Real-time Measurements and their Effects on State
Estimation of Distribution Power System
Xue Han∗ , Shi You∗ , Fannar Thordarson† , David Victor Tackie† , Sisse Merete Østberg‡ , Ole Michael Pedersen‡ ,
Henrik W. Bindner∗ , and Niels Christian Nordentoft†
∗ CEE,
Technical University of Denmark, Email: xueh, sy, hwbi@elektro.dtu.dk
Energy Association, Email: fth, dvt, ncn@danskenergi.dk
‡ DONG Energy, Email: simos, olemp@dongenergy.dk
† Danish
Abstract—This paper aims at analyzing the potential value of
using different real-time metering and measuring instruments applied in the low voltage distribution networks for state-estimation.
An algorithm is presented to evaluate different combinations of
metering data using a tailored state estimator. It is followed by a
case study based on the proposed algorithm. A real distribution
grid feeder with different types of meters installed either in
the cabinets or at the customer side is selected for simulation
and analysis. Standard load templates are used to initiate the
state estimation. The deviations between the estimated values
(voltage and injected power) and the measurements are applied
to evaluate the accuracy of the estimated grid states. Eventually,
some suggestions are provided for the distribution grid operators
on placing the real-time meters in the distribution grid.
I. I NTRODUCTION
The challenges introduced by the increasing integration of
Distributed Energy Resources (DERs) and new components,
push forward the necessity of additional real-time monitoring
system (referring to the concept that the operation states are
updated frequently comparing to the original energy billing
system) in the distribution grids, especially in low voltage
level (LV). Conventionally, the Distribution System Operators (DSOs) use Velander Correlation to estimate the peak
load, given the load templates (i.e., pseudo inputs). Apparently, these challenges cannot be sufficiently handled via this
method. The DSOs are facing a trade-off problem between the
visibility of the grid with a large quantity of active units (new
patterns) and the investment on metering system. To improve
the grid visibility, several key factors need to be addressed:
• Customer side smart meters: The smart meters are installed at the customer side to enable the hourly billing.
Average power in hourly (or higher) resolution is measurable. In some advanced meters, voltage and reactive
power can be measured as well. For political reasons, a
large scale roll-out is anticipated in the near future.
• Remote meters on grid side: Similar to the solution in
the transmission grid (as well as some MV distribution
grids), the remote meters are installed in the substations
and some special nodes. Three-phase voltage, current, and
power injection can be measured in hourly (or severalminute) intervals. Compared to the smart meters, they are
much more expensive.
• Pseudo measurements In unobservable areas or without
any measuring points, the estimation will fully depend
on the existing knowledge of the grid (i.e., pseudo measurements, like historical data, load templates, nominal
voltage value, average power factor, etc.). A better estimation result can be obtained if the pseudo measurements
are improved.
• State estimation method: Given the above inputs, DSOs
can apply the state estimation (SE) to obtain the best
approximation of the operation states. However, due to
the unique features of the LV grid (i.e., a huge number of nodes, radial topology, non-ignorable resistance
of the cables, etc.), the traditional estimation algorithm
(e.g., method introduced in [1]) is not applicable for the
distribution grid estimation. The methodology has been
improved by taking into account the features of the distribution grid in [2] and [3], i.e., the pseudo measurements
with around 20% uncertainty are considered as a complementary set for SE, and a three phase asymmetrical grid
model is used. Furthermore, some advises are provided on
placing the meters for grid operation [4]. Paper [5] studies
the influence of smart meters with advanced features onto
SE and suggests on the optimal positions considering the
grid features and the numbers of meters. However, new
problems arise, if the state estimator inputs consist of a
flexible combinations of pseudo data, real measurements,
which vary temporally and spatially, or if the measured
objects delivered from different sources are different from
each other in terms of voltage, power, etc. Thus, a valid
state estimator is necessary to enable the evaluation of
different metering portfolios, to maximize the potential
values of various metering options.
Hence, an evaluation procedure is proposed for the accuracy
of the estimation with respect to the number of meters and
their locations in the grid. In this procedure, a tailored state
estimator is developed and used.
II. E VALUATION A LGORITHM
A. Evaluation Procedure
To calculate the level of accuracy of the distribution grid
SE, using certain portfolios of limited numbers of meters,
simulations are conducted, following Fig. 1. The block ”Traditional state estimation” indicates the current knowledge on
the distribution grid from the DSOs, including the information
Power
meter
Traditional state
estimation
Comparison
Real state
Initial stateestimation error
All measurements
of the feeder
Real state
Initialization
Load profile
Load
template
Reduced error due
to measurements
Guidelines
Grid Model
& Rules
Cable parameters,
customer info
Cho
(from
Power flow
calculation
(U, I, PPF)
Comparison
state-estimation
errors with certain
combination
P
Area 3
All measurements
of the feeder
(PPF, V, I)
DTU Electrical Engineering, Technical University of Denmark
iPower WP3.2
No
B
Yes
Power flow
constraints
13-06-2013
S
Redundant
measurements
?
Cabinet meter
Area 2
Fig. 1. The evaluation procedure (Area 1: the reference case; Area 2: the
designed cases for measurements, i.e., certain portfolios of measurements;
Area 3: comparison and analysis).
5
Nominal voltage +
load template
(load)
Comparison
Area 1
State estimation
Combinations of
measurements
load
(load, V)
0 measurement
State estimation
By
min(wu∆U2+wi∆I2+
wp∆PPF2)
Weighting
factors
No
Result
All measurements
of annual billing-data and a 24-hour load template, estimated
on the basis of consumer type. Based on the comparisons of
various cases, i.e., different sets of available measurements, the
relation between the numbers of meters or different locations
are analysed by statistical approaches.
Powerby the following equation:
The accuracy level is given
load
Initialization
meter
n(load, V)
Load profile
6
Fig. 2.
Initialization
Choose the starting point
Any (other)
forward
buses?
where, i is the index of the selected state variables,
and err
(U, I, P )
is given by SEs compared to the real states.
errtrad,i gives the reference
value of errors for
the evaluation
P
Redundant
Cabinet meter
measurements
by following the procedure described byNo Area 1 ?in Fig. 1. erri
Yes
represent the errors when a certain portfolio of measurements
are involved in the estimation (Fig. 1 Area
2). Thus, the
State estimation
Weighting
By
designed portfolios and the corresponding
be
factors
min(w meters
∆U +w ∆I + can
w ∆P )
evaluated as in Area 3.
PF
p
Backward calculation
with P and U
2
Move to the
branching bus
2
No
Branching bus
= substation
?
Result
All measurements
B. Sate estimtation (SE) Approach
U, I, P
PF
i
U, I, P
Yes
Error
Within the proposed evaluation procedure, the tailored SE
T = T + (see
1
approach is designed and used for the simulations
Fig. 2).
The approach allows the possibility of several data sources for
SE. Before running the simulation, the data are matched with
6
the lowest sampling time,
and the possible time drift is checked
with redundant values. The measurement set consists of two
subsets: the real measurements (e.g., power flow information,
voltage magnitudes and angles), and the pseudo measurements
(e.g., load templates, predefined power factor). In the first step,
the load profiles are updated if the corresponding measurements are available. The weighting factors in SE are decided
by the specification of the measurement uncertainty in the
technical sheets.
In the second step, the hybrid backward-forward power flow
(see Fig. 3) is conducted based on the available information.
The LV feeder is usually in a radial topology. Thus, the
backward-forward method [6] can be applied. This hybrid
backward-forward method can converge very fast in the first
few iterations, and is not sensitive to the initial values and the
starting point. By using this method, the pseudo measurements
in the unobservable areas can be adjusted according to the
available information, i.e., the errors of the pseudo measurements is reduced. This step provides good initial values for
the later estimation.
DTU Electrical Engineering, Technical University of Denmark
forward
power flow
No
Power flow
constraints
2
Yes Backward-
Sweep backwards to
find branching bus
(PPF, V, I)
u
iPower W
(from substation to terminal buses)
Power flow
calculation
Cable parameters,
customer info
The SE algorithm
DTU Electrical Engineering, Technical University of Denmark
(1)
(load)
Error
T=T+1
Nominal voltage +
Load
loaditemplate
| errtrad,i | − | err
|
1X
template
accy =
n i=1 Grid Model| errtrad,i |
U, I, P
U, I, P
End
Fig. 3.
The hybrid backward-forward power flow
iPower WP3.2
06-06-2013
Similar to the traditional SE algorithm, voltage, current and
power could be regarded as the estimation variables. If there
are some redundant measurements to minimize the errors,
SE is applied. In the third step, by minimising the errors
between the available measured value and estimated value
using Weighted Least Square (WLS) method, the program will
update the SE results. The objective function is as follows:
J(x) = (z − H(x))0 W (z − H(x))
(2)
where
z is the measurement vector;
x is the state vector;
H is the transformation matrix, containing the linearised
relations in power flow;
and W is the weighting factor matrix, determined by the estimated uncertainty of the measurements, i.e., relative accuracy.
Different combinations of available measurements are provided for the calculations. Subsequently, the errors, as compared to the ”Real state” (Fig. 2), are further assessed.
Line1-2
Node 1
Line2-3
Time [hour]
Fig. 5.
Line4-5
Node 4
Line5-6
Node 5
Node 6
Load 5
Node 12
Line11-12
Load10
Node 10
Node 8 Line8-9 Node 9
Line6-8
Load 8
Node 11
Line11-13
Load 6
Line10-11
Line6-10
Node 7 Line6-7
Load 11
Node 13
Load 12
Load 13
Fig. 4.
80%
70%
60%
50%
40%
30%
20%
10%
0%
Pseudo
Real
ratio
Load 2
Load4
Load 3
Load 7
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
Node 2
Line2-4
Node 3
Active Power [kWh/h]
Connecting Point
Load 9
Remote meter:
Node 1, 2, 5, 6, 11
(P_ij, I_ij, U_i)
Smart meter:
Node 2, 4, 5, 6, 8, 10, 11
(P_i)
Node 3, 7, 9, 12, 13
(P_i, U_i)
rate of smart meters is very low. The valid range of current
values in the remote meters is 2.5A to 400A, which also affect
the power measurements.The uncertainty of the measurements
are listed as follows:
• Remote meters: ±2%;
• Power measurements from smart meters: ±1%;
• Voltage measurements from smart meters: ±5%.
Accordingly, the weighting factor of values used in SE should
be chosen depending on the data source.
C. Pseudo measurements
TABLE I
P SEUDO MEASUREMENTS
Variable
Voltage
Active power
Power factor
Topology of the test feeder with meter placements
III. C ASE STUDY
A. Network topology
The test network is a real LV feeder in Denmark [7]. It
consists of 13 nodes, 69 customers (involving 7 customer
types), and 3 PV systems. The nominal line-line voltage is
0.4kV. The topology is shown in Fig. 4. Two sources of the
measurements are investigated in this paper: remote meters in
the cabinets and smart meters at the customer side. Among
these 13 nodes, 5 remote meters are installed in the cabinets;
the smart meters are installed at all customers’ residence; and
5 additional smart meters are installed in the terminal nodes
to measure the voltage. All the lines are underground cables
with certain properties. The total length of the cables is 840
m.
B. Measurements
The remote meters measure three phase voltage magnitude,
current magnitude, and active power flow. The data is logged
in the database by sending SMS every 10 minutes. The smart
meters deliver the average active power on hourly basis (three
phases in total) via wireless internet. The additional 5 smart
meters log the three phase voltage in 10-minute intervals.
Currently, separate databases and different formats are used to
store the measurements. One-day measurements (18th April
2013) are used in the following simulations.
The missing rate of the remote meter data is around 1% – 10%,
but the missing strings are seldom consecutive. The missing
The load template vs. real measurements
Pseudo
nominal value
load template
constant value
Value
230V
–
0.95
When the information is not sufficient to support SE, the
pseudo measurements are involved in the calculations. TABLE
I lists several pseudo measurements.
A notable issue while doing the simulations is that the measured active power is much less than what is assumed in the
load templates. Fig. 5 shows the real measurements and the
template values of a certain load category. Apparently, the
error is very large and varying significantly (which violate
the hypothesis in the normal SE approach [2] and [3]). By
comparing the real and pseudo measurements, it is concluded
that the errors in the weekends are larger. To accommodate
such pseudo measurements, the SE approach should be robust
to avoid non-convergence.
D. Scenarios
To evaluate the effect of different combinations of available
real-time measurements, several scenarios are defined based
on the set-up stated as above:
Sc. 1 Reference scenario: using only pseudo measurements;
Sc. 2 Full observation: using all collected measurements;
Sc. 3 Power measurements from all smart meters available
with one additional voltage measurement from either
Node 1 (3a) or Node 3 (3b) as the reference voltage
(the measurements from different metering types);
Sc. 4 Power + voltage measurements on a single node
(i.e., 2, 3, 5, 6, 7, 9, 11, 12, 13) available (4a –
4i, respectively);
Injected power [kWh/h]
40
80
30
60
20
40
10
20
Voltage [p.u.]
0
1
2
3
4
5
6
7
8
9
10
11
12
13
0
1.02
1.02
1
1
0.98
0.98
0.96
1
2
3
Fig. 6.
4
5
6
7
8
Bus number
9
10
11
12
13
0.96
1
2
3
4
5
6
0
1
2
3
4
5
Sc. 1
Sc. 2
Sc. 3a
Sc. 3b
Sc. 4
Sc. 5
Sc. 6
6
8
7
9
8
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time [h]
Sc. 1
Sc. 3a
Sc. 3b
Comparison between Sc. 1, and Sc. 3 (the left column: fixed time; the right column: fixed bus)
TABLE II
T HE PORTFOLIO OF MEASUREMENTS IN EACH SCENARIO
Remote meter
(Power-flow)
–
All
–
–
Single node
–
All
7
Remote meter
(Voltage)
–
All
Node 1
–
(PF + U)
–
All
Smart meter Smart meter
(Power)
(Voltage)
–
–
All
All
All
–
All
Node 3
or Single node (P + U)
All
All
–
–
1 as a reference voltage to derive the remaining node voltages.
Since the voltage values on Node 1 and Node 3 are from
different sources, the results show a large difference between
Sc. 3a and Sc. 3b. The accuracy of the voltage estimation
is strongly dependent on the available voltage measurement,
as there is no redundant measurement in these scenarios.
Comparing the accuracy level of the voltage in Fig. 7, it is
obvious that the estimation result is biased by the less accurate
voltage value on Node 3.
B. Effect of the position of measurements
Sc. 5 All measurements from smart meters are available;
Sc. 6 All measurements from remote meters are available.
The scenarios are summed in TABLE II.
IV. R ESULTS AND ANALYSIS
A. Effect of the types of measurements
Fig. 6 shows the modified power flow results (i.e., the
injected power and the voltage). The two plots on the left
show the values at each bus in Hour 1, and the two plots on
the right show the values at the connecting point (Node 1) in
each hour. The huge difference between the load templates and
the real power consumption leads to a large difference in the
injected power values comparing Sc. 1 and Sc. 3, which may
lead to problems on plausibility and observability or biased
estimation result. However, the shape of diurnal variation is
similar. The real values is about 20% of the template values for
all customers. Thus, the load templates need to be modified to
obtain a reasonable prediction of the load consumption. This
error significantly affects the accuracy level of the feeder’s SE,
not only on the injected power but also on the voltage (see
Fig. 7: Sc. 1, Sc. 3a, and Sc. 3b).
The voltage drop along the feeder is reduced in Sc. 3 because
of less power flow in the feeder. The voltage magnitudes
depend mainly on the one and only voltage measurement, i.e.,
voltage on Node 1 (Sc. 3a) and on Node 3 (Sc. 3b). It replaces
the pseudo measurement (the nominal value as 1 p.u.) on Node
In Sc. 4, the meters (with voltage and load) are assigned to
the selected nodes one by one. In Fig. 7 it is observed that
if the load size is larger, a higher improvement is achieved.
The accuracy level of the injected power obtains 8% point
improvement with one meter installed in the feeder, whereas
the accuracy level of the voltage is improved approximately
15% point. The improvement of accyU is due to two reasons:
less power loss led by the updated load, and the available
voltage measurement. Comparing the sub-scenarios in Sc. 3,
it is seen that a higher accuracy is obtained if the node with
meters is in the beginning of the feeder.
C. Smart meter vs. remote meter
Fig. 8 shows the simulation results of Sc. 5 and Sc. 6, where
two types of meters with different measuring specifications
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
accyU
accyP
Sc1 Sc4a Sc4b Sc4c Sc4d Sc4e Sc4f Sc4g Sc4h Sc4i Sc3a Sc3b Sc5 Sc6 Sc2
Fig. 7. Accuracy level of different scenarios (relative scale: 0% refers to the
same error as in Sc. 1; Sc 2 has approximate 100% accuracy, due to the large
amount of redundant measuring points). accy refers to Eq. 1.
Injected power [kWh/h]
40
15
30
10
5
0
Voltage [p.u.]
20
10
1
2
3
4
5
6
7
8
9
10
11
12
13
0
1.02
1.02
1
1
0.98
0.98
0.96
1
2
3
4
5
6
7
8
9
10
11
12
13
0.96
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Sc. 5
Sc. 6
Time [h]
Bus number
Fig. 8.
Comparison between Sc. 5 and Sc. 6 (the left column: fixed time; the right column: fixed bus)
and locations (Fig. 4) are used. The difference of the voltage
estimates is almost constant along the feeder and in time, while
it is not the same for the injected power. This phenomenon
indicates that there might be calibrating errors, which can be
simply removed by recalibrating the meters. There would be
a big risk for voltage regulation solutions if such errors exist.
Looking at the accuracy level of Sc. 5 and Sc. 6 in Fig. 7, the
same results can be derived. By having all of measurements
available, a better estimation can be achieved.
D. Impacts of the metering data
While processing the measurements, some critical issues
regarding the metering data are identified, which need to be
solved in practice:
• About 4% of the data from the remote meters is missing
due to the unstable delivery of SMS service. The missing
data is usually not consecutive and, thus, can be estimated
from the neighbouring time instants. Otherwise, the corresponding node is regarded as non-measurable.
• The valid measuring range should be adapted to the
load or the feeder size, to send effective values to the
estimator. The invalid measurements in the remote meters
with regard to the current and power, is around 30% (less
than 2.5 A) due to the improper measuring range.
• The coordination between different sources could be a
risk on SE, not only due to the time step and the accuracy
of values, but also due to the reason that SE results may
be biased by the less accurate source (e.g., Sc. 5 and
Sc. 6). Moreover, the synchronization of the clocks and
the calibration of different data sources will lead to the
problem of convergence.
V. C ONCLUSION
This paper presents to what extent the estimation of the
grid operation can be improved by using different types of
real-time measurements in the LV distribution grids. With a
better estimation of the LV grid states, people can gain some
knowledge on the DER behaviours. It also enables the reliable
delivery of DER services to the grid. An evaluating algorithm
is described to estimate their values in a LV feeder, in which
a hybrid SE approach is presented to handle multiple sources
of the input values. Different combinations of measurements,
obtained from the real test feeder, are implemented in the
estimation. The accuracy level for each scenario is calculated.
The increasing numbers of meters or more types of measurements improve the overall accuracy of the estimation.
The redundant values can help on minimizing the measuring
errors. The accuracy of the injected power depends on the
error between the available power data and the corresponding
load templates used in the estimation. Power factors and the
unsymmetrical loads at the measuring nodes also affect the
accuracy. A higher accuracy of voltage can be anticipated if the
single voltage metering point is placed near the transformer.
Different sources of data and data quality are the barriers for
the SE approach. In the lack-of-measurement situations, the
insufficient data would potentially bias the estimation results.
In addition, the load template should be updated to approach
the real conditions of the feeder for various purposes (e.g.,
grid planning).
From the results, it can be suggested that a further preprocessing stage should be embedded in the estimation approach to obtain a robust SE. Based on the fact of the data
quality, a method to tune the weighting factor is important for
an automatic SE program.
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2003.
[3] B. Das, “Consideration of input parameter uncertainties in load flow
solution of three-phase unbalanced radial distribution system,” Power
Systems, IEEE Trans. on, vol. 21, no. 3, pp. 1088–1095, 2006.
[4] Distribution Fast Simulation and Modeling Technical Update: Stateof-the-Art, Prototype and Performance Analysis of Distribution State
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