost of the matching PCS for LBESS C_{unit,SC} Unit energy capacity cost of SCESS C_{PCS,SC} Acquisition cost of the matching PCS for SCESS C_{pen} Penalty cost without meeting the system power balance F Fixed value much larger than C_{equ,CESS} S_{LB} SOC of LBESS S_{min,LB} Minimum SOC of LBESS S_{max,LB} Maximum SOC of LBESS P_{clim,LB} Charging power limit of LBESS P_{dlim,LB} Discharging power limit of LBESS P_{clim,SC} Charging power limit of SCESS P_{dlim,SC} Discharging power limit of SCESS P_{r,LB} Required power rating of LBESS E_{r,LB} Required energy capacity of LBESS P_{r,SC} Required power rating of SCESS E_{r,SC} Required energy capacity of SCESS C_{acq,CESS} Acquisition cost of CESS C_{acq,LB} Acquisition cost of LBESS C_{acq,SC} Acquisition cost of SCESS
Acknowledgements
This work is supported by National High Technology Research and Development Program of China (863 Program) (No.2011AA05A107).
BIO
Fengbing Li He received his B.S. degree in 2008 from the School of Electrical Engineering, Chongqing University, Chongqing, China, where he is currently pursuing the Ph.D. degree in electrical engineering after coming back from the mountains to support minority education. His research interests include energy storage system and microgrids.
Kaigui Xie He received the Ph.D. degree from the School of Electrical Engineering, Chongqing University, Chongqing, China, in 2001. He is currently a Professor with the School of Electrical Engineering, Chongqing University, Chongqing, China. His research interests include power system planning and reliability, analysis, electricity market, distributed generation and microgrids.
Bo Zhao He received the Ph.D. degree from the Department of Electrical Engineering, Zhejiang University, Hangzhou, China, in 2005. He is currently an Engineer with the research Center, Electric Power Research Institute of State Grid Zhejiang Electric Power Corporation, Zhejiang, China. His research interests include distributed generation and microgrids.
Dan Zhou He received the Ph.D. degree from the Department of Electrical Engineering, Zhejiang University, Hangzhou, China, in 2011. He is currently an Engineer with the Research Center, Electric Power Research Institute of State Grid Zhejiang Electric Power Corporation, Zhejiang, China. His research interests include power electronics and microgrids.
Xuesong Zhang He received the Ph.D. degree from the Department of Electrical Engineering, Zhejiang University, Hangzhou, China, in 2006. He is currently an Engineer with the Research Center, Electric Power Research Institute of State Grid Zhejiang Electric Power Corporation, Zhejiang, China. His research interests include relay protection and microgrids.
Jiangping Yang She received the M.S. degree from the School of Electrical Engineering, Chongqing University, Chongqing, China, in 2012. She is currently an engineer with the Ministry of Construction, State Grid Sichuan Electric Power Corporation Meishan Power Supply Company, Sichuan, China. Her research interests include smart distribution grid and microgrids.
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