Optimization and Analysis of a Hybrid Energy Storage System in a Small-Scale Standalone Microgrid for Remote Area Power Supply (RAPS)
Abstract
:1. Introduction
2. A Small-Scale Standalone Microgrid and ESSs
2.1. System Structure of a Standalone Microgrid for RAPS
2.2. The Proposed Index Named ESS Effective Rate
2.3. General Mathematical Model of ESSs
3. Control Strategy of HESS
3.1. The Basic Control Strategy Considering Power Allocation Only
3.2. The Coordinated Control Strategy Based on State Cooperation
4. Cost Calculation and Life Quantification of HESS
4.1. Initial Investment Cost of HESS
4.2. Life Quantification and Loss Equivalent Cost of Storage Arrays in LB-ESS
4.3. Overall Life Quantification and Total Loss Equivalent Cost of HESS
4.4. Impact Analysis Models of Different Cost and Life Considerations
5. Comparative Analysis Models of ESSs under Different Application Schemes
5.1. SESS Used Only
5.2. SC-ESS Increased Newly Based on the Existing SESS
5.3. HESS Used Directly
6. Case Studies
6.1. System Demand and ESS Parameters
Parameter type | LB-ESS | SC-ESS |
---|---|---|
Operating range of SOC | 0.25~0.95 | 0.2~0.9 |
SOC threshold of over-charge protection | 0.9 | 0.85 |
SOC threshold of over-discharge protection | 0.3 | 0.25 |
Initial value of SOC | 0.8 | 0.8 |
Charge and discharge efficiency | 90% | 95% |
Self-discharge rate (%·s−1) | 0 | 0.00017 |
Unit capacity cost ($·kWh−1) | 655.7 | 157,377.0 |
Pr_PCS (kW) | 50 | 100 | 200 | 250 | 300 | 400 | 500 |
---|---|---|---|---|---|---|---|
CPCS_LB (104·$) | 1.00 | 1.97 | 3.77 | 4.61 | 5.41 | 6.89 | 8.20 |
CPCS_SC (104·$) | 1.21 | 2.36 | 4.52 | 5.54 | 6.49 | 8.26 | 9.84 |
6.2. Comparison of HESS Operation under Different Control Strategies
6.3. Comparative Analysis Based on Different Cost and Life Considerations
Optimal results | Optimized parameters | Optimized objectives | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Pr_LB (kW) | Er_LB (kWh) | Pr_SC (kW) | Er_SC (kWh) | Tf0 (s) | ΔSco_SC | Cinitial_HESSarr ($) | Cinitial_HESS ($) | Closs_LBarr ($) | Closs_HESS ($) | Cpen_ESS ($) | Copt_HESS ($) | |
opt1 | 500 | 779.4 | 300 | 1.73 | 15 | 0.52 | 78.3 × 104 | —— | —— | —— | 0 | 78.3 × 104 |
opt2 | 500 | 779.4 | 300 | 1.73 | 15 | 0.52 | —— | 93.0 × 104 | —— | —— | 0 | 93.0 × 104 |
opt3 | 500 | 749.6 | 300 | 5.92 | 43 | 0.68 | —— | —— | 406.3 | —— | 0 | 406.3 |
opt4 | 500 | 756.8 | 300 | 3.17 | 24 | 0.63 | —— | —— | —— | 467.9 | 0 | 467.9 |
Optimalresults | Initial investment cost | Loss equivalent cost | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Carray_LB (104·$) | CPCS_LB (104·$) | Carray_SC (104·$) | CPCS_SC (104·$) | Cinitial_HESS (104·$) | Closs_LBarr ($) | Closs_LB ($) | Closs_SCarr ($) | Closs_SC ($) | Closs_HESS ($) | |
opt1 | 51.1 | 8.2 | 27.2 | 6.5 | 93.0 | 443.2 | 465.7 | 25.2 | 27.0 | 492.7 |
opt2 | 51.1 | 8.2 | 27.2 | 6.5 | 93.0 | 443.2 | 465.7 | 25.2 | 27.0 | 492.7 |
opt3 | 49.2 | 8.2 | 93.2 | 6.5 | 157.0 | 406.3 | 428.7 | 44.8 | 46.6 | 475.3 |
opt4 | 49.6 | 8.2 | 49.9 | 6.5 | 114.2 | 415.9 | 438.3 | 27.8 | 29.6 | 467.9 |
- The initial investment cost of HESS is optimized in both Objective 1 and Objective 2, and the difference is whether to consider the cost of matched PCS. The optimized results are the same for both objectives, because PCSs in practical engineering applications are usually standard equipment packages. The rated output power of PCS has only a few optional specification values. This characteristic of non-continuous changes makes the initial investment cost of matched PCS relatively fixed. However, if this part of the cost has not counted in the project budget, a poor decision will be made. For example, an additional expense of 0.147 million dollars will be produced in this case study. Therefore, to minimize the amount of capital in initial investment of HESS, optimization using Objective 2 is more reasonable.
- The data comparing optimization when using Objective 2, Objective 3 and Objective 4 is analyzed to obtain the differences between minimizing the initial investment cost and minimizing the loss equivalent cost. The initial investment cost of whole HESS when using Objective 2 is 0.930 million dollars, which is 0.640 million dollars lower than using Objective 3 with a decline of 40.75%, and 0.212 million dollars lower than using Objective 4 with a decline of 18.55%. At the same time, the total loss equivalent cost of HESS when using Objective 2 is 492.7 dollars, which is 17.4 dollars more than using Objective 3 with an increase of 3.67%, and 24.8 dollars more than using Objective 4 with an increase of 5.29%. Compared with the cost when optimizing the loss equivalent cost, although the initial investment cost of whole HESS when optimizing the initial investment cost is lower, the total loss equivalent cost of HESS per unit time is significantly higher. As a result, from the point of life cycle cost, the overall performance of HESS is better when optimizing the loss equivalent cost.
- The life loss and cost conversion of storage arrays in LB-ESS are considered in Objective 3, and the life loss and cost conversion of whole HESS are considered in Objective 4. The life of storage arrays in LB-ESS is much less than the life of other components in HESS, so it is the main factor in HESS performance. As shown in Table 4, the minimum total loss equivalent cost of HESS is 467.9 dollars, i.e., the result when using Objective 4. When using Objective 3, the total loss equivalent cost of HESS is 475.3 dollars, which is only 7.3 dollars more than the optimal value with a difference of 1.57%. That is to say that, an approximately optimal value is obtained when using Objective 3. Meanwhile, the loss equivalent cost of storage arrays in LB-ESS is lowest when using Objective 3, which is 9.6 dollars lower than when using Objective 4 with a decline of 2.32%. The initial investment cost of whole HESS when using Objective 3 is 0.428 million dollars more than when using Objective 4 with an increase of 37.48%. Hence, the economic cost when using Objective 3 is difficult to accept, although the loss equivalent cost of storage arrays in LB-ESS can be lowest and an approximate minimum of total loss equivalent cost of HESS can be obtained.
6.4. Comparative Analysis Based on Different ESS Application Schemes
Optimal results | Optimized parameters | Loss equivalent cost | Initial investment cost | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Pr_LB (kW) | Er_LB (kWh) | Pr_SC (kW) | Er_SC (kWh) | Tf0 (s) | ΔSco_SC | Closs_LB ($) | Closs_SC ($) | Closs_HESS ($) | Cinitial_LB (104·$) | Cinitial_SC (104·$) | Cinitial_HESS (104·$) | |
SESS used only | 500 | 781.5 | —— | —— | —— | —— | 577.7 | —— | 577.7 | 59.4 | —— | 59.4 |
SC-ESS increased newly | —— | —— | 300 | 3.58 | 28 | 0.54 | 456.7 | 30.6 | 487.4 | —— | 62.8 | 122.3 |
HESS used directly | 500 | 756.8 | 300 | 3.17 | 24 | 0.63 | 438.3 | 29.6 | 467.9 | 57.8 | 56.4 | 114.2 |
- As shown in the optimal results of the three schemes, the loss equivalent cost of LB-ESS is 577.7, 456.7 and 438.3 dollars, respectively. Compared with the loss equivalent cost of LB-ESS when SESS is used alone, this cost is decreased by 20.9% when SC-ESS is newly increased, and decreased by 24.1% when HESS is used directly. The data analysis above shows that, compared with SESS used alone, the utilization of SC-ESS can effectively reduce the life loss equivalent cost of LB-ESS.
- Compared with SESS used alone, an additional initial investment cost of 0.628 million dollars is needed after SC-ESS is newly increased. However, the total loss equivalent cost of HESS in the simulation time is reduced from 577.7 dollars to 487.4 dollars, which is decreased by 15.6% based on the cost of SESS. This indicates that the initial investment cost is increased because of a newly increased SC-ESS, but the total loss of ESSs demanded by a standalone microgrid is effectively reduced in unit time, so the technical and economic characteristics are much better than SESS.
- After overall optimization of HESS used directly, the total loss equivalent cost has been decreased to 467.9 dollars, which represents a significant decreased amplitude of 19.0% compared with SESS used alone. In addition, compared with optimization of SC-ESS increased newly, the overall optimization of HESS used results in a decrease of the total initial investment cost from 1.223 to 1.142 million dollars, i.e., a savings 80.7 thousand dollars in the initial investment cost. Therefore, the technical and economic characteristics have a further enhance after overall optimization of HESS used directly.
7. Conclusions
Acknowledgments
Author Contributions
Nomenclature
PDG | Output power of distributed generations |
PLD | Power demand of loads |
Pnet_LD | Power demand of net loads |
Pout_ESS | Output power of ESS |
RESS | Effective rate of ESS |
ΔTcom | Time step of computation |
NT | Number of discrete data points in time T with in interval △Tcom |
Pref_ESS(n) | Output power reference of ESS at the nth time interval |
Pout_ESS(n) | Actual output power of ESS at the nth time interval |
Rset_ESS | Setting constraint of ESS effective rate |
Cpen_ESS | Penalty cost without satisfying Rset_ESS |
F | Fixed value much bigger than other cost |
Pclmt_ESS(n) | Charging power limit of ESS within the nth time interval |
Pdlmt_ESS(n) | Discharging power limit of ESS within the nth time interval |
Pcmax_ESS | Maximum charging power of ESS |
Pdmax_ESS | Maximum discharging power of ESS |
Er_ESS | Rated storage capacity of ESS |
Smax_ESS | Maximum SOC of ESS |
Smin_ESS | Minimum SOC of ESS |
SESS(n) | SOC of ESS at the nth time interval moment |
SESS(n-1) | SOC of ESS at the n-1th time interval moment |
σESS | Self-discharge rate of ESS |
ηc_ESS | Charging efficiency of ESS |
ηd_ESS | Discharging efficiency of ESS |
PHESS | Power command of HESS |
Pout_LB | Output power of LB-ESS |
Pout_SC | Output power of SC-ESS |
Tf | Filter time constant |
Tf0 | Initial value of Tf in power allocation |
ΔTf | Adjustment step of Tf |
Tfmin | Minimum of Tf Adjustment |
Tfmax | Maximum of Tf Adjustment |
SSC | SOC of SC-ESS |
Smin_SC | Minimum SOC of SC-ESS |
Smax_SC | Maximum SOC of SC-ESS |
SLBd_SC | SOC control objective of SC-ESS when LB-ESS discharges |
SLBc_SC | SOC control objective of SC-ESS when LB-ESS charges |
ΔSco_SC | SOC coordinated response margin of SC-ESS |
Er_LB | Rated storage capacity of LB-ESS |
Cunit_LB | Unit storage capacity cost of LB-ESS |
Er_SC | Rated storage capacity of SC-ESS |
Cunit_SC | Unit storage capacity cost of SC-ESS |
Cinitial_HESSarr | Total initial investment cost of storage arrays in HESS |
CPCS_LB | PCS cost of LB-ESS |
Cinitial_LB | Initial investment cost of LB-ESS |
CPCS_SC | PCS cost of SC-ESS |
Cinitial_SC | Initial investment cost of SC-ESS |
Cinitial_HESS | Initial investment cost of whole HESS |
Larray_LB | Lifetime loss coefficient of LB-ESS storage arrays |
M | Number of time interval in the life quantification of LB-ESS storage arrays |
ΔDLB(m) | Degenerate increment of LB-ESS storage capacity within the mth time interval |
Dlmt_LB | Degenerate limit of LB-ESS storage capacity |
D1, D2 | Intermediate variable of ΔDLB |
τ | Duration of the mth time interval |
Savg_LB | SOC average value of LB-ESS |
Sdev_LB | SOC normalized deviation of LB-ESS |
NLB | Equivalent throughput cycle of LB-ESS |
Tref | Reference temperature in degrees centigrade |
TLB | Operation temperature of LB-ESS storage arrays in degrees centigrade |
Ta_ref | Absolute temperature of Tref |
Ta_LB | Absolute temperature of TLB |
τlife_LB | Calendar lifetime estimate of LB-ESS storage arrays end of 80% initial capacity |
KT, Kco, Kex, KSOC | Empirical constant of specific LB-ESS storage arrays |
Closs_LBarr | Loss equivalent cost of LB-ESS storage arrays |
Larray_SC | Lifetime loss coefficient of SC-ESS storage arrays |
Ncycle_SC | Charge and discharge cycles of SC-ESS storage arrays |
Ntotal_SC | Total charge and discharge cycles of SC-ESS storage arrays |
Closs_SCarr | Loss equivalent cost of SC-ESS storage arrays |
Lloss_PCS | Lifetime loss coefficient of PCS |
T | Running time of PCS |
Tlife_PCS | Service lifetime of PCS |
Closs_LB | Loss equivalent cost of LB-ESS |
Closs_SC | Loss equivalent cost of SC-ESS |
Closs_HESS | Loss equivalent cost of HESS |
Copt1_HESS | Considered cost of HESS under optimization objective 1 |
Copt2_HESS | Considered cost of HESS under optimization objective 2 |
Copt3_HESS | Considered cost of HESS under optimization objective 3 |
Copt4_HESS | Considered cost of HESS under optimization objective 4 |
Pr_LB | Rated output power of LB-ESS |
Pr_SC | Rated output power of SC-ESS |
Pcmax_LB | Maximum charging power of LB-ESS |
Pdmax_LB | Maximum discharging power of LB-ESS |
SLB | SOC of LB-ESS |
Smin_LB | Minimum SOC of LB-ESS |
Smax_LB | Maximum SOC of LB-ESS |
Pcmax_SC | Maximum charging power of SC-ESS |
Pdmax_SC | Maximum discharging power of SC-ESS |
Copt_SESS | Loss equivalent cost of SESS used only |
Copt_SAESS | Loss equivalent cost of SC-ESS increased newly |
Copt_HESS | Loss equivalent cost of HESS used directly |
Ctotal_SESS | Total initial investment cost of SESS used only |
Ctotal_SAESS | Total initial investment cost of SC-ESS increased newly |
Ctotal_HESS | Total initial investment cost of HESS used directly |
Pr_PCS | Rated power of PCS |
Conflicts of Interest
References
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Share and Cite
Li, F.; Xie, K.; Yang, J. Optimization and Analysis of a Hybrid Energy Storage System in a Small-Scale Standalone Microgrid for Remote Area Power Supply (RAPS). Energies 2015, 8, 4802-4826. https://doi.org/10.3390/en8064802
Li F, Xie K, Yang J. Optimization and Analysis of a Hybrid Energy Storage System in a Small-Scale Standalone Microgrid for Remote Area Power Supply (RAPS). Energies. 2015; 8(6):4802-4826. https://doi.org/10.3390/en8064802
Chicago/Turabian StyleLi, Fengbing, Kaigui Xie, and Jiangping Yang. 2015. "Optimization and Analysis of a Hybrid Energy Storage System in a Small-Scale Standalone Microgrid for Remote Area Power Supply (RAPS)" Energies 8, no. 6: 4802-4826. https://doi.org/10.3390/en8064802