In this paper an Adaptive Neuro-Fuzzy Controller was designed to adaptively adjust the parameters of a power Oscillation Damper as the power system operating point changes due to change in operating point in a large interconnected Network fitted with FACTS device and Power Oscillation Damper. As a foundational work the generalized mathematic model of multi-machine power system with embedded FACTS was developes. The results obtained clearly reveals the effectiveness of this approach.

Most of the FACTS based damping controllers belong to the PI (Proportional + Integral) type and work effectively in single machine system [

Proposed Adaptive POD Controller

An attempt has been made to apply hybrid neuro-fuzzy approach for the coordination between the conventional power oscillation damping (POD) controllers for multi-machine power systems. With the help of MATLAB, a class of adaptive networks, that are functionally equivalent to fuzzy inference systems, is proposed. The proposed architecture is referred to as ANFIS (Adaptive Neuro-Fuzzy Inference System) [

The acronym ANFIS derives its name from adaptive neuro-fuzzy inference system. Using a given input/output data set, the toolbox function ANFIS constructs a fuzzy inference system (FIS) whose membership function parameters are tuned (adjusted) using either a back propagation algorithm alone, or in combination with a least squares type of method. This allows fuzzy systems to learn from the data they are modeling [

An unknown System as a Black Box

In the unknown system in Figure _{1} … … x_{n} and output y_{1} … … y_{n} can be measured. The mathematical description relating the input to the output can be a mathematical formula, such as a mapping or a function that relates the input to the output in the form

or a set of differential equations in the form

or a logical linguistic statement which can be quantified mathematically in the form:

Fuzzy systems modeling is to quantify the logical form of equation (3.51) by using Fuzzy logic and the mathematical functional model of equation (3.49) or by using Fuzzy logic together with the differential equation model of equation (3.50).

The fuzzy logic controller comprises of four stages: (1) fuzzification, a knowledge base, decision making and defuzzification. The fuzzification interface converts input data into suitable linguistic values that can be viewed as label fuzzy sets. To obtain a deterministic control action, a defuzzification strategy is required. Defuzzification is a mapping from a space of fuzzy control actions defined over an output universe of discourse into a space of nonfuzzy (crisp) control actions. The defuzzification of the variables into crisp outputs is tested by using the weighted average method.

After generating the fuzzy inference, the generated information describing the model’s structure and parameters of both the input and output variables are used in the ANFIS training phase. This information will be fine-tuned by applying the hybrid learning or the backpropagation schemes. The algorithm employed for ANFIS training is shown in Figure

Flowchart of ANFIS Training

Power Oscillation Dampers were designed for UPFC embedded in two test case study systems:

However the optimal performance of these PODs are only guaranteed at the particular operating points under consideration, but at any other operating points, different values of time constant must be determined for the damping to be effective

The training data and check data are generated by randomly varying the load (multiplying the load with a factor of 0.1) in the two areas of the test system. At each operating point the actual values of POD parameters T_{1} and T_{2} were calculated. The ANFIS parameter settings are as shown in

ANFIS Parameter Settings

numMFs | 5 |

mfType | 'gbellmf' |

epoch_n | 20 |

Training Data and ANFIS Output: Lead Time Constant

Check Data and ANFIS Output: Lead Time Constant

Prediction Error for Training Data and Check Data: Lead Time Constant

Training Data and ANFIS Output: Lag Time Constant

Check Data and ANFIS Output: Lag Time Constant

Prediction Error for Training Data and Check Data: Lag Time Constant

The data for training were obtained by randomly varying the load in different areas by a factor of 0.01 from low to medium and high values for about 500 scenarios, the data were divided into training data and check data. The lead-lag time constants were recorded as they change with operating conditions as well as the lead and lag time constants that provide the best damping under different operating conditions. The results obtained for lag time constant are as shown in Figures

Plot of ANFIS Data and Training Data: Lag Time Constant

Plot of ANFIS Data and Check Data: Lag Time Constant

Prediction Error for Training Data and Check Data

Plot of ANFIS Output and Training Data: Lead Time Constant

Plot of ANFIS Data and Check Data: Lead Time Constant

Prediction Error for Training Data and Check Data

Input Membership Function

ANFIS Adjusted Membership Function: Lag Time Constant

ANFIS Adjusted Membership Function: Lead Time Constant

In this work an adaptive neuro fuzzy controller has been developed for the purpose of coordinating the changes in power oscillation damper parameters with variation in power system operating point. The accuracy with which the controller was able to predict the values of POD parameters clearly reveals the effectiveness of the proposed approach.