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A New Strategy for the Charging/Discharging of Storage Devices

its peak during midday, and gradually decreases after midday. The surplus power at the PCC would also follow a similar trend. Therefore, a charging strategy where the charging rate gradually increases with the progress of the day, reaches its peak level during midday, and gradually decreases after the midday, would be more effective for PV impact mitigation, compared to a traditional constant charging strategy. Similarly, a discharging strategy where the discharging rate gradually increases from the start of the evening period, reaches its peak level during the evening peak load, and gradually decreases with the decrease of evening load, would be more effective for peak load support compared to a constant discharging strategy.

Further, since the energy storage devices have limited capacity (Ah) or energy (kWh), it is important to use it wisely. Charging the energy storage devices too fast, when there is reverse power flow, may cause the battery to be full too soon and therefore may result in unacceptable reverse power flow and a voltage-rise at an inconvenient time, for example at peak insolation period. But too slow charging of the storage device, when there is reverse power flow, may cause some of the capacity of the battery to be left unused.

A new charging/discharging strategy is proposed to better match the surplus PV generation/evening load profile. The methodology to obtain the appropriate charging/discharging rates to wisely use the limited storage capacity is described below using Fig. 6.7. Fig. 6.7(a) shows the load and the PV output profile at a given PCC, where the PV output is higher than the load demand for a period of the day, T. During this period, a surplus power will be available at the PCC. According to the proposed strategy, the storage device will be charged over the period T. The charging rate will be increased from zero at the start of the period T, (when the storage SoC is at the maximum depth of discharge DoDmax) at a Slope of Charging Rate (SCR) defined in per-unit of time, until the SoC reaches a threshold level, ToS1. This is shown in Fig.

6.7(b). From this point, the storage will be charged at a constant saturated charging rate, CRSat. Once the SoC reaches the second threshold, ToS2, less capacity of the storage is

available and therefore the charging rate will be decreased using the same SCR, until the storage device attains the state of maximum charge, SoCmax, at the end of period T.

Fig. 6.7. Proposed charging/discharging strategy. (a) load and PV generation profile; (b) methodology to obtain charging/discharging rates; (c) a constant charging profile; (d) a triangular charging profile.

According to this strategy, the charging rate at the k-th time instant can be expressed as given in (6.8).

   

   

 

   

 





max

2 2 1

Sat

1

SoC 1

SoC if 0

ToS 1

SoC if SCR 1

CR

ToS 1

SoC ToS

if CR

ToS 1

SoC if SCR 1

CR CR

k ,

k ,

k

k ,

k ,

k

k    (6.8) 

To obtain the appropriate values of the parameters SCR and CRSat to be used in (6.8), the following facts are considered.

The amount of charge lost for not charging the battery at a constant charging rate over the entire charging period will have to be recovered in the overall charging period.

Mathematically, this constraint can be expressed using the geometrical relationships in

Fig. 6.7(b) as given below.

 

2 1 SCR2 12 0

2

2 h T h h

h    (6.9) 

where, h1 is the constant charging rate that charges the battery in T amount of time, h2

is the amount of increase in the constant charging rate to recover the charge lost for not using the constant charging rate over the whole charging period.

Again, the charge stored during the constant charging period is equal to the amount of charge between the first and second threshold of SoC, ToS1 and ToS2 respectively. This can be expressed using (6.10) below.

 

  

ToS ToS

C 0

SCR 2 SCR

2

1 2 2

2 1

1    

 

  

h h

T h

h    (6.10)

It is observed that in (6.9) and (6.10), h2 and SCR are the only unknown parameters;

h1 is known from the battery capacity, and T is the period for which the battery is intended to be charged, which can be estimated from historical load and PV output profile as shown in Fig. 6.7(a), ToS1 and ToS2 are the choices to shape the charging rate profile. Therefore, h2 and SCR can be obtained by solving (6.9) and (6.10) simultaneously using a Newton based numerical technique. By varying the difference between ToS1 and ToS2, different charging profiles can be obtained and the pattern of usage of the available storage capacity can be controlled. For example, if ToS1 and ToS2

are set to DoDmax and SoCmax, respectively, a constant charging profile is obtained, as shown in Fig. 6.7(c). Again, if the difference between ToS1 and ToS2 is zero, then a triangular charging profile is obtained, as shown in Fig. 6.7(d).

A similar strategy will be followed for the discharge operation; however, in this case the discharge rate (DR) will be increased at a Slope of Discharge Rate (SDR) defined in per-unit of time, until the SoC drops to ToS2 from the SoCmax level, and then the discharge will continue at a constant saturated discharge rate DRSat. When the SoC drops below ToS1, the battery discharge rate is decreased at the same SDR until DoDmax

is reached. At a given k--th instant, this can be expressed as,

 

 

   

 

   

 





max

1 1 2

Sat

2

DoD 1

SoC if 0

ToS 1

SoC if SDR 1

DR

ToS 1

SoC ToS

if DR

ToS 1

SoC if SDR 1

DR DR

k ,

k ,

k

k ,

k ,

k

k    (6.11)

The values of SDR and DRSat can be obtained from (6.9)-(6.10). In this case, T will be the intended period of discharge. This is the duration of the peak load support and will depend on the limited amount of the stored energy in the battery. To make an effective use of the available stored energy, it needs to be discharged in a period that includes the maximum evening peak, as shown in Fig. 6.8.

An estimate of the discharge period, T, can be obtained initially using the historical load curves of the specific household where the storage device is to be installed. If the available energy is fully discharged during the evening peak, the following expression will hold true.

SoC DoD

2

 

0

max 1

max    

VB

tt PL t dt

B (6.12)

where, (t2 - t1)= T, as shown in Fig. 6.8, tmax is the time of occurrence of the maximum demand, VB is the nominal battery voltage, B is the battery energy efficiency and PL(t) is the load demand at time, t. T can be obtained by solving (6.12) iteratively and can be used in (6.9) and (6.10) to obtain SDR and DRSat. Normally, the time of occurrence of the peak load and the length of evening load period would not be significantly different between two consecutive days. Therefore, once the system is installed and commissioned using the initial historical load curve, the information on t1 and t2 can be updated daily from measurements at the PCC to accurately estimate the intended period of discharge.

Fig. 6.8. Determination of evening peak support interval.

PL(t), PPV(t)

The flow chart of the charge and discharge control system for a given time step is shown in Fig. 6.9(a) and 9(b), respectively. The storage device is normally charged if there is no sudden decrease in PV output at the PCC and also a reverse power flow greater than a threshold level is found. The charging rate is obtained using (6.8) based on the parameters obtained from (6.9)-(6.10). The storage is normally discharged if the PCC voltage is found to be lower than a threshold level and also when no sudden dip in the PCC voltage is observed, as shown Fig. 6.9(b). The discharge rate is obtained using (6.11) based on the parameters obtained from (6.9)-(6.10).

Fig. 6.9. Storage control flow charts. (a) charging operation (b) discharging operation

The PV output may be suddenly decreased by irregularities in the sun irradiance levels due to unstable weather conditions causing fluctuations in the PCC net power and voltage. In the event of a sudden decrease in the PV output, the storage is put into a short-term discharge (STD) mode, as shown in Fig. 6.9(a). The short-term discharge-support is limited to avoid a significant drainage of charge.

To ensure an effective use of the available storage capacity, it is necessary to make-up for the charge lost during the short- term discharge period, and also during the unavailability of enough surplus power at the PCC caused by changing cloudiness of the sky. The lost charge can be replenished by adjusting the charging rate at each instant of time to attain a reference SoC level. The reference SoC level is the one which is not affected by any unstable weather condition and can be obtained using the charging rate expressions given in (6.8). The strategy for performing the adjustment in charging rate is shown in Fig. 6.10.

Fig. 6.10. Adjustment of charging rate to make-up for charge lost due to unstable weather condition. If the storage is not charged at the (k-1)-th time instant, the SoC will remain at the same value as in the previous time instant. Again, if the storage is discharged at the (k-1)-th time instant, the SoC level will be reduced than the previous SoC. Therefore, an adjustment of the charging rate has to be performed at the beginning of the k-th time instant to make-up for the charge not stored, or lost, during the (k-1)-th instant, as given below.

 

           

t

t k k

k k

k ref

 

  SoC -SoC 1 CR

CR R

C     (6.13) 

where, CR k is the adjusted charging rate, SoCref is the reference level of SoC, t is the time between two consecutive time instants, and  is a parameter defining the percentage of the deviation to be met which can be controlled to limit the adjustment in the charging rate, if required. This adjustment of charging rate ensures an effective utilization of a storage device compared to a constant charging rate strategy in the event of irregularities in PV output which is difficult to anticipate.

Similarly, in the evening, it may be required to discharge the storage at a rate higher than the normal rate to support any abrupt voltage drop, such as a voltage-dip event caused by a sudden increase in the load demand. In this situation, the storage is put into at a short-term high discharge (STHD) mode as presented in Fig. 6.9(b), depending on the intensity of the sudden increase in the momentary load demand. This will result an additional charge to be drained during the higher discharge operation. Therefore, the discharge rate is adjusted by using (6.14) to reduce the deviation with the reference SoC

level.

           

t

t k k

k k

k ref

 

  SoC -SoC 1 DR

DR R

D  (6.14)

All of the distributed storage units in the feeder operate according to the control strategy described above, based on the local information at the PCC, such as the PV output, the local demand, and the PCC voltage.

Although this thesis proposes a storage control strategy based on local parameters only, a coordinated control strategy of multiple storage devices in the feeder may also be possible if a communication system become available as envisaged in the future smart grid. In such a coordinated operation, the storage devices at different locations would be able to exchange information on the available storage capacity and the surplus power at different PCCs using the communication systems, to make a better use of the total storage capacity available in the feeder to store an optimum amount of total excess PV generation in the feeder.

The present thesis mainly discusses the mitigation of reverse power flow caused by active power injection from rooftop solar PV in LV distribution feeders, resulting in the avoidance of a voltage-rise, although the system does not intentionally control the voltage. As there is no voltage control set-point in the proposed strategy, it is different than an on load tap-changer or voltage regulator located in medium voltage system where a feed-back arrangement is used to control the voltage at the load centre. For the same reason, it will not interfere with the operation of the on load tap-changer or the voltage regulator. The only effect of this controller is to make the on-load tap changer and the voltage regulator to have less switching operation and hence less stress. With a communication system, the battery storage system can be coordinated with the on-load tap changer as presented in [9].