Fig. 1. Eigen values of the closed loop system in the z-plane: 110MW ( ~) and 330 MW ( ). Fig. 2. Simple heat exchanger model. 776 T. IEE Japan, Vol.

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Application of Nonlinear System Identification Method to Thermal Power Plants Yukihiro Toyoda, Member (Bailey Japan Co., Ltd.), Kiyoshi Wada, Member (Kyushu University) Electric power companies will pay their attention to the load following capability and economical operation of a thermal power plant with once-through boilers. However conventional PID controllers embedded on DCSs cannot always give the optimum solution to such subjects. To cope with these problems, we have discussed a model-based advanced control system. Prior to study of the advanced control system, we develop a nonlinear system identification method based on the exogenous variable-dependent ARX model considering the charac teristics of a power plant dynamics. We verify its effectiveness through simulation tests by using measurement data collected in the field tests and simulation tests with SIMULINK-based boiler-turbine dynamic models.

Fig. 1. Eigen values of the closed loop system in the z-plane: 110MW ( ~) and 330 MW ( ). Fig. 2. Simple heat exchanger model. 776 T. IEE Japan, Vol. 120-C, No. 6, 2000

ě(t)=[Ċy(t)Ċu(t)Ċw(t)] c c c c c c c c c c(3) Ċy(t)=[y(t)y(t- 1)...y(t-na+1)]T Ċu (t)=[u(t)u(t-1)...u(t-nb+1)]t Ċu,(t)=[ w(t) w(t-1)... w(t-na+1)]t w(t)=w(t)-w(t-1) y(t+1)=y{ě)(t)}+e>(f+1) c c c c c c c c c c(2) c c c c c c c c c c (4) c c c c c c c c c c (5) Table 1. Behavior of the eigen values due to steam flow rate.

Fig. 3. Example of the application of the exogenous variable-dependent ARK model to data collected in the identification tests by using the actual power plant. 778 T. IEE Japan, Vol. 120-C, No. 6, 2000

Fig. 4. Example of the application of the exgenous variable-dependent ARX model to the actual drum boiler.

Fig. 5. Boiler/Turbine dynamic models with existing controllers by using MATLAB Simulink. Fig. 6. Step-response due to manipulated variables at higher load and lower load. Fig. 7. Conceptual diagram of the system at the identification test. 780 T. IEE Japan, Vol. 120-C, No. 6, 2000

非 線 形 シス テ ム制 御 系設 計 の た め の同 定 (a)同 定 試験 時 実 測値 のWavelet解 Fig. 8. Results 析結 果 (b)同 定試 験 時予 測値 のWavelet解 析結果 図8 ラ ン プ状 負 荷 変 化 時 の 実 測 値/予 測 値 時 系 列 のWavelet解 析 of Wavelet analysis for measured and estimated data at rampwise load changes. プ ロ セ ス の 動 特 性 を 精 度 よ く 同 定 す る た め に, MWDを ラ ン プ 状 に 変 化 さ せ な が ら,同 FF, SP1, SP2, RGDと してM系 時 に 各 種 バ イ ア ス信 号 列 信 号 を用 い て プ ロセ ス を励 振 す る(図7) 図8か ら明 ら か な よ う に,非 運転 条 件 に も か か わ ら ず,提 線 形 性 が 強 く現 わ れ て い る 案手 法 を用 いれ ば全 域 にわ た って 高 い 予 測 精 度 が 得 られ る こ とが 確 認 で き た な お,こ の と きの 外 生 変 数 依 存 型ARXモ 1, 2は25%と90%の デ ル の 基 準 負 荷wj0, j= 二 つ の負荷 帯 を選 ん だ こ こで は ラ ン プ状 負 荷 変 化 時 の 予 測 モ デ ル の 妥 当 性 を評 価 す る方 法 と し て,時 考 慮 し,実 間 的 に周 波 数特 性 が変 化 す る ことを 測 値 と予 測 値 の 時 系 列 デ ー タ にWavelet解 を行 う方 法 を 試 み た(8) こ れ に よ れ ば,負 析 荷 変 化 時 に どの 程度 の帯域 まで 予測 モ デ ルが 有 効 で あ るか を評価 す る こ と がで きる 図8(a)は 実 測 値 の, して お り,横 周 波 数(Hz)を (b)図 軸 は 時 点(サ は予 測値 のゲ イ ン特性 を表 ン プ リ ン グ 周 期90s),縦 一 時 刻 で の 濃 度 を比 較 す る こ と に よ り予 測 精 度 が 有 効 な 帯 域 を知 る こ と が で き,予 120巻6号,平 成12年 従 来線 形 補 間方 式 と提案 方 式 の予測 精 度 の 比較 Fig. 9. Comparison between conventional interpo lation method using linear models and the proposed それ ぞ れ表 す ゲ イ ンの 大 き さ に濃 度 を 対 応 させ て い る の で,同 電 学 論C, 図9 軸 は method using ARX model 測 モ デル 781 the exogenous variable-dependent

Fig. 10. Dependency of each parameters of the exogenous variable-dependent ARX model on load level. (1) H. Nakamura and H. Akaike: "Statistical Identification for Optimal Supercritical Thermal Power Control of Plants", "Optimal Reg Automation-J. IFAC, 17, 143 `155 (1981) (2) S. Miyazuka, H. Kishimoto, H. Shioya, and H. Nakamura: ulator Implementation by Microprocessor based Distributed Control System", 1989 Conference on Power Plant Controls and Automation (1989) (3) H. Nakamura and Y. Toyoda: "Statistical Identification and Optimal Control of Thermal power Plants", Ann. Inst. Statist. Matte. 40, No. 1, 1-28 (1988) (4) V. Haggan and T. Ozaki: "Modeling Nonlinear Random Vibrations Using an Amplitude-dependent Autoregressive Time Series Model", Bioini trika 68, 189-196 (1981) ( 5) Y. Toyoda, K. Oda, and T. Ozaki: "The Nonlinear System Identification Method for The Advanced Control of The Fossil Power Plant", 11th IFAC Syrnp. On System IdentiJica., 3, 1273-1278 (1997) (6) The MathWorks, Inc. SIMULINK User's Guide (1993) 782 T. IEE Japan, Vol. 120-C, No. 6, 2000

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