04-09-2014, 11:19 AM
MODELING POWER SYSTEM LOAD USING INTELLIGENT METHODS
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Abstract
Modern power systems are integrated, complex, dynamic systems. Due to the
complexity, power system operation and control need to be analyzed using numerical
simulation. The load model is one of the least known models among the many components in
the power system operation. The two different load models are the static and dynamic models.
The ZIP load model has been extensively studied. This has widely applied to composite
load models that could maintain constant impedance, constant current, and/or constant power. In
this work, various Neural Networks algorithms and fuzzy logic have been used to obtain these
ZIP load model coefficients for determining the percentage of constant impedance, current, or
power for the various load buses. The inputs are a combination of voltage, voltage change, and
power change, or voltage and power, and the outputs consist of the ZIP load model coefficients
for determining the type and the percentage of load at the bus. The trained model is used to
predict the type and percentage of constant load at other buses using simulated transient data
from the 16-generator system. A small study was also done using a dynamic induction machine
model in addition to the ZIP load model. As expected, the results show that the dynamic model
is more difficult to determine than the static model.
Introduction and Motivation
On August 14, 2003, a blackout took place in the North American Eastern
Interconnection that included most of New York State, parts of Pennsylvania, Ohio, Michigan,
and Ontario, Canada. About 63 GW of load was interrupted. This magnitude equals
approximately 11% of the total load distributed in the Eastern Interconnection of the North
American system. Another important discovery was that there were significant reactive power
supply problems in the states of Indiana and Ohio prior to noon. The first important event was
the outage that took place in First Energy’s Eastlake unit 5 generator as the area was generating
high levels of reactive power. As a result, the Eastlake unit 5 voltage regulator tripped because
of over-excitation.
Due to the cascading loss of major tie lines in Ohio and Michigan, a huge 3700 MW
reverse power flow was serving load in the Ohio and Michigan system and caused heavy loading
on the transmission around the region. In the end, this whole series of events resulted in a
cascading outage of several hundred lines and generators tripped in the entire region.
The primary causes were summarized as inadequate understanding of the system,
inadequate level of situation awareness, inadequate level of vegetation management (tree
trimming), and an inadequate level of support from the reliability coordinator. The figure for the
August 14, 2003 cascading outage is shown below.
Objective of the Research
Load modeling is not an easy task in a complex power system. A load bus representation
in stability research consists of a combination of devices including fluorescent and incandescent
lamps, refrigerators, heaters, compressors, motors, furnaces, and so on. The exact components of
a load are very hard to describe mathematically or physically. The composition of the load will
also change during the day and season, as well as with the weather conditions and the state of the
economy. There are virtually millions of components in the total load supplied by the power
systems. Hence, it becomes quite impractical to display all load components in a load model.
To effectively study the load representation in a power system, we therefore really need to have a
simplified model [3]. This thesis will describe simple load modeling concepts, load composition
and characteristics as well as the obtaining of load model parameters.
Overview of Research
This research used various intelligent techniques to do a load modeling. The two
preliminary work categories included using pseudo inverse and manual calculations to find load
parameters. The later sections used various techniques including Levenberg-Marqauardt
algorithm, Widow-Hoff backpropagation, Default Scaled Conjugate gradient Algorithm,
Adaptive-Neural Fuzzy Inference Systems (ANFIS), and traditional neural networks method to
find the parameters of the load model both in static and dynamic models. The objectives and
approaches to achieve the goals are outlined as below.
Simple Modeling:
Organization of Thesis
The structure of the thesis is outlined as follows.
This chapter describes the power system load and the power system failure or collapse in
recent years. Also, it gives the motivation and the need for the work and research.
Chapter 2 discusses the background of load modeling. The recent study and research
done by others on load modeling are reviewed. The reviews of voltage stability aspects are
described.
Chapter 3 talks about the problems and the preparation for this research. It explains the
models and methods used at the early stage of the research and the shortcomings for these early
experiments. Test cases are shown to prepare for this early research. It introduces different
methods to solve load models. ZIP model parameters and various other forms of representation
are introduced. Methods including pseudo-inverse, manual equation methods and inverse matrix
methods are described. The advantages and disadvantages of these methods will be discussed.
Voltage and Load Stability
The constant change in the electricity industry creates a new feature of our power
systems. It is represented by complex interconnections, and the applying of a large variety of
controllers for improving the system operation and the utilizing of available sources.
Furthermore, the deregulation also causes the interconnected power network to be more
complex. Therefore, the need for power networks to understand channels for the transfer of
electricity from points of production to points of consumption is crucial. This process depends
on a competitive system and time varying factors. The complexity of the system, the nature of
the dynamics that cause it and the external factors interfering simultaneously require extra care,
in order to maintain a suitably operated power system. The system must supply high reliability
at minimum cost and ensure the smallest impact on the natural environment. To avoid
inconvenience to customers and technical problems which lead to higher costs, the system needs
to handle the frequent variations in active and reactive load. High levels of system security,
availability of “spinning” reserve of active and reactive power, high quality in the design of the
system components and availability of different paths for the delivery of the energy to the
customers are very important [4]. The load representation in these stability studies is discussed
later on in this chapter.
History of Load Modeling
As the current trend shows, load modeling has gained interest as the power system load
becomes the new area of research within power system stability. A couple of studies, [5 and 6]
have demonstrated the key effect of load representation in voltage stability studies. Because of
that, there is a need to find more accurate load models than those already used traditional ones
(e.g. all constant impedance or all constant power).
As voltage collapses only took several minutes in the past “real world” cases, the older
load modeling work was focused on induction machines, critical in the range of some seconds
after a disturbance. The load response was taken as a function of voltage [7]. The use of
dynamic load models has become increasingly popular compared to the static load models.
Although knowledge has been acquired from power system load in the recently years, it is one of
the most difficult and unknown areas of study in the midst of the power system models. This is
because of the diverse and complex load components, the high distribution and variation during
the time of day and year, weather, and the lack of information for the load. The new techniques
for the load modeling will result in better understanding of the load and better representation of
the load in simulations of the system. This will help to have a positive impact for the control,
operation, and reliability of the power system. The accurate load model and a real-time
monitoring application will help to introduce more competiveness for the electric industry and
contribute to the development of smart grid information structure [8].
The Structure of Load and Load ModeI
The mathematical representation of the relationship between a bus voltage (magnitude
and frequency) and the power (active and reactive) or current flowing into the bus load is called
a load model [9]. It is important for the design, planning, and operation of a power system.
Since the load parameters are usually non-linear, it is a challenging problem to describe the
dynamic characteristics of the load.
As discussed previously, load models can be constructed based on two different
approaches. One approach is measuring the voltage and frequency sensitivity of the active and
reactive powers at the substation or load bus. The second approach constructs a composite load
model for a given substation or load bus, according to the mix of load classes at the substation
INTELLIGENT TECHNIQUES FOR STATIC LOAD MODELS
As briefly touched on in the last section, the conventional matrix calculations do not
work too well for power system load parameter identification. Other techniques need to be
sought to solve the problems. The main idea here is to find the parameters p1, p2, p3, q1, q2, q3
that will form the components of the load model. The general search and use of load parameters
are shown below.
Simple parameter identification training
In order for the training model to work well, we need to have a set of rules for the
training and testing. The trained model should be able to predict the parameters for itself if the
inputs are given. Training and validation need to be done on the same system making the
training model legitimate and useful. For instance, a set of data is used to train the model, and
the rest of the set of data is used to validate and to observe the mean square error between real
and simulated outputs. Consequently, the trained model should be applicable to the other load
buses in other parts of the power systems. The trained model is useful if it can be used to predict
the unknown parameters for the other load buses based on their values of v, P, and Q. Since
compared to the other inputs, the frequency had less effect on the system; we neglect this
component for simplifying our study in this thesis.
Widow-Hoff Backpropagation Method
In reference [44], the author used Widow-Hoff delta learning rule with multiple-layer
networks and non-linear transfer functions are used in this Matlab backpropagation method. A
gradient descent algorithm where the network weights are moved along the negative of the
gradient of the function is the standard backpropagation. Inputs are applied to the network, the
outputs are calculated, and the resulting error is used to adjust the weights in a back to front type
order. The general structure is shown below in Figure 4.12. The backpropagation usually uses
MSE to evaluate the real outputs and the generated outputs. The difference is recorded and will
be used to refine the backward calculation until the real and generated results match closely.
Generally the rule of thumb is the more hidden neurons and the more layers, the better the
results. However, in a very big training set, more layers and hidden neurons will also greatly
delay the computational training time. Figure 4.12 below shows a diagram of a Widow-Hoff
backpropagation method.
Analyze Strategies and Methods with Best Training Approach
In this section, we trained the data from selected buses (assumed to be the known buses)
with different training methods and strategies. The different training methods are described in a
later part of this section. The training strategies described here involve constructing the model
by selecting data from various combinations of buses from Table 4.7 on the next page for
training. With the specified strategy and method, the weights and models obtained from the
training will be used to test and predict the data (load parameters p1, p2, p3, q1, q2, and q3) from the
unselected buses (assumed to be the unknown buses) as well as the known buses. The mean
square errors between the simulated data and the actual data were recorded from ten trials in each
method and strategy. In this Section 4.4, only the results from the best trials were recorded and
used for comparison between the effectiveness of each strategy and method. Parameters from
these methods, especially ANFIS method were optimized by hand. In ANFIS method, the
member function and epoch numbers were also adjusted in order to train the data more
accurately and with an allowable reasonable time. Section 4.5 later on will do a slightly different
comparison.
Conclusions
In this thesis, we discussed ways to solve parameter identification problems. For
instance, the simple power system was developed to work with mathematical calculations and
ZIP load model verification. Although pseudo inverse and linear programming will solve for the
parameters, the parameters will have infeasible solutions that do not represent the percentage of
constant power, constant current and constant impedance. As a result, intelligent techniques
were used to train intelligent systems that will be used to determine the models for loads that do
not have information about their parameters.
Several intelligent methods were used in this research, included:
Levenberg-Marquardt
Widow-Hoff Backpropagation
ANFIS (or Adaptive Network-Based Fuzzy Inference System)
Default Scaled Conjugate gradient
A series of combined strategies were used to train and test the load buses as well. These
strategies are trained on two main fault conditions. Namely load buses at fault 41-42 and fault
44-43. The buses that were trained are listed below with their symbol of representation.
Single bus training: A1(37), A2(41), A3(42), A4(52), A5(36), A6(44), A7(43),
and A8(51).
Double bus training: B1(41, 42), B2(44, 43), B3(37,41), B4(36,44), B5(37,42),
B6(36,43), B7(41,52), and B8(44, 51).
Triple bus training: C1(37, 41, 42), C2(36, 44, 43), C3(41, 42, 52), and C4(44, 43,
51).
Quadruple bus training: D1(36, 41, 42, 52) and D2(36, 44, 43, 51).
Mixed bus training: E1(41,42,44,43), E2(37, 52, 36, 51), E3(37,41,36,43), and
E4(42,52, 44, 51).