JP2005048637A - Turbine reference output calculating device and its method, and computer program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a turbine reference output calculating device and its method for calculating the reference output of a turbine as a deterioration reference, and to provide a computer program. <P>SOLUTION: A reference value for the output of the turbine is calculated in accordance with a reference expression stored in a reference expression storage means and a coefficient stored in a coefficient storage means. By applying a heat insulating heat drop ΔH to the reference expression, the theoretical output of the turbine is calculated to be the reference value for the output of the turbine. The reference value can be properly updated by reflecting the condition of the turbine. It is compared with an actually measured value of the output of the turbine to determine the deterioration of the turbine. A quadratic expression Q1 for a mass flow rate Vm of operating fluid and a quadratic expression Q2 for a specific volume Sp of the operating fluid are used for properly reflecting a change in the efficiency of the turbine with a change in the mass flow rate Vm to the reference value. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

ここで、
κ：比熱比（＝Ｃｐ（低圧比熱）／Ｃｖ（定容比熱））
Ｐ１：タービン入口側圧力
Ｐ２：タービン出口側圧力
である。
【００４７】
ΔＨを断熱熱落差としたことから、ΔＨ・Ｖ_ｍは理論上のタービンの最大出力である理論出力Ｐｒｅｆとしての意味を持ち、式（１）は次の式（３）に置き換えることができる。
Ｐ＝Ｐ_ｒｅｆ・η ……式（３）
【００４８】
図４は、質量流量Ｖ_ｍとタービン効率ηおよびタービン出力Ｐの関係を表すグラフである。図４に示すように、一般にタービン効率はＶ_ｍを横軸にとると上に凸の曲線となる。
この曲線を二次近似すると、次の式（４）の関係が導出できる。
η＝（ａＶ_ｍ ^２＋ｂＶ_ｍ＋ｃ） ……式（４）
ここで、ａ〜ｃ：係数 である。
【００４９】
しかしながら、式（４）を式（１）に代入した次の式（５）について種々の検討を重ねたところ、式（５）は必ずしも測定値と一致しないことが判った。
Ｐ＝ΔＨ・Ｖ_ｍ・（ａＶ_ｍ ^２＋ｂＶ_ｍ＋ｃ） ……式（５）
【００５０】
その後に様々な調査を行ったところ、比体積Ｓｐあるいは体積流量Ｖｖを用いて補正することで、基準式を実際の値と非常によく一致させられることが判った。これは例えば、次の式（６）である。
【００５１】

ここで、

である。
【００５２】
式（６）は、体積流量Ｖｍの二次式Ｑ１と比体積Ｓｐの二次式Ｑ２の積の形で表されている。
式（６）では比体積Ｓｐを用いて補正する場合を示しているが、次の式（７）に示すように比体積Ｓｐに換えて体積流量Ｖｖを用いて補正することも可能である。

【００５３】
式（６）、（７）では、比体積Ｓｐの二次式Ｑ２，体積流量Ｖｖの二次式Ｑ３の係数は同一に表されているが、実際の値としては異なる値が用いられることとなる。
式（６）、（７）では、どちらかと言えば式（６）の方が広い範囲の質量流量Ｖ_ｍで、タービンＴの出力と一致する。しかしながら、式（７）でも質量流量Ｖ_ｍの変化幅がそれほど大きくなければ、出力の基準値の算出に用いて差し支えない。
なお、式（６）、（７）では、比体積Ｓｐまたは体積流量Ｖｖの２次項までを用いて近似精度を向上しているが、これは必ずしも絶対的なものではなく、１次項まであるいは３次項以上を用いることができる。
【００５４】
Ｂ．複数タービンの場合
複数のタービンが１つの軸で接続されている場合には、全体の出力の基準値Ｐｗはこれら複数のタービンの出力を加算したものとなる。
例えば、図１で示したような蒸気タービンＳＴ（高圧タービンＨＴ、中圧タービンＩＴ、低圧タービンＬＴ）、ガスタービンＧＴ、空気圧縮機ＣＰが接続されている場合の出力基準値Ｐｗは以下の式（１０）により表される。
【００５５】
Ｐ_Ｗ＝−Ｐ_ＣＰ＋Ｐ_ＧＴ＋Ｐ_ＨＴ＋Ｐ_ＩＴ＋Ｐ_ＬＴ＋Ｃ ……式（１０）
ここで、Ｐ_ＣＰ：空気圧縮機ＣＰの出力（実際には入力なので−がつく）
Ｐ_ＧＴ：ガスタービンＧＴの出力
Ｐ_ＨＴ：高圧タービンＨＴの出力
Ｐ_ＩＴ：中圧タービンＩＴの出力
Ｐ_ＬＴ：低圧タービンＬＴの出力
Ｃ：近似定数
であり、それぞれ式（１１）〜（１５）のように表される。
【００５６】
空気圧縮機ＣＰについては、軸方向の成分と周方向の成分に分けて近似式が適用される。以下に示す圧縮機出力等の軸方向／周方向成分の比率は、空気圧縮機ＣＰの入口に設けられた案内羽根の角度により変化する。
Ｐ_ＣＰ＝Ｐ_{ＣＰ＿ｒｅｆ}・（ａ_１Ｖ_ａｆ＿ｍ ^２＋ｂ_１Ｖ_ａｆ＿ｍ＋ｃ_１）・（α_１Ｖ_{ａｆ＿ ｖ} ^２＋β_１Ｖ_{ａｆ＿ ｖ}＋γ_１）＋Ｐ_{ＣＰ＿ｒｅｆ＿ｒ}・（ａ_２Ｖ_{ａｆ ｒ ＿ｍ} ^２＋ｂ_２Ｖ_{ａｆ ｒ ＿ｍ}＋ｃ_２）・（α_２Ｖ_{ａ ｆ ｒ ＿ ｖ} ^２＋β_２Ｖ_{ａｆ ｒ ＿ ｖ}＋γ_２） …式（１１）
【００５７】
ここで、
Ｐ_{ＣＰ＿ｒｅｆ}（＝ΔＨ_ｃｏｍｐ・Ｖ_ａｆ＿ｍ） ：圧縮機理論出力の軸方向成分
Ｐ_{ＣＰ＿ｒｅｆ＿ｒ}（＝ΔＨ_ｃｏｍｐ・Ｖ_{ａｆ ｒ ＿ｍ}）：圧縮機理論出力の周方向成分
Ｖ_ａｆ＿ｍ：圧縮機空気質量流量の軸方向成分
Ｖ_ａｆ＿ｖ：圧縮機空気体積流量の軸方向成分
Ｖ_{ａｆｒ＿ｍ}：圧縮機空気質量流量の周方向成分
Ｖ_{ａｆｒ＿ ｖ}：圧縮機空気体積流量の周方向成分
である。
【００５８】
Ｐ_ＧＴ＝Ｐ_{ＧＴ＿ｒｅｆ}・（ａ_３Ｖ_ＧＴ＿ｍ ^２＋ｂ_３Ｖ_ＧＴ＿ｍ＋ｃ_３）・（α_３Ｖ_ＧＴ＿ｖ ^２＋β_３Ｖ_{ＧＴ＿ ｖ}＋γ_３） …式（１２）
ここで、
Ｐ_{ＧＴ＿ｒｅｆ}（＝ΔＨ_ＧＴ・Ｖ_ＧＴ＿ｍ） ：ガスタービン理論出力
Ｖ_ＧＴ＿ｍ：ガスタービン入口燃焼ガス質量流量
Ｖ_ＧＴ＿ｖ：ガスタービン入口燃焼ガス体積流量
である。
【００５９】
Ｐ_ＨＴ＝Ｐ_{ＨＴ＿ｒｅｆ}・（ａ_４Ｖ_ＨＴ＿ｍ ^２＋ｂ_４Ｖ_ＨＴ＿ｍ＋ｃ_４）・（α_４Ｖ_ＨＴ＿ｖ ^２＋β_４Ｖ_{ＨＴ＿ ｖ}＋γ_４） …式（１３）
ここで、
Ｐ_{ＨＴ＿ｒｅｆ}（＝ΔＨ_ＨＴ・Ｖ_ＨＴ＿ｍ）：高圧タービン理論出力
Ｖ_ＨＴ＿ｍ：高圧タービン入口蒸気質量流量
Ｖ_ＨＴ＿ｖ：高圧タービン入口蒸気体積流量
である。
【００６０】
Ｐ_ＩＴ＝Ｐ_{ＩＴ＿ｒｅｆ}・（ａ_５Ｖ_ＩＴ＿ｍ ^２＋ｂ_５Ｖ_ＩＴ＿ｍ＋ｃ_５）・（α_５Ｖ_ＩＴ＿ｖ ^２＋β_５Ｖ_{ＩＴ＿ ｖ}＋γ_５） …式（１４）
ここで、
Ｐ_{ＩＴ＿ｒｅｆ}（＝ΔＨ_ＩＴ・Ｖ_ＩＴ＿ｍ） ：中圧タービン理論出力
Ｖ_ＩＴ＿ｍ：中圧タービン入口蒸気質量流量
Ｖ_ＩＴ＿ｖ：中圧タービン入口蒸気体積流量
である。
【００６１】
Ｐ_ＬＴ＝Ｐ_{ＬＴ＿ｒｅｆ}・（ａ_６Ｖ_ＬＴ＿ｍ ^２＋ｂ_６Ｖ_ＬＴ＿ｍ＋ｃ_６）・（α_６Ｖ_ＬＴ＿ｖ ^２＋β_６Ｖ_{ＬＴ＿ ｖ}＋γ_６）＋δＶ_ａｃ …式（１５）
ここで、
Ｐ_{ＬＴ＿ｒｅｆ}（＝ΔＨ_ＬＴ・Ｖ_ＬＴ＿ｍ）：低圧タービン理論出力
Ｖ_ＬＴ＿ｍ：低圧タービン入口蒸気質量流量
Ｖ_ＬＴ＿ｖ：低圧タービン入口蒸気体積流量
δＶ_ａｃ：真空度による補正項
（Ｖ_ａｃ＝復水器真空度／Ｖ_ＬＴ＿ｍ・Ｐ_{ＬＴ＿ｒｅｆ}）
である。
【００６２】
式（１０）に式（１１）〜（１５）を代入することで、それぞれのタービンＴの状態（入口側温度Ｔ１、入口側圧力Ｐ２、出口側圧力Ｐ２、質量流量Ｖｍ）から、発電システムＧＳ全体としての出力の基準値を算出することができる。
【００６３】
Ｃ．重回帰分析等による係数の決定
式（１１）〜（１５）における係数ａ_ｎ〜ｃ_ｎ（ｎ：１〜６）、α_ｎ〜γ_{ｎ 、}δ、Ｃは、実際には未知数である。これを実際の発電システムＧＳに合わせて算出する必要がある。即ち、Ｐ_Ｗが基準としたい状態の発電機Ｇの出力実測値Ｐｍに近づくような係数ａ_ｎ〜ｃ_ｎ、α_ｎ〜γ_{ｎ 、}δ、Ｃを算出する。
具体的には、式（１１）〜（１５）を展開して式（１０）に代入し、重回帰分析を行うことにより係数ａ_ｎ等を求めることができる。例えば、ガスタービンＧＴの式（１２）を展開すると、次の式（２０）のように表せ、重回帰分析により係数Ａ〜Ｉを導出できる。
【００６４】
Ｐ_ＧＴ＝Ａ・Ｐ_{ＧＴ＿ｒｅｆ}・Ｖ_ＧＴ＿ｍ ^２・Ｖ_ＧＴ＿ｖ ^２＋Ｂ・Ｐ_{ＧＴ＿ｒｅｆ}・Ｖ_ＧＴ＿ｍ ^２・Ｖ_ＧＴ＿ｖ＋Ｃ・Ｐ_{ＧＴ＿ｒｅｆ}・Ｖ_ＧＴ＿ｍ ^２＋Ｄ・Ｐ_{ＧＴ＿ｒｅｆ}・Ｖ_ＧＴ＿ｍ・Ｖ_ＧＴ＿ｖ ^２＋Ｅ・Ｐ_{ＧＴ＿ｒｅｆ}・Ｖ_ＧＴ＿ｍ・Ｖ_ＧＴ＿ｖ＋Ｆ・Ｐ_{ＧＴ＿ｒｅｆ}・Ｖ_ＧＴ＿ｍ＋Ｇ・Ｐ_{ＧＴ＿ｒｅｆ}・Ｖ_ＧＴ＿ｖ ^２＋Ｈ・Ｐ_{ＧＴ＿ｒｅｆ}・Ｖ_ＧＴ＿ｖ＋Ｉ・Ｐ_{ＧＴ＿ｒｅｆ} …式（２０）
【００６５】
係数の算出に使用するデータは、例えば次のａ，ｂのようなデータを利用することができる。多様なデータの取得が可能であることから、どちらかといえば、ａの性能試験データの方が利用するデータとして好ましいものの、いずれのデータを利用しても係数の算出が可能である。
ａ．発電システムＧＳの性能試験データ
性能試験では、発電システムＧＳを異なる運転条件下に置きそれぞれ異なる出力を得ることができる。
【００６６】
ｂ．発電システムＧＳの実績運転データ（例えば、一年間）
発電システムＧＳを通常運転下に置いて、そのときに得られる出力データを蓄積する。このときには、平均的運転条件に対応するように係数ａ_ｎ等が決定されることになる。
【００６７】
Ｄ．基本状態値の推定
式（１０）から判るように、断熱熱落差ΔＨの算出には、入口側温度Ｔ１、入口側圧力Ｐ１、出口側圧力Ｐ２が必要となり、これらのパラメータが計測されていることが望ましい。
しかしながら、次のような手法を適用することで、一部のパラメータが何らかの理由により（例えば、測定器が備えられていない）欠けている場合でも、対応することができる。
【００６８】
ａ．ガスタービンＧＴの場合
入口側温度Ｔ１について、以下▲１▼、▲２▼の方法を適用して算出できる。
▲１▼燃料成分と燃料・空気流量から計算
次の式（３０）の両辺が等しくなるような温度Ｔ１を算出する。燃料の成分、流量が燃料の熱量Ｑ_ＦＬの算出に、空気の流量が空気の熱量Ｑ_ＣＰの算出に用いられる。
Ｑ_ＦＬ＋Ｑ_ＣＰ＝Ｑ_Ｎ２＋Ｑ_Ｏ２＋Ｑ_ＣＯ２＋Ｑ_Ｈ２Ｏ …式（３０）
【００６９】
ここで、
Ｑ_ＦＬ：燃料の熱量
Ｑ_ＣＰ：空気圧縮機ＣＰ出口温度（燃焼前）における燃焼用空気の熱量
Ｑ_Ｎ２：ガスタービンＧＴ入口温度Ｔ１における燃焼後の窒素の熱量
Ｑ_Ｏ２：ガスタービンＧＴ入口温度Ｔ１における燃焼後の酸素の熱量
Ｑ_ＣＯ２：ガスタービンＧＴ入口温度Ｔ１における燃焼後の二酸化炭素の熱量
Ｑ_Ｈ２Ｏ：ガスタービンＧＴ入口温度Ｔ１における燃焼後の水分の熱量
である。
【００７０】
▲２▼出口側温度Ｔ２が判っている場合には、タービンＴ内での作動流体の変化がポリトロープ変化だとして入口側温度Ｔ１を計算できる。
Ｔ１＝Ｔ２・（Ｐ１／Ｐ２）^{（ｎ−１）／ｎ} ……式（４０）
ここで、
ｎ：ポリトロープ係数
Ｐ１，Ｐ２：入口側、出口側圧力
Ｔ１，Ｔ２：入口側、出口側温度
である。
【００７１】
ｂ．中圧タービンＩＴの場合
出口側圧力Ｐ２について、以下▲１▼、▲２▼の方法を適用できる。
▲１▼中圧タービン入口側圧力Ｐ１と復水器真空度Ｐ_ＣＤから低圧蒸気流量、クロスオーバー管等の影響を考慮して、算出できる。
具体的には、次の式（５１）に基づき、出口側圧力Ｐ２を算出することができる。
Ｐ２＝Ｐ１・Ｋ１^ｍ１ ……式（５１）
【００７２】
ここで、
ｍ１：中圧タービンＩＴの段落数
Ｋ１：中圧タービン一段当たりの圧力降下率
＝ｎ段の入口圧力／（ｎ−１）段の入口圧力
＝［Ｐ_ＣＤ／（Ｐ１・Ｋ２・Ｋ３^ｍ２）］^{１／（ｍ１＋ｍ２）}
ｍ２：低圧タービンＬＴの段落数
Ｋ２：クロスオーバ管の圧力降下率
＝クロスオーバ管後の圧力／クロスオーバ管前の圧力
Ｋ３：低圧タービン流量比
＝中圧タービン出口流量／低圧タービン入口流量／Ａ
Ａ：低圧タービンＬＴの入口面積・車室数／中圧タービン最終段面積
である。
【００７３】
▲２▼中圧タービン排気部の車室温度ｔを使い、低圧蒸気熱量とのバランスから算出できる。
具体的には、以下の式（５２）において、両辺が等しくなるのに必要な圧力Ｐを算出する。
ｈ１・Ｆ１＝ｈ２・（Ｆ１＋Ｆ２）−ｈ３・Ｆ２ …式（５２）
【００７４】
ここで、
Ｋ２：クロスオーバ管の圧力降下率
ｈ１：温度ｔ（車室温度ｔと等しいとする）、圧力Ｐにおける中圧タービンの出口側エンタルピー
ｈ２：（低圧タービン入口側）温度ｔ２、圧力Ｐ・Ｋ２における低圧タービンの入口側エンタルピー
ｈ３：（低圧主蒸気）温度ｔ３、圧力Ｐ３における低圧主蒸気エンタルピー
Ｆ１：中圧タービン蒸気流量
Ｆ２：低圧主蒸気流量
である。
【００７５】
ｃ．低圧タービンＬＴの場合
入口側圧力について、中圧タービンＩＴと同様の手法を適用できる。
具体的には、次の式（５３）に基づき、出口側圧力Ｐ２を算出することができる。
Ｐ２＝Ｐ１・Ｋ２ ……式（５３）
【００７６】
ここで、
Ｐ１：中圧タービン入口側圧力
Ｋ２：クロスオーバ管の圧力降下率
＝クロスオーバ管後の圧力／クロスオーバ管前の圧力
である。
【００７７】
入口側温度については、中圧タービン排気部の車室温度ｔを使い、低圧蒸気熱量とのバランスから計算により求めることができる。
具体的には、以下の式（５４）において、両辺が等しくなるのに必要な温度ｔ２を算出する。
ｈ２・（Ｆ１＋Ｆ２）＝ｈ１・Ｆ１＋ｈ３・Ｆ２ …式（５４）
【００７８】
ここで、
Ｋ２：クロスオーバ管の圧力降下率
ｈ１：温度ｔ（車室温度ｔと等しいとする）、圧力Ｐにおける中圧タービンの出口側エンタルピー
ｈ２：（低圧タービン入口側）温度ｔ２、圧力Ｐ・Ｋ２における低圧タービンの入口側エンタルピー
ｈ３：（低圧主蒸気）温度ｔ３、圧力Ｐ・Ｋ２３における低圧主蒸気エンタルピー
Ｆ１：中圧タービン蒸気流量
Ｆ２：低圧主蒸気流量
である。
なお、中圧タービン排気部の車室温度ｔが中圧タービンの排気と低圧蒸気とを混合した後での温度と見なせる場合は、車室温度ｔにその温度を用いることができる。
【００７９】
（発電システムＧＳの管理）
Ａ．発電システムＧＳ全体の管理
式（１０）を用いて、発電システムＧＳの管理を行うことができる。
これは次のように、式（１０）から得られた出力基準値Ｐｗと発電システムＧＳの出力実測値Ｐｍとを比較することで行える。これは図３のステップＳ２５で既述の出力の比較に対応する。
ΔＰ＝Ｐｗ−Ｐｍ ……式（６０）
ここで、ΔＰ：出力偏差 である。
【００８０】
さらに、この出力偏差ΔＰを用いて、効率の変化Δηを算出することができる。
Δη＝ΔＰ／Ｑｔ ……式（６１）
ここで、Ｑｔ：使用した燃料から発せられた総熱量（Ｊ） である。
【００８１】
ここで、式（６０）で表される出力偏差ΔＰの意味を再度説明する（式（１）に関連して一旦説明済み）。
既述のように、出力基準値Ｐｗは発電システムＧＳのある時点での出力実測値に一致するように係数が設定される。これはその時点での発電システムＧＳの性能に対応するように式（１０）が設定されたことを意味する。従い、出力偏差ΔＰは、性能の変化に対応するものと考えられる。
【００８２】
タービンや圧縮機の内部において性能に影響を及ぼすような変化があった場合、出口側温度の変化により出力が変動するが、上のように求めた基準出力は出口側温度の要素を含まないため、実績の出力との比較を行うと性能の変化分が出力の偏差として算出される。
【００８３】
Ｂ．個別的な管理
式（１０）をタービンＴ毎に評価することが可能であり、例えばガスタービンＧＴ側、蒸気タービンＳＴに分離することができる。
式（１０）から、以下の２つの式（６２）、（６３）を取り出すことができる。
【００８４】
Ｐ_ＧＴ０＝−Ｐ_ＣＰ＋Ｐ_ＧＴ ……式（６２）
Ｐ_{ＳＴ ０}＝Ｐ_ＨＴ＋Ｐ_ＩＴ＋Ｐ_ＬＴ ……式（６３）
ここで、
Ｐ_ＧＴ０：全ガスタービン出力（作動流体に空気・燃焼ガスを利用する空気圧縮機ＣＰとガスタービンＧＴの出力合計）
Ｐ_ＳＴ０：全蒸気タービン出力（作動流体に蒸気を利用する蒸気タービンＳＴの出力）
である。
【００８５】
ガスタービンＧＴ、蒸気タービンＳＴそれぞれの実績出力を採取して（基準出力算出に使用したデータと同じ時期に、データを採取するのが便宜）、全ガスタービン出力Ｐ_ＧＴ０の算出値（Ｐ_ＧＴ０ｃ）と実測値（Ｐ_ＧＴ０ｍ）、全蒸気タービン出力Ｐ_ＳＴの算出値（Ｐ_ＳＴ０ｃ）と実測値（Ｐ_ＳＴｍ）それぞれの関係を示す近似式や図を作成しておけば、ガスタービンＧＴ側、蒸気タービンＳＴ側の基準出力となりうる（ＧＴ基準線、ＳＴ基準線の作成）。
【００８６】
なお、全ガスタービン出力の実測値（Ｐ_ＧＴ０ｍ）、全蒸気タービン出力の実測値（Ｐ_ＳＴ０ｍ）は、次のａ，ｂのような手法で全出力Ｐｗから分離することができる。
【００８７】
ａ．入出熱法
ガスタービンＧＴと蒸気タービンＳＴそれぞれで、入った熱Ｑ１と出た熱Ｑ２を求め、これを出力に換算することができる。具体的には、次の式（５５）を用いる。
【００８８】

ここで、
Ｑ２_ＧＴ， Ｑ１_ＧＴ： ガスタービンＧＴでの熱の入力、出力
Ｑ２_ＳＴ， Ｑ１_ＳＴ： 蒸気タービンＳＴでの熱の入力、出力
ΔＰ（＝Ｐ_ＧＴ０−Ｐ_ＳＴ０）： ガスタービンＧＴと蒸気タービンＳＴの出力差
Ａ：換算値
である。
【００８９】
式（６５）で算出された出力差ΔＰを全体出力の実測値Ｐｗｍとの差をとることで、ガスタービンＧＴと蒸気タービンＳＴそれぞれの出力Ｐ０_ＧＴ、Ｐ_ＳＴ０を算出できる。
Ｐ_ＳＴ０＝（Ｐｗｍ−ΔＰ）／２
Ｐ_ＧＴ０＝（Ｐｗｍ＋ΔＰ）／２ …式（６６）
【００９０】
ｂ．計測法
軸トルク計等を用いて、ガスタービンＧＴと蒸気タービンＳＴの境界に加わるトルクＴを測定し、この測定結果を基に出力差ΔＰ（物理的意味合いは、式（６５）と同様）を算出する。その後は、式（６６）を用いてガスタービンＧＴと蒸気タービンＳＴそれぞれの出力Ｐ_ＧＴ０、Ｐ_ＳＴ０を算出できる。
【００９１】
（実験結果）
以下、本発明を適用して計算した結果を示す。
図５は、本発明に係るタービン基準出力算出装置において式（６０）に基づき計算された出力偏差ΔＰの具体例を示すグラフである。また、図６は、図５の比較例を表すグラフである。これらのグラフでは、横軸：時間（ｔ）、縦軸：出力（ＭＷ）となっている。この具体例、比較例ではそれぞれ式（６）、（５）に基づき出力偏差ΔＰを算出している。
図５，６を比較すれば判るように、本発明を適用した図５では誤差が小さいことが判る。
【００９２】
図７は、本発明に係るタービン基準出力算出装置により計算されたガスタービンＧＴの基準値Ｐと実測値Ｐｍの相関の具体例を表すグラフ（横軸：基準値Ｐ、縦軸：実測値Ｐｍ）である。また、図８は、この比較例を表すグラフである。この具体例、比較例ではそれぞれ式（６）、（５）に基づき出力偏差ΔＰを算出している。
図７，８を比較すれば判るように、本発明を適用した図７では基準値Ｐと実測値Ｐｍの相関が高いことが判る。
【００９３】
図９〜１１は、本発明に係るタービン基準出力算出装置によって式（６）に基づき算出された出力偏差ΔＰの時間的な経過を発電出力全体、ガスタービンＧＴ、蒸気タービンＳＴのそれぞれについて表したグラフである。
ガスタービンＧＴの水洗の前後で、図９，１０では出力偏差ΔＰが変動しているが、図１１ではあまり変動していない。このことは、ガスタービンＧＴと蒸気タービンＳＴの出力の分離が、適切に行えていることを意味すると考えられる。
【００９４】
【発明の効果】
以上説明したように、本発明によれば、タービンの劣化の基準となる基準出力を算出するタービン基準出力算出装置、タービン基準出力算出方法、およびコンピュータ・プログラムを提供することができる。
【図面の簡単な説明】
【図１】本発明の１実施形態に係るタービン基準出力算出装置の構成を示すブロック図である。
【図２】図１に表されたタービン基準出力算出装置の基準式記憶手段に記憶された基準式に含まれる二次式Ｑ１，Ｑ２の係数の算出を行う手順を表すフロー図である。
【図３】図１に表されたタービン基準出力算出装置により発電システムの出力の基準値の算出を行う手順を表すフロー図である。
【図４】質量流量Ｖ_ｍとタービン効率ηおよびタービン出力Ｐの関係を表すグラフである。
【図５】本発明に係るタービン基準出力算出装置により計算された出力偏差ΔＰの具体例を示すグラフである。
【図６】出力偏差ΔＰの比較例を示すグラフである。
【図７】本発明に係るタービン基準出力算出装置により計算されたガスタービンＧＴの基準値Ｐと実測値Ｐｍの相関の具体例を表すグラフである。
【図８】ガスタービンＧＴの基準値Ｐと実測値Ｐｍの相関の比較例を表すグラフである。
【図９】本発明に係るタービン基準出力算出装置によって算出された発電出力全体での出力偏差ΔＰの時間的な経過を表すグラフである。
【図１０】本発明に係るタービン基準出力算出装置によって算出されたガスタービンＧＴでの出力偏差ΔＰの時間的な経過を表すグラフである。
【図１１】本発明に係るタービン基準出力算出装置によって算出された蒸気タービンＳＴでの出力偏差ΔＰの時間的な経過を表すグラフである。
【符号の説明】
１０…タービン基準出力算出装置
１１…基準式記憶手段
１２…係数算出手段
１３…係数記憶手段
１４…基準出力算出手段
１５…出力比較手段
１６…入力手段
１７…出力手段[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a turbine reference output calculation device, a turbine reference output calculation method, and a computer program that calculate a reference value of an output of a turbine such as a steam turbine or a gas turbine.
[0002]
[Prior art]
In power plants, steam turbines, gas turbines, and combined cycle turbines that combine these are used for power generation. The characteristics of these turbines may be deteriorated due to aging or the like, and the deterioration is detected. A technique for detecting deterioration is disclosed in Patent Document 1.
[Patent Document 1]
JP-A-8-326555 (refer to the claims)
[0003]
[Problems to be solved by the invention]
However, detection of turbine degradation is not always easy. When the turbine is operated under a certain condition (for example, at a rated output condition) and the output value is stable, the deterioration of the turbine characteristics can be easily estimated from the temporal fluctuation of the turbine output itself. However, the use condition of the turbine is not always constant, and it is not always easy to estimate the deterioration of the turbine from only the temporal fluctuation of the output. In addition, there may be a time delay in the output fluctuation.
When a plurality of turbines are combined (for example, a combined cycle), it is difficult to determine which turbine has deteriorated characteristics.
[0004]
The present invention has been made to solve such a problem, and provides a turbine reference output calculation device, a turbine reference output calculation method, and a computer program for calculating a reference output that serves as a reference for turbine deterioration. It is aimed.
[0005]
[Means for Solving the Problems]
A. In order to achieve the above object, the turbine reference output calculation apparatus according to the present invention includes a quadratic expression Q1 of the adiabatic heat drop ΔH and the mass flow rate Vm of the working fluid flowing into and out of the turbine. A reference expression storage means for storing a reference expression representing a reference value of the output of the turbine, and a reference expression storage means for storing the reference expression of the output of the turbine. Coefficient storage means for storing the coefficients of the quadratic expressions Q1 and Q2 of the mass flow rate Vm and the specific volume Sp included in the reference expression, the reference expression stored in the reference expression storage means, and the coefficient stored in the coefficient storage means And a reference output calculating means for calculating a reference value of the output of the turbine.
[0006]
In the turbine reference output calculation apparatus according to the present invention, the reference value of the turbine output can be calculated based on the reference expression stored in the reference expression storage means and the coefficient stored in the coefficient storage means.
Since the reference equation includes an adiabatic heat drop ΔH (a heat drop when the state change of the working fluid in the turbine is performed in an adiabatic state (change in enthalpy H)), The meaning output is calculated and used as a reference value for the turbine output. This reference value can be appropriately updated to reflect the state of the turbine (for example, the volume flow rate of the working fluid, the pressure on the turbine inlet side, the pressure on the turbine outlet side, etc.).
Thus, since the reference value of the turbine output calculated by the reference equation can be updated according to the state of the turbine, the deterioration of the turbine or the like can be obtained by comparing this reference value with the actual measured value of the turbine output. Can be determined.
The quadratic formula Q1 of the mass flow rate Vm of the working fluid and the quadratic formula Q2 of the specific volume Sp of the working fluid are for reflecting changes in the efficiency of the turbine due to changes in the mass flow rate Vm and the like in the reference value. The reference value can always be a value that can be compared with the actual measurement value.
[0007]
(1) The turbine reference output calculation device outputs an input means for inputting an actual measurement value of the turbine output, and an output for comparing the actual measurement value input by the input means with the reference value calculated by the reference output calculation means. A comparison means may be further provided.
The calculated reference value can be automatically compared with the actual measurement value, and the state of the turbine can be easily monitored.
The measured value of the turbine output input from this input means may be data appropriately sent from a detector installed in the turbine (for example, in real time) or once accumulated in another device. Even time-series data can be used. That is, the present invention can be applied to both so-called real-time processing and batch processing.
[0008]
(2) The reference output calculation means may include means for calculating the adiabatic heat drop based on the inlet side temperature, the inlet side pressure, and the outlet side pressure of the turbine.
The adiabatic heat drop can be calculated based on measured values of the turbine inlet side temperature, inlet side pressure, and outlet side pressure.
However, even if any of these cannot be measured directly, if the reference output calculation means includes means for estimating at least one of the inlet side temperature, the inlet side pressure, and the outlet side pressure of the turbine, the adiabatic heat The head can be calculated.
[0009]
(3) The turbine reference output calculation device further includes coefficient calculation means for calculating coefficients of quadratic expressions Q1 and Q2 of the mass flow rate Vm and the specific volume Sp based on the actual measurement value of the turbine output. Also good.
By determining the coefficients of the secondary expressions Q1 and Q2 so that the reference expression matches the actual measurement value of the turbine output at that time, the reference value calculated from the reference expression can be easily compared with the actual measurement value. .
The coefficient calculation means can calculate the coefficients of the respective quadratic expressions Q1 and Q2 by regression analysis, for example.
[0010]
The coefficient calculating means may include means for calculating the adiabatic heat drop based on an inlet side temperature, an inlet side pressure, and an outlet side pressure of the turbine.
The adiabatic heat drop can be calculated based on measured values of the turbine inlet side temperature, inlet side pressure, and outlet side pressure.
However, even if any of these cannot be measured directly, if the reference output calculation means includes means for estimating at least one of the inlet side temperature, the inlet side pressure, and the outlet side pressure of the turbine, the adiabatic heat The head can be calculated.
[0011]
(4) The reference formula stored in the reference formula storage means may include a secondary formula Q3 of the volumetric flow rate of the working fluid as an element instead of the secondary formula Q2 of the specific volume Sp of the working fluid.
The combination of the secondary equation Q1 for the mass flow rate Vm of the working fluid and the secondary equation Q3 for the volumetric flow rate reflects the change in turbine efficiency accompanying changes in the mass flow rate Vm in the reference value, and the reference value is always measured. And can be made a comparable value.
[0012]
(5) The turbine may be a multistage turbine including a plurality of turbines.
In the case of multiple stages of turbines, the output reference value for the entire turbine can be calculated by summing the outputs calculated for each turbine.
[0013]
Here, the reference output calculation means may separately calculate the reference outputs of a plurality of turbines.
When the output of a plurality of turbines can be measured separately, the reference value and the actual measurement value can be easily compared.
In addition, this “separate” means to allow a plurality of turbines to be calculated individually or collectively to some extent. For example, when the whole turbine is composed of a combination of a steam turbine composed of a high-pressure, medium-pressure, and low-pressure turbine and a gas turbine, the case where the reference output is divided into the steam turbine and the gas turbine and calculated.
[0014]
B. The turbine reference output calculation method according to the present invention includes a quadratic expression Q1 of the adiabatic heat drop ΔH in the turbine of the working fluid flowing into and out of the turbine, the mass flow rate Vm of the working fluid, and the specific volume of the working fluid. A reference expression storage step that includes the quadratic expression Q2 of Sp as an element and stores a reference expression representing a reference value of the output of the turbine in the reference expression storage means; and the reference expression storage means in the reference expression storage means A coefficient calculating step for calculating the coefficients of the quadratic expressions Q1 and Q2 of the mass flow rate Vm and specific volume Sp included in the stored reference equation, and the mass flow rate Vm and specific volume Sp calculated in the coefficient calculating step, respectively. A coefficient storage step for storing the coefficients of the quadratic expressions Q1 and Q2 in the coefficient storage means, and the reference expression stored in the reference expression storage means in the reference expression storage step and the coefficient storage step. Based on the coefficients stored in the coefficient storage means flop, characterized by comprising a reference output calculation step of calculating a reference value of the output of the turbine.
[0015]
In the turbine reference output calculation method according to the present invention, the reference value of the turbine output can be calculated based on the reference expression stored in the reference expression storage means and the coefficient stored in the coefficient storage means.
Since the adiabatic heat drop ΔH is included in the reference equation, the output in the theoretical sense of the turbine is calculated and used as the reference value of the turbine output. Since this reference value can be appropriately updated to reflect the state of the turbine, it is possible to easily determine deterioration of the turbine or the like by comparing this reference value with an actual measurement value of the turbine output.
The quadratic formula Q1 of the mass flow rate Vm of the working fluid and the quadratic formula Q2 of the specific volume Sp of the working fluid are for reflecting changes in the efficiency of the turbine due to changes in the mass flow rate Vm and the like in the reference value. The reference value is always a value that can be compared with the actual measurement value.
[0016]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
FIG. 1 is a block diagram showing a configuration of a turbine reference output calculation device 10 according to an embodiment of the present invention, together with a power generation system GS that is a reference output calculation target.
The turbine reference output calculation device 10 is a device that calculates a reference output of the power generation system GS.
[0017]
(About power generation system GS)
The power generation system GS will be described first.
The power generation system GS includes a generator G, a steam turbine ST (high pressure turbine HT, medium pressure turbine IT, low pressure turbine LT), a condenser CD, an air compressor CP, a gas turbine GT, an exhaust heat recovery boiler (HRSG). : Heat Recovery Steam Generator) SG, with chimney VT.
[0018]
An air compressor CP, a gas turbine GT, and a steam turbine ST are connected to the generator G. The generator G is driven by the gas turbine GT and the steam turbine ST to generate electricity.
[0019]
The air AR compressed by the air compressor CP is mixed with the fuel FL in a combustion chamber (not shown) and burned to generate combustion gas CG. This combustion gas CG drives the gas turbine GT, and is then used to generate and reheat steam in the exhaust heat recovery boiler SG, and is discharged from the chimney VT to the outside.
The high-pressure steam HS generated from the exhaust heat recovery boiler SG is given a driving force to the high-pressure turbine HT and then reheated by the exhaust heat recovery boiler SG to become an intermediate-pressure steam IS to give a driving force to the intermediate-pressure turbine IT. The driving force is applied to the low-pressure turbine LT by becoming LS1. In addition to the low-pressure steam LS1, low-pressure steam LS2 obtained by heating the condensate CW from the condenser CD is input to the low-pressure turbine LT. That is, the low-pressure steam LS includes a flow that circulates through the low-pressure turbine LT, the condenser CD, and the exhaust heat recovery boiler SG.
[0020]
The above power generation system GS is a so-called combined cycle in which a steam turbine ST and a gas turbine GT are combined. The combustion gas CG drives the gas turbine GT, generates steam, and finally the steam turbine ST and the gas turbine GT. Since it is used for both driving, the thermal efficiency is good.
[0021]
(Configuration of turbine reference output calculation device 10)
The turbine reference output calculation device 10 includes a computer including a central processing unit (CPU), a storage device (which may be either a main storage device such as a memory or an auxiliary storage device such as a hard disk) and its peripheral devices, It is composed of a combination of computer programs that drive the computer, and calculates a reference output of the power generation system GS.
[0022]
As shown in FIG. 1, specifically, the turbine reference output calculation device 10 includes a reference expression storage unit 11, a coefficient calculation unit 12, a coefficient storage unit 13, a reference output calculation unit 14, an output comparison unit 15, and an input unit 16. Output means 17.
Among these, the reference expression storage unit 11 and the coefficient storage unit 13 are appropriately arranged and configured on a storage area on the storage device. The coefficient calculation means 12 and the reference output calculation means 14 are configured by a combination of a CPU and a computer program. The input means 16 and the output means 17 are input / output devices for the computer to input / output information from / to the outside. The computer program may be configured using either a dedicated program or a general-purpose program. For example, it is possible to configure using Microsoft Excel.
[0023]
The reference expression storage means 11 is a storage means for storing a reference expression of the output of the power generation system GS. The reference expressions stored here are, for example, expressions (6), (7), and (10) to be described later, the adiabatic heat drop ΔH in the turbine of the working fluid flowing into and out of the turbine, and the working fluid flowing into the turbine The secondary expression Q1 of the mass flow rate Vm and the secondary expression Q2 of the specific volume Sp (in some cases, the secondary expression Q3 of the volume flow rate Vv of the working fluid) are included as elements.
[0024]
The original thermodynamic input to the turbine is represented by the heat drop of the working fluid (change in the enthalpy of the working fluid before and after the input to the turbine). Here, a kind of idealization is performed and the theoretical turbine output is calculated on the assumption that the working fluid adiabatically changes in the turbine, and the output calculated by this reference formula has the meaning as the reference value of the turbine output. . The secondary equations Q1 and Q2 are for reflecting changes in the efficiency of the turbine due to changes in the mass flow rate Vm, etc., in the reference value, and for making the reference value always comparable to the actual measurement value. is there.
The details will be described later. In addition, the term “as an element” here means “as a substantial element of the formula”. For example, in place of the specific volume Sp (volume flow rate Vv / mass flow rate Vm) There seems to be no change.
[0025]
The coefficient calculation means 12 is a calculation means for calculating the coefficients of the secondary expressions Q1 and Q2 of the mass flow rate Vm and the specific volume Sp included in the reference expression stored in the reference expression storage means 11. If the measured values of the turbine output with respect to the adiabatic heat drop ΔH, the mass flow rate Vm, and the specific volume Sp are known, the quadratic expressions Q1 and Q2 can be used so that the measured values correspond to the reference values calculated by the reference equation. The coefficient can be calculated appropriately. A statistical method such as regression analysis (including multiple regression analysis) can be used to calculate this coefficient.
[0026]
The coefficient storage means 13 is a storage means for storing the coefficients of the quadratic expressions Q1 and Q2 of the mass flow rate Vm and the specific volume Sp included in the reference expression stored in the reference expression storage means 11.
[0027]
The reference output calculation means 14 is a calculation means for calculating a reference value of the turbine output based on the reference expression stored in the reference expression storage means 11 and the coefficients of the secondary expressions Q1 and Q2 stored in the coefficient storage means 13. is there.
[0028]
The output comparison unit 15 is a comparison unit that compares the reference value of the turbine output calculated by the reference output calculation unit 14 with the measured value of the turbine output. This comparison can be performed simply by subtracting the reference value from the measured value. Furthermore, various processes (for example, a warning corresponding to the degree of change) may be performed according to the magnitude of the difference.
[0029]
The input means 16 includes the coefficients in the coefficient calculation means 12 and the reference output calculation means 14 and information necessary for calculating the reference value (for example, the mass flow rate Vm in the power generation system GS, the inlet side pressure P1 in the turbine T, the outlet side This is a means for inputting the pressure P2 and the turbine output actual measurement value Pm). The input means 16 may be directly input a measurement value from a detector installed in the power generation system GS, or may be measured from a storage device (database or the like) in which data from the detector is recorded in time series. It does not matter if the value is entered indirectly. In other words, the input means 16 includes input means for both real-time processing and batch processing, and includes a case where data is input via a network.
[0030]
The output unit 17 is a unit that outputs a comparison result with the calculated reference value or actual measurement value of the power generation system GS. For example, the output unit 17 includes a display device (CRT, LCD, etc.), a printer, and some media (flexible disk). , CD-ROM, and an external communication line).
[0031]
(Operation of Turbine Reference Output Calculation Device 10)
2 and 3 are flowcharts showing the operation procedure of the turbine reference output calculation device 10.
FIG. 2 shows a procedure for calculating the coefficients of the quadratic expressions Q1 and Q2 of the mass flow rate Vm and the specific volume Sp included in the reference expression stored in the reference expression storage means 11, and FIG. 3 shows the reference expression storage means. 11 represents a procedure for calculating the reference value of the output of the power generation system GS based on the reference equation stored in 11 and the calculated coefficient. Hereinafter, a description will be given with reference to FIGS.
[0032]
A. Calculation of coefficients (Figure 2)
(1) Coefficient calculation data is collected (step S11).
As will be described later, this data may be either performance test data for the power generation system GS or actual operation data. It is sufficient if the basic state value described later can be calculated.
[0033]
(2) The basic state value is calculated based on the collected data (step S12).
The basic state value here refers to the adiabatic heat drop ΔH, the mass flow rate Vm, and the specific volume Sp (in some cases, the volume flow rate Vv) in each turbine (GT, HT, IT, LT).
The adiabatic heat drop ΔH can be calculated from the inlet-side temperature T1, the inlet-side pressure P1, and the outlet-side pressure P2 using equation (2) described later. However, when a part of the inlet side temperature T1, the inlet side pressure P1, and the outlet side pressure P2 is not known, it can be estimated by a method described later.
[0034]
(3) The coefficients of the quadratic equations Q1 and Q2 for the mass flow rate Vm and the specific volume Sp are calculated (step S13).
This calculation can be performed by determining a coefficient by regression analysis or the like so that the reference value calculated when the basic state value is substituted into the reference expression matches the measured value.
In addition, after this calculation, the gas turbine GT and the steam turbine ST are configured so that the reference values in the gas turbine GT and the steam turbine ST (the high pressure turbine HT, the intermediate pressure turbine IT, and the low pressure turbine LT) can be calculated quickly. It is convenient to summarize the relationship between the basic state value and the reference value as a reference line (GT reference line, ST reference line).
[0035]
(4) Store the calculated coefficients of the secondary expressions Q1 and Q2 (step S14).
The calculated coefficient is stored in the coefficient storage unit 13. When the GT reference line and the ST reference line are created, these reference lines are also stored in the storage unit.
[0036]
B. Management of the power generation system GS based on the calculated coefficient (Fig. 3)
(1) Collect data for managing the power generation system GS (step S21).
The data to be collected may be directly collected from a detector installed in the power generation system GS, or may be indirectly collected via a database or the like.
[0037]
(2) The basic state value is calculated based on the collected data (step S22).
The basic state value here refers to the adiabatic heat drop ΔH, the mass flow rate Vm, and the specific volume Sp (in some cases, the volume flow rate Vv) in each turbine (GT, HT, IT, LT) as in step S12. The adiabatic heat drop ΔH can be calculated from the inlet-side temperature T1, the inlet-side pressure P1, and the outlet-side pressure P2, and if some of these are not known, it can be estimated as in step S12.
[0038]
(3) The reference value of the output of each turbine (GT, HT, IT, LT) is calculated (step S23).
This calculation can be performed by substituting the basic state value into the reference equation corresponding to each turbine T.
[0039]
(4) The reference value of the output in the entire power generation system GS, gas turbine GT, and steam turbine ST is calculated (step S24).
This calculation can be performed by adding the reference value calculated for each turbine T in the entire power generation system GS, the gas turbine GT, and the steam turbine ST. It is convenient to use a GT reference line and an ST reference line stored in the calculation.
[0040]
(5) The reference value of the output of the power generation system GS is compared with the measured value. This comparison is performed in the entire power generation system GS, the gas turbine GT, and the steam turbine ST.
As a result of this comparison, when the difference between the reference value and the actual measurement value is large, a warning is issued as necessary, and each component device of the power generation system GS is inspected.
[0041]
(Explanation of standard formula)
Details of the reference formula stored in the reference formula storage unit 11 will be described below.
A. Single turbine case
Generally, the output P of the turbine T (both the steam turbine and the gas turbine) is expressed by the following formula (1).
P = ΔH ・ V_m・ Η ... Formula (1)
here,
ΔH (= H1−H2): heat drop of working fluid per unit mass (change in enthalpy H at the turbine inlet and outlet)
V_m : Mass flow rate of working fluid (kg / sec)
η: Turbine efficiency
It is.
[0042]
This expression (1) is an expression corresponding to the output of the turbine T itself, but the heat drop ΔH in the expression (1) is changed to the adiabatic heat drop (the change of the working fluid in the turbine T is performed in an adiabatic state). By substituting it for (the heat drop at the time), it is possible to give a meaning as a reference value of the output of the turbine T as follows.
[0043]
When ΔH is a heat drop, the output calculated by the equation (1) corresponds to the measured value of the output of the turbine T. On the other hand, when ΔH is an adiabatic heat drop, this value is irrelevant to the outlet side temperature T2 of the turbine T as shown in the following formula (2), and is a kind of idealization. It becomes a state.
[0044]
When the performance of the turbine T is deteriorated, only part of the enthalpy is used for the driving force of the turbine T when the working fluid in the same state is input. For this reason, the enthalpy of the working fluid discharged from the turbine T is kept at a relatively high state, in other words, the outlet side temperature T2 becomes high.
[0045]
When ΔH is a heat drop, the influence of the outlet side temperature T2 is incorporated into the equation (1), and the calculated output of the turbine T changes (in other words, the equation (1) is used as a reference for the output of the turbine T). It is difficult to use for calculation of values). On the other hand, when ΔH is an adiabatic heat drop, the change in the outlet temperature T2 of the turbine T due to the deterioration of the characteristics of the turbine T is not incorporated in the equation (1), and the equation (1) is It can be used to calculate the output reference value.
Hereinafter, ΔH is defined as an adiabatic heat drop in order to give the expression (1) a meaning as a reference value of the output of the turbine T.
[0046]
The adiabatic heat drop ΔH per unit mass of the working fluid is the inlet side temperature T1, the inlet side pressure P1, the outlet side pressure P2, and the mass flow rate V._mCan be calculated based on the following equation (2).

here,
κ: Specific heat ratio (= Cp (low pressure specific heat) / Cv (constant volume specific heat))
P1: Turbine inlet side pressure
P2: Turbine outlet side pressure
It is.
[0047]
Since ΔH is adiabatic heat drop, ΔH · V_mHas the meaning as the theoretical output Pref which is the maximum output of the theoretical turbine, and the equation (1) can be replaced by the following equation (3).
P = P_ref・ Η ...... Formula (3)
[0048]
4 shows the mass flow rate V_mAnd a turbine efficiency η and a turbine output P. As shown in FIG. 4, in general, the turbine efficiency is V_mIf the horizontal axis is taken, it becomes a convex curve.
By quadratic approximation of this curve, the relationship of the following formula (4) can be derived.
η = (aV_m ²+ BV_m+ C) ...... Formula (4)
Here, a to c are coefficients.
[0049]
However, when various studies were made on the following equation (5) obtained by substituting equation (4) into equation (1), it was found that equation (5) does not necessarily match the measured value.
P = ΔH ・ V_m・ (AV_m ²+ BV_m+ C) ...... Formula (5)
[0050]
After various investigations, it was found that the reference equation can be made to match the actual value very well by correcting using the specific volume Sp or the volume flow rate Vv. This is, for example, the following formula (6).
[0051]

here,

It is.
[0052]
Expression (6) is expressed in the form of the product of the secondary expression Q1 of the volume flow rate Vm and the secondary expression Q2 of the specific volume Sp.
Although the equation (6) shows a case where correction is performed using the specific volume Sp, it is also possible to correct using the volume flow rate Vv instead of the specific volume Sp as shown in the following equation (7).

[0053]
In the equations (6) and (7), the coefficients of the quadratic expression Q2 of the specific volume Sp2 and the quadratic expression Q3 of the volume flow rate Vv are expressed the same, but different values are used as actual values. Become.
In Equations (6) and (7), if anything, Equation (6) has a wider mass flow rate V_mThus, it matches the output of the turbine T. However, even in equation (7), mass flow rate V_mIf the change width is not so large, it may be used to calculate the output reference value.
In the equations (6) and (7), the approximation accuracy is improved by using up to the second order term of the specific volume Sp or the volume flow rate Vv, but this is not necessarily absolute, and up to the first order term or 3 The following terms can be used.
[0054]
B. For multiple turbines
When a plurality of turbines are connected by one shaft, the reference value Pw of the total output is the sum of the outputs of these turbines.
For example, the output reference value Pw when the steam turbine ST (high pressure turbine HT, intermediate pressure turbine IT, low pressure turbine LT), gas turbine GT, and air compressor CP as shown in FIG. It is represented by (10).
[0055]
P_W= -P_CP+ P_GT+ P_HT+ P_IT+ P_LT+ C ...... Formula (10)
Where P_CP: Output of air compressor CP (It is-because it is actually input)
P_GT: Output of gas turbine GT
P_HT: Output of high-pressure turbine HT
P_IT: Output of medium pressure turbine IT
P_LT: Output of low-pressure turbine LT
C: Approximate constant
And are expressed as in the equations (11) to (15), respectively.
[0056]
For the air compressor CP, an approximate expression is applied separately for an axial component and a circumferential component. The ratio of axial / circumferential components such as compressor output shown below varies depending on the angle of guide vanes provided at the inlet of the air compressor CP.
P_CP= P_{CP_ref}・ (A₁V_{af_m} ²+ B₁V_{af_m}+ C₁) ・ (Α₁V_{af_ v} ²+ Β₁V_{af_ v}+ Γ₁) + P_{CP_ref_r}・ (A₂V_{af r _M} ²+ B₂V_{af r _M}+ C₂) ・ (Α₂V_{a f r _ v} ²+ Β₂V_{af r _ v}+ Γ₂) ... Formula (11)
[0057]
here,
P_{CP_ref}(= ΔH_comp・ V_{af_m}: Axial component of compressor theoretical output
P_{CP_ref_r}(= ΔH_comp・ V_{af r _M}): Circumferential component of compressor theoretical output
V_{af_m}: Axial component of compressor air mass flow
V_{af_v}: Axial component of compressor air volume flow
V_{afr_m}: Compressor air mass flow circumferential component
V_{afr_ v}: Compressor air volume flow circumferential component
It is.
[0058]
P_GT= P_{GT_ref}・ (A₃V_{GT_m} ²+ B₃V_{GT_m}+ C₃) ・ (Α₃V_{GT_v} ²+ Β₃V_{GT_ v}+ Γ₃) ... Formula (12)
here,
P_{GT_ref}(= ΔH_GT・ V_{GT_m}: Gas turbine theoretical output
V_{GT_m}: Gas turbine inlet combustion gas mass flow rate
V_{GT_v}: Gas turbine inlet combustion gas volume flow rate
It is.
[0059]
P_HT= P_{HT_ref}・ (A₄V_{HT_m} ²+ B₄V_{HT_m}+ C₄) ・ (Α₄V_{HT_v} ²+ Β₄V_{HT_ v}+ Γ₄) ... Formula (13)
here,
P_{HT_ref}(= ΔH_HT・ V_{HT_m}: High pressure turbine theoretical output
V_{HT_m}: High-pressure turbine inlet steam mass flow rate
V_{HT_v}: High-pressure turbine inlet steam volume flow
It is.
[0060]
P_IT= P_{IT_ref}・ (A₅V_{IT_m} ²+ B₅V_{IT_m}+ C₅) ・ (Α₅V_{IT_v} ²+ Β₅V_{IT_ v}+ Γ₅) ... Formula (14)
here,
P_{IT_ref}(= ΔH_IT・ V_{IT_m}: Medium pressure turbine theoretical output
V_{IT_m}: Medium-pressure turbine inlet steam mass flow rate
V_{IT_v}: Medium pressure turbine inlet steam volume flow
It is.
[0061]
P_LT= P_{LT_ref}・ (A₆V_{LT_m} ²+ B₆V_{LT_m}+ C₆) ・ (Α₆V_{LT_v} ²+ Β₆V_{LT_ v}+ Γ₆) + ΔV_ac                            ... Formula (15)
here,
P_{LT_ref}(= ΔH_LT・ V_{LT_m}: Low pressure turbine theoretical output
V_{LT_m}: Low-pressure turbine inlet steam mass flow rate
V_{LT_v}: Low-pressure turbine inlet steam volume flow
δV_ac: Correction term depending on the degree of vacuum
(V_ac= Condenser vacuum level / V_{LT_m}・ P_{LT_ref})
It is.
[0062]
By substituting Equations (11) to (15) into Equation (10), the power generation system GS can be obtained from the state of each turbine T (inlet side temperature T1, inlet side pressure P2, outlet side pressure P2, mass flow rate Vm). The reference value of the output as a whole can be calculated.
[0063]
C. Coefficient determination by multiple regression analysis etc.
Coefficient a in equations (11) to (15)_n~ C_n(N: 1-6), α_n~ Γ_{n ,}δ and C are actually unknown numbers. It is necessary to calculate this according to the actual power generation system GS. That is, P_WIs a coefficient a that approaches the actual output value Pm of the generator G in the state that it is desired to use as a reference_n~ C_n, Α_n~ Γ_{n ,}δ and C are calculated.
Specifically, the equations (11) to (15) are expanded and substituted into the equation (10), and the coefficient a is obtained by performing multiple regression analysis._nEtc. can be obtained. For example, when the equation (12) of the gas turbine GT is developed, it can be expressed as the following equation (20), and the coefficients A to I can be derived by multiple regression analysis.
[0064]
P_GT= AP_{GT_ref}・ V_{GT_m} ²・ V_{GT_v} ²+ B ・ P_{GT_ref}・ V_{GT_m} ²・ V_{GT_v}+ C ・ P_{GT_ref}・ V_{GT_m} ²+ DP_{GT_ref}・ V_{GT_m}・ V_{GT_v} ²+ E ・ P_{GT_ref}・ V_{GT_m}・ V_{GT_v}+ F ・ P_{GT_ref}・ V_{GT_m}+ G ・ P_{GT_ref}・ V_{GT_v} ²+ H ・ P_{GT_ref}・ V_{GT_v}+ I ・ P_{GT_ref}                            ... Formula (20)
[0065]
For example, the following data a and b can be used as the data used for calculating the coefficients. Since a variety of data can be acquired, the performance test data of “a” is preferable as the data to be used, but the coefficient can be calculated by using any of the data.
a. Performance test data of power generation system GS
In the performance test, the power generation system GS can be placed under different operating conditions to obtain different outputs.
[0066]
b. Actual operation data of power generation system GS (for example, one year)
The power generation system GS is placed under normal operation, and output data obtained at that time is accumulated. At this time, the coefficient a corresponds to the average operating condition._nEtc. will be determined.
[0067]
D. Estimating basic state values
As can be seen from equation (10), the calculation of the adiabatic heat drop ΔH requires the inlet side temperature T1, the inlet side pressure P1, and the outlet side pressure P2, and these parameters are preferably measured.
However, by applying the following method, even if some parameters are missing for some reason (for example, a measuring instrument is not provided), it is possible to cope with it.
[0068]
a. For gas turbine GT
The inlet side temperature T1 can be calculated by applying the methods (1) and (2) below.
(1) Calculated from fuel components and fuel / air flow rates
A temperature T1 is calculated such that both sides of the following equation (30) are equal. Fuel component, flow rate is fuel heat quantity Q_FLThe air flow rate is calculated based on the air heat quantity Q_CPUsed to calculate
Q_FL+ Q_CP= Q_N2+ Q_O2+ Q_CO2+ Q_H2O    ... Formula (30)
[0069]
here,
Q_FL: Fuel heat quantity
Q_CP: Combustion air heat at the air compressor CP outlet temperature (before combustion)
Q_N2: Heat quantity of nitrogen after combustion at gas turbine GT inlet temperature T1
Q_O2: Heat quantity of oxygen after combustion at gas turbine GT inlet temperature T1
Q_CO2: Calorie of carbon dioxide after combustion at gas turbine GT inlet temperature T1
Q_H2O: Heat quantity of water after combustion at gas turbine GT inlet temperature T1
It is.
[0070]
(2) When the outlet side temperature T2 is known, the inlet side temperature T1 can be calculated assuming that the change of the working fluid in the turbine T is a polytropic change.
T1 = T2 · (P1 / P2)^{(N-1) / n}    ...... Formula (40)
here,
n: Polytropic coefficient
P1, P2: inlet side, outlet side pressure
T1, T2: inlet side, outlet side temperature
It is.
[0071]
b. For medium pressure turbine IT
The following methods (1) and (2) can be applied to the outlet side pressure P2.
(1) Medium pressure turbine inlet side pressure P1 and condenser vacuum degree P_CDCan be calculated taking into account the effects of low-pressure steam flow, crossover pipes, etc.
Specifically, the outlet side pressure P2 can be calculated based on the following equation (51).
P2 = P1 ・ K1^m1                    ...... Formula (51)
[0072]
here,
m1: Number of paragraphs of medium pressure turbine IT
K1: Pressure drop rate per stage of medium pressure turbine
= N stage inlet pressure / (n-1) stage inlet pressure
= [P_CD/ (P1, K2, K3^m2]]^{1 / (m1 + m2)}
m2: Number of paragraphs of low-pressure turbine LT
K2: Pressure drop rate of crossover pipe
= Pressure after crossover pipe / Pressure before crossover pipe
K3: Low-pressure turbine flow ratio
= Medium-pressure turbine outlet flow rate / Low-pressure turbine inlet flow rate / A
A: Entrance area of low-pressure turbine LT, number of passenger compartments / medium-pressure turbine final stage area
It is.
[0073]
(2) It can be calculated from the balance with the low-pressure steam heat quantity using the cabin temperature t of the exhaust section of the intermediate pressure turbine.
Specifically, in the following formula (52), the pressure P required to make both sides equal is calculated.
h1 · F1 = h2 · (F1 + F2) −h3 · F2 Formula (52)
[0074]
here,
K2: Pressure drop rate of crossover pipe
h1: outlet side enthalpy of intermediate pressure turbine at temperature t (assuming equal to cabin temperature t) and pressure P
h2: (Low-pressure turbine inlet side) Low-pressure turbine inlet-side enthalpy at temperature t2 and pressure P · K2
h3: (Low pressure main steam) Low pressure main steam enthalpy at temperature t3 and pressure P3
F1: Medium-pressure turbine steam flow rate
F2: Low-pressure main steam flow rate
It is.
[0075]
c. For low-pressure turbine LT
For the inlet side pressure, a method similar to that of the intermediate pressure turbine IT can be applied.
Specifically, the outlet side pressure P2 can be calculated based on the following equation (53).
P2 = P1 · K2 (Formula 53)
[0076]
here,
P1: Medium pressure turbine inlet side pressure
K2: Pressure drop rate of crossover pipe
= Pressure after crossover pipe / Pressure before crossover pipe
It is.
[0077]
The inlet side temperature can be obtained by calculation from the balance with the low-pressure steam heat quantity using the cabin temperature t of the intermediate pressure turbine exhaust section.
Specifically, in the following formula (54), a temperature t2 required to make both sides equal is calculated.
h2 · (F1 + F2) = h1 · F1 + h3 · F2 Formula (54)
[0078]
here,
K2: Pressure drop rate of crossover pipe
h1: outlet side enthalpy of intermediate pressure turbine at temperature t (assuming equal to cabin temperature t) and pressure P
h2: (Low-pressure turbine inlet side) Low-pressure turbine inlet-side enthalpy at temperature t2 and pressure P · K2
h3: (Low pressure main steam) Low pressure main steam enthalpy at temperature t3 and pressure P · K23
F1: Medium-pressure turbine steam flow rate
F2: Low-pressure main steam flow rate
It is.
In addition, when the passenger compartment temperature t of the intermediate pressure turbine exhaust part can be regarded as the temperature after mixing the exhaust of the intermediate pressure turbine and the low pressure steam, the temperature can be used as the passenger compartment temperature t.
[0079]
(Management of power generation system GS)
A. Management of the entire power generation system GS
The power generation system GS can be managed using Expression (10).
This can be done by comparing the output reference value Pw obtained from the equation (10) with the actual output value Pm of the power generation system GS as follows. This corresponds to the output comparison described above in step S25 of FIG.
ΔP = Pw−Pm Equation (60)
Here, ΔP: output deviation.
[0080]
Further, the efficiency change Δη can be calculated using the output deviation ΔP.
Δη = ΔP / Qt Equation (61)
Here, Qt is the total amount of heat (J) generated from the used fuel.
[0081]
Here, the meaning of the output deviation ΔP represented by the equation (60) will be described again (it has already been explained in relation to the equation (1)).
As described above, the coefficient is set so that the output reference value Pw matches the actual output value at a certain point in time of the power generation system GS. This means that Expression (10) is set so as to correspond to the performance of the power generation system GS at that time. Therefore, the output deviation ΔP is considered to correspond to a change in performance.
[0082]
When there is a change that affects the performance inside the turbine or compressor, the output fluctuates due to the change in the outlet side temperature, but the reference output obtained as above does not include the element of the outlet side temperature. When the comparison is made with the actual output, the change in performance is calculated as the output deviation.
[0083]
B. Individual management
Formula (10) can be evaluated for each turbine T, and can be separated into, for example, the gas turbine GT side and the steam turbine ST.
From the equation (10), the following two equations (62) and (63) can be extracted.
[0084]
P_GT0 = -P_CP+ P_GT                    ... Formula (62)
P_{ST 0}= P_HT+ P_IT+ P_LT                  ...... Formula (63)
here,
P_GT0: Output of all gas turbines (total output of air compressor CP and gas turbine GT using air / combustion gas as working fluid)
P_ST0: Total steam turbine output (output of steam turbine ST using steam as working fluid)
It is.
[0085]
Collect the actual output of each of the gas turbine GT and steam turbine ST (it is convenient to collect data at the same time as the data used to calculate the reference output), and the total gas turbine output P_GTCalculated value of 0 (P_GT0c) and measured value (P_GT0m), all steam turbine output P_STCalculated value of (P_ST0c) and measured value (P_STm) If approximate expressions and diagrams showing the respective relationships are prepared, the reference outputs on the gas turbine GT side and the steam turbine ST side can be obtained (creation of GT reference line and ST reference line).
[0086]
In addition, the actual measurement value (P_GT0m), measured value of total steam turbine output (P_ST0m) can be separated from the total output Pw by the following methods a and b.
[0087]
a. Heat input / output method
In each of the gas turbine GT and the steam turbine ST, the heat Q1 that has entered and the heat Q2 that has come out can be obtained and converted into outputs. Specifically, the following equation (55) is used.
[0088]

here,
Q2_GT, Q1_GT: Heat input and output in gas turbine GT
Q2_ST, Q1_ST: Heat input and output at steam turbine ST
ΔP (= P_GT0-P_ST0): Output difference between gas turbine GT and steam turbine ST
A: Conversion value
It is.
[0089]
By taking the difference between the output difference ΔP calculated by the equation (65) and the actual measurement value Pwm of the total output, the output P0 of each of the gas turbine GT and the steam turbine ST is obtained._GT, P_ST0 can be calculated.
P_ST0 = (Pwm−ΔP) / 2
P_GT0 = (Pwm + ΔP) / 2 Formula (66)
[0090]
b. Measurement method
A torque T applied to the boundary between the gas turbine GT and the steam turbine ST is measured using an axial torque meter or the like, and an output difference ΔP (the physical meaning is the same as that of the equation (65)) is calculated based on the measurement result. . Thereafter, the output P of each of the gas turbine GT and the steam turbine ST is expressed using the equation (66)._GT0, P_ST0 can be calculated.
[0091]
(Experimental result)
The results calculated by applying the present invention are shown below.
FIG. 5 is a graph showing a specific example of the output deviation ΔP calculated based on the equation (60) in the turbine reference output calculation apparatus according to the present invention. FIG. 6 is a graph showing a comparative example of FIG. In these graphs, the horizontal axis is time (t), and the vertical axis is output (MW). In this specific example and the comparative example, the output deviation ΔP is calculated based on the equations (6) and (5), respectively.
As can be seen by comparing FIGS. 5 and 6, it can be seen that the error is small in FIG. 5 to which the present invention is applied.
[0092]
FIG. 7 is a graph showing a specific example of the correlation between the reference value P of the gas turbine GT and the actual measurement value Pm calculated by the turbine reference output calculation device according to the present invention (horizontal axis: reference value P, vertical axis: actual measurement value Pm). ). FIG. 8 is a graph showing this comparative example. In this specific example and the comparative example, the output deviation ΔP is calculated based on the equations (6) and (5), respectively.
As can be seen by comparing FIGS. 7 and 8, it can be seen that the correlation between the reference value P and the actual measurement value Pm is high in FIG. 7 to which the present invention is applied.
[0093]
9 to 11 show the time course of the output deviation ΔP calculated by the turbine reference output calculation apparatus according to the present invention based on the equation (6) for the entire power generation output, the gas turbine GT, and the steam turbine ST. It is a graph.
Before and after the water washing of the gas turbine GT, the output deviation ΔP varies in FIGS. 9 and 10, but does not vary much in FIG. This is considered to mean that the outputs of the gas turbine GT and the steam turbine ST are appropriately separated.
[0094]
【The invention's effect】
As described above, according to the present invention, it is possible to provide a turbine reference output calculation device, a turbine reference output calculation method, and a computer program that calculate a reference output that is a reference for turbine deterioration.
[Brief description of the drawings]
FIG. 1 is a block diagram showing a configuration of a turbine reference output calculation apparatus according to an embodiment of the present invention.
2 is a flowchart showing a procedure for calculating coefficients of secondary equations Q1 and Q2 included in the reference equation stored in the reference equation storage means of the turbine reference output calculating device shown in FIG. 1; FIG.
FIG. 3 is a flowchart showing a procedure for calculating a reference value of the output of the power generation system by the turbine reference output calculation device shown in FIG. 1;
[Figure 4] Mass flow rate V_mAnd a turbine efficiency η and a turbine output P.
FIG. 5 is a graph showing a specific example of an output deviation ΔP calculated by the turbine reference output calculation device according to the present invention.
FIG. 6 is a graph showing a comparative example of output deviation ΔP.
FIG. 7 is a graph showing a specific example of the correlation between the reference value P of the gas turbine GT and the actual measurement value Pm calculated by the turbine reference output calculation device according to the present invention.
FIG. 8 is a graph showing a comparative example of the correlation between the reference value P of the gas turbine GT and the actual measurement value Pm.
FIG. 9 is a graph showing the time course of the output deviation ΔP in the entire power generation output calculated by the turbine reference output calculation device according to the present invention.
FIG. 10 is a graph showing the time course of the output deviation ΔP in the gas turbine GT calculated by the turbine reference output calculation device according to the present invention.
FIG. 11 is a graph showing the time course of the output deviation ΔP in the steam turbine ST calculated by the turbine reference output calculation device according to the present invention.
[Explanation of symbols]
10 ... Turbine reference output calculation device
11 ... Standard expression storage means
12: Coefficient calculation means
13. Coefficient storage means
14: Reference output calculation means
15 ... Output comparison means
16 ... Input means
17 ... Output means

Claims (15)

The element includes a quadratic expression Q1 of the adiabatic heat drop ΔH in the turbine of the working fluid flowing into and out of the turbine, a mass flow rate Vm of the working fluid, and a quadratic expression Q2 of the specific volume Sp of the working fluid. And a reference expression storage means for storing a reference expression representing a reference value of the output of the turbine;
Coefficient storage means for storing coefficients of quadratic expressions Q1, Q2 of the mass flow rate Vm and specific volume Sp included in the reference expression stored in the reference expression storage means;
Reference output calculation means for calculating a reference value of the output of the turbine based on the reference expression stored in the reference expression storage means and the coefficient stored in the coefficient storage means; Calculation device. Input means for inputting an actual measurement value of the output of the turbine;
The turbine reference output calculation apparatus according to claim 1, further comprising output comparison means for comparing the actual measurement value input by the input means with the reference value calculated by the reference output calculation means. The turbine reference output calculation device according to claim 1, wherein the reference output calculation means includes means for calculating the adiabatic heat drop based on an inlet side temperature, an inlet side pressure, and an outlet side pressure of the turbine. The turbine reference output calculation device according to claim 3, wherein the reference output calculation means includes means for estimating at least one of an inlet side temperature, an inlet side pressure, and an outlet side pressure of the turbine. The turbine according to claim 1, further comprising coefficient calculation means for calculating coefficients of quadratic expressions Q1 and Q2 for the mass flow rate Vm and the specific volume Sp based on the measured value of the output of the turbine. Reference output calculation device. The turbine reference output calculation device according to claim 5, wherein the coefficient calculation means calculates the coefficients of the respective quadratic expressions Q1 and Q2 by regression analysis. The turbine reference output calculation apparatus according to claim 6, wherein the coefficient calculation means includes means for calculating the adiabatic heat drop based on an inlet side temperature, an inlet side pressure, and an outlet side pressure of the turbine. The turbine reference output calculation device according to claim 7, wherein the coefficient calculation means includes means for estimating at least one of an inlet side temperature, an inlet side pressure, and an outlet side pressure of the turbine. The reference equation stored in the reference equation storage means includes a quadratic equation Q3 of the volume flow rate of the working fluid as an element instead of the quadratic equation Q2 of the specific volume Sp of the working fluid. Item 5. The turbine reference output calculation device according to Item 1. The turbine reference output calculation device according to claim 1, wherein the turbine is a multistage turbine including a plurality of turbines. The turbine reference output calculation apparatus according to claim 10, wherein the reference output calculation means calculates the reference outputs of the plurality of turbines separately. The element includes a quadratic expression Q1 of the adiabatic heat drop ΔH in the turbine of the working fluid flowing into and out of the turbine, a mass flow rate Vm of the working fluid, and a quadratic expression Q2 of the specific volume Sp of the working fluid. And a reference expression storage step for storing a reference expression representing a reference value of the output of the turbine in the reference expression storage means;
A coefficient calculating step of calculating coefficients of secondary equations Q1 and Q2 of the mass flow rate Vm and specific volume Sp included in the reference equation stored in the reference equation storage means in the reference equation storage step;
A coefficient storage step for storing the coefficients of the quadratic expressions Q1 and Q2 of the mass flow rate Vm and the specific volume Sp calculated in the coefficient calculation step in a coefficient storage unit;
A reference output calculation step of calculating a reference value of the output of the turbine based on the reference equation stored in the reference equation storage unit in the reference equation storage step and the coefficient stored in the coefficient storage unit in the coefficient storage step; A turbine reference output calculation method comprising: The turbine reference output calculation method according to claim 12, further comprising an output comparison step of comparing the actual measurement value of the turbine with the reference value calculated by the reference output calculation means. A computer program for causing a computer to function as the turbine reference output calculation device according to claim 1. A computer program for causing a computer to execute the turbine reference output calculation method according to claim 12.

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