09-09-2013, 03:32 PM
Kalman Filter-Based Distributed Predictive Control of Large-Scale Multi-Rate Systems: Application to Power Networks
Kalman Filter-Based Distributed.pdf (Size: 3.36 MB / Downloads: 51)
Abstract
In this paper, a novel distributed Kalman filter (KF)
algorithm along with a distributed model predictive control (MPC)
scheme for large-scale multi-rate systems is proposed. The decom-
posed multi-rate system consists of smaller subsystems with linear
dynamics that are coupled via states. These subsystems are multi-
rate systems in the sense that either output measurements or input
updates are not available at certain sampling times. Such systems
can arise, e.g., when the number of sensors is smaller than the
number of variables to be controlled, or when measurements of
outputs cannot be completed simultaneously because of practical
limitations. The multi-rate nature gives rise to lack of information,
which will cause uncertainty in the system’s performance. To cir-
cumvent this problem, we propose a distributed KF-based MPC
scheme, in which multiple control and estimation agents each de-
termine actions for their own parts of the system. Via communica-
tion, the agents can in a cooperative way take one another’s actions
into account. The main task of the proposed distributed KF is to
compensate for the information loss due to the multi-rate nature of
the systems by providing optimal estimation of the missing infor-
mation. A demanding two-area power network example is used to
demonstrate the effectiveness of the proposed method.
INTRODUCTION
Recently, considerable attention has been devoted to control
and estimation problems in large-scale systems and numerous
distributed control [2], [8]–[12] and estimation [13]–[15]
methods have been proposed. In a distributed control structure,
the whole system is decomposed into a number of small subsys-
tems. Each subsystem is controlled by a so-called agent, which
solves its own, local control and estimation problem. State
estimators can be employed to compute important states of the
system that are often difficult to measure, using partly available
measurement. The structure of a state estimator involves a
dynamical model of the system, which is simulated in parallel
to the real system using the same inputs and initial conditions
as the real system. Then the simulation error, defined as the
difference between the real measurements and the simulated
ones, is used as feedback in the simulated model for correction.
This error comes into play as the initial conditions are often
not known exactly, the process is subject to disturbances, or
model-plant mismatch exists. In such cases, if no feedback is
used, there is no guarantee that the predictions are close or
equal to the real states.
Problem Statement
Distributed Kalman filtering [3], [17]–[19] involves state es-
timation using a set of local KFs that communicate with all
other agents. However, in multi-rate state estimation an addi-
tional issue needs to be considered which is the multi-rateness
of the system. The main issue that is addressed by our proposed
method is to introduce a novel state estimation approach for
multi-rate linear discrete-time systems in which measurements
are only available at certain sampling times.
Synchronous Agent Case
In Fig. 4, the simulation results corresponding to the case
where the input sampling rate for both agents (power areas) is 6
times faster than the output sampling rate, are presented. It can
be observed that the performance of the proposed multi-rate KF
method is close to that of the single-rate (perfect) case; the total
simulated performance loss
is 3.98% in comparison to
78.39% in the fully decentralized KF case (see Table III). This
means that the multi-rate KF algorithm is more effective in com-
pensating for the information loss due to the infrequent output
measurements. Notice that the constraints on the load reference
set-point variables imposed in (68) are respected at all times
during operation of the controller.
CONCLUSION AND FUTURE WORK
In this paper, a new KF-based distributed model predictive
control algorithm has been proposed for multi-rate large-scale
systems. The proposed framework consists of two main parts,
control and estimation. In the control part, a distributed MPC
via a Nash game has been studied for multi-rate sampled-data
systems and in the estimation part a distributed KF has been
proposed to provide the state values for inter-sampling times.
The algorithm provides a reliable control and estimation and
compensation mechanism for the information loss due to the
multi-rate nature of the systems using the proposed distributed
KF. In a simulation study involving a two-area power system the
proposed method has been compared with a single-rate KF (in
plots), centralized KF (in tables) scheme and also with a decen-
tralized multi-rate KF demonstrating significant levels of per-
formance improvement. Several simulation scenarios including
slow and fast input sampling as well as slow and fast output sam-
pling in both synchronous and asynchronous arrangements have
been considered showing feasibility and high effectiveness.