WCCI 2012 IEEE World Congress on Computational Intelligence June, 10-15, 2012 - Brisbane, Australia
IJCNN
A Scalable Wide Area Monitoring System using Cellular Neural Networks Karthikeyan Balasubramaniam, Bipul Luitel and Ganesh Kumar Venayagamoorthy, Senior Member, IEEE Real-Time Power and Intelligent Systems Laboratory Holcombe Department of Electrical and Computer Engineering Clemson University, Clemson, SC 29634, USA
[email protected],
[email protected], and
[email protected] Abstract— Synchrophasor systems make power grids more observable by collecting data from various locations, time-align and process them as a coherent data set. Better observability results in better control actions. A limiting factor to this approach is communication delays. Power system wide area communication delays range from several milliseconds to several seconds depending on the communication media and distance. One way to deal with this is to have an intelligent system which can predict state values for one or more time steps ahead of time. A novel four dimensional scalable multirate cellular neural network (CNN) architecture for use as wide area monitoring system (WAMS) is proposed. Recurrent neural network (RNN) is used as computational engine for each cell as RNNs have dynamic memory. By using information from phasor measurement units (PMUs) that are optimally located in a power system, each layer predicts a state variable for one or more time steps. Data from remote PMUs are replaced by the respective CNN cells’ time delayed predicted state values for next time step. This enables local controllers to take real-time control action with system wide information. A 12-bus test power system is used to develop and demonstrate the effectiveness of the proposed CNN framework for WAMS. Keywords- Cellular neural networks, Recurrent neural networks, State estimation, Synchrophasors, Wide area monitoring and control.
I. INTRODUCTION Synchrophasor systems have made power grids more observable by collecting data from different locations, timealign them and process them as coherent data sets [1]. These data sets are then used for monitoring and control. In power systems, optimal power flow dispatch is updated every five minutes. Variations between dispatches are handled by local controllers with little or no system wide knowledge [2]. A limiting factor in implementing real-time control with system wide information is communication delays. Communication delays in power system can range from few milliseconds to several seconds depending on distance and communication media [3]. A possible solution to this problem is proposed in this paper through the use of cellular neural networks (CNN) [4] framework. The proposed framework is used to predict This work is supported by the National Science Foundation (NSF) of the United States, under grant # EFRI 1238097 and CAREER ECCS #1231820. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of National Science Foundation.
U.S. Government work not protected by U.S. copyright
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system states for future time instances. By transmitting predicted state values ahead of time we can effectively compensate for communication delays. Thus, for any nominal frequency all the required data will be made available to controllers for real-time control. Power systems can be modeled with a set of differential algebraic equations (DAEs), solution to which would give all the required system states. Neural networks (NNs) on the other hand are good at identifying system dynamics without the need for a detailed system model. NNs can be made to learn system dynamics by training them with historical data. However, they suffer from the problem of scalability. CNNs on the other hand make scaling linear by dividing the problem at hand to several sub-problems. These aspects make the proposed CNN framework suitable for real-time applications as it is computationally less intensive. Furthermore, it is possible to capture spatial dynamics of a power system through the use of CNN architecture where each cell is connected to other cells according to system topology. The fascinating aspect of this proposed CNN framework for WAMS is its flexibility. In this paper, a ‘layer’ is defined as a group of interconnected cells performing a similar task, for example, prediction of a state variable for one or more time steps ahead of time. It is possible to have several of these layers, where each layer predicts one state variable. In this paper, four layers are modeled: speed deviation prediction layer, voltage prediction layer, active power output prediction layer and line flow prediction layer. Layers are coupled with each other in specific ways to mimic coupling that exists between various power system parameters [5]. Each cell models a power system component depending on the layer where the cell exists. For example, each cell in speed deviation prediction layer would represent a generator. Likewise, each cell in voltage prediction layer would represent a bus in the system. Each cell is represented as a computational engine that is used to learn the dynamics of the particular component it represents. Recurrent neural networks (RNNs) are used as the computational engine in all cells, but it is also possible to use heterogeneous computational engines where different cells have different type of computational engine as reported in [6]. Spatial dynamics are captured by connecting individual cells in each layer according to power system topology while temporal dynamics of the system are captured by RNNs as
they have dynamic memory. The remaining sections of the paper are arranged as follows: In Section II, use of four dimensional CNN framework for WAMS is discussed. Methodology and implementation are covered in Section III, CNN training and testing is discussed in Section IV, results are presented and discussed in Section V and conclusions make up Section VI. II. FOUR DIMENSIONAL CELLULAR NEURAL NETWORK The proposed architecture of CNN has four layers. Each layer predicts one state variable. The four state variables that are being predicted are generator speed deviation, terminal voltage at all buses, generator active power output and line flow. It is to be noted that only optimally located PMU information is used by each cell, remaining information comes from time-delayed predicted values of other cells. This way, we can compensate for communication delays. Fig. 1 shows the proposed architecture. As shown in the diagram, each layer has a number of individual units called cells. Depending on the layer, each individual cell represents a power system component and is modeled using a RNN. Each cell in every layer is connected to other cells in the layer in specific ways that represent the physical system’s topology. In addition to this, cells are also vertically connected across layers. This coupling is illustrated in Fig. 2. Output from one layer is fed as input to another layer. For example, generator number 2 represents bus number 10 in the system. Hence, time delayed predicted value of speed deviation of generator 2 is used as one of the inputs for voltage prediction of bus number 10. Generator 2 governor dynamics are captured in speed deviation signal and using this as input for cell 10 in voltage prediction layer improves terminal voltage prediction at bus 10.
are addressed this way and with this framework real-time control can be formulated with system wide information. It is well known that group of generators swing together. In other words, primary oscillation of a generator is influenced by nearby group of generators to which it is connected. Secondary and tertiary oscillations are influenced by the rest of the generators spread across the system. This principle has been used in cell to cell connections where connectivity is predominantly based on local neighbors. To identify secondary and tertiary oscillations, specific generators from different ‘cluster of generators’ are connected in specific ways, where ‘cluster of generators’ implies a group of generators that swing together when there is a change in system. For speed deviation prediction, ∆ ,∆ 1 , and ∆ 2 , ∆ and ∆ are ∆ used as inputs. Where, ∆ and its time delayed versions generator. ∆ is are actual speed deviations of time delayed predicted value of change in reference signal of exciter and ∆ is the change in reference signal of generator. ∆ is the time delayed governor for the value of predicted speed deviations of neighboring cells from cell receives inputs. These inputs are used by which the each cell in speed deviation layer to predict ∆ 1 i.e. generator for time the predicted value of speed deviation of t+1. Each cell predicts speed deviation of one generator and there are four generators in the system. Hence, there are four cells in this layer. In Fig. 3, connection scheme for 12-bus test system speed deviation layer is shown. CNN cells are superimposed on top of one line diagram to show how cells capture spatial dynamics.
The proposed CNN framework is decentralized and asynchronous. The approach is decentralized because each cell performs prediction using information that is relevant and important to that particular layer and cell and by virtue of being connected with other cells and layers in specific ways, the details of which are discussed in Section III. Learning is typically asynchronous where each cell learns at its own rate and when required. For example, system disturbances although global, have a more pronounced effect closer to the point of disturbance. As a result, cells that predict state variables in the vicinity of the disturbance will have more learning to do than cells that represent locations further away from disturbance area. Hence, asynchronous learning is used in this work. Thus, each cell learns when required and at its own rate. III.
METHODOLOGY AND IMPLEMENTATION
A. Speed Deviation Prediction Layer CNN is a decentralized approach where state variables are predicted based on inputs from locally placed phasor measurement units (PMUs) and time delayed predicted values of neighboring cells. Since each cell is going to predict for one or more time steps in future, time delayed values of predicted states from neighboring cells will be available to other cells that are connected to it before next set of calculations for control are to be performed. Problem of communication delays
Figure 1. Each block represents a cell, where RNN is used as computational engine. Spatial dynamics are captured by connectivity i.e. information flow between cells, while temporal dynamics are captured by RNN. The four different layers predict speed deviation, terminal voltage, generator active power output and line flows. In addition to cells being connected to each other within a layer, there is also information flow between layers. This coupling enables better prediction.
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Figure 2. Each block represents a layer. The four different layers that predict speed deviation, terminal voltage, generator active power output and line flows are coupled as shown. Information flow between layers is shown as directed lines. Figure 4. Voltage prediction layer connectivity is shown. Cells are superimposed on top of one line diagram of 12 bus test system. Voltage prediction at all the 12 buses is to be carried out and hence there are 12 cells. The blue dashed lines represent the connectivity between each cell where direction of information flow is indicated by directed arrows.
B. Voltage Prediction Layer Unlike speed deviation prediction, voltage variations are system wide phenomenon. Hence, each cell’s connectivity is set exactly the same way as in real system. Here each cell represents a bus and is connected to other cells the same way buses are connected in the real system. Two different input schemes are followed for this layer. For terminal voltage prediction at generator buses, time delayed predicted speed deviation value ∆ and time delayed predicted value of generator ∆ are used. control signal of exciter at , 1 , 2 , and In addition to this, are also used, where and are time delayed predicted values of terminal voltage from neighboring cells 1 to N and , 1 , 2 are current and time delayed values of terminal voltage at generator. The reasoning is that voltage variations at generator buses depend on control actions taken by exciter and governor in addition to changes at load buses to which it is connected. It is to be noted that ∆ is time delayed predicted value of speed deviation from speed deviation layer. Governor dynamics are captured through this input. A simpler input scheme is used for load bus voltage prediction. In this input scheme, voltage of only the buses to which bus is connected are used as inputs in addition to current and time delayed
Figure 3. Speed deviation layer connectivity is shown. Each block represents a generator. Blue dashed lines represent the connectivity between each cell where direction of information flow is indicated by directed arrows. Cells are superimposed on top of one line diagram of 12 bus test system to show how spatial dynamics are captured by cells.
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values of terminal voltage of that particular bus. Connection between cells for voltage prediction layer is shown in Fig. 4.
signal by a large value, RNN would learn a wide range of operating conditions.
C. Generator Active Power Output Prediction Layer Active power output of a generator is directly related to its speed deviation. By coupling this layer with speed deviation layer, the output of which has internal dynamics of speed and voltage control, all the required dynamics are fed as input for prediction. Connections between cells follow the same principle as that of speed deviation layer as the dynamics are similar.
Online training scheme is used for training RNN. Training is done using standard backpropagation algorithm [10], [11] where error during each time instance is backpropagated and subsequent adjustment to weights are made. To reduce training time, one cell is trained with historic data to required error tolerance and other cells start their learning process with this cell’s weights as starting point.
Inputs ∆ , ∆ 1 , ∆ 2 and ∆ 1 . For single step prediction, are used to predict ∆ coupling from speed deviation layer could be replaced by data from locally placed PMUs i.e. ∆ from speed deviation layer could be replaced with ∆ from PMU but for multistep prediction coupling is required. In order to maintain a uniform general representation for single and multi-step predictions, time delayed predicted values from speed deviation layer is used. D. Line Flow Prediction Layer Power transfer between two buses is given by (1) and (2) [7]:
To test if neural network has learned, it needs to be tested on a different data set (test data) than the one it is trained with. Test data is obtained in two different ways. First, PRBS is varied by an amount that is within the training set perturbation range i.e. for example by +x% to –x% where x is a number lesser than 5 for governor control signal and lesser than 10 for exciter control signal. For the second method, 12-bus power system is perturbed a little from its steady state value and before the system settles to a new operating point, PRBS is applied. This ensures that the system has a new set of initial conditions. Constructing test data this way makes it possible to check if neural network has learned. Once training is completed, test data generated by methods mentioned above are presented to each layer and the obtained results are presented in Fig. 7 through 11. Since it is impossible to train each layer under every operating condition,
Hence, next state can be predicted by using voltage information along with current and time delayed value of apparent power flow between lines. For voltage information, voltage prediction layer is directly coupled to line flow layer. By using 2 values in addition , 1 and to coupling from voltage prediction layer, apparent power flow in lines for next time instance, 1 , is predicted. Subscript FT represents ‘from’ to ‘to’ end.
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E. Test System 12-bus power system from [8] is used to demonstrate feasibility of CNN framework for power system applications. All four generators are modeled with full transient dynamics in PSCAD [9]. All four generators are assumed to be gas turbine with a ramp rate of 18MW/min. Loads are modeled as 50% dynamic and 50% static loads. Generator and load details are given in appendix.
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IV. CNN TRAINING AND TESTING Training data is generated in PSCAD using pseudorandom binary signal (PRBS) as perturbation. Perturbation in the form of PRBS is applied to governor and exciter control of generator 2, 3 and 4. For governor, PRBS is varied between +5% and 5% while for exciter, PRBS is varied between +10% and -10%. Each set of perturbation is applied in sequence. For the first 400 seconds, governor is perturbed with PRBS and from 401500 seconds, exciter is perturbed with PRBS. Care is taken to not apply high values of PRBS to all generators at the same time. PRBS is varied from individual high to low in a sequential manner so as to not drive the system unstable. The idea behind applying PRBS is that by perturbing the control
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each cell is allowed to learn with a small learning gain when error between its predicted and actual values goes above 3% of relative error. Such a condition indicates that the system is now at some new operating point under which the neural network was not trained. V.
RESULTS AND DISCUSSION
Fig. 7 represents speed deviation prediction layer results. Speed deviations of all four generators are shown. Fig. 8 (a) through (c) shows terminal voltage prediction for buses 1 through 12. Fig. 9 is generator active power output prediction. Fig. 10 (a) through (d) are line flows. In all the plots, blue curve represents the actual value of state variables and red curve indicates the predicted value. The results shown are for single step ahead prediction. Good tracking performance for all four layers is obtained. As proof of scalability, generator speed deviation prediction for IEEE 68-bus test case is implemented and results are presented in Fig. 11. Training with coupling between layers is a challenging task. Each cell in each layer has its own error and when this is fed as input to other cells and layers, the system quickly diverges. To avoid this, during training phase, each layer is trained separately using historical data without interconnection between layers. Once good tracking performance is obtained, the layers are coupled. During online operation, if relative error goes above 3% it is indicative of the fact that the system is now at an operating point that the neural network was not trained under. Under such circumstances specific cells that need weight updates are allowed to learn with a small learning gain. This way each CNN cell is allowed to continuously fine tune itself to achieve good tracking performance. During training phase, CNN is trained under different operating conditions with a wide range of perturbation signals. During this phase CNN learns the dynamics of the system over a wide range. Hence, only fine tuning of neural network weights is required to achieve good tracking performance under new operating conditions. Connection between cells, layers and inputs to each cell in each layer are all based on real world phenomenon. Control signals to governor and exciter systems alter system state. By using these as inputs, along with carefully interconnected cells whose connection is based on topology, neural network in each cell (RNN in this study) receives all necessary inputs to predict how system would be at next time step. The whole idea of this CNN framework for WAMS is to overcome the problem of communication delay to enable real-time control using system wide information. Communication delays play a major part when information source is far away. By using time-delayed predicted values which effectively compensate for communication delays, all the required inputs at current time can be made available to the controller to perform real-time control using system wide information. In power systems, optimal dispatch is updated every five minutes which is based on forecast, and variations within this window period are handled by linear controllers with little to no system wide information. With increasing penetration of intermittent renewable energy sources such as wind, conditions of high variability and uncertainty are introduced.
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Hour ahead wind prediction models have around 10% error. With energy production from renewable energy sources set to increase at a faster pace in the coming years it is important to take control actions with as much system wide information as possible. With the advent of synchrophasor systems, power grid has become more observable but the use of this information for use in real-time control of controllers is limited by power system communication delays which can range from a few milliseconds to several seconds based on communication media and distance. Intelligent predictive methods offer a potential solution to this problem because communication delays can be compensated by predicting state values ahead of time. A substation based dynamic state estimator has been used as WAMS in [12] that provides abilities to predict instabilities before they occur. Although various techniques are being used and developed for wide area monitoring, there are still major challenges in their use for control. These challenges are related to extracting dynamics of the system without knowing the system model, mining and interpreting huge amount of data available from monitoring devices and assessment of the overall dynamics of the system based on wide area information [13]. By employing the type of WAMS presented in this paper in tandem with novel control schemes such as adaptive critics design based control scheme as given in [2] or with conventional controllers we can realize control schemes with system wide information as communication delays will be compensated by predicting for future time instances. As long as duration of n-step ahead prediction is bigger than communication delay, all the required information at time t will be made available to controllers. VI.
CONCLUSIONS
Feasibility of cellular neural network (CNN) framework for use as wide area monitoring systems (WAMS) has been demonstrated for a 12-bus test power system modeled with full transient dynamics. CNN framework is developed in MATLAB [14]. Communication delay is compensated by predicting future state values. This is particularly important with increased penetration of intermittent energy sources such as wind and solar. These sources add high uncertainty and variability to forecasts, using which optimal dispatch is calculated. Linear controllers which handle variations in the window period between dispatches with little to no system wide knowledge perform poorly under high variability conditions and could eventually drive the system unstable. Having system wide information would enable controllers to take best possible control action. Distributed nature of CNN architecture can be exploited to implement the framework in a cluster using parallel computing. In such a configuration, each cell would be represented by a processor. Such architecture would allow real-time implementation of large systems with many variables. The proposed research is a framework where various ‘computational engines’ can be used. As progress is made in biologically inspired artificial neural network (BIANN) architectures the prospect of using BIANN as computational engine in CNN framework is an interesting possibility.
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Figure 6. (a) Wide area measurement signal transmission delay in WAMS is shown. Speed deviation signal received at generator 3 at time t is the signal of generator 1 transmitted at time i.e. ∆ is received at generator 3 at time t with a delay of . (b) In the proposed framework communication delay is overcome by transmitting predicted values of future time instances. By predicting n-steps ahead, at time t, predicted value of speed deviation for generator 1 i.e. ∆ ∆ is transmitted and is received at generator 3, at time t as ∆ because of communication delay. Here ∆ i.e. the difference between n-step ahead prediction and communication delay. The diagram shown is for a generalized n-step ahead prediction model. Results presented in this paper are for single step ahead prediction at 10Hz.
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Table I Generator Data for 12-bus Test System from [8] Bus 9(G1) 10(G2) 11(G3) 12(G4)
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