Skip to content

Commit

Permalink
preliminary equations
Browse files Browse the repository at this point in the history
  • Loading branch information
@zhen0427
zhen0427 committed Nov 16, 2023
1 parent 385c679 commit c3ff31b
Showing 1 changed file with 126 additions and 11 deletions.
137 changes: 126 additions & 11 deletions docs/user_manual/components.md
View file
Original file line number Diff line number Diff line change
Expand Up @@ -133,6 +133,14 @@ if any of the faults in any of the scenarios within a batch are not three-phase
(i.e. `fault_type` is not `FaultType.three_phase`).
```

#### Electric Model

`line` is described by π model,
where z_series =`r`+j`x`, and y_shunt = 2πf`c`/(tan𝛿 + 1j), and f is system frequency.




### Link

* type name: `link`
Expand All @@ -142,6 +150,10 @@ two busbars inside a substation. It has a very high admittance (small impedance)
(equivalent to 10e6 siemens for 10kV network). Therefore, it is chosen by design that no sensors can be coupled to a `link`.
There is no additional attribute for `link`.

#### Electric Model:
`link` is modeled by using an constant value y_series=1e-6.


### Transformer

`transformer` is a {hoverxreftooltip}`user_manual/components:branch` which connects two nodes with possibly different voltage
Expand Down Expand Up @@ -181,6 +193,38 @@ It can happen that `tap_min > tap_max`. In this case the winding voltage is decr
increased.
```

#### Electric Model
`transformer` is described by π model, where z_series and y_shunt can be computed by following equations:

$$
$$

z_base = `sn`/(`u2`^2)

|z_series| = |`uk`|/z_base

Re(z_series) = (`pk`/`sn`)/z_base

Im(z_series) = sign(`uk`) * sqrt(|z_series|^2-Re(z_series)^2)

base_i_to = base_power_3p / u2_rated / sqrt(3),

base_y_to = base_i_to^2 / base_power_1p

y_series = (1/z_seires) / base_y_to

y_shunt_abs = `i0` * `sn` / `u2`^2

Re(y_shunt) = `p0` / (`u2`^2)

Im(y_shunt) = 0 (if Re(y_shunt) > y_shunt_abs) or = -sqrt(y_shunt_abs^2-Re(y_shunt)^2)

y_shunt = y_shunt / base_y_to

where base_power_3p = 1e6, and base_power_1p = base_power_3p / 3. u2_rated is a constant value, which is normally set to 10e3.


## Branch3

* type name: `branch3`
Expand Down Expand Up @@ -287,6 +331,11 @@ It can happen that `tap_min > tap_max`. In this case the winding voltage is decr
increased.
```

#### Electrical Model

For positive sequence,


## Appliance

* type name: `appliance`
Expand Down Expand Up @@ -339,6 +388,28 @@ with an internal impedance. The impedance is specified by convention as short ci
| `rx_ratio` | `double` | - | R to X ratio | ❌ default 0.1 | ❌ | `>= 0` |
| `z01_ratio` | `double` | - | zero sequence to positive sequence impedance ratio | ❌ default 1.0 | ❌ | `> 0` |

#### Electric Model
`source` is modeled by using an internal constant impedance r+jx with positive sequence and zero sequence.

The value of impedance can be computed using following equations:

For positive sequence,
z_s = s_base/sk

x1 = z_s * sqrt(1+ rx_ratio*rx_ratio)

r1= rx_ratio * x1

where s_base is a constant value 1e6.

For zero sequence,
zs_0 = z_s * z01_ratio

x0 = zs_0 * sqrt(1+ rx_ratio*rx_ratio)

r0= rx_ratio * x0


### Generic Load and Generator

* type name: `generic_load_gen`
Expand Down Expand Up @@ -369,6 +440,22 @@ However, the reference direction and meaning of `RealValueInput` is different, a
| `p_specified` | `RealValueInput` | watt (W) | specified active power | ✨ only for power flow | ✔ |
| `q_specified` | `RealValueInput` | volt-ampere-reactive (var) | specified reactive power | ✨ only for power flow | ✔ |

##### Electric model

`generic_load_gen` are modelled by using the so-called ZIP load model in power-grid-model,
where a load/generator is represented as a composition of constant power (P), constant current (I) and constant impedance (Z).

The injection current I_inj of each ZIP model type can be computed from s = `p_specified` + j`q_specified`as:

For constant impedance (Z) load: I_inj = S*u

For Constant current (I) load: I_inj = S*|u|/u = S

For constant power (P) load: I_inj = S/u

Here u is the input variable `u_rated` of a corresponding node. Polarities of load and generator are opposite.


### Shunt

* type name: `shunt`
Expand All @@ -392,6 +479,10 @@ if any of the faults in any of the scenarios within a batch are not three-phase
(i.e. `fault_type` is not `FaultType.three_phase`).
```

#### Electric Model
`shunt` is modelled by a fixed admittance which equals to `g` + j`b`


## Sensor

* type name: `sensor`
Expand Down Expand Up @@ -421,6 +512,7 @@ a `node`.
| --------- | --------- | -------- | --------------------------------------------------------------------------------------------------------------- | :--------------------------------: | :------: | :----------: |
| `u_sigma` | `double` | volt (V) | standard deviation of the measurement error. Usually this is the absolute measurement error range divided by 3. | ✨ only for state estimation | ✔ | `> 0` |


#### Voltage Sensor Concrete Types

There are two concrete types of voltage sensor. They share similar attributes:
Expand All @@ -446,6 +538,16 @@ voltage is a line-to-line voltage. In a `asym_voltage_sensor` the measured volta
| `u_residual` | `RealValueOutput` | volt (V) | residual value between measured voltage magnitude and calculated voltage magnitude |
| `u_angle_residual` | `RealValueOutput` | rad | residual value between measured voltage angle and calculated voltage angle (only possible with phasor measurement units) |

#### Electric Model
`generic_voltage_sensor` is modeled by following equations:

u_residual = u_measured - “u_node” ,

u_angle_residual = u_angle_measured - "u_angle_node",

where “u_node” and "u_angle_node" are the steady state output variables`u` and `u_angle` of corresponding `node`


### Generic Power Sensor

* type name: `generic_power_sensor`
Expand Down Expand Up @@ -508,6 +610,16 @@ See the documentation on [state estimation calculation methods](calculations.md#
| `p_residual` | `RealValueOutput` | watt (W) | residual value between measured active power and calculated active power |
| `q_residual` | `RealValueOutput` | volt-ampere-reactive (var) | residual value between measured reactive power and calculated reactive power |

#### Electric Model
`Generic Power Sensor` is modeled by following equations:

p_residual = p_measured - “p_node” ,

q_residual = q_measured - “q_node” ,

where “p_node” and "q_node" are the steady state output variables `p` and `q` of corresponding `node`


## Fault

* type name: `fault`
Expand Down Expand Up @@ -537,17 +649,6 @@ If any of the faults in any of the scenarios within a batch are not `three_phase
the calculation is treated as asymmetric.
```

##### Default values for `fault_phase`

In case the `fault_phase` is not specified or is equal to `FaultPhase.default_value`, the power-grid-model assumes the following fault phases for different values of `fault_type`.

| `fault_type` | `fault_phase` |
| ---------------------------------- | ---------------- |
| `FaultType.three_phase` | `FaultPhase.abc` |
| `FaultType.single_phase_to_ground` | `FaultPhase.a` |
| `FaultType.two_phase` | `FaultPhase.bc` |
| `FaultType.two_phase_to_ground` | `FaultPhase.bc` |

#### Steady state output

A `fault` has no steady state output.
Expand All @@ -558,3 +659,17 @@ A `fault` has no steady state output.
| ----------- | ----------------- | ---------- | ------------- |
| `i_f` | `RealValueOutput` | ampere (A) | current |
| `i_f_angle` | `RealValueOutput` | rad | current angle |

#### Electric Model
Four types of short circuit fault are included in power-grid-model.

| `fault_type` | `fault_phase` | description |
| ---------------------------------- | ---------------- |-------------------------------------------------------------------|
| `FaultType.three_phase` | `FaultPhase.abc` | Three phases are connected with impedance `z` =`r_f` + j`r_f`. |
| `FaultType.single_phase_to_ground` | `FaultPhase.a` | One phase grounded with impedance `z`, and other phases are open. |
| `FaultType.two_phase` | `FaultPhase.bc` | Two phases are connected with impedance `z`. |
| `FaultType.two_phase_to_ground` | `FaultPhase.bc` | Two phases are connected with impedance `z` then grounded. |

In case the `fault_phase` is not specified or is equal to `FaultPhase.default_value`, the power-grid-model assumes the following fault phases for different values of `fault_type`.


0 comments on commit c3ff31b

Please sign in to comment.