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Table 2 Summary of Analytical Models

From: Tractable lithium-ion storage models for optimizing energy systems

Model Approximations
  Voltage Energy Content Limits Efficiency
C/C/C \(\begin {aligned} V = \left \{ \begin {array}{lr} \boldsymbol {V}_{\boldsymbol {nom,d}} & : P < 0\\ \boldsymbol {V}_{\boldsymbol {nom,c}} & : P \geq 0 \end {array} \right. \end {aligned}\) \(\begin {aligned} &\bar {\boldsymbol {a}}_{\boldsymbol {1}}n \\ &\bar {\boldsymbol {a}}_{\boldsymbol {2}}n \end {aligned}\) \(\begin {aligned} &\bar {\boldsymbol {\eta }}_{\boldsymbol {d}}\\ &\bar {\boldsymbol {\eta }}_{\boldsymbol {c}} \end {aligned}\)
C/L/C \(\begin {aligned} V = \left \{ \begin {array}{lr} \boldsymbol {V}_{\boldsymbol {nom,d}} & : P < 0\\ \boldsymbol {V}_{\boldsymbol {nom,c}} & : P \geq 0 \end {array} \right. \end {aligned}\) a1(P)=u1(P/Vnom,d)+v1na2(P)=u2(P/Vnom,c)+v2n \(\begin {aligned} & \bar {\boldsymbol {\eta }}_{\boldsymbol {d}} \\ &\bar {\boldsymbol {\eta }}_{\boldsymbol {c}} \end {aligned}\)
C/L/L \(\begin {aligned} V = \left \{ \begin {array}{lr} \boldsymbol {V}_{\boldsymbol {nom,d}}\unboldmath & : P < 0\\ \boldsymbol {V}_{\boldsymbol {nom,c}} & : P \geq 0 \end {array} \right. \end {aligned}\) a1(P)=u1(P/Vnom,d)+v1na2(P)=u2(P/Vnom,c)+v2n \(\begin {aligned} &\eta _{d}(P) = 1- P R_{id}/n\boldsymbol {V}_{\boldsymbol {nom,d}}^{2}\\ &\eta _{c}(P) = 1 - P R_{ic}/n\boldsymbol {V}_{\boldsymbol {nom,c}}^{2} \end {aligned}\)
L/L/Q \(\begin {aligned} &V = \boldsymbol {x}_{\boldsymbol {00}} + \frac {\boldsymbol {x}_{\boldsymbol {10}}}{n}I + \frac {\boldsymbol {x}_{\boldsymbol {01}}}{n}b \end {aligned}\) a1(I)=u1I+v1na2(I)=u2I+v2n ηd(I,V)=1−IRid/nVηc(I,V)=1−IRic/nV
  1. Note: x00, x01, x10, u1, u2, v1, and v2 are fitted parameters. Bolded parameters are affected by the OR