Composite Neural Network Load Models for Power
System Stability Analysis
Ali Keyhani, Fellow, IEEE, Wenzhe Lu, Student Member, IEEE, Gerald T. Heydt, Fellow, IEEE
Abstract — Proper load models are essential to power system
stability analysis. This paper proposes a methodology for the
development of neural network (NN) based composite load mod-
els for power system stability analysis. A two-step modeling pro-
cedure is proposed. First knowledge is acquired from a test bed
of power systems based on detail load models of a bus to the dis-
tribution level. Then, the test bed data is used to develop a com-
posite NN model. The developed NN model is updated based on
measurements. A case study on a power inverter controling an
induction motor load is presented.
Index Terms — Artificial neural networks, composite load model-
ing, power systems, stability analysis.
N power system stability analysis, all power system compo-
nents are represented by their models. Generally, detailed
data about components such as generators, transformers, and
transmission lines are available, and accurate models can be
obtained for them. However, corresponding data for individual
loads are not always available, which makes the modeling of
loads an important area of research. Increasingly nonlinear
dynamic loads have been connected into power systems; such
as variable speed drives, robotic factories and power electron-
ics loads. This adds to the complexity of load modeling. In
distribution systems, there are often multiple loads connected
to a single bus, as shown in Figure 1. Normally the power of
individual load is not measured or not available, but the total
power transmitted through the bus is measured. In these cases,
the loads can be considered as one composite load, which con-
sists of static loads and dynamic or nonlinear loads. In recent
years, many different techniques have been proposed to model
such loads [1-9]. However, most of them are based on an as-
sumed load equation and the parameters of the equation are
estimated through curve fitting. Because of the complexity of
modern loads (for example, power electronics loads), the as-
sumed models may not capture power, frequency, and voltage
phenomena simultaneously and accurately. It is necessary to
investigate new load modeling techniques and establish accu-
rate load models for power system stability analysis.
Ali Keyhani and Wenzhe Lu are with the Department of Electrical Engineer-
ing, The Ohio State University, Columbus, OH 43210 (e-mail: key-
Gerald Thomas Heydt is with the Arizona State University, Tempe, AZ
Static P/Q Loads
Figure 1 Composite load in a distribution system
In this paper, a neural network based composite load model is
proposed. The methodology for the development of the model
is given in details. First, a simulation testbed is setup based on
the nominal parameters of the loads. The simulation data will
be collected to develop a two-layer recurrent neural network
(NN), which estimates the load power from terminal voltage
and system frequency. The developed composite neural net-
work will be retrained using the measured data.
II. KNOWLEDGE ACQUISITION FROM A TEST-BED OF
TRANSIENT STABILITY CASE STUDY
Because of the nonlinear nature of the load power with respect
to voltage and frequency, a neural network is proposed to map
their relationship. To obtain an adequate representation of
complex loads, the neural network needs to be trained with
large set of data in expected operating conditions. In power
system normal operation, the voltage and frequency only vary
in a very narrow range. If the neural network is trained with
only with these data, then the NN will not characterize the
load dynamics during operation when the voltage or frequency
varies outside nominal operating conditions.
To address this problem, a two-step procedure is used in the
composite NN load model development. In the first step, a
simulation test bed of transient stability is constructed on a
system bus with detail load models using the nominal parame-
ters in the distribution systems. In the modeling of distribution
systems, the motor loads of large industrial systems are mod-
eled in detail with associated converters. P-Q load models are
used for all buses except the bus for which a composite load
model would be developed. At each time step of the transient
stability studies, voltages are computed from a load flow
based on constant P and Q. Detailed load data of the bus under
study for a composite NN load model would be collected
when the system is subjected to line outages for up to five
seconds of the disturbance. In addition, the system frequency
will also be collected for NN modeling. The data collected
from the test bed would be utilized to develop an NN load
model as described in the next section.
III. RECURRENT NEURAL NETWORK LOAD MODELS
Neural networks are composed of simple elements operating
in parallel. These elements are inspired by biological systems.
As in nature, the network function is determined largely by the
connections between elements. It is possible to train a neural
network to perform a particular function by adjusting the val-
ues of the connections (weights) between elements. Com-
monly neural networks are adjusted, or trained, so that a par-
ticular input leads to a specific target output.
The simplest type of neural network is the feedforward NN,
which has no feedback in the structure. Therefore, it can only
perform a “memoryless” mapping: at any time instant, the
output of the neural network is determined by the current in-
Another type of neural network is the recurrent NN, which has
feedback from the output of later layers to the input of previ-
ous layers in the structure, with appropriate delays. The delay
in the recurrent connection stores values from previous time
steps, which can be used in the current time step. The recur-
rent connection allows the neural network to both detect and
generate time-varying patterns.
The structure of the proposed NN is shown in Figure 2. The
input quantities to the neural network are the voltage ( ),
and frequency f (instantaneous values and/or values with ap-
propriate delays), and the output is the load power P or Q.
(used also as the training objective).
The output of the first layer is fed back to the input with some
delays to form a recurrent neural network. Because active
power P and reactive power Q have different characteristics, it
is suggested to utilize two distinct neural networks to map
A hyperbolic tangent sigmoid transfer function – “tansig(…)”
is chosen to be the activation function of the input layer,
which gives the following relationship between its inputs and
+×+ bfIW k
= ntansiga . (1)
A pure linear function is chosen to be the activation of the
output layer, which gives,
222 )()( nnpurelinaQorP === . (2)
The combination of these transfer functions can approximate
any function (with a finite number of discontinuities) with
arbitrary accuracy .
Input First Layer Second Layer Output
Figure 2 Structure of a recurrent neural network for composite load modeling
IV. OFFLINE KNOWLEDGE ACQUISITION FROM
At time step t, k=0
∆−=Since the simulation testbed is based on nominal parameters of
the loads, it is not accurate enough to fully represent the char-
acteristics of the real loads. The neural network based model
trained with the simulation data cannot be directly used in
power system stability analysis. It must be improved by meas-
ured data. However, the substantial a priori information based
on the nominal load data can be used to establish an adequate
first pass estimation of the complex loads in a compact NN
modelfVV ,, 2
During normal operation and occasional systems disturbances
such as fault and line switching, the bus data such as power,
voltage, and frequency are measured and recorded. These data
will be used to retrain the neural network developed in Section
II. After retraining, the load model will represent the loads at
normal operating condition very accurately. Since the NN
model is also trained using the disturbance data, the NN model
gives an adequate representation of load dynamic perform-
V. UTILIZATION IN POWER SYSTEM STABILITY
When the neural network based load model is well trained, it
can be applied directly to power system stability analysis.
Here it is assumed that the general stability analysis program,
which takes the load power (P, Q) as input will produce out-
puts as the voltage V (and frequency f).
At each time step t, the digital model first uses the voltage and
frequency obtained from previous time step to estimate load
power P and Q. Subsequently the power levels are used to
compute the voltage and frequency. Since this estimated load
power might not be accurate, the calculated V and f may
propagate the error. Iterations will generally be needed to at-
tain convergent model parameters: first update P and Q with
the calculated V and f; and then calculate new values of V and
f. This process is repeated until convergence is attained (with
ε≤−=∆ −1kk VVV , where k is the iteration step). A flowchart of
the process is shown in Figure 3.
The developed NN model is a recurrent NN model in which
the time step represents the simulation time step in transient
stability studies. This class of NN reflects the changing dy-
namics of the loads due to the changes in frequency and volt-
age magnitude when the system is subjected to disturbances in
the two cycles time frame of stability studies. It should be
pointed out that the weights of the NN model remain the same,
however the expected loads change as the input to the NN
changes during the disturbance.
Figure 3 Flowchart: utilizing composite NN load model in power
system stability analysis
VI. CASE STUDY
To test the proposed load model, a case study has been per-
formed on a power inverter controlled induction motor load in
simulation. The depiction in Figure 4 represents a composite
load – an induction motor that connects to power system
through a rectifier and an IGBT power inverter. The load
torque connected to the motor is a function of the rotor speed.
In addition, a speed controller is implemented to control the
In simulation, the motor is operated in the steady state, and the
supply voltage is decreased / increased over the range of 0.0 to
1.2 p.u., with different rates. The active power P and reactive
power Q at the load terminals are computed and recorded.
Similar simulations are performed at different system frequen-
cies (55 Hz through 65 Hz). All data are collected for neural
network training and load model validation.
The data collected from simulation are separated into two
parts. One part is used to train the neural network; the other is
used to test the validity of the results. After the neural net-
works are trained by one part of the collected data, the NNs
are validated with the other part of data. The procedure is to
send the recorded sequence of voltage and frequency to the
neural networks, and compare the estimated power sequence
with recorded power sequences. Figure 5 shows one of the
validation results. In Fig. 5, the voltage is shown as a dashed
curve; the simulated power is shown as a solid curve; and the
Figure 4 Simulation testbed: a composite load – induction motor controlled by power inverters
(a) Validation of active power P
(b) Validation of reactive power Q
Figure 5 Model validation results from noise-free data
estimated power (from neural network) is shown as small cir-
cles. Note that in this simulation, the motor is initially running
at rated voltage, and then the voltage is decreased to zero. Af-
ter reaching steady state, the voltage is increased from 0.0 to
1.2 p.u. Finally, the voltage is returned to rated value. Due to
the performance of the speed controller, the load power
changes nonlinearly. In view of this behavior, simple load
models will not capture the phenomenon accurately. But from
the results here, one can see that the proposed neural network
based load model captures the load dynamics very well. The
mean of estimation error for P is 3.07x10-4 p.u., and that for
Q is 4.04x10-5 p.u. thus suggesting a satisfactory estimation.
The validation of other data shows similar results.
This paper presents a methodology for development of neural
network based load models which can be used in power sys-
tem stability analysis. A two-step procedure is proposed to
first develop a recurrent neural network with simulation data
and then update it with measured data. A case study on an
induction motor load proves the availability of the suggested
NN load model.
This work is supported in part by NSF Grant NSF
 Les M. Hajagos, Behnam Danai, “Laboratory Measurements
and Models of Modern Loads and Their Effect on Voltage
Stability Studies,” IEEE Transactions on Power Systems, Vol.
13, No. 2, May 1998, pp. 584-592.
 IEEE Task Force on Load Representation for Dynamic Per-
formance, “Standard Load Models for Power Flow and Dy-
Parameters of Testbed:
50HP, 460V, 60Hz
662.1 mkgJ ⋅=
IGBT Switching: Vector-
namic Performance Simulation,” IEEE Transactions on
Power Systems, Vol. 10, No. 3, August 1995, pp. 1302-1313.
 Les Pereira, Dmitry Kosterev, Peter Mackin, Donald Davies,
John Undrill, and Wenchun Zhu, “An Interim Dynamic In-
duction Motor Model for Stability Studies in the WSCC,”
IEEE Transactions on Power Systems, Vol. 17, No. 4, No-
vember 2002, pp. 1108-1115.
 M. K. Pai, “Voltage Stability: Analysis Needs, Modeling
Requirements, and Modeling Adequacy,” IEE Proceedings-C,
Vol. 140, No. 4, July 1993, pp. 279-286.
 A. Borghetti, R. Caldon, A. Mari, C. A. Nucci, “On Dynamic
Load Models for Voltage Stability Studies,” IEEE Transac-
tions on Power Systems, Vol. 12, No. 1, February 1997, pp.
 S. Z. Zhu, Z. Y. Dong, K. P. Wang, and Z. H. Wang, “Power
System Dynamic Load Identification and Stability,” Proceed-
ing of International Conference on Power System Technology
2000, Vol. 1, Dec. 4-7, 2000, pp. 13-18.
 Y. G. Zeng, A. Berizzi, and P. Marannino, “Voltage Stability
Analysis Considering Dynamic Load Model,” Proceeding of
International Conference on Advances in Power Sys-
tem Control, Operation and Management, APSCOM-97,
Hong Kong, November 1997, pp. 396-401.
 David J. Hill, “Nonlinear Dynamic Load Models with Recov-
ery for Voltage Stability Studies,” IEEE Transactions on
Power Systems, Vol. 8, No. 1, , February 1993, pp. 166-176.
 Y. Baghzouz, Craig Quist, “Composite Load Model Deriva-
tion from Recorded Field Data,” IEEE Power Engineering
Society 1999 Winter Meeting, Vol. 1, Jan. 31 - Feb. 4 1999,
pp. 713 –718.
 William W. Price, Kim A. Wirgau, Alexander Murdoch,
James V. Mitsche, Ebrahim Vaahedi, and Moe A. El-Kady,
“Load Modeling for Power Flow and Transient Stability
Computer Studies,” IEEE Transactions on Power Systems,
Vol. 3, No. 1, February 1988, pp. 180-187.
 Y. Kataoka, “A Probabilistic Nodal Loading Model and
Worst Case Solutions for Electric Power System Voltage Sta-
bility Assessment,” IEEE Transactions on Power Sys-
tems, Vol. 18, Issue 4, Nov. 2003, pp. 1507-1514.
 J. R. Shin, B. S. Kim, M. S. Chae, S. A. Sebo, “Improvement
of Precise P/V Curve Considering Effects of Voltage-
Dependent Load Models and Transmission Losses for Volt-
age Stability Analysis,” IEE Proceedings on Generation,
Transmission and Distribution, Vol. 149, No. 4, July 2002, pp.
 Qisheng Liu, Yunping Chen, Dunfeng Duan, “The Load
Modeling and Parameters Identification for Voltage Stability
Analysis,” Proceedings of 2002 International Conference on
Power System Technology. Vol. 4, Oct. 2002, pp. 2030-2033.
 Dingguo Chen, R. R. Mohler, “Neural Network Based Load
Modeling and its Use in Voltage Stability Analysis,” IEEE
Transactions on Control System Technology, Vol. 11, No.
4, July 2003, pp. 460-470.
 Elman, J. L., "Finding Structure in Time," Cognitive Science,
vol. 14, 1990, pp. 179-211.
Wenzhe Lu (S’00) received his BS from Xi’an Jiaotong University, Xi’an,
China in 1993, and MS from Tsinghua University, Beijing, China in 1996,
respectively. Now he is a PhD student in Electrical Engineering Department
of The Ohio State University, Columbus, Ohio. Mr. Lu's research interests
include power system modeling and analysis, and modeling and control of
switched reluctance motors for electric vehicle applications.
Ali Keyhani (S’72-M’76-SM’89-F’98) received his Ph.D degree from Pur-
due University, West Lafayette, Indiana in 1975. From 1976 to 1980, he was a
professor of Electrical Engineering at Tehran Polytechnic, Tehran, Iran. Cur-
rently, Dr. Keyhani is a Professor of Electrical Engineering at the Ohio State
University, Columbus, Ohio.
Gerald Thomas Heydt (S’62–M’71–SM’79–F’91) received the B.E.E.E.
degree from the Cooper Union, New York, and the M.S.E.E. and Ph.D. de-
grees from Purdue University, West Lafayette, IN. Currently, he is a Regents’
Professor of Electrical Engineering at Arizona State University, Tempe, AZ.
Dr. Heydt is a member of that National Academy of Engineering.