Super capacitorsThe irregular fluctuations and hard transients would fast degrade their performance Many solutions based on the combination of supercapacitors and batteries have been presented in literature so that the hard transients are supplied or absorbed by the supercapacitors

Supercapacitors store energy by physically separating positive and negative charges instead of chemically storing charge as batteries do [5] Consequently supercapacitors benefit from a longer life than batteries and have fast charge and discharge times They are able to provide a high power over a very short period of time Unlike batteries after hundreds of thousands of chargedischarge cycles their characteristics do not degrade so much Their operation is less affected by temperature and their efficiciency is higher However they can not provide energy over a long period of time as batteries do To take advantage of both high power and high energy densities their combination has been subject of research in power supply systemsThe main goal of using supercapacitors as a complement of batteries is to suppress hard transient states and smooth strong and short-time power bursts of the renewable sources or the load [14] The battery would basically supply or absorb the average power to the load In all these systems the demanding power is subtracted from the power generated by the renewable energy generators and is filtered so that the high frequency part of the missing energy is supplied by the supercapacitors

The non-isolated bidirectional buck-boost converter which interfaces the batteries and the dc bus

(represented in Fig 8) allows to protect the battery respecting its safe output voltages and dischargecharge current besides keeping the dc bus voltage constant at 100 V

In the second case the battery is setting the dc bus voltage without any power interface and supercapacitors are connected to the dc bus using a non-isolated bidirectional buck-boost converter as interface This converter is used to control the battery current so that the high frequency harmonic components are supplied by the supercapacitorThis system has the advantage of requiring one converter less than the others that include supercapacitors The other systems have two bidirectional dc-dc convertersIn the third and in the fourth systems the dc bus is controlled by the converter interfacing the battery Thefourth one is an improvement of the third presented in [711] An adaptation of the high pass filter was applied [10] because the filtered signal presents unwanted features such as zero crossing when the signal being filtered increases or decreases (even without zero crossing) and for exceeding this original signalIn the latter the root mean square (rms) value of the battery current (Irms) and the battery state of charge stress factors (SOCstressREL) of all the considered systems are compared to that of system 1 which is the system without

supercapacitor The stress factor [10] is a measure of how deep the battery is charged and discharged as a function of frequency It is defined by the following equation

Power Smoothing of Large Solar PV Plant Using Hybrid Energy Storage

A hybrid energy storage system (HESS) composed of a vanadium redox battery and a supercapacitor bank is used to smooth the fluctuating output power of the PV plant The power management ofThe HESS is purposely designed to reduce the required power rating of the SCB to only one-fifth of the VRB rating and to avoid the operation of the VRB at low power levels thus increasing its overall efficiencyThe traditional concept of the power sharing is based on the response times of each technology the high-frequency power oscillations are assigned to the short-term storage device and the low-frequency oscillations are handled by the long-term storage deviceThe proposed power management (PM) of the PV power plant is a rule-based algorithm which consists of two stages an incremental power sharing scheme between the VRB and SC bank (SCB) and the rules managing the operation modes of the PV power plant The main advantages of the proposed PM with respect to conventional techniques are as follows reducing the required power rating of the SCB to only one-fifth of the VRB rating and avoiding the operation of theVRB at low power levels thus increasing its overall efficiency

In order to maximise the value of the solar energy a hybrid electricity storage consisting of batteries and supercapacitors is used with the PV system This paper proposes a control strategy focusing on the DC power at the DC link rather than at the grid-connected inverter

the complementary characteristics of batteries and supercapacitors make them an attractive choice for a hybrid electricity storage system in which the battery is chosen as the long-term storage device to meet the demand and the supercapacitor provides the short-term storage device to absorb the fast high-frequency fluctuations of the PV Also the supercapacitor can operate at any state of charge since it stores energy by physically separating positive and negative charges which means that it can be operated fully charged or fully dischargedfor the batteries the state of charge SOC must be controlled to maintain an appropriate level to ensure a long cycle-life The supercapacitor can therefore be used to protect the battery from short duration transients and help prolong the life of the battery

Modelling super capacitors

The equivalent circuit of a basic supercapacitor in which the variable capacitance C plays the most important role and the resistance R2 describes the self-discharge of the super capacitor The capacitance Cp together with the resistance Rp represents the fast dynamic changes of the super capacitor Cp is lower than C The resistance R1 which is connected in series represents the energy loss during the charging or discharging period while the resistance R3 is added in case of over-voltage The variable capacitances C and Cp should be chosen and regulated by the size the super capacitor [11]

where iSC is current through supercapacitor CSC is overall capacitance of supercapacitor and uSC

is terminal voltage of supercapacitor

Due to the high power density and the low energy density the discharging time of the supercapacitor is very short and its response is very fast The supercapacitor plays the role of absorbing the high-frequency power fluctuations from the PV and maintaining the voltage of the

DC link in a proper range The random nature of these fluctuations is a key factor of the PV system and the instantaneous change in the output power is unpredictable The supercapacitoralways charges or discharges in a shorter time than the battery therefore the battery is protected from the high frequency fluctuationsThe voltage of the DC link is monitored and compared with the reference value V_DC resulting in the error signal which is the input of the PI controller The reference current of thesupercapacitor I_SC is usedwith themonitored supercapacitor current Isc to create the control signals for the BuckBoost DCDC converter through the current-tracking PWM

RL Spyker RM Nelms ldquoClassical Equivalent Circuit Parameters for a Double Layer Capacitorrdquo IEEE Tranactions in aerospace and electronic systems vol 36 no 3 pp 829-836 July 2000

Supercapacitor ModelFig 9 shows the classical equivalent circuit model for the supercapacitor [15] The model consists of three components the capacitance the equivalent series resistance (ESR) and the equivalent parallel resistance (EPR) The ESR is a loss term that models the internal heating in the capacitor and is most important during charging and discharging The EPR models the current leakage effect and will impact the long term energy storage performance of the supercapacitor and C is the capacitance Equations (7)-(9) describe the ESR EPR and terminal voltage of the supercapacitor

The function of the voltage-dependent capacitor C can be obtained with curve fitting from thechargingdischarging measurements The model is verified with Nesscap 27V600F supercapacitor Fig 10 shows the 10A charging rest and 5A discharging of the model with an ESR of 1m1049101 and an EPR of 2581049101

The capacitance C is responsible for the most important phenomenon in the model Itdetermines how charge is handled in the circuit The amount of energy stored and the rate of energy level variations are both determined mainly by the capacitance value The resistance R2 that is connected in parallel with the capacitor is meant to represent the self discharge effect The series resistance R1 represents the losses during charge and discharge These losses occur because the conducting element in the supercapacitor has a resistance so the connection is not ideal The over voltage protection provided by R3 and the switch controlling its connection to the circuit is necessary to prevent damage to the capacitor elements by balancing the voltage level The voltage balancing is needed because otherwise the voltage in one separate cell can increase higher than the others resulting in gassing or explosion This voltage difference can occur if one cell has a lower capacitance than the others since that results in more energy being stored The resistance Rp and the capacitance Cp are included in the circuit to model some of the fast dynamics in the behaviour of the supercapacitor

Table 3 Component values for basic model in Simulink The capacitance value is included because it isused for initial tests before the variable capacitance is implementedComponent R1 [m_] R2 [k_] R3 [m_] Rp [m_] C [F] Cp [F]Value 6 18 52 3 35 C13

Main capacitance calculation

The non-isolated bidirectional buck-boost converter which interfaces the batteries and the dc bus

(represented in Fig 8) allows to protect the battery respecting its safe output voltages and dischargecharge current besides keeping the dc bus voltage constant at 100 V

In the second case the battery is setting the dc bus voltage without any power interface and supercapacitors are connected to the dc bus using a non-isolated bidirectional buck-boost converter as interface This converter is used to control the battery current so that the high frequency harmonic components are supplied by the supercapacitorThis system has the advantage of requiring one converter less than the others that include supercapacitors The other systems have two bidirectional dc-dc convertersIn the third and in the fourth systems the dc bus is controlled by the converter interfacing the battery Thefourth one is an improvement of the third presented in [711] An adaptation of the high pass filter was applied [10] because the filtered signal presents unwanted features such as zero crossing when the signal being filtered increases or decreases (even without zero crossing) and for exceeding this original signalIn the latter the root mean square (rms) value of the battery current (Irms) and the battery state of charge stress factors (SOCstressREL) of all the considered systems are compared to that of system 1 which is the system without

supercapacitor The stress factor [10] is a measure of how deep the battery is charged and discharged as a function of frequency It is defined by the following equation

Power Smoothing of Large Solar PV Plant Using Hybrid Energy Storage

A hybrid energy storage system (HESS) composed of a vanadium redox battery and a supercapacitor bank is used to smooth the fluctuating output power of the PV plant The power management ofThe HESS is purposely designed to reduce the required power rating of the SCB to only one-fifth of the VRB rating and to avoid the operation of the VRB at low power levels thus increasing its overall efficiencyThe traditional concept of the power sharing is based on the response times of each technology the high-frequency power oscillations are assigned to the short-term storage device and the low-frequency oscillations are handled by the long-term storage deviceThe proposed power management (PM) of the PV power plant is a rule-based algorithm which consists of two stages an incremental power sharing scheme between the VRB and SC bank (SCB) and the rules managing the operation modes of the PV power plant The main advantages of the proposed PM with respect to conventional techniques are as follows reducing the required power rating of the SCB to only one-fifth of the VRB rating and avoiding the operation of theVRB at low power levels thus increasing its overall efficiency

In order to maximise the value of the solar energy a hybrid electricity storage consisting of batteries and supercapacitors is used with the PV system This paper proposes a control strategy focusing on the DC power at the DC link rather than at the grid-connected inverter

the complementary characteristics of batteries and supercapacitors make them an attractive choice for a hybrid electricity storage system in which the battery is chosen as the long-term storage device to meet the demand and the supercapacitor provides the short-term storage device to absorb the fast high-frequency fluctuations of the PV Also the supercapacitor can operate at any state of charge since it stores energy by physically separating positive and negative charges which means that it can be operated fully charged or fully dischargedfor the batteries the state of charge SOC must be controlled to maintain an appropriate level to ensure a long cycle-life The supercapacitor can therefore be used to protect the battery from short duration transients and help prolong the life of the battery

Modelling super capacitors

The equivalent circuit of a basic supercapacitor in which the variable capacitance C plays the most important role and the resistance R2 describes the self-discharge of the super capacitor The capacitance Cp together with the resistance Rp represents the fast dynamic changes of the super capacitor Cp is lower than C The resistance R1 which is connected in series represents the energy loss during the charging or discharging period while the resistance R3 is added in case of over-voltage The variable capacitances C and Cp should be chosen and regulated by the size the super capacitor [11]

where iSC is current through supercapacitor CSC is overall capacitance of supercapacitor and uSC

is terminal voltage of supercapacitor

Due to the high power density and the low energy density the discharging time of the supercapacitor is very short and its response is very fast The supercapacitor plays the role of absorbing the high-frequency power fluctuations from the PV and maintaining the voltage of the

DC link in a proper range The random nature of these fluctuations is a key factor of the PV system and the instantaneous change in the output power is unpredictable The supercapacitoralways charges or discharges in a shorter time than the battery therefore the battery is protected from the high frequency fluctuationsThe voltage of the DC link is monitored and compared with the reference value V_DC resulting in the error signal which is the input of the PI controller The reference current of thesupercapacitor I_SC is usedwith themonitored supercapacitor current Isc to create the control signals for the BuckBoost DCDC converter through the current-tracking PWM

RL Spyker RM Nelms ldquoClassical Equivalent Circuit Parameters for a Double Layer Capacitorrdquo IEEE Tranactions in aerospace and electronic systems vol 36 no 3 pp 829-836 July 2000

Supercapacitor ModelFig 9 shows the classical equivalent circuit model for the supercapacitor [15] The model consists of three components the capacitance the equivalent series resistance (ESR) and the equivalent parallel resistance (EPR) The ESR is a loss term that models the internal heating in the capacitor and is most important during charging and discharging The EPR models the current leakage effect and will impact the long term energy storage performance of the supercapacitor and C is the capacitance Equations (7)-(9) describe the ESR EPR and terminal voltage of the supercapacitor

The function of the voltage-dependent capacitor C can be obtained with curve fitting from thechargingdischarging measurements The model is verified with Nesscap 27V600F supercapacitor Fig 10 shows the 10A charging rest and 5A discharging of the model with an ESR of 1m1049101 and an EPR of 2581049101

The capacitance C is responsible for the most important phenomenon in the model Itdetermines how charge is handled in the circuit The amount of energy stored and the rate of energy level variations are both determined mainly by the capacitance value The resistance R2 that is connected in parallel with the capacitor is meant to represent the self discharge effect The series resistance R1 represents the losses during charge and discharge These losses occur because the conducting element in the supercapacitor has a resistance so the connection is not ideal The over voltage protection provided by R3 and the switch controlling its connection to the circuit is necessary to prevent damage to the capacitor elements by balancing the voltage level The voltage balancing is needed because otherwise the voltage in one separate cell can increase higher than the others resulting in gassing or explosion This voltage difference can occur if one cell has a lower capacitance than the others since that results in more energy being stored The resistance Rp and the capacitance Cp are included in the circuit to model some of the fast dynamics in the behaviour of the supercapacitor

Table 3 Component values for basic model in Simulink The capacitance value is included because it isused for initial tests before the variable capacitance is implementedComponent R1 [m_] R2 [k_] R3 [m_] Rp [m_] C [F] Cp [F]Value 6 18 52 3 35 C13

Main capacitance calculation

(represented in Fig 8) allows to protect the battery respecting its safe output voltages and dischargecharge current besides keeping the dc bus voltage constant at 100 V

In the second case the battery is setting the dc bus voltage without any power interface and supercapacitors are connected to the dc bus using a non-isolated bidirectional buck-boost converter as interface This converter is used to control the battery current so that the high frequency harmonic components are supplied by the supercapacitorThis system has the advantage of requiring one converter less than the others that include supercapacitors The other systems have two bidirectional dc-dc convertersIn the third and in the fourth systems the dc bus is controlled by the converter interfacing the battery Thefourth one is an improvement of the third presented in [711] An adaptation of the high pass filter was applied [10] because the filtered signal presents unwanted features such as zero crossing when the signal being filtered increases or decreases (even without zero crossing) and for exceeding this original signalIn the latter the root mean square (rms) value of the battery current (Irms) and the battery state of charge stress factors (SOCstressREL) of all the considered systems are compared to that of system 1 which is the system without

supercapacitor The stress factor [10] is a measure of how deep the battery is charged and discharged as a function of frequency It is defined by the following equation

Power Smoothing of Large Solar PV Plant Using Hybrid Energy Storage

A hybrid energy storage system (HESS) composed of a vanadium redox battery and a supercapacitor bank is used to smooth the fluctuating output power of the PV plant The power management ofThe HESS is purposely designed to reduce the required power rating of the SCB to only one-fifth of the VRB rating and to avoid the operation of the VRB at low power levels thus increasing its overall efficiencyThe traditional concept of the power sharing is based on the response times of each technology the high-frequency power oscillations are assigned to the short-term storage device and the low-frequency oscillations are handled by the long-term storage deviceThe proposed power management (PM) of the PV power plant is a rule-based algorithm which consists of two stages an incremental power sharing scheme between the VRB and SC bank (SCB) and the rules managing the operation modes of the PV power plant The main advantages of the proposed PM with respect to conventional techniques are as follows reducing the required power rating of the SCB to only one-fifth of the VRB rating and avoiding the operation of theVRB at low power levels thus increasing its overall efficiency

In order to maximise the value of the solar energy a hybrid electricity storage consisting of batteries and supercapacitors is used with the PV system This paper proposes a control strategy focusing on the DC power at the DC link rather than at the grid-connected inverter

the complementary characteristics of batteries and supercapacitors make them an attractive choice for a hybrid electricity storage system in which the battery is chosen as the long-term storage device to meet the demand and the supercapacitor provides the short-term storage device to absorb the fast high-frequency fluctuations of the PV Also the supercapacitor can operate at any state of charge since it stores energy by physically separating positive and negative charges which means that it can be operated fully charged or fully dischargedfor the batteries the state of charge SOC must be controlled to maintain an appropriate level to ensure a long cycle-life The supercapacitor can therefore be used to protect the battery from short duration transients and help prolong the life of the battery

Modelling super capacitors

The equivalent circuit of a basic supercapacitor in which the variable capacitance C plays the most important role and the resistance R2 describes the self-discharge of the super capacitor The capacitance Cp together with the resistance Rp represents the fast dynamic changes of the super capacitor Cp is lower than C The resistance R1 which is connected in series represents the energy loss during the charging or discharging period while the resistance R3 is added in case of over-voltage The variable capacitances C and Cp should be chosen and regulated by the size the super capacitor [11]

where iSC is current through supercapacitor CSC is overall capacitance of supercapacitor and uSC

is terminal voltage of supercapacitor

Due to the high power density and the low energy density the discharging time of the supercapacitor is very short and its response is very fast The supercapacitor plays the role of absorbing the high-frequency power fluctuations from the PV and maintaining the voltage of the

DC link in a proper range The random nature of these fluctuations is a key factor of the PV system and the instantaneous change in the output power is unpredictable The supercapacitoralways charges or discharges in a shorter time than the battery therefore the battery is protected from the high frequency fluctuationsThe voltage of the DC link is monitored and compared with the reference value V_DC resulting in the error signal which is the input of the PI controller The reference current of thesupercapacitor I_SC is usedwith themonitored supercapacitor current Isc to create the control signals for the BuckBoost DCDC converter through the current-tracking PWM

RL Spyker RM Nelms ldquoClassical Equivalent Circuit Parameters for a Double Layer Capacitorrdquo IEEE Tranactions in aerospace and electronic systems vol 36 no 3 pp 829-836 July 2000

Supercapacitor ModelFig 9 shows the classical equivalent circuit model for the supercapacitor [15] The model consists of three components the capacitance the equivalent series resistance (ESR) and the equivalent parallel resistance (EPR) The ESR is a loss term that models the internal heating in the capacitor and is most important during charging and discharging The EPR models the current leakage effect and will impact the long term energy storage performance of the supercapacitor and C is the capacitance Equations (7)-(9) describe the ESR EPR and terminal voltage of the supercapacitor

The function of the voltage-dependent capacitor C can be obtained with curve fitting from thechargingdischarging measurements The model is verified with Nesscap 27V600F supercapacitor Fig 10 shows the 10A charging rest and 5A discharging of the model with an ESR of 1m1049101 and an EPR of 2581049101

The capacitance C is responsible for the most important phenomenon in the model Itdetermines how charge is handled in the circuit The amount of energy stored and the rate of energy level variations are both determined mainly by the capacitance value The resistance R2 that is connected in parallel with the capacitor is meant to represent the self discharge effect The series resistance R1 represents the losses during charge and discharge These losses occur because the conducting element in the supercapacitor has a resistance so the connection is not ideal The over voltage protection provided by R3 and the switch controlling its connection to the circuit is necessary to prevent damage to the capacitor elements by balancing the voltage level The voltage balancing is needed because otherwise the voltage in one separate cell can increase higher than the others resulting in gassing or explosion This voltage difference can occur if one cell has a lower capacitance than the others since that results in more energy being stored The resistance Rp and the capacitance Cp are included in the circuit to model some of the fast dynamics in the behaviour of the supercapacitor

Table 3 Component values for basic model in Simulink The capacitance value is included because it isused for initial tests before the variable capacitance is implementedComponent R1 [m_] R2 [k_] R3 [m_] Rp [m_] C [F] Cp [F]Value 6 18 52 3 35 C13

Main capacitance calculation

supercapacitor The stress factor [10] is a measure of how deep the battery is charged and discharged as a function of frequency It is defined by the following equation

Power Smoothing of Large Solar PV Plant Using Hybrid Energy Storage

A hybrid energy storage system (HESS) composed of a vanadium redox battery and a supercapacitor bank is used to smooth the fluctuating output power of the PV plant The power management ofThe HESS is purposely designed to reduce the required power rating of the SCB to only one-fifth of the VRB rating and to avoid the operation of the VRB at low power levels thus increasing its overall efficiencyThe traditional concept of the power sharing is based on the response times of each technology the high-frequency power oscillations are assigned to the short-term storage device and the low-frequency oscillations are handled by the long-term storage deviceThe proposed power management (PM) of the PV power plant is a rule-based algorithm which consists of two stages an incremental power sharing scheme between the VRB and SC bank (SCB) and the rules managing the operation modes of the PV power plant The main advantages of the proposed PM with respect to conventional techniques are as follows reducing the required power rating of the SCB to only one-fifth of the VRB rating and avoiding the operation of theVRB at low power levels thus increasing its overall efficiency

In order to maximise the value of the solar energy a hybrid electricity storage consisting of batteries and supercapacitors is used with the PV system This paper proposes a control strategy focusing on the DC power at the DC link rather than at the grid-connected inverter

the complementary characteristics of batteries and supercapacitors make them an attractive choice for a hybrid electricity storage system in which the battery is chosen as the long-term storage device to meet the demand and the supercapacitor provides the short-term storage device to absorb the fast high-frequency fluctuations of the PV Also the supercapacitor can operate at any state of charge since it stores energy by physically separating positive and negative charges which means that it can be operated fully charged or fully dischargedfor the batteries the state of charge SOC must be controlled to maintain an appropriate level to ensure a long cycle-life The supercapacitor can therefore be used to protect the battery from short duration transients and help prolong the life of the battery

Modelling super capacitors

The equivalent circuit of a basic supercapacitor in which the variable capacitance C plays the most important role and the resistance R2 describes the self-discharge of the super capacitor The capacitance Cp together with the resistance Rp represents the fast dynamic changes of the super capacitor Cp is lower than C The resistance R1 which is connected in series represents the energy loss during the charging or discharging period while the resistance R3 is added in case of over-voltage The variable capacitances C and Cp should be chosen and regulated by the size the super capacitor [11]

where iSC is current through supercapacitor CSC is overall capacitance of supercapacitor and uSC

is terminal voltage of supercapacitor

Due to the high power density and the low energy density the discharging time of the supercapacitor is very short and its response is very fast The supercapacitor plays the role of absorbing the high-frequency power fluctuations from the PV and maintaining the voltage of the

DC link in a proper range The random nature of these fluctuations is a key factor of the PV system and the instantaneous change in the output power is unpredictable The supercapacitoralways charges or discharges in a shorter time than the battery therefore the battery is protected from the high frequency fluctuationsThe voltage of the DC link is monitored and compared with the reference value V_DC resulting in the error signal which is the input of the PI controller The reference current of thesupercapacitor I_SC is usedwith themonitored supercapacitor current Isc to create the control signals for the BuckBoost DCDC converter through the current-tracking PWM

RL Spyker RM Nelms ldquoClassical Equivalent Circuit Parameters for a Double Layer Capacitorrdquo IEEE Tranactions in aerospace and electronic systems vol 36 no 3 pp 829-836 July 2000

Supercapacitor ModelFig 9 shows the classical equivalent circuit model for the supercapacitor [15] The model consists of three components the capacitance the equivalent series resistance (ESR) and the equivalent parallel resistance (EPR) The ESR is a loss term that models the internal heating in the capacitor and is most important during charging and discharging The EPR models the current leakage effect and will impact the long term energy storage performance of the supercapacitor and C is the capacitance Equations (7)-(9) describe the ESR EPR and terminal voltage of the supercapacitor

The function of the voltage-dependent capacitor C can be obtained with curve fitting from thechargingdischarging measurements The model is verified with Nesscap 27V600F supercapacitor Fig 10 shows the 10A charging rest and 5A discharging of the model with an ESR of 1m1049101 and an EPR of 2581049101

The capacitance C is responsible for the most important phenomenon in the model Itdetermines how charge is handled in the circuit The amount of energy stored and the rate of energy level variations are both determined mainly by the capacitance value The resistance R2 that is connected in parallel with the capacitor is meant to represent the self discharge effect The series resistance R1 represents the losses during charge and discharge These losses occur because the conducting element in the supercapacitor has a resistance so the connection is not ideal The over voltage protection provided by R3 and the switch controlling its connection to the circuit is necessary to prevent damage to the capacitor elements by balancing the voltage level The voltage balancing is needed because otherwise the voltage in one separate cell can increase higher than the others resulting in gassing or explosion This voltage difference can occur if one cell has a lower capacitance than the others since that results in more energy being stored The resistance Rp and the capacitance Cp are included in the circuit to model some of the fast dynamics in the behaviour of the supercapacitor

Table 3 Component values for basic model in Simulink The capacitance value is included because it isused for initial tests before the variable capacitance is implementedComponent R1 [m_] R2 [k_] R3 [m_] Rp [m_] C [F] Cp [F]Value 6 18 52 3 35 C13

Main capacitance calculation

the complementary characteristics of batteries and supercapacitors make them an attractive choice for a hybrid electricity storage system in which the battery is chosen as the long-term storage device to meet the demand and the supercapacitor provides the short-term storage device to absorb the fast high-frequency fluctuations of the PV Also the supercapacitor can operate at any state of charge since it stores energy by physically separating positive and negative charges which means that it can be operated fully charged or fully dischargedfor the batteries the state of charge SOC must be controlled to maintain an appropriate level to ensure a long cycle-life The supercapacitor can therefore be used to protect the battery from short duration transients and help prolong the life of the battery

Modelling super capacitors

The equivalent circuit of a basic supercapacitor in which the variable capacitance C plays the most important role and the resistance R2 describes the self-discharge of the super capacitor The capacitance Cp together with the resistance Rp represents the fast dynamic changes of the super capacitor Cp is lower than C The resistance R1 which is connected in series represents the energy loss during the charging or discharging period while the resistance R3 is added in case of over-voltage The variable capacitances C and Cp should be chosen and regulated by the size the super capacitor [11]

where iSC is current through supercapacitor CSC is overall capacitance of supercapacitor and uSC

is terminal voltage of supercapacitor

Due to the high power density and the low energy density the discharging time of the supercapacitor is very short and its response is very fast The supercapacitor plays the role of absorbing the high-frequency power fluctuations from the PV and maintaining the voltage of the

DC link in a proper range The random nature of these fluctuations is a key factor of the PV system and the instantaneous change in the output power is unpredictable The supercapacitoralways charges or discharges in a shorter time than the battery therefore the battery is protected from the high frequency fluctuationsThe voltage of the DC link is monitored and compared with the reference value V_DC resulting in the error signal which is the input of the PI controller The reference current of thesupercapacitor I_SC is usedwith themonitored supercapacitor current Isc to create the control signals for the BuckBoost DCDC converter through the current-tracking PWM

RL Spyker RM Nelms ldquoClassical Equivalent Circuit Parameters for a Double Layer Capacitorrdquo IEEE Tranactions in aerospace and electronic systems vol 36 no 3 pp 829-836 July 2000

Supercapacitor ModelFig 9 shows the classical equivalent circuit model for the supercapacitor [15] The model consists of three components the capacitance the equivalent series resistance (ESR) and the equivalent parallel resistance (EPR) The ESR is a loss term that models the internal heating in the capacitor and is most important during charging and discharging The EPR models the current leakage effect and will impact the long term energy storage performance of the supercapacitor and C is the capacitance Equations (7)-(9) describe the ESR EPR and terminal voltage of the supercapacitor

The function of the voltage-dependent capacitor C can be obtained with curve fitting from thechargingdischarging measurements The model is verified with Nesscap 27V600F supercapacitor Fig 10 shows the 10A charging rest and 5A discharging of the model with an ESR of 1m1049101 and an EPR of 2581049101

The capacitance C is responsible for the most important phenomenon in the model Itdetermines how charge is handled in the circuit The amount of energy stored and the rate of energy level variations are both determined mainly by the capacitance value The resistance R2 that is connected in parallel with the capacitor is meant to represent the self discharge effect The series resistance R1 represents the losses during charge and discharge These losses occur because the conducting element in the supercapacitor has a resistance so the connection is not ideal The over voltage protection provided by R3 and the switch controlling its connection to the circuit is necessary to prevent damage to the capacitor elements by balancing the voltage level The voltage balancing is needed because otherwise the voltage in one separate cell can increase higher than the others resulting in gassing or explosion This voltage difference can occur if one cell has a lower capacitance than the others since that results in more energy being stored The resistance Rp and the capacitance Cp are included in the circuit to model some of the fast dynamics in the behaviour of the supercapacitor

Table 3 Component values for basic model in Simulink The capacitance value is included because it isused for initial tests before the variable capacitance is implementedComponent R1 [m_] R2 [k_] R3 [m_] Rp [m_] C [F] Cp [F]Value 6 18 52 3 35 C13

Main capacitance calculation

where iSC is current through supercapacitor CSC is overall capacitance of supercapacitor and uSC

is terminal voltage of supercapacitor

Due to the high power density and the low energy density the discharging time of the supercapacitor is very short and its response is very fast The supercapacitor plays the role of absorbing the high-frequency power fluctuations from the PV and maintaining the voltage of the

DC link in a proper range The random nature of these fluctuations is a key factor of the PV system and the instantaneous change in the output power is unpredictable The supercapacitoralways charges or discharges in a shorter time than the battery therefore the battery is protected from the high frequency fluctuationsThe voltage of the DC link is monitored and compared with the reference value V_DC resulting in the error signal which is the input of the PI controller The reference current of thesupercapacitor I_SC is usedwith themonitored supercapacitor current Isc to create the control signals for the BuckBoost DCDC converter through the current-tracking PWM

RL Spyker RM Nelms ldquoClassical Equivalent Circuit Parameters for a Double Layer Capacitorrdquo IEEE Tranactions in aerospace and electronic systems vol 36 no 3 pp 829-836 July 2000

Supercapacitor ModelFig 9 shows the classical equivalent circuit model for the supercapacitor [15] The model consists of three components the capacitance the equivalent series resistance (ESR) and the equivalent parallel resistance (EPR) The ESR is a loss term that models the internal heating in the capacitor and is most important during charging and discharging The EPR models the current leakage effect and will impact the long term energy storage performance of the supercapacitor and C is the capacitance Equations (7)-(9) describe the ESR EPR and terminal voltage of the supercapacitor

The function of the voltage-dependent capacitor C can be obtained with curve fitting from thechargingdischarging measurements The model is verified with Nesscap 27V600F supercapacitor Fig 10 shows the 10A charging rest and 5A discharging of the model with an ESR of 1m1049101 and an EPR of 2581049101

The capacitance C is responsible for the most important phenomenon in the model Itdetermines how charge is handled in the circuit The amount of energy stored and the rate of energy level variations are both determined mainly by the capacitance value The resistance R2 that is connected in parallel with the capacitor is meant to represent the self discharge effect The series resistance R1 represents the losses during charge and discharge These losses occur because the conducting element in the supercapacitor has a resistance so the connection is not ideal The over voltage protection provided by R3 and the switch controlling its connection to the circuit is necessary to prevent damage to the capacitor elements by balancing the voltage level The voltage balancing is needed because otherwise the voltage in one separate cell can increase higher than the others resulting in gassing or explosion This voltage difference can occur if one cell has a lower capacitance than the others since that results in more energy being stored The resistance Rp and the capacitance Cp are included in the circuit to model some of the fast dynamics in the behaviour of the supercapacitor

Table 3 Component values for basic model in Simulink The capacitance value is included because it isused for initial tests before the variable capacitance is implementedComponent R1 [m_] R2 [k_] R3 [m_] Rp [m_] C [F] Cp [F]Value 6 18 52 3 35 C13

Main capacitance calculation

DC link in a proper range The random nature of these fluctuations is a key factor of the PV system and the instantaneous change in the output power is unpredictable The supercapacitoralways charges or discharges in a shorter time than the battery therefore the battery is protected from the high frequency fluctuationsThe voltage of the DC link is monitored and compared with the reference value V_DC resulting in the error signal which is the input of the PI controller The reference current of thesupercapacitor I_SC is usedwith themonitored supercapacitor current Isc to create the control signals for the BuckBoost DCDC converter through the current-tracking PWM

RL Spyker RM Nelms ldquoClassical Equivalent Circuit Parameters for a Double Layer Capacitorrdquo IEEE Tranactions in aerospace and electronic systems vol 36 no 3 pp 829-836 July 2000

Supercapacitor ModelFig 9 shows the classical equivalent circuit model for the supercapacitor [15] The model consists of three components the capacitance the equivalent series resistance (ESR) and the equivalent parallel resistance (EPR) The ESR is a loss term that models the internal heating in the capacitor and is most important during charging and discharging The EPR models the current leakage effect and will impact the long term energy storage performance of the supercapacitor and C is the capacitance Equations (7)-(9) describe the ESR EPR and terminal voltage of the supercapacitor

The function of the voltage-dependent capacitor C can be obtained with curve fitting from thechargingdischarging measurements The model is verified with Nesscap 27V600F supercapacitor Fig 10 shows the 10A charging rest and 5A discharging of the model with an ESR of 1m1049101 and an EPR of 2581049101

The capacitance C is responsible for the most important phenomenon in the model Itdetermines how charge is handled in the circuit The amount of energy stored and the rate of energy level variations are both determined mainly by the capacitance value The resistance R2 that is connected in parallel with the capacitor is meant to represent the self discharge effect The series resistance R1 represents the losses during charge and discharge These losses occur because the conducting element in the supercapacitor has a resistance so the connection is not ideal The over voltage protection provided by R3 and the switch controlling its connection to the circuit is necessary to prevent damage to the capacitor elements by balancing the voltage level The voltage balancing is needed because otherwise the voltage in one separate cell can increase higher than the others resulting in gassing or explosion This voltage difference can occur if one cell has a lower capacitance than the others since that results in more energy being stored The resistance Rp and the capacitance Cp are included in the circuit to model some of the fast dynamics in the behaviour of the supercapacitor

Table 3 Component values for basic model in Simulink The capacitance value is included because it isused for initial tests before the variable capacitance is implementedComponent R1 [m_] R2 [k_] R3 [m_] Rp [m_] C [F] Cp [F]Value 6 18 52 3 35 C13

Main capacitance calculation

The function of the voltage-dependent capacitor C can be obtained with curve fitting from thechargingdischarging measurements The model is verified with Nesscap 27V600F supercapacitor Fig 10 shows the 10A charging rest and 5A discharging of the model with an ESR of 1m1049101 and an EPR of 2581049101

The capacitance C is responsible for the most important phenomenon in the model Itdetermines how charge is handled in the circuit The amount of energy stored and the rate of energy level variations are both determined mainly by the capacitance value The resistance R2 that is connected in parallel with the capacitor is meant to represent the self discharge effect The series resistance R1 represents the losses during charge and discharge These losses occur because the conducting element in the supercapacitor has a resistance so the connection is not ideal The over voltage protection provided by R3 and the switch controlling its connection to the circuit is necessary to prevent damage to the capacitor elements by balancing the voltage level The voltage balancing is needed because otherwise the voltage in one separate cell can increase higher than the others resulting in gassing or explosion This voltage difference can occur if one cell has a lower capacitance than the others since that results in more energy being stored The resistance Rp and the capacitance Cp are included in the circuit to model some of the fast dynamics in the behaviour of the supercapacitor

Table 3 Component values for basic model in Simulink The capacitance value is included because it isused for initial tests before the variable capacitance is implementedComponent R1 [m_] R2 [k_] R3 [m_] Rp [m_] C [F] Cp [F]Value 6 18 52 3 35 C13

Main capacitance calculation

The capacitance C is responsible for the most important phenomenon in the model Itdetermines how charge is handled in the circuit The amount of energy stored and the rate of energy level variations are both determined mainly by the capacitance value The resistance R2 that is connected in parallel with the capacitor is meant to represent the self discharge effect The series resistance R1 represents the losses during charge and discharge These losses occur because the conducting element in the supercapacitor has a resistance so the connection is not ideal The over voltage protection provided by R3 and the switch controlling its connection to the circuit is necessary to prevent damage to the capacitor elements by balancing the voltage level The voltage balancing is needed because otherwise the voltage in one separate cell can increase higher than the others resulting in gassing or explosion This voltage difference can occur if one cell has a lower capacitance than the others since that results in more energy being stored The resistance Rp and the capacitance Cp are included in the circuit to model some of the fast dynamics in the behaviour of the supercapacitor

Table 3 Component values for basic model in Simulink The capacitance value is included because it isused for initial tests before the variable capacitance is implementedComponent R1 [m_] R2 [k_] R3 [m_] Rp [m_] C [F] Cp [F]Value 6 18 52 3 35 C13

Main capacitance calculation

Table 3 Component values for basic model in Simulink The capacitance value is included because it isused for initial tests before the variable capacitance is implementedComponent R1 [m_] R2 [k_] R3 [m_] Rp [m_] C [F] Cp [F]Value 6 18 52 3 35 C13

Main capacitance calculation