地域毎に、以下の制約を考慮することができる。
- 需給バランス制約
- GF&LFC調整力制約
- 三次調整力制約
- RE電源の予測値と予測最小値の差を補償する上げ調整力と、予測値と予測最大値の差を補償する下げ調整力の2種類がある。
- 必要慣性定数制約
各添字、集合、定数、決定変数の定義は以下のページを参照。
$$
\begin{align}
\sum_{g \in G_{a}}
p_{t,g}+ P_{t,a,\text{Others}}
+ \sum_{ess \in ESS_{a}} \left(
p_{t,ess}^{\text{discharge}} - p_{t,ess}^{\text{charge}} \right) \notag
\\
+ P_{t,a,\text{PV}}^{\text{output}} - p_{t,a,\text{PV}}^{\text{suppr}}
+ P_{t,a,\text{WF}}^{\text{output}} - p_{t,a,\text{WF}}^{\text{suppr}} \notag
\\
+ \sum_{tie \in TIE_{\text{to}=a}}
\left( p_{t,tie}^{\text{forward}} - p_{t,tie}^{\text{counter}} \right) \notag
\\
+ \sum_{tie \in TIE_{\text{from}=a}}
\left( p_{t,tie}^{\text{counter}} - p_{t,tie}^{\text{forward}} \right) \notag
\\
+ p_{t,a}^{\text{short}} - p_{t,a}^{\text{surplus}}
& = D_{t,a}
& \forall t \in T, \forall a \in A
\end{align}
$$
$$
\begin{align}
\sum_{g \in G_{a}} p_{t,g}^{\text{GF\&LFC},\text{UP}}
+ \sum_{ess \in ESS_{a}} p_{t,ess}^{\text{GF\&LFC},\text{UP}}
+ p_{t,a,\text{PV}}^{\text{GF\&LFC},\text{UP}}
+ p_{t,a,\text{WF}}^{\text{GF\&LFC},\text{UP}} \notag
\\
+ \sum_{tie \in TIE_{\text{to}=a}} \left(
p_{t,tie}^{\text{GF\&LFC},\text{UP, forward}} - p_{t,tie}^{\text{GF\&LFC},\text{UP, counter}} \right) \notag
\\
+ \sum_{tie \in TIE_{\text{from}=a}} \left(
p_{t,tie}^{\text{GF\&LFC},\text{UP, counter}} - p_{t,tie}^{\text{GF\&LFC},\text{UP, forward}} \right)
& \geq D_{t,a}^{\text{GF\&LFC},\text{UP, req}} \notag
\\
& \forall t \in T, \forall a \in A
& \qquad (1)
\end{align}
$$
$$
\begin{align}
\sum_{g \in G_{a}} p_{t,g}^{\text{GF\&LFC},\text{UP}}
+ \sum_{ess \in ESS_{a}} p_{t,ess}^{\text{GF\&LFC},\text{UP}}
+ p_{t,a,\text{PV}}^{\text{GF\&LFC},\text{UP}}
+ p_{t,a,\text{WF}}^{\text{GF\&LFC},\text{UP}} \notag
\\
+ \sum_{tie \in TIE_{\text{to}=a}} \left(
p_{t,tie}^{\text{GF\&LFC},\text{UP, forward}} - p_{t,tie}^{\text{GF\&LFC},\text{UP, counter}} \right) \notag
\\
+ \sum_{tie \in TIE_{\text{from}=a}} \left(
p_{t,tie}^{\text{GF\&LFC},\text{UP, counter}} - p_{t,tie}^{\text{GF\&LFC},\text{UP, forward}} \right)
& \geq p_{t,a,\text{PV}}^{\text{GF\&LFC},\text{UP, req}} \notag
\\
& \forall t \in T, \forall a \in A
& \qquad (2)
\end{align}
$$
$$
\begin{align}
\sum_{g \in G_{a}} p_{t,g}^{\text{GF\&LFC},\text{UP}}
+ \sum_{ess \in ESS_{a}} p_{t,ess}^{\text{GF\&LFC},\text{UP}}
+ p_{t,a,\text{PV}}^{\text{GF\&LFC},\text{UP}}
+ p_{t,a,\text{WF}}^{\text{GF\&LFC},\text{UP}} \notag
\\
+ \sum_{tie \in TIE_{\text{to}=a}} \left(
p_{t,tie}^{\text{GF\&LFC},\text{UP, forward}} - p_{t,tie}^{\text{GF\&LFC},\text{UP, counter}} \right) \notag
\\
+ \sum_{tie \in TIE_{\text{from}=a}} \left(
p_{t,tie}^{\text{GF\&LFC},\text{UP, counter}} - p_{t,tie}^{\text{GF\&LFC},\text{UP, forward}} \right)
& \geq p_{t,a,\text{WF}}^{\text{GF\&LFC},\text{UP, req}} \notag
\\
& \forall t \in T, \forall a \in A
& \qquad (3)
\end{align}
$$
$$
\begin{align}
\sum_{g \in G_{a}} p_{t,g}^{\text{GF\&LFC},\text{DOWN}}
+ \sum_{ess \in ESS_{a}} p_{t,ess}^{\text{GF\&LFC},\text{DOWN}}
+ p_{t,a,\text{PV}}^{\text{GF\&LFC},\text{DOWN}}
+ p_{t,a,\text{WF}}^{\text{GF\&LFC},\text{DOWN}} \notag
\\
+ \sum_{tie \in TIE_{\text{to}=a}} \left(
p_{t,tie}^{\text{GF\&LFC},\text{DOWN, forward}} - p_{t,tie}^{\text{GF\&LFC},\text{DOWN, counter}} \right) \notag
\\
+ \sum_{tie \in TIE_{\text{from}=a}} \left(
p_{t,tie}^{\text{GF\&LFC},\text{DOWN, counter}} - p_{t,tie}^{\text{GF\&LFC},\text{DOWN, forward}} \right)
& \geq D_{t,a}^{\text{GF\&LFC},\text{DOWN, req}} \notag
\\
& \forall t \in T, \forall a \in A
& \qquad (4)
\end{align}
$$
$$
\begin{align}
\sum_{g \in G_{a}} p_{t,g}^{\text{GF\&LFC},\text{DOWN}}
+ \sum_{ess \in ESS_{a}} p_{t,ess}^{\text{GF\&LFC},\text{DOWN}}
+ p_{t,a,\text{PV}}^{\text{GF\&LFC},\text{DOWN}}
+ p_{t,a,\text{WF}}^{\text{GF\&LFC},\text{DOWN}} \notag
\\
+ \sum_{tie \in TIE_{\text{to}=a}} \left(
p_{t,tie}^{\text{GF\&LFC},\text{DOWN, forward}} - p_{t,tie}^{\text{GF\&LFC},\text{DOWN, counter}} \right) \notag
\\
+ \sum_{tie \in TIE_{\text{from}=a}} \left(
p_{t,tie}^{\text{GF\&LFC},\text{DOWN, counter}} - p_{t,tie}^{\text{GF\&LFC},\text{DOWN, forward}} \right)
& \geq p_{t,a,\text{PV}}^{\text{GF\&LFC},\text{DOWN, req}} \notag
\\
& \forall t \in T, \forall a \in A
& \qquad (5)
\end{align}
$$
$$
\begin{align}
\sum_{g \in G_{a}} p_{t,g}^{\text{GF\&LFC},\text{DOWN}}
+ \sum_{ess \in ESS_{a}} p_{t,ess}^{\text{GF\&LFC},\text{DOWN}}
+ p_{t,a,\text{PV}}^{\text{GF\&LFC},\text{DOWN}}
+ p_{t,a,\text{WF}}^{\text{GF\&LFC},\text{DOWN}} \notag
\\
+ \sum_{tie \in TIE_{\text{to}=a}} \left(
p_{t,tie}^{\text{GF\&LFC},\text{DOWN, forward}} - p_{t,tie}^{\text{GF\&LFC},\text{DOWN, counter}} \right) \notag
\\
+ \sum_{tie \in TIE_{\text{from}=a}} \left(
p_{t,tie}^{\text{GF\&LFC},\text{DOWN, counter}} - p_{t,tie}^{\text{GF\&LFC},\text{DOWN, forward}} \right)
& \geq p_{t,a,\text{WF}}^{\text{GF\&LFC},\text{DOWN, req}} \notag
\\
& \forall t \in T, \forall a \in A
& \qquad (6)
\end{align}
$$
$$
\begin{align}
D_{t,a}^{\text{GF\&LFC},\text{UP, req}}
& = D_{t,a} \frac{R_{t,a}^{\text{GF\&LFC},\text{UP}}}{100}
& \forall t \in T, \forall a \in A
& \qquad (1)
\\
p_{t,a,\text{PV}}^{\text{GF\&LFC},\text{UP, req}}
& = \left( P_{t,a,\text{PV}}^{\text{output}} - p_{t,a,\text{PV}}^{\text{suppr}} \right)
\frac{R_{t,a,\text{PV}}^{\text{GF\&LFC},\text{UP}}}{100}
& \forall t \in T, \forall a \in A
& \qquad (2)
\\
p_{t,a,\text{WF}}^{\text{GF\&LFC},\text{UP, req}}
& = \left( P_{t,a,\text{PV}}^{\text{output}} - p_{t,a,\text{PV}}^{\text{suppr}} \right)
\frac{R_{t,a,\text{PV}}^{\text{GF\&LFC},\text{UP}}}{100}
& \forall t \in T, \forall a \in A
& \qquad (3)
\end{align}
$$
$$
\begin{align}
D_{t,a}^{\text{GF\&LFC},\text{DOWN, req}}
& = D_{t,a} \frac{R_{t,a}^{\text{GF\&LFC},\text{UP}}}{100}
& \forall t \in T, \forall a \in A
& \qquad (4)
\\
p_{t,a,\text{PV}}^{\text{GF\&LFC},\text{DOWN, req}}
& = \left( P_{t,a,\text{PV}}^{\text{output}} - p_{t,a,\text{PV}}^{\text{suppr}} \right)
\frac{R_{t,a,\text{PV}}^{\text{GF\&LFC},\text{DOWN}}}{100}
& \forall t \in T, \forall a \in A
& \qquad (5)
\\
p_{t,a,\text{WF}}^{\text{GF\&LFC},\text{DOWN, req}}
& = \left( P_{t,a,\text{WF}}^{\text{output}} - p_{t,a,\text{WF}}^{\text{suppr}} \right)
\frac{R_{t,a,\text{WF}}^{\text{GF\&LFC},\text{DOWN}}}{100}
& \forall t \in T, \forall a \in A
& \qquad (6)
\end{align}
$$
各式を考慮するか否かは、設定ファイルの記載を編集することで、簡単に変更することができる。各設定値は以下の通りである。
| 条件名 |
デフォルト値 |
設定ファイル上での設定名 |
Falseとしたときの必要GF＆LFC調整力の変更内容 |
| 需要起因の必要GF&LFC上向き調整力の有無 |
True |
consider_required_gf_lfc_up_by_demand |
式（1）の右辺を0にする |
| 太陽光起因の必要GF&LFC上向き調整力の有無 |
True |
consider_required_gf_lfc_up_by_pv |
式（2）の右辺を0にする |
| 風力起因の必要GF&LFC上向き調整力の有無 |
True |
consider_required_gf_lfc_up_by_wf |
式（3）の右辺を0にする |
| 需要起因の必要GF&LFC下向き調整力の有無 |
False |
consider_required_gf_lfc_down_by_demand |
式（4）の右辺を0にする |
| 太陽光起因の必要GF&LFC下向き調整力の有無 |
False |
consider_required_gf_lfc_down_by_pv |
式（5）の右辺を0にする |
| 風力起因の必要GF&LFC下向き調整力の有無 |
False |
consider_required_gf_lfc_down_by_wf |
式（6）の右辺を0にする |
$$
\begin{align}
\sum_{g \in G_{a}} p_{t,g}^{\text{Tert},\text{UP}}
+ \sum_{ess \in ESS_{a}} p_{t,ess}^{\text{Tert},\text{UP}}
+ p_{t,a,\text{PV}}^{\text{Tert},\text{UP}}
+ p_{t,a,\text{WF}}^{\text{Tert},\text{UP}} \notag
\\
+ \sum_{tie \in TIE_{\text{to}=a}} \left(
p_{t,tie}^{\text{Tert},\text{UP, forward}} - p_{t,tie}^{\text{Tert},\text{UP, counter}} \right) \notag
\\
+ \sum_{tie \in TIE_{\text{from}=a}} \left(
p_{t,tie}^{\text{Tert},\text{UP, counter}} - p_{t,tie}^{\text{Tert},\text{UP, forward}} \right)
+ p_{t,a}^{\text{Tert},\text{UP, short}} \notag
& \geq p_{t,a,\text{PV}}^{\text{Tert},\text{UP, req}} \notag
\\
& \forall t \in T, \forall a \in A
& \qquad (1)
\end{align}
$$
$$
\begin{align}
\sum_{g \in G_{a}} p_{t,g}^{\text{Tert},\text{UP}}
+ \sum_{ess \in ESS_{a}} p_{t,ess}^{\text{Tert},\text{UP}}
+ p_{t,a,\text{PV}}^{\text{Tert},\text{UP}}
+ p_{t,a,\text{WF}}^{\text{Tert},\text{UP}} \notag
\\
+ \sum_{tie \in TIE_{\text{to}=a}} \left(
p_{t,tie}^{\text{Tert},\text{UP, forward}} - p_{t,tie}^{\text{Tert},\text{UP, counter}} \right) \notag
\\
+ \sum_{tie \in TIE_{\text{from}=a}} \left(
p_{t,tie}^{\text{Tert},\text{UP, counter}} - p_{t,tie}^{\text{Tert},\text{UP, forward}} \right)
+ p_{t,a}^{\text{Tert},\text{UP, short}}
& \geq p_{t,a,\text{WF}}^{\text{Tert},\text{UP, req}} \notag
\\
& \forall t \in T, \forall a \in A
& \qquad (2)
\end{align}
$$
$p_{t,a,\text{PV}}^{\text{Tert},\text{UP, req}}$ 、 $p_{t,a,\text{WF}}^{\text{Tert},\text{UP, req}}$ は負の値を取る可能性があるため、
上げ調整力の合計値が0以上でなくていはいけない制約を式（3）として加える。
$$
\begin{align}
\sum_{g \in G_{a}} p_{t,g}^{\text{Tert},\text{UP}}
+ \sum_{ess \in ESS_{a}} p_{t,ess}^{\text{Tert},\text{UP}}
+ p_{t,a,\text{PV}}^{\text{Tert},\text{UP}}
+ p_{t,a,\text{WF}}^{\text{Tert},\text{UP}} \notag
\\
+ \sum_{tie \in TIE_{\text{to}=a}} \left(
p_{t,tie}^{\text{Tert},\text{UP, forward}} - p_{t,tie}^{\text{Tert},\text{UP, counter}} \right) \notag
\\
+ \sum_{tie \in TIE_{\text{from}=a}} \left(
p_{t,tie}^{\text{Tert},\text{UP, counter}} - p_{t,tie}^{\text{Tert},\text{UP, forward}} \right)
+ p_{t,a}^{\text{Tert},\text{UP, short}} \notag
& \geq 0
\\
& \forall t \in T, \forall a \in A
& \qquad (3)
\end{align}
$$
$$
\begin{align}
\sum_{g \in G_{a}} p_{t,g}^{\text{Tert},\text{DOWN}}
+ \sum_{ess \in ESS_{a}} p_{t,ess}^{\text{Tert},\text{DOWN}}
+ p_{t,a,\text{PV}}^{\text{Tert},\text{DOWN}}
+ p_{t,a,\text{WF}}^{\text{Tert},\text{DOWN}} \notag
\\
+ \sum_{tie \in TIE_{\text{to}=a}} \left(
p_{t,tie}^{\text{Tert},\text{DOWN, forward}} - p_{t,tie}^{\text{Tert},\text{DOWN, counter}} \right) \notag
\\
+ \sum_{tie \in TIE_{\text{from}=a}} \left(
p_{t,tie}^{\text{Tert},\text{DOWN, counter}} - p_{t,tie}^{\text{Tert},\text{DOWN, forward}} \right)
+ p_{t,a}^{\text{Tert},\text{DOWN, short}} \notag
& \geq p_{t,a,\text{PV}}^{\text{Tert},\text{DOWN, req}}
\\
& \forall t \in T, \forall a \in A
& \qquad (4)
\end{align}
$$
$$
\begin{align}
\sum_{g \in G_{a}} p_{t,g}^{\text{Tert},\text{DOWN}}
+ \sum_{ess \in ESS_{a}} p_{t,ess}^{\text{Tert},\text{DOWN}}
+ p_{t,a,\text{PV}}^{\text{Tert},\text{DOWN}}
+ p_{t,a,\text{WF}}^{\text{Tert},\text{DOWN}} \notag
\\
+ \sum_{tie \in TIE_{\text{to}=a}} \left(
p_{t,tie}^{\text{Tert},\text{DOWN, forward}} - p_{t,tie}^{\text{Tert},\text{DOWN, counter}} \right) \notag
\\
+ \sum_{tie \in TIE_{\text{from}=a}} \left(
p_{t,tie}^{\text{Tert},\text{DOWN, counter}} - p_{t,tie}^{\text{Tert},\text{DOWN, forward}} \right)
+ p_{t,a}^{\text{Tert},\text{DOWN, short}} \notag
& \geq p_{t,a,\text{WF}}^{\text{Tert},\text{DOWN, req}}
\\
& \forall t \in T, \forall a \in A
& \qquad (5)
\end{align}
$$
$$
\begin{align}
p_{t,a,\text{PV}}^{\text{Tert},\text{UP, req}}
& = \left( P_{t,a,\text{PV}}^{\text{output}} - p_{t,a,\text{PV}}^{\text{suppr}} - P_{t,a,\text{PV}}^{\text{lower}} \right) U^{\text{Tert}}
& \forall t \in T, \forall a \in A
& \qquad (1)
\\
p_{t,a,\text{WF}}^{\text{Tert},\text{UP, req}}
& = \left( P_{t,a,\text{WF}}^{\text{output}} - p_{t,a,\text{WF}}^{\text{suppr}} - P_{t,a,\text{WF}}^{\text{lower}} \right) U^{\text{Tert}}
& \forall t \in T, \forall a \in A
& \qquad (2)
\end{align}
$$
$$
\begin{align}
p_{t,a,\text{PV}}^{\text{Tert},\text{DOWN, req}}
& = \left( P_{t,a,\text{PV}}^{\text{upper}} - P_{t,a,\text{PV}}^{\text{output}}+ p_{t,a,\text{PV}}^{\text{suppr}} \right) U^{\text{Tert}}
& \forall t \in T, \forall a \in A
& \qquad (3)
\\
p_{t,a,\text{WF}}^{\text{Tert},\text{DOWN, req}}
& = \left( P_{t,a,\text{WF}}^{\text{upper}} - P_{t,a,\text{WF}}^{\text{output}}+ p_{t,a,\text{WF}}^{\text{suppr}} \right) U^{\text{Tert}}
& \forall t \in T, \forall a \in A
& \qquad (4)
\end{align}
$$
各式を考慮するか否かは、設定ファイルの記載を編集することで、簡単に変更することができる。各設定は以下の通りである。
| 条件名 |
デフォルト値 |
設定ファイル上での設定名 |
Falseとしたときの必要三次調整力の変更内容 |
| 太陽光起因の必要三次上向き調整力の有無 |
True |
consider_required_tert_up_by_pv |
式（1）の右辺を0にする |
| 風力起因の必要三次上向き調整力の有無 |
True |
consider_required_tert_up_by_wf |
式（2）の右辺を0にする |
| 太陽光起因の必要三次下向き調整力の有無 |
False |
consider_required_tert_down_by_pv |
式（3）の右辺を0にする |
| 風力起因の必要三次下向き調整力の有無 |
False |
consider_required_tert_down_by_wf |
式（4）の右辺を0にする |
$$
\begin{align}
\sum_{g \in G_{N\&T,a}} P_{g}^{\text{MAX}} u_{t,g} M_{g}
+ \sum_{g \in G_{HYDRO,a}} P_{g}^{\text{MAX}} M_{g} \notag
\\
+ \sum_{ess \in ESS_{a}} P_{ess}^{\text{discharge},\text{MAX}} dchg_{t,ess} M_{p}
& \geq D_{t,a} M_{t,a}^{\text{req}}
& \forall t \in T, \forall a \in A
\end{align}
$$
上記式を考慮するか否かは、設定ファイルの記載を編集することで、簡単に変更することができる。設定は以下の通りである。
| 条件名 |
デフォルト値 |
設定ファイル上での設定名 |
Falseとしたときの必要慣性定数制約の変更内容 |
| 慣性定数必要量の有無 |
True |
consider_require_inertia |
上記式の右辺を0にする |