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Theoretic analysis shows that the output power of the distributed generation system is nonlinear and chaotic. And it is coupled with the microenvironment meteorological data. Chaos is an inherent property of nonlinear dynamic system. A predicator of the output power of the distributed generation system is to establish a nonlinear model of the dynamic system based on real time series in the reconstructed phase space. Firstly, chaos should be detected and quantified for the intensive studies of nonlinear systems. If the largest Lyapunov exponent is positive, the dynamical system must be chaotic. Then, the embedding dimension and the delay time are chosen based on the improved C-C method. The attractor of chaotic power time series can be reconstructed based on the embedding dimension and delay time in the phase space. By now, the neural network can be trained based on the training samples, which are observed from the distributed generation system. The neural network model will approximate the curve of output power adequately. Experimental results show that the maximum power point of the distributed generation system will be predicted based on the meteorological data. The system can be controlled effectively based on the prediction.

As the energy and environmental stresses increased, the distributed generation system has become the best energy supply options. The distributed generation system has been noted by many countries and regions as one of the first elements which saves primary energy and reduces greenhouse gas emissions [

The operation and control of distributed generation system are facing a stringent challenge to keep the efficiency and stability of the system [

The output power of the distributed generation system and the environmental meteorology are strongly coupled. The chaotic time series of the microenvironment meteorological data and the output power are obtained by analysis of the previous meteorology rules in this region. In this paper, we build the model of the microenvironment meteorology and the output power of the distributed generation system based on neural network and chaos time series forecasting. The neural network is trained based on the training samples, which are chaotic time series obtained from the distributed generation system. The neural network approximates the curve of output power adequately. The functional relationships between the output power and the meteorological data are fitted to build the chaos forecasting model of the output power. The maximum power point is tracked by the chaos forecasting model in the conversion process between the renewable energy sources and the conventional energy sources. Then, different kinds of energy system are controlled harmoniously and banded together closely. The model of the system is mostly established based on accurate data. The error is general among experimental data owing to the disturbance. The precision of forecasting model based on neural network depends on the generalization of neural network. In order to improve the neural network predictor, the structure and parameters of the model should be optimized.

With the increasing demand for energy, the shortage of energy sources in the world is becoming more and more serious. At the same time, the consumption of the traditional energy sources aggravates the environmental pollution. Therefore, the utilization and the critical technology of renewable energy source have been paid more and more attention. The combined cooling, heating, and power systems have been considered as the best solution of future energy supply [

The combined heating and cooling system.

The cooling subsystem

The heating subsystem

The distributed generation system can be conceptually seen as being composed of the combination of local subsystems producing electricity, heat, cooling, and so on. Figure

The block diagram of distributed generation system.

The chemical reaction is the process in which biomass gas is converted to electrical energy in the biomass gas generating system. The available solid biomass resources with low calorific value are convertible to gas. Small electricity generators are powered by biogas or natural gas. As one bioenergy technology, biomass gas generating technology can provide clean energy. The biomass gas generating system consumes large amounts of solid reject and generates enormous amounts of thermal and electrical energy. The waste heat of the generating unit is used to drive the lithium bromide absorption refrigeration cycle and the plate heat exchanger.

The heat exchanging processes are physical reactions. The refrigerant vapour is generated in evaporator of the lithium bromide absorption refrigerator. Then, the lithium bromide solution will become dilute because amount of vapour is absorbed by the solution in absorber. The dilute solution is sent back to the heat exchanger by the circulating pump. The solution is concentrated and further heated by steam or hot water in the generator. The temperature of cool dilute solution rises through heat exchanger between the generator and the absorber. The metal plates are used to transfer heat between two fluids in a plate heat exchanger. The lithium bromide solution and refrigerant water are fed into tubes of the plate heat exchangers. The system also includes monitoring system, energy management system, and control system. The safe and stable running of the distributed generation system is ensured.

The powers of different subsystems are all subject to the fluctuation of the external environmental state, meaning the renewable energy is intermittent. The efficient control is a serious challenge in long cycle, security, and steady running. Therefore, it is very necessary for the prediction research of the renewable energy system. The real information can be supplied to distribution system if applicable. The short-term power forecasting can improve system operating efficiency and flexibility.

Generally, only a single scalar time series can be measured from a real physical system. So the phase space reconstruction from time series is the first stage in nonlinear time series analysis of data from chaotic systems [

Supposing that a continuous time dynamical system is described as follows:

The phase space reconstruction system is an orthogonal projection from

The forecasting model is derived from the expression of the mapping equation (see (

The delay time and embedding dimension play an important role in the phase space reconstruction according to a scalar time series. However, it is often extremely difficult to choose the parameters such as embedding dimension and delay time for phase space reconstruction. Normally, the delay time and embedding dimension are chosen independently. However, in recent years, some researchers contend that the delay time and embedding dimension are interrelated; that is, the delay time window should be estimated firstly for the choice of delay time and embedding dimension [

Echo state network (ESN) is a new-style recurrent neural network with a sparsely connected hidden layer [

Architecture of echo state network.

The training of echo state network can be done in two stages: sampling and weight computation. During the sampling stage of the training, the echo state network is driven by the input sequence

The mean squared training error is defined as

Nonlinear time series forecasting is an important portion of current science and technology [

The forecasting methods of nonlinear time series include indirect forecasting and direct forecasting. The method of single-step forecasting has higher accuracy in practical applications. The direct multisteps forecasting model is concerned with the estimation of the system output at some time steps based on the mapping of input and output. There is no accumulation error for direct forecasting algorithms without the feedback of errors. However, with the increase of time steps, the forecasting model will be more complex. The single-step forecasting model can carry out indirect multisteps forecasting through iterations. But the error of forecasting model accumulates along with time. The method of direct multisteps forecasting is applied to forecast the time series of distributed generation system power in this paper. A detailed description of each implement step of the forecasting algorithm is as follows:

The chaotic analysis: calculate the value of the largest Lyapunov exponent to check whether the scalar time series is chaotic. Positive largest Lyapunov exponent shows the dynamic system is chaotic.

The selection of system parameters: the embedding dimension

Phase space reconstruction: reconstruct an

The training samples: the input vectors are

The initialization of the forecasting model: the forecasting model based on ESN is initialized according to the learning algorithm of ESN. The output weights matrix is calculated based on (

Prediction of the observation: the prediction value of energy in time domain

The equations of the distributed generation system are normally unknown. The interaction among the subsystems can be analyzed based on the dynamics system theory. The system law in the multidimensional phase space will be investigated based on the evolution track of the maximum power. During the operation of the distributed generation system, the maximum power was recorded every day. We gained a rich supply of data which would normally be accessible. In this paper, we collected 1000 data points, including 800 training datasets and 200 test data sequences. The data collection system consists of two parts, data acquisition and normalization processing. The process of data normalization can suppress the electromagnetic interferences and improve the generalization ability of neural network model. The method of normalization processing is provided. The equation of linear transformation can be represented as shown below:

The problem of detecting and quantifying chaos is a key step for the intensive studies of nonlinear systems. The Lyapunov exponents are the important indexes to quantify the sensitivity on initial conditions for a dynamical system. If the dynamical system is chaotic, at least one Lyapunov exponent must be positive. Therefore, we only need to calculate the largest Lyapunov exponent to judge the chaotic characters. The largest Lyapunov exponent characterizes the rate exponential divergence of the nearby trajectories in the reconstructed phase space. There are also lots of algorithms to estimate the largest Lyapunov exponent of an experimental time series. In this paper, the largest Lyapunov exponent was calculated with small amount of data. The estimate of the largest Lyapunov exponent is 0.13 bit/s (shown in Figure

The largest Lyapunov exponent.

The embedding dimension

The attractor of chaotic power time series.

The neural network model is trained based on the training samples. The teacher signal is written into the output unit for times

The result of direct prediction based on echo state network for the maximum power series of the distributed generation system is shown in Figure

The estimated output and observations.

The error of the predictions.

The error of the traditional multilayer perceptron.

The microenvironment meteorological data are coupled with the output power of the distributed generation system. Theoretical proof and experimental results show that the output power of the distributed generation system is chaotic time series. The prediction of chaotic time series is to establish a nonlinear model of the dynamic system based on real time series in the reconstructed phase space. Firstly, we should detect and quantify chaos for the intensive studies of nonlinear systems. If the largest Lyapunov exponent is positive, the dynamical system must be chaotic. Secondly, the embedding dimension and the delay time are chosen based on the improved C-C method. The attractor of chaotic power time series can be reconstructed based on the embedding dimension and delay time in the phase space. Lastly, the neural network model is trained based on the training samples, which are obtained from the distributed generation system. The neural network will approximate the curve of output power adequately. The maximum power point of the distributed generation system will be tracked based on the meteorological data.

The measuring errors are unavoidable among experimental data due to the disturbance and many other factors. The prediction precision of the neural network model is largely dependent on the generalization of neural network. Therefore, we should optimize the structure and parameters of the model for better performance. Experimental results show that the prediction model based on echo state network has high accuracy. The chaotic prediction model can approximate the mapping between the maximum power point of the distributed generation system and the meteorological data. The echo state network model can make rather remarkably accurate predictions about the maximum power of the distributed generation system.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is supported by the National Natural Science Foundation of China (nos. 61473174, 61105100, and 51376110), the Specialized Research Fund for the Doctoral Program of Higher Education (no. 20130131130006), Project funded by China Postdoctoral Science Foundation (no. 2014M551907), and Independent Innovation Foundation of Shandong University (no. 2013ZRQP002).