ESTIMATION OF CVR EFFECTIVENESS WITH AGGREGATED
LOAD MODELING
A Project
Presented to the faculty of the Department of Electrical and Electronic Engineering
California State University, Sacramento
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
Electrical and Electronic Engineering
by
Musie Tesfasilassie
FALL
2013
© 2013
Musie Tesfasilassie
ALL RIGHTS RESERVED
ii
ESTIMATION OF CVR EFFECTIVENESS WITH AGGREGATED
LOAD MODELING
A Project
by
Musie Tesfasilassie
Approved by:
__________________________________, Committee Chair
Mahyar Zarghami
__________________________________, Second Reader
Mohammad Vaziri
____________________________
Date
iii
Student: Musie Tesfasilassie
I certify that this student has met the requirements for format contained in the University
format manual, and that this project is suitable for shelving in the Library and credit is to
be awarded for the project.
__________________________, Graduate Coordinator___________________
Preetham B. Kumar
Date
Department of Electrical and Electronic Engineering
iv
Abstract
of
ESTIMATION OF CVR EFFECTIVENESS WITH AGGREGATED
LOAD MODELING
by
Musie Tesfasilassie
In order to develop an estimate of the benefits of Conservation Voltage
Reduction (CVR) in the distribution system, the composite characteristics of system loads
have been extracted from measurements of electrical quantities at the main substation.
Real and reactive power measurements at the secondary bus of the substation are used as
inputs to the parameter identification procedure based on the least square optimization
approach for finding aggregated ZIP load model parameters. This knowledge is further
used in finding a quantitative estimation approach for predicting the effectiveness of
substation transformer tap changes in reducing total power demand during different
distribution system load conditions. The proposed algorithm is implemented on the IEEE
34 bus test system and the results are demonstrated. It is shown that the method can
predict the effectiveness of CVR with acceptable accuracy.
_______________________, Committee Chair
Mahyar Zarghami
______________________
Date
v
TABLE OF CONTENTS
Page
List of Tables ........................................................................................................ vii
List of Figures ...................................................................................................... viii
Chapter
1. INTRODUCTION ...................................................................................................1
2. LOAD MODELING ................................................................................................4
3. PARAMETER ESTIMATION USING LEAST SQUARE METHOD ..................8
4. CVR EFFECTS BASED ON 𝑑𝑆/𝑑𝑉 ....................................................................10
5. SIMULATION PARAMETERS AND RESULTS ...............................................13
5.1.1. Simulation Parameters ..................................................................................13
5.1.2. Simulations of Different Scenarios and Results ...........................................16
6. CONCLUSIONS AND FUTURE CONSIDERATIONS ......................................32
Appendix. MatLab Code ........................................................................................34
References ..............................................................................................................36
vi
LIST OF TABLES
Tables
Page
1.
Simulation Data, Scenario 1, without downstream compensation ........................16
2.
Simulation Data, Scenario 1, with downstream compensation..............................19
3.
Simulation Data, Scenario 2, without downstream compensation ........................21
4.
Simulation Data, Scenario 2, with downstream compensation..............................24
5.
Simulation Data, Scenario 3, without downstream compensation ........................26
6.
Simulation Data, Scenario 3, with downstream compensation..............................29
vii
LIST OF FIGURES
Figures
Page
1.
IEEE 34-bus, 69KV/24.9 kV distribution test feeder ............................................13
2.
CVR impacts for Scenario 1 without downstream compensation .........................17
3.
Voltage profile for Scenario 1 with no downstream compensation .......................18
4.
CVR impacts for Scenario 1with downstream compensation ...............................20
5.
Voltage profile for Scenario 1with downstream compensation .............................20
6.
CVR impacts for Scenario 2 without downstream compensation .........................22
7.
Voltage profile for Scenario 2 without downstream compensation.......................23
8.
CVR impacts for Scenario 2 with downstream compensation ..............................25
9.
Voltage profile for Scenario 2 with downstream compensation ...........................25
10.
CVR impacts for Scenario 3 without downstream compensation .........................27
11.
Voltage profile for Scenario 3 without downstream compensation.......................28
12.
CVR impacts for Scenario 3 with downstream compensation ..............................30
13.
Voltage profile for Scenario 3 with downstream compensation ...........................31
viii
1
1. INTRODUTION
The introduction of smart grid technologies in the electricity supply industry and an
increasing cost of energy in today’s market have increased the desire of the electric
utilities in implementing effective and efficient demand reduction by exploring some
forms of CVR. The goal of CVR is to save energy by reducing the voltage level of the
electrical distribution network as low as possible within the ANSI residential voltage
limits (120 ± 5% V). In many cases, providing voltage to the customer in the lower part
of the ANSI C84.1 range (114 to 120 V) results in energy savings without causing any
danger or any loss of performance by end use appliances. Some of the methods which
electric utilities use to achieve the benefits of CVR are through application of voltage
regulators, capacitors and load tap changing transformers [1, 2, and 3].
Energy savings achieved from the implementation of CVR on distribution circuits are
highly dependent on system configuration and its load types. One method of modeling a
load without a thermal cycle is to use a polynomial ZIP load form. The ZIP load model is
composed of time invariant constant impedance (Z), constant current (I), and constant
power (P) elements [4, 5]. Change in power consumption resulting from reduction of
voltage depends on the composition of ZIP load parameters. Dependency of power on
voltage magnitude can be described using basic Ohm’s and Joule’s laws as follow: For
constant impedance loads such as incandescent lights, power consumption decreases in
quadratic relation with the reduction of voltage. This is seen from the power and voltage
relation |𝑆| = |𝑉|2 ⁄|𝑍|. In constant current loads, as compact fluorescent lighting, power
consumption is decreased linearly with the increase of voltage to maintain a constant
2
current at the load according to the equation |𝑆| = |𝑉| × |𝐼|. On the other hand, constant
power loads such as motors, computers, and TV sets increase power consumption when
voltage is reduced. This is because of the increase in current as a result of reduction in
voltage, which also increases the line losses given by |𝐼|2 × 𝑅𝑙𝑖𝑛𝑒 and |𝐼|2 × 𝑋𝑙𝑖𝑛𝑒
components.
Energy reduction resulting from reduction of voltage is quantified by CVR factor, which
is expressed as the ratio of percentage change in energy to percentage change in voltage
described by%∆𝐸 ⁄%∆𝑉 . Different studies show different ranges of CVR factor. A field
study conducted on 12 circuits in the Snohomish County Public Utilities found a CVR
factor of 0.34 to 1.103 [6], while CVR test conducted on 32 high voltage distribution
circuits at the Northeast Utilities revealed a 1% reduction in voltage resulting in a 1%
reduction in energy consumption at the substation low side bus [4]. A study conducted in
Bonneville Power Administration (BPA) shows a CVR factor of 0.765 and 0.991 for
residential and commercial sectors respectively [3].
The focus of this paper is on the evaluation of CVR effect by estimation of consumed
power at different voltage levels using aggregated load model parameters computed at the
secondary bus of a substation. The IEEE 34-bus distribution test system is used to show
the dependency of CVR on system loads and estimation of power consumption using
load model parameters. The approach is implemented through ZIP load model parameters
based on the least square optimization technique. The paper is organized as follows:
Section II introduces different load modeling approaches. Section III elaborates details on
3
ZIP load modeling based on the least square optimization. Section IV describes
evaluation of CVR effect from load model parameters. In section V the test circuit and
simulation results are discussed. Future recommendations and concluding remarks are
presented in section VI.
4
2. LOAD MODELING
In electrical power systems, a load is defined as a device that is connected to the system
for consuming power. A load model is defined as a set of mathematical equations which
relate both voltage magnitude and frequency with its active and reactive power
consumption [7]. Load modeling is always a difficult task to accomplish because of the
time variant features of load. The two methodologies adopted in load modeling are the
component based and the measurement based approaches. The component based load
modeling approach develops load model from information on its constituent parts. This
approach is very tedious and expensive to implement especially in large systems when
load model parameters change with time so frequently [5, 7]. The measurement based
load modeling approach uses data from field measurements to identify parameters of the
load. In this approach it is easy to update the parameters of the load modeling when the
load characteristics change. As stated in [7], load modeling practice has three steps: data
collection, load aggregation and load model validation. Both the component based and
the measurement based approaches use these three steps in load modeling practice for
steady state and dynamic study analysis. In the component based approach, the data
needed for load modeling are predefined and obtained by theoretical analyses and
laboratory measurements and once determined, they will be used by all power utilities
[8]. Different projects conducted by Electric Power Research Institute (EPRI) determined
and documented much of such data. Typical load component characteristics are
demonstrated in [9, 10]. Load composition data and load class mix data are other
information needed for the component based load modeling approach. Load composition
5
data is the fractional composition of the load by load components, and load class mix data
is the fractional composition of the bus load by load classes. Data needed for the
measurement based approach are collected by electronic measurement devices installed
in the system. These devices record voltage magnitude and frequency and active and
reactive power consumption at the point where the load is modeled. These recorded data
are used as inputs for load modeling. Once data needed for load modeling is collected
from either component constituent or from field measurements, the next step is to
develop a mathematical relationship between the voltage (magnitude and frequency) and
power at the point of aggregation. There are three different approaches to relate these
measured data for proper representation of a load. These are static, dynamic and
composite load models. A static load model describes the relationship between the bus
voltage and the load power at a given instant of time. This model is applicable for system
steady-state analysis. There are two forms of static load model, polynomial load model
also called the ZIP load model and exponential load model. The polynomial function
representation of a load may contain loads of constant impedance, constant current,
constant power or any of the combination of these types. Polynomial load model or the
ZIP model relates the voltage and power at a load bus using the equations of the form:
𝑉 2
𝑉
𝑃 = 𝑃0 (𝑍𝑝 (𝑉 ) + 𝐼𝑝 (𝑉 ) + 𝑃𝑝 )
0
0
𝑉 2
𝑉
𝑄 = 𝑄0 (𝑍𝑞 (𝑉 ) + 𝐼𝑞 (𝑉 ) + 𝑃𝑞 )
0
0
(1)
(2)
6
In (1)-(2),𝑍𝑖 , 𝐼𝑖 and 𝑃𝑖 , (𝑖 = 𝑝, 𝑞) are the constant components of impedance, current and
power for active and reactive powers, 𝑃0 and 𝑄0 are the base active and reactive powers
consumed at nominal voltage 𝑉0, and 𝑃 and 𝑄 are the total consumed active and reactive
powers at the point of interest, respectively.
In this paper the ZIP load model representation is used to represent the aggregated load at
the secondary bus of the substation transformer. The other form of static load model is
the exponential load model. This load model uses exponential functions of the form (3)
and (4) to relate voltage and power at the point of load aggregation.
𝑉 𝛼
𝑃 = 𝑃0 (𝑉 )
0
𝑉 𝛽
𝑄 = 𝑄0 (𝑉 )
0
(3)
(4)
Where 𝛼 and 𝛽 are the active and reactive power exponents of the aggregated load
respectively. 𝑃0 and 𝑄0 are the base active and reactive powers consumed at nominal
voltage 𝑉0, and 𝑃 and 𝑄 are the total consumed active and reactive powers at the point of
interest, respectively.
The dynamic load modeling uses differential and difference equations to represent a load
at any instant of time as a function of the bus voltage. This load model is used to
represent the load during small and large disturbances [7, 11]. The composite load model
is a combination of static and dynamic load models. It is represented by an equivalent
induction motor in parallel with a static load [12]. This model is used in stability studies
7
where more accurate dynamic representation of the load is required [7]. The final step in
load modeling is to test the validation of the developed mathematical model using new
field data.
8
3. PARAMETER ESTIMATION USING LEAST SQUARE METHOD
The Least Square (LS) optimization is a technique used to fit mathematical models into
observations. It is mostly used to solve unconstrained optimization problems [13]. It is
also applicable to polynomial functions of the form shown in equations (1) and (2) [14].
Application of LS optimization for solving active power load model parameters of
equation (1) can be realized by minimizing (5). A similar approach can be used for
derivation of reactive power coefficients. For ‘n’ number of measurements, (5) represents
the objective function for the load model of equation (1):
𝜆=
∑𝑛𝑖=1 (𝑍𝑝
2
𝑉𝑖 2
𝑉𝑖
𝑃𝑖
0
0
(𝑉 ) + 𝐼𝑝 (𝑉 ) + 𝑃𝑝 − (𝑃 ))
0
(5)
where 𝑉𝑖 and 𝑃𝑖 are the 𝑖 𝑡ℎ measured line to neutral voltage magnitude and the single
phase active power at the bus of interest, assuming balanced operation. In load modeling,
the objective is to find the coefficients 𝑍𝑝 , 𝐼𝑝 and 𝑃𝑝 which minimize 𝜆. This can be
achieved by setting the partial derivatives of equation (5) with respect to each of the
coefficient variables to zero as shown in equations (6) to (8).
𝑑𝜆
𝑑𝑍𝑝
𝑑𝜆
𝑑𝐼𝑝
𝑑𝜆
𝑑𝐼𝑃
2
𝑉
2
𝑉
𝑉
𝑃
= ∑𝑛𝑖=1 2 (𝑉𝑖 ) × (𝑍𝑝 (𝑉𝑖 ) + 𝐼𝑝 (𝑉𝑖 ) + 𝑃𝑝 − (𝑃 𝑖 )) = 0
0
0
𝑉
𝑉
0
2
0
𝑉
𝑃
= ∑𝑛𝑖=1 2 × 𝑉𝑖 × (𝑍𝑝 (𝑉𝑖 ) + 𝐼𝑝 (𝑉𝑖 ) + 𝑃𝑝 − (𝑃 𝑖 )) = 0
0
0
𝑉
2
0
𝑉
0
𝑃
= ∑𝑛𝑖=1 2 × (𝑍𝑝 (𝑉𝑖 ) + 𝐼𝑝 (𝑉𝑖 ) + 𝑃𝑝 − (𝑃𝑖 )) = 0
0
0
0
(6)
(7)
(8)
9
Equations (6) through (8) can be rearranged and simplified in a matrix form of (9):
∑𝑛𝑖=1 2𝑉𝑖 4
[∑𝑛𝑖=1 2𝑉𝑖 3
∑𝑛𝑖=1 2𝑉𝑖 2
∑𝑛𝑖=1 2𝑉𝑖 3
∑𝑛𝑖=1 2𝑉𝑖 2
∑𝑛𝑖=1 𝑉𝑖
∑𝑛𝑖=1 2𝑉𝑖 2
𝑍𝑝
∑𝑛𝑖=1 2𝑃𝑖 𝑉𝑖 2
∑𝑛𝑖=1 𝑉𝑖 ] × [ 𝐼𝑝 ] = [ ∑𝑛𝑖=1 2𝑃𝑖 𝑉𝑖 ]
𝑃𝑝
∑𝑛𝑖=1 2𝑃𝑖
2𝑛
(9)
From (9), values of load model parameters 𝑍𝑝 , 𝐼𝑝 and 𝑃𝑝 can be determined. Similar
equations can be derived for reactive power load model parameters as shown in (10):
∑𝑛𝑖=1 2𝑉𝑖 4
[∑𝑛𝑖=1 2𝑉𝑖 3
∑𝑛𝑖=1 2𝑉𝑖 2
∑𝑛𝑖=1 2𝑉𝑖 3
∑𝑛𝑖=1 2𝑉𝑖 2
∑𝑛𝑖=1 𝑉𝑖
∑𝑛𝑖=1 2𝑉𝑖 2
𝑍𝑞
∑𝑛𝑖=1 2𝑄𝑖 𝑉𝑖 2
∑𝑛𝑖=1 𝑉𝑖 ] × [ 𝐼𝑞 ] = [ ∑𝑛𝑖=1 2𝑄𝑖 𝑉𝑖 ] (10)
𝑃𝑞
∑𝑛𝑖=1 2𝑄𝑖
2𝑛
10
4. CVR EFFECTS BASED ON 𝒅𝑺⁄𝒅𝑽
In previous works done on CVR, the quantification of the benefits of CVR in terms of
energy savings is calculated using the ratio of percentage reduction in energy to 1%
reduction in voltage. In this paper we use the parameters of the load model found in
equations (9) and (10) to solve CVR factor as the ratio of change in total apparent power
to change in voltage. This approach for evaluation of CVR factor helps to estimate the
power consumption at an arbitrary voltage level given the initial voltage and power
values. At a given instant of time, the complex power of a bus is determined from its
active and reactive powers by:
𝑆̅ = 𝑃 + 𝑗𝑄
(11)
The magnitude of the complex power known as apparent power is given by:
𝑆 = √𝑃2 + 𝑄 2
(12)
It is clearly seen in equation (12) that the apparent power at the bus is a function of
voltage, as both active and reactive powers of the bus are functions of voltage described
by equations (1) and (2). Using the principle of derivatives, the change in total power
due to change in voltage can be solved by differentiating equation (12) with respect to the
variable voltage. This differentiation is represented in equation (13):
𝑑𝑆
𝑑𝑉
=
𝑑𝑃
𝑑𝑄
+𝑄
𝑑𝑉
𝑑𝑉
√𝑃2 +𝑄2
𝑃
(13)
11
Where
𝑑𝑆
𝑑𝑉
is the derivative of apparent power with respect to voltage, and
𝑑𝑃
𝑑𝑉
and
𝑑𝑄
𝑑𝑉
are the derivatives of active power and reactive power with respect to voltage,
respectively.
The expression for the derivatives
𝑑𝑃
𝑑𝑉
and
𝑑𝑄
𝑑𝑉
are evaluated from equations (1) and (2)
and are shown in equations (14) and (15) as:
𝑑𝑃
= 𝑃0 (
𝑑𝑉
𝑑𝑄
𝑑𝑉
2𝑍𝑝 𝑉
= 𝑄0 (
𝑉0
2𝑍𝑞 𝑉
𝑉0
𝐼𝑝
+ )
𝑉
(14)
0
𝐼𝑞
+ )
𝑉
(15)
0
By substitution of equations (3), (4), (14) and (15) into equation (13), the expression of
CVR factor can be found as shown in equation (16). In this equation, the CVR factor
𝑑𝑆⁄𝑑𝑉 is expressed by the ZIP load model parameters:
𝑉 2
𝑑𝑆
𝑑𝑉
=
2𝑍𝑝 𝑉
𝑉
𝐼𝑝
𝑉 2
𝑉
2𝑍𝑞 𝑉
𝐼𝑞
(𝑃0 2 ×(𝑍𝑝 (𝑉 ) +𝐼𝑝 (𝑉 )+𝑃𝑝 )×( 𝑉 +𝑉 ))+(𝑄0 2 ×(𝑍𝑞 (𝑉 ) +𝐼𝑞 (𝑉 )+𝑃𝑞 )×( 𝑉 +𝑉 ))
0
0
0
0
0
0
0
0
2
2
2
2
√(𝑃0 (𝑍𝑝 ( 𝑉 ) +𝐼𝑝 ( 𝑉 )+𝑃𝑝 )) +(𝑄0 (𝑍𝑞 ( 𝑉 ) +𝐼𝑞 ( 𝑉 )+𝑃𝑞 ))
𝑉0
𝑉0
𝑉0
𝑉0
(16)
Similarly the derivative (𝑑𝑆⁄𝑑𝑉) of the total apparent power (S) with respect to the
variable voltage (V) found in equation (16) can be evaluated as the ratio of change of
total power (∆𝑆) to change in voltage (∆𝑉) as shown in equation (17) :
𝑑𝑆
𝑑𝑉
=
𝑆2 −𝑆1
𝑉2 −𝑉1
(17)
12
Equating (16) and (17) and solving for 𝑆2 as shown in (18), an estimation of the total
consumed apparent power at a new voltage level can be found using existing voltage and
power values:
𝑑𝑆
𝑆2 = 𝑆1 + 𝑑𝑉 (𝑉2 − 𝑉1 )
(18)
In the experiments conducted in this paper equation (18) is used to estimate the effect of
CVR (implemented through transformer tap changer) in reducing the total power
consumed at the secondary bus of the substation transformer.
13
5. SIMULATION PARAMETERS AND RESULTS
5.1 Simulation Parameters
The IEEE 34-bus, 24.9 kV test feeder of Figure 1 with single-phase and three-phase
laterals feeding different spot and distributed loads was used for simulations using the
utility grade computer program CYMEDIST. The “balanced voltage drop” feature of
CYMEDIST which divides the total load equally between the three phases was adopted
for simulations.
32
31
15
28
14
1
22
10
2
3
4
6
7
8
11
24
12
26
23
21
25
9
29
34
20
27
33
5
30
19
16
13
18
17
Figure 1. IEEE 34-bus, 69/24.9 kV distribution test feeder.
The system consists of 6 spot and 19 distributed loads of different values with a total of
1769KW at nominal voltage. Each load in the system is represented by a ZIP model.
Other than the 2500KVA, 69/24.9 kV main substation transformer, there is a 500KVA,
24.9/4.16 kV step down connected between buses 20 and 33. The tap changer on the
primary side of the substation transformer is used as a means of voltage control at the
secondary bus of the substation where the load modeling data is collected. There are two
14
capacitors of rating 150kVAr/phase and 100kVAr/phase installed in the system at buses
32 and 28, respectively. There are also two voltage regulators of terminal voltage output
value of 122V on a base of 120V connected between buses 7 and 8 and buses 19 and 20.
For modeling and estimation of the CVR effects, three distinct scenarios have been
conducted. In each scenario, the model of each load is changed to constant impedance
(Z), constant current (I) and constant power (PQ) components based on the following
compositions:
1. 70% of the total active power in the system (1238KW) represented by constant
impedance loads (Z), 20% of the total active power (354KW) by constant power
loads (PQ) and the rest 10% (177KW) by constant current loads (I).
2. 70% of the total active power demand in the system (1238KW) represented by
constant power loads (PQ), 20% of the total active power demand (354KW) by
constant current loads (I) and the rest 10% (177KW) by constant impedance loads
(Z).
3. 70% of the total active power in the system (1238KW) represented by constant
current loads (I), 20% of the total active power demand (354KW) by constant
impedance loads (Z) and the rest 10% of the total demand (177KW) by constant
power loads (PQ).
In each experiment, it is assumed that the load and its model will remain unchanged,
representing a period in which load profiles have little variations. Each of the above
scenarios is simulated twice, with and without the presence of capacitors and voltage
15
regulators in order to observe the effect of voltage regulating devices on the load
modeling practice and CVR effect. In the load modeling practice, data needed for
determination of load parameters are collected by simulating the system at various
substation primary voltages changing from 72.45KV (1.05pu) to 65.55KV (0.95pu) in
steps of 0.69KV (0.01pu). At each primary voltage, a balanced load flow analysis is
performed, and line to neutral voltage and single phase active and reactive powers at the
secondary bus of the substation are gathered. The collected data are then fed to a
MATLAB code to find ZIP load model parameters using LS approach.
In order to estimate the change in total power consumption at the secondary of the
substation due to controlled voltage change, the tap setting of the substation transformer
is manually changed while the primary bus voltage is kept at 69kV (1pu). By considering
the results of load flow at 100% tap as initial values, power consumption in each test is
estimated at a different tap setting using equation (18) and the result is compared with the
actual measured value using percentage error which is defined as the percentage of
deviation of apparent power over its actual measured value as seen in equation (19).
𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒−𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑉𝑎𝑙𝑢𝑒
𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟(%) = (
𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑉𝑎𝑙𝑢𝑒
) × 100
(19)
In this paper, measured value refers to the power flow simulation results and estimated
value refers to the value obtained from equation (18) after substitution of parametric
values.
16
5.2 Simulations of Different Scenarios and Results
Scenario 1: System with load composition of constant Z = 70%, constant PQ = 20% and
constant I = 10%.
A- Without capacitors and voltage regulators (with no downstream compensation)
In this case, capacitors and voltage regulators are disconnected from the system. Data
measured at the secondary bus of the substation transformer for different voltage values
at the primary side is shown in Table 1 below.
Substation primary
voltage
(pu)
1.05
1.04
1.03
1.02
1.01
1.00
0.99
0.98
0.97
0.96
0.95
Line to line
Voltage (kV)
72.45
71.76
71.07
70.38
69.69
69.00
68.31
67.62
66.93
66.24
65.65
Substation secondary
bus data
Line to neutral
Voltage (kV)
14.649
14.509
14.369
14.228
14.088
13.948
13.807
13.667
13.526
13.386
13.245
Single-phase
active power (kW)
580.440
570.236
560.128
550.116
540.199
530.380
520.656
511.028
501.497
492.061
482.722
Single-phase
reactive power (kVAr)
242.854
238.707
234.599
230.531
226.501
222.509
218.557
214.644
210.769
206.934
203.138
Table 1. Simulation Data, Scenario 1, without downstream compensation.
When the data in columns 3 to 5 of Table 1 are fed into MATLAB code shown in the
appendix to evaluate aggregated load parameters based on equations (9) and (10), it
17
results in the following active and reactive aggregated load parameters at the secondary
bus of the substation:
𝑍𝑝 = 0.903424, 𝐼𝑝 = 0.031806, 𝑃𝑝 = 0.06477
𝑍𝑞 = 0.873248, 𝐼𝑞 = 0.037573, 𝑃𝑞 = 0.089179
When the load model parameters are substituted in equation (16), a CVR effect of
75.170587 kVA/kV is obtained. Estimated power from equation (18) and simulated
power at the secondary bus of the substation transformer for this scenario is shown in
Figure 2. As seen, voltage reduction has resulted in reduced power demand. In this case,
maximum estimated error using equation (19) is around 0.23% which shows a good
approximation.
640
630
Max Error = -0.228341%
620
S(KVA)
610
600
590
580
570
560
550
0.95
Measured KVA
Estimated KVA
0.96
0.97
0.98
0.99
V(pu)
1
1.01
1.02
1.03
Figure 2. CVR impacts for Scenario 1 without downstream compensation.
18
Voltage profile of the system shown in Figure 3 for this case is monotonically decreasing
from the substation since no reactive power compensation has been implemented.
1.04
1.02
1
V-bus(pu)
0.98
0.96
0.94
tap-102
tap-101
tap-100
tap-99
tap-98
tap-97
tap-96
tap-95
0.92
0.9
0.88
0.86
0.84
1
3
5
7
9
11 13
15 17 19
bus
21 23 25 27
29 31 3334
Figure 3. Voltage profile for Scenario 1 with no downstream compensation.
B- With capacitors and voltage regulators included (with downstream compensation)
In this case, capacitors and voltage regulators are included in simulations to determine
how their operation may impact ZIP load parameters and CVR effect. Results of the
simulation with different substation primary voltages are shown in Table 2:
19
Substation primary
voltage
Line to line
(pu) voltage (kV)
1.05
72.45
1.04
71.76
1.03
71.07
1.02
70.38
1.01
69.69
1.00
69.00
0.99
68.31
0.98
67.62
0.97
66.93
0.96
66.24
0.95
65.65
Line to neutral
Voltage (kV)
14.917
14.768
14.619
14.471
14.323
14.174
14.025
13.877
13.728
13.579
13.432
Substation secondary
bus data
Single-phase
Single-phase reactive
active power (kW)
power (kVAr)
602.052
43.012
603.040
44.659
603.852
46.277
605.658
47.807
607.196
49.298
607.429
50.819
608.487
52.232
609.269
53.600
609.773
54.924
609.999
56.203
609.979
56.523
Table 2. Simulation Data, Scenario 1, with downstream compensation.
The aggregated ZIP load model parameters in this case are calculated as:
𝑍𝑝 = -1.332001, 𝐼𝑝 = 2.502586, 𝑃𝑝 = -0.176076
𝑍𝑞 = -5.312904, 𝐼𝑞 = 7.676377, 𝑃𝑞 = -1.376265
When the load model parameters are substituted in equation (16), a CVR factor of 6.04619 kVA/kV is found. Estimated and simulated voltages for this scenario are shown
in Figure 4. As seen, reduced voltage has not resulted in reduced power demand. Voltage
profile of the system in this case is not monotonically decreasing, because of the effect of
voltage regulators and capacitors. This case clearly shows that voltage reduction may not
result in demand reduction at all times. Careful attention must be paid when compensator
action is considered on a distribution feeder. Results also show a good estimation of
power demand with a maximum error of 0.18%.
20
614
Max Error = -0.178712%
613
612
S(KVA)
611
610
609
608
607
Measured KVA
Estimated KVA
606
0.95
0.96
0.97
0.98
0.99
V(pu)
1
1.01
1.02
Figure 4. CVR impacts for Scenario 1 with downstream compensation.
1.03
1.02
1.01
V-bus(pu)
1
0.99
tap-102
tap-102
tap-101
tap-100
tap-99
tap-98
tap-97
0.98
0.97
0.96
0.95
0.94
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 3334
bus
Figure 5. Voltage profile for Scenario 1 with downstream compensation.
21
Scenario 2: Load composition of constant PQ = 70%, constant I = 20% and constant Z =
10%.
A- Without capacitors and voltage regulators
In this case, simulation results at the substation secondary bus are shown in Table 3.
Substation primary
voltage
Line to line
(pu) Voltage (kV)
1.05
72.45
1.04
71.76
1.03
71.07
1.02
70.38
1.01
69.69
1.00
69.00
0.99
68.31
0.98
67.62
0.97
66.93
0.96
66.24
0.95
65.65
Line to neutral
voltage (kV)
14.616
14.463
14.309
14.156
14.002
13.848
13.693
13.538
13.383
13.228
13.072
Substation secondary
bus data
Single-phase
Single-phase reactive
active power (kW)
power (kVAr)
607.710
262.105
607.360
265.043
607.028
267.989
606.719
270.950
606.432
273.926
606.169
276.921
605.933
279.936
605.724
282.975
605.544
286.042
605.395
289.139
605.279
292.270
Table 3. Simulation Data, Scenario 2, without downstream compensation.
ZIP load parameters in this case are evaluated as:
𝑍𝑝 = 0.176424, 𝐼𝑝 = -0.302330, 𝑃𝑝 = 1.125891
𝑍𝑞 = 0.198801, 𝐼𝑞 = -1.435164, 𝑃𝑞 = 2.236303.
CVR factor in this case has been evaluated as -6.66916 kVA/kV. Estimated and
simulated results in Figure 6 show that reducing voltage has resulted in demand increase,
22
since the majority of loads in the system are of constant power type. As seen in Figure 7,
voltage profile of the system is monotonically decreasing in this case.
668
Measured KVA
Estimated KVA
Max Error = -0.086513%
667
S(KVA)
666
665
664
663
662
661
0.95
0.96
0.97
0.98
0.99
V(pu)
1
1.01
1.02
Figure 6. CVR impacts for Scenario 2 without downstream compensation.
23
1.02
1
V-bus(pu)
0.98
0.96
0.94
0.92
tap-101
tap-100
tap-99
tap-98
tap-97
tap-96
tap-95
0.9
0.88
0.86
0.84
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 3334
bus
Figure 7. Voltage profile for Scenario 2 without downstream compensation.
B- With capacitors and voltage regulators included
Power flow results in this case are shown in Table 4.ZIP load parameters in this case are
calculated as:
𝑍𝑝 = -0.021134, 𝐼𝑝 = 0.076626, 𝑃𝑝 = 0.944355
𝑍𝑞 = 16.164164, 𝐼𝑞 = -34.094921, 𝑃𝑞 = 18.968708
Based on these results, CVR factor at the secondary bus of the substation is found as
0.911196 kVA/kV.
24
Substation primary
voltage
Line to line
(pu) voltage (kV)
1.05
72.45
1.04
71.76
1.03
71.07
1.02
70.38
1.01
69.69
1.00
69.00
0.99
68.31
0.98
67.62
0.97
66.93
0.96
66.24
0.95
65.65
Line to neutral
voltage (kV)
14.912
14.765
14.618
14.472
14.326
14.178
14.031
13.884
13.732
13.584
13.436
Substation secondary
bus data
Single-phase
Single-phase
active power (kW)
reactive power (kVAr)
606.341
45.946
606.158
46.517
605.981
47.199
605.770
47.181
605.558
47.318
605.392
48.338
605.191
48.767
604.993
49.364
604.638
53.264
604.447
54.215
604.260
55.341
Table 4. Simulation Data, Scenario 2, with downstream compensation.
Estimated and simulated results in Figure 8 show that reducing voltage has resulted in
demand reduction. System voltage profile in Figure 9 indicates that because of reactive
power compensation, voltage reduction at the main substation has resulted in total power
demand reduction.
25
608
Max Error = -0.026222%
607.8
607.4
607.2
607
Measured KVA
Estimated KVA
606.8
0.95
0.96
0.97
0.98
0.99
V(pu)
1
1.01
1.02
Figure 8. CVR impacts for Scenario 2 with downstream compensation.
1.03
1.02
1.01
1
V-bus(pu)
S(KVA)
607.6
0.99
tap-103
tap-102
tap-101
tap-100
tap-99
tap-98
tap-97
0.98
0.97
0.96
0.95
0.94
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 3334
bus
Figure 9. Voltage profile for Scenario 2 with downstream compensation.
26
Scenario 3: Load composition of constant I = 70%, constant Z = 20% and constant PQ =
10%
A- Without capacitors and voltage regulators
In this case, simulation results are shown in Table 5.
Substation primary
voltage
Line to line
(pu) voltage (kV)
1.05
72.45
1.04
71.76
1.03
71.07
1.02
70.38
1.01
69.69
1.00
69.00
0.99
68.31
0.98
67.62
0.97
66.93
0.96
66.24
0.95
65.65
Line to neutral
voltage (kV)
14.63628
14.49071
14.34512
14.19953
14.05392
13.90831
13.76268
13.61704
13.47139
13.32572
13.18005
Substation secondary
bus data
Single-phase
Single-phase
active power (kW) reactive power (kVAr)
590.9956
250.4176
584.836
249.1753
578.6835
247.9126
572.5381
246.6294
566.3997
245.3258
560.2684
244.0018
554.1441
242.6572
548.0268
241.2922
541.9165
239.9068
535.8132
238.5008
529.7169
237.0743
Table 5. Simulation Data, Scenario 3, without downstream compensation.
The aggregate load model parameters using equations (7) and (8) are found as:
𝑍𝑝 = 0.063112, 𝐼𝑝 = 0.920919, 𝑃𝑝 = 0.015968
𝑍𝑞 = -0.399800, 𝐼𝑞 =1.304311, 𝑃𝑞 =0.095489
Equation (12) together with the above load model parameters results in a CVR effect of
42.238887 kVA/kV. Estimated and measured powers shown in Figure 10 indicate that
voltage reduction results in load reduction in this case.
27
645
Max Error = -0.0028%
640
635
S(KVA)
630
625
620
615
610
605
0.95
Measured KVA
Estimated KVA
0.96
0.97
0.98
0.99
V(pu)
1
1.01
1.02
1.03
Figure 10. CVR impacts for Scenario 3 without downstream compensation.
The voltage profile of the system in this case decreases monotonically starting from the
substation as shown in Figure 11, since no reactive power compensation has been
implemented.
28
1.05
1.03
1.01
V-bus(pu)
0.99
0.97
0.95
0.93
tap-101
tap-100
tap-99
tap-98
tap-97
tap-96
tap-95
0.91
0.89
0.87
0.85
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 3334
bus
Figure 11. Voltage profile for Scenario 3 without downstream compensation.
B- With capacitors and voltage regulators included
Power flow results in this case are shown in Table 6.
29
Substation primary
voltage
Line to line
(pu) voltage (kV)
1.05
72.45
1.04
71.76
1.03
71.07
1.02
70.38
1.01
69.69
1.00
69.00
0.99
68.31
0.98
67.62
0.97
66.93
0.96
66.24
0.95
65.65
Line to neutral
voltage (kV)
14.915
14.767
14.619
14.471
14.323
14.175
14.027
13.878
13.729
13.581
13.432
Substation secondary
bus data
Single-phase
Single-phase
active power (kW) reactive power (kVAr)
603.106
43.759
603.987
45.167
604.757
46.597
606.029
47.653
607.136
48.748
607.557
50.259
608.377
51.426
609.029
52.636
609.515
53.889
609.832
55.184
609.979
56.523
Table 6. Simulation Data, Scenario 3, with downstream compensation.
The load model parameters evaluated from the above data are:
𝑍𝑝 = -0.896215, 𝐼𝑝 = 1.658901, 𝑃𝑝 = 0.233997
𝑍𝑞 = -0.108687, 𝐼𝑞 = -2.349386, 𝑃𝑞 = 3.466025
CVR effect in this case is -5.276863KVA/KV. Figure 12 shows estimated and measured
powers at different secondary voltage values. As seen in Figure 12, power consumption
increases with the reduction of voltage.
30
613
Measured KVA
Estimated KVA
Max Error = -0.178712%
612
S(KVA)
611
610
609
608
607
0.95
0.96
0.97
0.98
0.99
V(pu)
1
1.01
1.02
Figure 12. CVR impacts for Scenario 3 with downstream compensation.
The voltage profile of the system as seen in figure 13 is not monotonically decreasing,
because of the effect of voltage regulators and capacitors in the system.
31
1.03
1.02
1.01
V-bus(pu)
1
0.99
tap-103
tap-102
tap-101
tap-100
tap-99
tap-97
tap-96
0.98
0.97
0.96
0.95
0.94
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 3334
bus
Figure 13. Voltage profile for Scenario 3 with downstream compensation.
32
6. CONCLUSIONS AND FUTURE CONSIDERATIONS
Utility companies supply power to the end use customer with a voltage level defined by
the ANSI C84.1 standards. The standard voltage defined for the end use voltage level is
120 ± 5% V (114 to 120 V on a 120 volts base) in USA. Utilities practice principle of
CVR to conserve energy and minimize losses by operating the end-user load on the lower
half of the ANSI standard without exposing customers to unacceptable under-voltage
conditions. Reduction of voltage may reduce or increase total power consumption
depending on the end-user load type and local reactive power compensation. In this
paper, it has been shown that effectiveness of CVR in reducing total power demand can
be approximated using an aggregated load model viewed from a point of interest, such as
the main substation.
This paper has discussed the estimation of the total power consumption by finding the
ZIP load model parameters using the least square optimization approach. The IEEE 34bus distribution test feeder has been used to conduct various experiments for different
loading conditions. For each load composition in the system, two distinct scenarios have
been simulated, with and without the presence of capacitors and voltage regulators in the
system, to see the effect of voltage regulating devices in the load modeling and power
demand estimation. As can be seen from the results, total power demand can be
accurately estimated using CVR effect. It has been shown that when composition of the
aggregated load is dominated by constant impedance or constant current loads, CVR is
most effective. However, an important observation is that using local reactive power
compensation downstream of the main substation can reverse the effect of CVR in these
33
cases. On the other hand, it was observed that when aggregated load is dominated by
constant power loads, voltage reduction may not result in demand reduction. However,
with local reactive power compensation in such cases, it is possible to reduce total
demand using CVR.
The approach of identification of aggregated load model parameters and estimation of
power consumption explained in this paper is based on manual changes of voltage at the
main substation using tap-changing transformer. Moreover, it has been assumed that
during each experiment, the load in the system remains unchanged. In practice, however,
loads change continuously with changes in temperature, wind speed, cloud cover,
humidity and human action [15]. For improvement of this work in the future, it is
recommended to incorporate more sophisticated load modeling approaches, which
include natural variations of the load in the process of identification. Moreover, impacts
of distributed generations such as renewable energy sources in the CVR effect need to be
investigated.
34
Appendix
MatLab Code
clear all
clc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
LData = 'Book1.xls'; %%excel sheet which holds data from power flow result.
A = 1;
fprintf('--------------------------------------------------------\n');
P = xlsread(LData,a);
V1 = (P(:,3))';
P1 = (P(:,4))';
Q1 = (P(:,5))';
%%% input the nominal values (V,P and Q) at bus 1 from the measured data
V01 = input(prompt); %% nominal voltage in the system
P01 = input(NomialPower); %% nominal real power in the system
Q01 = input(NomianlReaPower); %%% nominal reactive power in the system
Vmat1 = [sum(2*((V1/V01).^4)) sum(2*((V1/V01).^3)) sum(2*((V1/V01).^2))
35
sum(2*((V1/V01).^3)) sum(2*((V1/V01).^2)) sum(2*(V1/V01))
sum(2*((V1/V01).^2)) sum(2*(V1/V01))
2*length(V1)];
% V matrix for the
%% least sqr method
Pmat1 = [sum(2*(P1/P01).*((V1/V01).^2))
sum(2*(P1/P01).*(V1/V01))
sum(2*(P1/P01))];
% P matrix for the least sqr method
Qmat1 = [sum(2*(Q1/Q01).*((V1/V01).^2))
sum(2*(Q1/Q01).*(V1/V01))
sum(2*(Q1/Q01))];
ZIP1p = (Vmat1^-1)*Pmat1;
% Q matrix for the least sqr method
%ZIP load components for real power consumption
%%% from equation 9
ZIP1q = (Vmat1^-1)*Qmat1; %% ZIP load components for reactive power
%%consumption from equation 10
fprintf('\nZp1 = %f Ip1 = %f Pp1 = %f \n',ZIP1p(1),ZIP1p(2),ZIP1p(3));
fprintf('Zq1 = %f Iq1 = %f Pq1 = %f\n',ZIP1q(1),ZIP1q(2),ZIP1q(3));
36
References
[1] Triplett, J.M.; Kufel, S.A., "Implementing CVR through voltage regulator LDC
settings," Rural Electric Power Conference (REPC), 2012 IEEE , vol., no., pp.B21,B2-5, 15-17 April 2012
[2] Wilson, T.L., "Energy conservation with voltage reduction-fact or fantasy," Rural
Electric Power Conference, 2002. 2002 IEEE , vol., no., pp.C3,C3_6, 2002
[3] De Steese, J. G.; Merrick, S. B.; Kennedy, B.W., "Estimating methodology for a large
regional application of conservation voltage reduction," Power Systems, IEEE
Transactions on , vol.5, no.3, pp.862,870, Aug 1990
[4] Schneider, Kevin P., Jason C. Fuller, Francis K. Tuffner, and Ruchi Singh.
Information Bridge: DOE Scientific and Technical Information. Proc. of Evaluation
of Conservation Voltage Reduction (CVR) on a National Level. N.p., 29 Sept. 2010.
[5] Shi, J.H.; He Renmu, "Measurement-based load modeling-model structure," Power
Tech Conference Proceedings, 2003 IEEE Bologna , vol.2, no., pp.5 pp. Vol.2,, 23-26
June 2003
[6] Kennedy, B.W.; Fletcher, R.H., "Conservation voltage reduction (CVR) at
Snohomish County PUD,"
Power Systems, IEEE Transactions on , vol.6, no.3,
pp.986,998, Aug 1991
[7] Jia Hou; Zhao Xu; Zhao-Yang Dong, "Load modeling practice in a smart grid
environment," Electric Utility Deregulation and Restructuring and
Power
Technologies (DRPT), 2011 4th International Conference on , vol., no., pp.7,13, 6-9
July 2011
37
[8] Ribeiro J. R., F. J. Lange, "A New Aggregation Method for Determining Composite
Load Characteristics," IEEE Trans. PAS-101, no.8, pp. 2869-75, Aug. 1982.
[9] Concordia C. , S. Ihara. "Load Representation in Power System Stability Studies,"
IEEE Trans. PAS-101, No. 4, pp. 969-77, Apr. 1982.
[10]
IEEE Task Force, “Standard Load Models for Power Flow and Dynamic
Performance Simulations,” IEEE Trans. Power Systems, Vol. 10, No. 3, August
1995.
[11]
Stojanovic, D., L. Korunovic, and J. Milanovic. "Dynamic Load Modelling Based
on Measurements in Medium Voltage Distribution Network." Electric Power Systems
Research 78.2 (2008): 228-38. Print.
[12]
Ju, P.; Wu, F.; Shao, Z.-Y.; Zhang, X. -P; Fu, H.-J.; Zhang, P.-F.; He, N.-Q.;
Han, J.-D., "Composite load models based on field measurements and their
applications in dynamic analysis," Generation, Transmission & Distribution, IET ,
vol.1, no.5, pp.724,730, September 2007
[13]
Gill, P.E. and W. Murray: Algorithms for the solution of the nonlinear least-
square problems, SIAM J. Num. Anal. Vol. 15(1978) pp. 977-992
[14]
Sadeghi, M.; Sarvi, G.A., "Determination of ZIP parameters with least squares
optimization method," Electrical Power & Energy Conference (EPEC), 2009 IEEE ,
vol., no., pp.1,6, 22-23 Oct. 2009
38
[15]
Asber, D.; Lefebvre, S.; Saad, M.; Desbiens, C., "Modeling of Distribution Loads
for Short and Medium-Term Load Forecasting," Power Engineering Society General
Meeting, 2007. IEEE , vol., no., pp.1,5, 24-28 June 2007