# 辅导案例-KNE446

Semester 1 2020

KNE446: Electrical Power Design (SDUST)

Student Name: Signature

Student ID: Date:

Instructions for students:

Development Component
Introduction
As distribution systems become larger and more complex, power system designers face an evolving
challenge. Monitoring the network for areas of improvement requires measurement devices through
the network, but these devices are expensive and cannot be placed on every bus. Transmission
systems rarely meet this issue – they tend to have a small number of buses and a metering device on
each. In this task, you are going to develop a state estimator for a distribution system that will be given
to you.

Aim
You will each be emailed a unique power system. For this power system:
1. Calculate an estimate for the state of the network. Measurement devices have the following
standard deviations:
a. Power injection measurements have a standard deviation of 0.012 p.u.
b. Power flow measurements have a standard deviation of 0.007 p.u.
c. Voltage magnitude measurements have a standard deviation of 0.003 p.u.
2. Demonstrate that the network is observable (see the notes in this document).
3. A new customer has requested that they be connected to your network. Information related
to their request is given at the end of the document detailing the network. Determine if you
expect there to be any violations of operational constraints if they were to connect to the
network. Also, determine where additional measurement devices may be required to ensure
the network is still observable.

Requirements
This assignment is open-ended, however the minimum requirements are:
• Develop a state estimator in MATLAB (and submit this on MyLO).
• Estimate the state of the network using the state estimator, and determine whether there are
any voltage violations (operational constraint is ±0.05p.u).
• Complete an observability analysis.
• Prepare a report detailing your analysis of the system, and what recommendations you would
make regarding additional measurements, operational requirements, and anything else you
may have noticed.
Additionally, you may investigate various methods of completing state estimation, as well as other
topics on top of just a WLS state estimator. This might include bad data detection, parameter
estimation, optimal meter placement, robust estimation, etc.

State Estimation and Network Observability
In the lecture notes on distribution system design, you can find information on how to develop a
weighted least-squares state estimator. You will need this formulation to complete the task, however
there is some work required to ensure that we can actually obtain a state estimate using our estimator.
Imagine a power system with one measurement unit. Despite getting a measurement, you can
imagine that it isn’t possible to guess what the measurements on all other buses are, even
probabilistically. What we need to know is whether we have enough measurement devices to ensure
we get an estimate. If we do, we call the network observable. If we don’t, what we get are a number
of observable islands, and we need to add more measurement devices to guarantee a unique
estimate. We also want to ensure we don’t have more measurement devices than we need (as
measurement devices are expensive). Both observability analysis and redundancy analysis are
discussed below.
Graphs, Networks and Observability
All power networks can be analysed using topology. This is necessary for observability analysis. A brief
description of the required steps is given here.
Firstly, we need to find a spanning tree of a network, and then classify its links. A spanning tree is
simply a collection of edges in a graph where moving along the tree allows every node to be reached.
See the following graph with four nodes for an example.

In this example, the spanning tree is:
= {12, 24, 34}
{13, 23}
Note this is not a unique classification, however you should assign one spanning tree set and one link
set and stick with them in your network!
We can also define a fundamental loop. This is the loop linking the spanning tree with each link
individually, and there are as many fundamental loops as there are links. In this case, the fundamental
loops are:
1 = {13, 12, 24, 34}
And
e24
1 2
3 4
e12
e34
e13
e23
2 = {23, 24, 34}.

Now, for our observability analysis, we need to use directed graphs. This is simply the network drawn
with arrows in arbitrary directions. It is most useful to have the spanning tree pointing all one way. An
example is shown here.

Now, this graph is directed, and a branch-to-bus incidence matrix can be created. This is a matrix
indicating the connections between buses with only a 1, -1 or 0 depending on the arrow direction.
Note that we put the edges in the spanning tree first, then the links next. Columns correspond to each
bus number (negative if directed toward, positive if directed away). For this network, we get:
=
12
24
34
13
23

[

1 −1 0 0
0 1 0 −1
0 0 −1 1
1 0 −1 0
0 1 −1 0 ]

Now, we are ready to determine where our observable islands may exist within the network. We will
work with the network as a power system and add some measurement devices (black squares indicate
line power flow measurements and black arrows indicate bus power injection measurements). For
this section, we also de-couple the power and voltage components, since voltage angle will mostly
determine the active power , and voltage magnitude will mostly determine the reactive power .

Since all we are looking at here is whether we have enough measurements to ‘see’ all the buses, we
don’t need to worry about the line impedances. To make things simple, we will set these all to
1.0 . . Similarly, all voltage magnitudes can also be set to 1.0 . . To determine observability, we
need only look at active power flows and bus voltage angles. These are related using as follows:
e24
1 2
3 4
e12
e34
e13
e23
e24
1 2
3 4
e12
e34
e13
e23
=
Where is a vector of branch power flows, is the branch-to-bus incidence matrix and is the vector
of bus voltage phase angles.

We need to develop one more matrix – a modified Jacobian Measurement Matrix, . This matrix
encodes the information that the measurement devices actually tell us, and is based on simple power
flow equations with branch reactances and voltages magnitudes all set to unity. To build this matrix,
use these steps:
1. For line power flow measurements, we get
= −
So, we get a +1 in location , and a −1 in location in the matrix.
2. For injection measurements, we know:
= + = − + − = 2 − −
Where bus is the bus the measurement was taken on, and buses and are buses adjacent
to bus (of course there can be any number of adjacent buses).
For our system,
=
1
12
34
[
2 −1 −1 0
1 −1 0 0
0 0 −1 1
]
This matrix, when multiplied by the state vector , should give us all of our system measurements
(usually denoted ):
=

We now need to use a seemingly unintuitive fact to complete our observability analysis. If all voltages
angles in a network were zero, we would have no power flows. That is, if = [0,0, … ,0], then =
[0,0, … ,0]. Of course, this implies that we would measure no power flows, so = [0,0,… ,0]. However,
this implication does not hold in the opposite direction. It is not necessarily true that, if all
measurements in were zero, then the system has a completely zero state. That is, if = 0, but
= ≠ 0, then our measurements have not told us all of the information about the system, and
some part of the system must not have been observed by the measurements. This is the fact we need
to use to work out if we have enough measurements in the system.

To proceed, assume that all measurements = [0,0,… ,0]. So,
= 0
⇒ (
) = 0
Hopefully, you remember that
= , the gain matrix (ignoring the standard deviations of
measurements). We can use LU factorisation of the gain matrix to allow us to determine observability.
If the upper matrix contains more than one zero pivot (that is, more than one zero on the diagonal),
then the network is not observable, since will not lead to a zero result.

By adding other measurements to the system, we can restore observability. This is something you can
explore in as much detail as you would like. Note that you must demonstrate whether your network
is observable or not through basic observability analysis, and you must recommend where to place
new measurement points to return observability to your system. How you do this can be quite open-
ended, but will need to be explained in your report. There are a number of (sometimes complicated)
methods that are available to research in literature on network observability and state estimation,
and the more sophisticated your algorithm, the more likely you are to achieve a fully observable
system with the least number of measurements  Email:51zuoyejun

@gmail.com