Each of the solar PV units installed in an LV feeder contributes to the change in network behaviour depending on its capacity. However, to analyse the PV impacts on an overall feeder, a development of numerical indices considering the impacts of all the PV units in a feeder is necessary. The level of PV impact from feeder to feeder will vary depending on the impedance, loading, and level of PV penetration. The use of the numerical indices would also be beneficial to analyse and compare the impacts on different feeders in a distribution system. Indices developed to quantify solar PV impacts in terms of voltage deviation, feeder power flow, MV/LV substation capacity and feeder power loss will be used in the proposed approach. The following proposed indices will be used to investigate the PV impacts using the measured data and also using the results from the load flow analysis for any intended scenario analysis considering changes in the network, such as, increase in PV penetration.

Voltage rise is one of the most discussed impacts of solar PV integration. It can affect the voltage quality of the network by creating a long-duration overvoltage problem [11].

The maximum amount of voltage rise observed among different nodes of a feeder at any
given time is used to estimate voltage deviation in the feeder and is defined as the
Maximum Voltage Deviation Index (MVDI). At the k^{th} time instant, this can be
obtained using,

###

*nom*
*nom*

*V*

*k*
*V*

*k* *V* ^{max}

MVDI (4.2)

Here, V* ^{nom}* is the nominal voltage which can either be a constant, or vary according to
the load condition or time of the day, based on the operational policy of the utility;

*V*max(k) is the voltage at the LV feeder node where the maximum amount of voltage
variation is observed at the k-th time instant. It is to be noted that MVDI needs to be
determined for all the phases separately. The MVDI is an index calculated at any
particular instant of time to assess the maximum voltage rise impact of the rooftop solar
PV integration in the low voltage network, as given in (4.2). The index is based on the
nominal value of the feeder voltage and therefore, it can provide an indication of the
deviation of feeder voltage affected by the level of PV penetration. The index can have

both positive and negative value. Without PV integration, the voltages at different points in the feeder are generally lower than the nominal voltage and hence the MVDI will be generally positive. A negative value indicates that the solar PV integration may have produced a voltage-rise. The index can also be used to determine whether the feeder is experiencing overvoltage or undervoltage, by comparing the index with the specified limits for the distribution feeder. For example in Australia, the upper limit is 10% over the nominal value. An MVDI value which is more negative than -0.1 indicates an overvoltage has occurred. Similarly, undervoltage can be indicated by comparing the MVDI with the minimum limit.

An Average Feeder Loading Index (AFLI) of an LV feeder can be formulated as the
weighted average of loading levels of all the feeder segments with respect to their
lengths. The AFLI at k^{th} instance can be expressed as,

###

^{s}

*j* *j*

*j*
*f*
*j*

*C*
*k*
*S*
*L*
*k* *l*

1

AFLI (4.3)

For an LV feeder, the length of the j^{th} segment l*j*, total feeder length L*f* and load
carrying capacity of the j^{th} segment C*j *are constants. The AFLI will, therefore, depend
only on the complex power flow through all the line segments at the k^{th} time instant,
*S**j*(k), where j = 1, 2…, s and s is the total number of segments in the feeder. The AFLI
index provides an average indication of the degree of loading of a given feeder. It
indicates the loading of a distribution feeder as a whole, and not for any particular
segment. This index can be used to compare the impact on the loading of a given feeder
for different scenarios of PV generation. The AFLI value is zero if no power flow takes
place in the feeder segments. The AFLI value will increase with an increase in feeder
power flow to serve the customers. However, with a high penetration of PV resources,
AFLI can also increase due to a high amount of reverse power flow.

The amount of the load demand locally served by solar PV units contributes to the release of MV/LV substation capacity of an LV feeder. An index is defined to assess the PV impact on the available capacity of substations using a Substation Reserve Capacity Index (SRCI) as given below.

###

*sub*
*c*
*b*

*a*

*S*

*k*
*S*
*k*
*S*
*k*

*k* 1 *S*^{1} ^{1} ^{1}

SRCI

(4.4)

Here, S1*a*, S1*b*, and S1*c* are the complex power flows from phase a, b and c of the LV
substation bus and S*sub* is the rated capacity of the substation. A value of SRCI equal to
*one means substation capacity is fully available whereas a value equal to zero means no *
substation capacity is left unused. With PV units serving local loads, SRCI will decrease
with PV integration. However, above a certain level of PV penetration, reverse power
flow will cause a higher level of substation capacity to be used and SRCI will decrease.

The import of power from the upstream network will be less due to the availability of local PV generation. Therefore, power loss in the distribution feeder will be reduced. To quantify this, an index is developed using the ratio of the total loss incurred in the feeder to the total load served by the feeder and is referred to as the Feeder Loss to Load Ratio (FLLR), as shown below.

###

###

*k*

*P*

###

*k*

*P*

###

*k*

*P*

*k*
*P*
*k*
*P*
*k*
*k* *P*

*c*
*dem*
*b*

*dem*
*a*

*dem*

*c*
*loss*
*b*

*loss*
*a*

*loss*

FLLR (4.5)

Here, *P**loss**a*, *P**loss**b* and P*loss**c* are power losses incurred and P*dem**a*, *P**dem**b* and P*dem**c* are
the load demands in phase a, b and c of an LV feeder. FLLR is an index obtained from
the ratio of the loss in the feeder to the load demand of the feeder. Its value increases
significantly during midday when the PV output is the highest and the load demand is
usually low. During that period, the power loss through the feeder is high due to a high
amount of reverse power flow, but since the load demand is typically lower, therefore,
the ratio of the loss to the load demand becomes significantly high.

Indices of the Moving Averages (MA) of the variables associated with the PV impact in the sliding windows is required to understand the overall trend of the changes in network behaviour caused by the level of solar PV.

The moving average of the voltage deviation index at any given sliding window, w, with a width of W can be defined as,

*W*
*k*

*W*
*w*

*w*
*k*
*w*

###

^{}

^{}

1

MVDI

MVDI (4.6)

Similarly, the moving averages of the other impact indices, AFLIw, SRCIw and FLLRw will be obtained, as given in (4.7)-(4.9). The moving average provides a useful indicator of the long term trend of the variables associated with the PV impact.

*W*
*k*

*W*
*w*

*w*
*k*
*w*

###

^{}

^{}

1

AFLI

AFLI (4.7)

*W*
*k*

*W*
*w*

*w*
*k*
*w*

###

^{}

1

SRCI

SRCI (4.8)

*W*
*k*

*W*
*w*

*w*
*k*
*w*

###

^{}

^{}

1

FLLR

FLLR (4.9)