Measurement Model

The JuliaGrid supports the composite type Measurement to preserve measurement data, with the following fields: voltmeter, ammeter, wattmeter, varmeter, and pmu. These fields contain information pertaining to measurements such as bus voltage magnitude, branch current magnitude, active power flow and injection, reactive power flow and injection measurements, and measurements of bus voltage and branch current phasors.

The composite type Measurement can be created using a function:

• measurement.

JuliaGrid supports two modes for populating the Measurement type: using built-in functions or using HDF5 files.

It is recommended to use the HDF5 format for large-scale systems. To facilitate this, JuliaGrid has the function:

• saveMeasurement.

Once the Measurement type has been established, we can incorporate voltmeters, ammeters, wattmeters, varmeters, and phasor measurement units (PMUs) using the following functions:

• addVoltmeter!,
• addAmmeter!,
• addWattmeter!,
• addVarmeter!,
• addPmu!.

Also, JuliaGrid provides macros @voltmeter, @ambmeter, @wattmeter, @varmeter, and @pmu to define templates that aid in creating measurement devices. These templates help avoid entering the same parameters repeatedly.

Moreover, it is feasible to modify the parameters of measurement devices. When these functions are executed, all relevant fields within the Measurement composite type will be automatically updated. These functions include:

• updateVoltmeter!,
• updateAmmeter!,
• updateWattmeter!,
• updateVarmeter!,
• updatePmu!.

Finally, the user has the capability to randomly alter the measurement set by activating or deactivating devices through the following function:

• status!.

Furthermore, we provide users with the ability to modify each specific measurement set by utilizing the functions:

• statusVoltmeter!,
• statusAmmeter!,
• statusWattmeter!,
• statusVarmeter!,
• statusPmu!.

Build Model

The measurement function generates the Measurement composite type and requires a string-formatted path to HDF5 files as input. Alternatively, the Measurement can be created without any initial data by initializing it as empty, allowing the user to construct the measurements from scratch.

HDF5 File

In order to use the HDF5 file as input to create the Measurement type, it is necessary to have saved the data using the saveMeasurement function beforehand. Let us say we saved the measurements as measurements14.h5 in the directory C:\hdf5. Then, the following code can be used to construct the Measurement type:

device = measurement("C:/hdf5/measurements14.h5")

Model from Scratch

To start building a model from the ground up, the initial step involves constructing a power system, which facilitates the addition of measurement devices to buses or branches. As an illustration:

system = powerSystem()
device = measurement()

addBus!(system; label = "Bus 1")
addBus!(system; label = "Bus 2")
addBranch!(system; label = "Branch 1", from = "Bus 1", to = "Bus 2", reactance = 0.12)

addVoltmeter!(system, device; bus = "Bus 1", magnitude = 1.0, variance = 1e-3)
addWattmeter!(system, device; from = "Branch 1", active = 0.2, variance = 1e-4, noise = true)

In this context, we have created the voltmeter responsible for measuring the bus voltage magnitude at Bus 1, with associated mean and variance values expressed in per-units:

julia> [device.voltmeter.magnitude.mean device.voltmeter.magnitude.variance]1×2 Matrix{Float64}:
 1.0  0.001

Furthermore, we have established the wattmeter to measure the active power flow at the from-bus end of Branch 1, with corresponding mean and variance values also expressed in per-units:

julia> [device.wattmeter.active.mean device.wattmeter.active.variance]1×2 Matrix{Float64}:
 0.192995  0.0001

Save Model

Once the Measurement type has been created using one of the methods outlined in Build Model, the current data can be stored in the HDF5 file by using saveMeasurement function:

saveMeasurement(device; path = "C:/hdf5/measurement.h5")

All electrical quantities saved in the HDF5 file are in per-units and radians.

Add Voltmeter

We have the option to add voltmeters to a loaded measurement type or to one created from scratch. As an example, we can initiate the Measurement type and then incorporate voltmeters by utilizing the addVoltmeter! function:

system = powerSystem()
device = measurement()

addBus!(system; label = "Bus 1")

addVoltmeter!(system, device; bus = "Bus 1", magnitude = 0.9, variance = 1e-4)
addVoltmeter!(system, device; bus = "Bus 1", magnitude = 1.0, variance = 1e-3, noise = true)

In this example, we have established two voltmeters designed to measure the bus voltage magnitude at Bus 1. In the case of the second voltmeter, the measurement value is generated internally by introducing white Gaussian noise with the variance added to the magnitude value. As a result, we obtain the following data:

julia> [device.voltmeter.magnitude.mean device.voltmeter.magnitude.variance]2×2 Matrix{Float64}:
 0.9      0.0001
 1.00498  0.001

Customizing Input Units for Keywords

By default, the magnitude and variance keywords are expected to be provided in per-units (pu). However, users have the flexibility to specify these values in volts (V) if they prefer. For instance, consider the following example:

@voltage(kV, rad, V)

system = powerSystem()
device = measurement()

addBus!(system; label = "Bus 1", base = 135e3)

addVoltmeter!(system, device; bus = "Bus 1", magnitude = 121.5, variance = 0.0135)
addVoltmeter!(system, device; bus = "Bus 1", magnitude = 135, variance = 0.135, noise = true)

In this example, we have chosen to specify magnitude and variance in kilovolts (kV). It is important to note that even though we have used kilovolts as the input units, these keywords will still be stored in the per-units:

julia> [device.voltmeter.magnitude.mean device.voltmeter.magnitude.variance]2×2 Matrix{Float64}:
 0.9      0.0001
 1.00207  0.001

Add Ammeter

Users can introduce ammeters into either an existing measurement type or one that they create from the ground up by making use of the addAmmeter! function, as demonstrated in the following example:

system = powerSystem()
device = measurement()

addBus!(system; label = "Bus 1")
addBus!(system; label = "Bus 2")
addBranch!(system; label = "Branch 1", from = "Bus 1", to = "Bus 2", reactance = 0.12)

addAmmeter!(system, device; from = "Branch 1", magnitude = 0.8, variance = 1e-3)
addAmmeter!(system, device; to = "Branch 1", magnitude = 0.9, variance = 1e-1, noise = true)

In this scenario, we have established one ammeter to measure the branch current magnitude at the from-bus end of Branch 1, as indicated by the use of the from keyword. Similarly, we have added an ammeter to measure the branch current magnitude at the to-bus end of the branch by utilizing the to keyword.

For the first ammeter, we assume that the measurement value is already known, defined by the magnitude. In contrast, for the second ammeter, the measurement value is generated by adding white Gaussian noise with the variance to the magnitude value. These actions result in the following outcomes:

julia> [device.ammeter.magnitude.mean device.ammeter.magnitude.variance]2×2 Matrix{Float64}:
 0.8      0.001
 0.75193  0.1

Customizing Input Units for Keywords

By default, the magnitude and variance keywords are expected to be provided in per-unit (pu). However, users have the flexibility to express these values in amperes (A) if they prefer. Take a look at the following example:

@current(A, rad)

system = powerSystem()
device = measurement()

addBus!(system; label = "Bus 1", base = 135e3)
addBus!(system; label = "Bus 2", base = 135e3)
addBranch!(system; label = "Branch 1", from = "Bus 1", to = "Bus 2", reactance = 0.12)

addAmmeter!(system, device; from = "Branch 1", magnitude = 342.13, variance = 0.428)
addAmmeter!(system, device; to = "Branch 1", magnitude = 385, variance = 42.8, noise = true)

In this example, we have opted to specify the magnitude and variance in amperes (A). It is worth noting that, despite using amperes as the input units, these keywords will still be stored in the per-unit system:

julia> [device.ammeter.magnitude.mean device.ammeter.magnitude.variance]2×2 Matrix{Float64}:
 0.799992  0.00100078
 0.864891  0.100078

Add Wattmeter

Users can include wattmeters in either an existing measurement type or one that they create from scratch by utilizing the addWattmeter! function, as demonstrated in the following example:

system = powerSystem()
device = measurement()

addBus!(system; label = "Bus 1")
addBus!(system; label = "Bus 2")
addBranch!(system; label = "Branch 1", from = "Bus 1", to = "Bus 2", reactance = 0.12)

addWattmeter!(system, device; bus = "Bus 1", active = 0.6, variance = 1e-3)
addWattmeter!(system, device; from = "Branch 1", active = 0.3, variance = 1e-2)
addWattmeter!(system, device; to = "Branch 1", active = 0.1, variance = 1e-3, noise = true)

In this scenario, one wattmeter has been added to measure the active power injection at Bus 1, as indicated by the use of the bus keyword. Additionally, two wattmeters have been introduced to measure the active power flow on both sides of Branch 1 using the from and to keywords.

For the first and second wattmeters, we assume that the measurement values are already known, defined by the active. In contrast, for the third wattmeter, the measurement value is generated by adding white Gaussian noise with the variance to the active value. As a result, the measurement data is as follows:

julia> [device.wattmeter.active.mean device.wattmeter.active.variance]3×2 Matrix{Float64}:
 0.6       0.001
 0.3       0.01
 0.147162  0.001

Customizing Input Units for Keywords

By default, the active and variance keywords are expected to be provided in per-unit (pu) values. However, users have the option to express these values in watts (W) if they prefer, as demonstrated in the following example:

@power(MW, pu, pu)

system = powerSystem()
device = measurement()

addBus!(system; label = "Bus 1")
addBus!(system; label = "Bus 2")
addBranch!(system; label = "Branch 1", from = "Bus 1", to = "Bus 2", reactance = 0.12)

addWattmeter!(system, device; bus = "Bus 1", active = 60, variance = 1e-1)
addWattmeter!(system, device; from = "Branch 1", active = 30, variance = 1)
addWattmeter!(system, device; to = "Branch 1", active = 10, variance = 1e-1, noise = true)

In this example, we have chosen to specify the active and variance in megawatts (MW), but even though we have used megawatts as the input units, these keywords will still be stored in the per-unit system:

julia> [device.wattmeter.active.mean device.wattmeter.active.variance]3×2 Matrix{Float64}:
 0.6       0.001
 0.3       0.01
 0.043435  0.001

Add Varmeter

To include varmeters, the same approach as described in the Add Wattmeter section can be applied, but here, we make use of the addVarmeter! function, as demonstrated in the following example:

system = powerSystem()
device = measurement()

addBus!(system; label = "Bus 1")
addBus!(system; label = "Bus 2")
addBranch!(system; label = "Branch 1", from = "Bus 1", to = "Bus 2", reactance = 0.12)

addVarmeter!(system, device; bus = "Bus 1", reactive = 0.2, variance = 1e-3)
addVarmeter!(system, device; from = "Branch 1", reactive = 0.1, variance = 1e-2)
addVarmeter!(system, device; to = "Branch 1", reactive = 0.05, variance = 1e-3, noise = true)

In this context, one varmeter has been added to measure the reactive power injection at Bus 1, as indicated by the use of the bus keyword. Additionally, two varmeters have been introduced to measure the reactive power flow on both sides of Branch 1 using the from and to keywords. As a result, the following outcomes are observed:

julia> [device.varmeter.reactive.mean device.varmeter.reactive.variance]3×2 Matrix{Float64}:
 0.2        0.001
 0.1        0.01
 0.0427086  0.001

Customizing Input Units for Keywords

Just as we explained for the previous device, users have the flexibility to select units different from per-units. In this case, they can opt for volt-ampere reactive (VAr), as illustrated in the following example:

@power(pu, MVAr, pu)

system = powerSystem()
device = measurement()

addBus!(system; label = "Bus 1")
addBus!(system; label = "Bus 2")
addBranch!(system; label = "Branch 1", from = "Bus 1", to = "Bus 2", reactance = 0.12)

addVarmeter!(system, device; bus = "Bus 1", reactive = 20, variance = 1e-1)
addVarmeter!(system, device; from = "Branch 1", reactive = 10, variance = 1)
addVarmeter!(system, device; to = "Branch 1", reactive = 5, variance = 1e-1, noise = true)

JuliaGrid will still store the values in the per-unit system:

julia> [device.varmeter.reactive.mean device.varmeter.reactive.variance]3×2 Matrix{Float64}:
  0.2         0.001
  0.1         0.01
 -0.00512005  0.001

Add PMU

Users have the capability to incorporate PMUs into either an existing measurement type or create one from scratch by utilizing the addPmu! function, as demonstrated in the following example:

system = powerSystem()
device = measurement()

addBus!(system; label = "Bus 1")
addBus!(system; label = "Bus 2")
addBranch!(system; label = "Branch 1", from = "Bus 1", to = "Bus 2", reactance = 0.12)

addPmu!(system, device; bus = "Bus 1", magnitude = 1.1, angle = 0.1, varianceMagnitude = 1e-3)
addPmu!(system, device; from = "Branch 1", magnitude = 1.0, angle = -0.2, noise = true)
addPmu!(system, device; to = "Branch 1", magnitude = 0.9, angle = 0.0, varianceAngle = 1e-2)

In this context, one PMU has been added to measure the bus voltage phasor at Bus 1, as indicated by the use of the bus keyword. Additionally, two PMUs have been introduced to measure the branch current phasors on both sides of Branch 1 using the from and to keywords.

For the first and third PMUs, we assume that the measurement values are already known, defined by the magnitude and angle keywords. However, for the second PMU, we generate the measurement value by adding white Gaussian noise with varianceMagnitude and varianceAngle to the magnitude and angle values, respectively. It is important to note that when we omit specifying variance values, we rely on their default settings, both of which are equal to 1e-5. As a result, we observe the following outcomes:

julia> [device.pmu.magnitude.mean device.pmu.magnitude.variance]3×2 Matrix{Float64}:
 1.1      0.001
 1.00403  1.0e-5
 0.9      1.0e-5
julia> [device.pmu.angle.mean device.pmu.angle.variance]3×2 Matrix{Float64}:
  0.1       1.0e-5
 -0.198452  1.0e-5
  0.0       0.01

Coordinate Systems and Correlated Measurement Errors

When users add PMUs, the incorporation of these measurements into the state estimation model is always in the rectangular coordinate system. In this scenario, the real and imaginary components of the phasor measurements become correlated, although typically these correlations are disregarded. However, if users want to consider these error correlations, the keyword correlated = true is provided for support.

Further, in the AC state estimation model, users have the flexibility to integrate PMU outputs in the polar coordinate system by specifying polar = true.

For example, let us add PMUs:

addPmu!(system, device; bus = "Bus 2", magnitude = 0.9, angle = 0, correlated = true)
addPmu!(system, device; bus = "Bus 2", magnitude = 0.9, angle = 0, polar = true)

In the case of linear state estimation using PMUs only, both PMUs will be integrated into the rectangular coordinate system because the polar keyword is only related to AC state estimation. The treatment of the first PMU assumes error correlation between the real and imaginary parts. Conversely, the treatment of the second PMU assumes no correlation, as it defaults to correlated = false.

Next, in AC state estimation, the first PMU measurement will be integrated into the rectangular coordinate system where correlation between the real and imaginary parts exists. The second PMU will be integrated in the polar coordinate system. It is noteworthy that representing measurements in polar coordinates can cause ill-conditioned problems arising from small current magnitudes.

Customizing Input Units for Keywords

By default, the magnitude and varianceMagnitude keywords are expected to be provided in per-unit (pu), while the angle and varianceAngle keywords are expected to be provided in radians (rad). However, users have the flexibility to express these values in different units, such as volts (V) and degrees (deg) if the PMU is set to a bus, or amperes (A) and degrees (deg) if the PMU is set to a branch. This flexibility is demonstrated in the following:

@voltage(kV, deg, V)
@current(A, deg)

system = powerSystem()
device = measurement()

addBus!(system; label = "Bus 1", base = 135e3)
addBus!(system; label = "Bus 2", base = 135e3)
addBranch!(system; label = "Branch 1", from = "Bus 1", to = "Bus 2", reactance = 0.12)

addPmu!(system, device; bus = "Bus 1", magnitude = 148.5, angle = 5.73, varianceAngle = 0.06)
addPmu!(system, device; from = "Branch 1", magnitude = 167.35, angle = -11.46, noise = true)
addPmu!(system, device; to = "Branch 1", magnitude = 150.61, angle = 0.0)

In this example, we have opted to specify kilovolts (kV) and degrees (deg) for the PMU located at Bus 1, and amperes (A) and degrees (deg) for the PMUs located at Branch 1. It is important to note that regardless of the units used, the values will still be stored in per-units and radians:

julia> [device.pmu.magnitude.mean device.pmu.magnitude.variance]3×2 Matrix{Float64}:
 1.1       1.0e-5
 0.389913  1.0e-5
 0.352167  1.0e-5
julia> [device.pmu.angle.mean device.pmu.angle.variance]3×2 Matrix{Float64}:
  0.100007  0.0010472
 -0.203037  1.0e-5
  0.0       1.0e-5

Add Templates

The functions addVoltmeter!, addAmmeter!, addWattmeter!, addVarmeter!, and addPmu! are employed to introduce measurement devices. In cases where specific keywords are not explicitly defined, default values are automatically assigned to certain parameters.

Default Keyword Values

When utilizing the addVoltmeter! function, the default variance is set to variance = 1e-2 per-unit, and the voltmeter's operational status is automatically assumed to be in-service, as indicated by the setting of status = 1.

Similarly, for the addAmmeter! function, the default variances are established at variance = 1e-2 per-unit, and the operational statuses are configured to status = 1. This means that if a user places an ammeter at either the from-bus or to-bus end of a branch, the default settings are identical. However, as we will explain in the following subsection, users have the flexibility to fine-tune these default values, differentiating between the two locations.

In alignment with ammeters, the addWattmeter! and addVarmeter! functions feature default variances set at variance = 1e-2 per-unit, and statuses are automatically assigned as status = 1, regardless of whether the wattmeter or varmeter is placed at the bus, the from-bus end, or the to-bus end. Users have the ability to customize these default values, making distinctions between the three positions of the measurement devices.

For the addPmu! function, variances for both magnitude and angle measurements are standardized to varianceMagnitude = 1e-5 and varianceAngle = 1e-5 in per-units. Likewise, operational statuses are uniformly set to statusMagnitude = 1 and statusAngle = 1, regardless of whether the PMU is positioned on the bus, the from-bus end, or the to-bus end. Once more, users retain the option to tailor these default values to their specific needs, allowing for distinctions between these three locations of the measurement devices. Additionally, the coordinate system utilized for AC state estimation is consistently configured with polar = false, while correlation in the rectangular system is disabled with correlated = false.

Across all measurement devices, the method for generating measurement means is established as noise = false.

Change Default Keyword Values

In JuliaGrid, users have the flexibility to customize default values and assign personalized settings using the @voltmeter, @ammeter, @wattmeter, @varmeter, and @pmu macros. These macros create voltmeter, ammeter, wattmeter, varmeter, and pmu templates that are employed each time functions for adding measurement devices are called. Here is an example of creating these templates with tailored default values:

system = powerSystem()
device = measurement()

addBus!(system; label = "Bus 1")
addBus!(system; label = "Bus 2")
addBranch!(system; label = "Branch 1", from = "Bus 1", to = "Bus 2", reactance = 0.12)

@voltmeter(variance = 1e-4, noise = true)
addVoltmeter!(system, device; label = "Voltmeter 1", bus = "Bus 1", magnitude = 1.0)

@ammeter(varianceFrom = 1e-3, varianceTo = 1e-4, statusTo = 0)
addAmmeter!(system, device; label = "Ammeter 1", from = "Branch 1", magnitude = 1.1)
addAmmeter!(system, device; label = "Ammeter 2", to = "Branch 1", magnitude = 0.9)

@wattmeter(varianceBus = 1e-3, statusFrom = 0, noise = true)
addWattmeter!(system, device; label = "Wattmeter 1", bus = "Bus 1", active = 0.6)
addWattmeter!(system, device; label = "Wattmeter 2", from = "Branch 1", active = 0.3)
addWattmeter!(system, device; label = "Wattmeter 3", to = "Branch 1", active = 0.1)

@varmeter(varianceFrom = 1e-3, varianceTo = 1e-3, statusBus = 0)
addVarmeter!(system, device; label = "Varmeter 1", bus = "Bus 1", reactive = 0.2)
addVarmeter!(system, device; label = "Varmeter 2", from = "Branch 1", reactive = 0.1)
addVarmeter!(system, device; label = "Varmeter 3", to = "Branch 1", reactive = 0.05)

@pmu(varianceMagnitudeBus = 1e-4, statusAngleBus = 0, varianceAngleFrom = 1e-3)
addPmu!(system, device; label = "PMU 1", bus = "Bus 1", magnitude = 1.1, angle = -0.1)
addPmu!(system, device; label = "PMU 2", from = "Branch 1", magnitude = 1.0, angle = -0.2)
addPmu!(system, device; label = "PMU 3", to = "Branch 1", magnitude = 0.9, angle = 0.0)

For instance, when adding a wattmeter to the bus, the varianceBus = 1e-3 will be applied, or if it is added to the from-bus end of the branch, these wattmeters will be set as out-of-service according to statusFrom = 0.

Similarly, when adding a PMU to the bus, the variance of the bus voltage magnitude will be defined in accordance with varianceMagnitudeBus = 1e-4, while the bus voltage angle measurements will be configured as out-of-service based on the statusAngleBus = 0.

It is important to note that changing input units will also impact the templates accordingly.

Multiple Templates

In the case of calling the macros multiple times, the provided keywords and values will be combined into a single template for the corresponding measurement device.

Reset Templates

To reset the measurement device templates to their default settings, users can utilize the following macros:

@default(voltmeter)
@default(ammeter)
@default(wattmeter)
@default(varmeter)
@default(pmu)

Additionally, users can reset all templates using the macro:

@default(template)

Labels

JuliaGrid necessitates a unique label for each voltmeter, ammeter, wattmeter, varmeter, or pmu. These labels are stored in order dictionaries, functioning as pairs of strings and integers. The string signifies the distinct label for the particular device, while the integer tracks the internal numbering of measurement devices.

In all the previous examples, with the exception of the last one, we relied on automatic labeling by omitting the label keyword. This allowed JuliaGrid to independently assign unique labels to measurement devices. In such cases, JuliaGrid utilizes a sequential set of increasing integers for labeling the devices. The last example demonstrates the user labeling approach.

Integer-Based Labeling

If users prefer to utilize integers as labels in various functions, this is acceptable. However, it is important to note that despite using integers, these labels are still stored as strings. Let us take a look at the following illustration:

system = powerSystem()
device = measurement()

addBus!(system; label = "Bus 1")
addBus!(system; label = "Bus 2")
addBranch!(system; label = "Branch 1", from = "Bus 1", to = "Bus 2", reactance = 0.12)

addVoltmeter!(system, device; label = 1, bus = "Bus 1", magnitude = 1.0)

addAmmeter!(system, device; label = 1, from = "Branch 1", magnitude = 1.1)
addAmmeter!(system, device; label = 2, to = "Branch 1", magnitude = 0.9)

Automated Labeling Using Templates

Furthermore, users can create labels using templates and include the symbol ? an incremental set of integers at any position. In addition, users have the option to use the symbol ! to insert the location of the measurement device into the label. For example:

system = powerSystem()
device = measurement()

addBus!(system; label = "Bus 1")
addBus!(system; label = "Bus 2")
addBranch!(system; label = "Branch 1", from = "Bus 1", to = "Bus 2", reactance = 0.12)

@voltmeter(label = "Voltmeter ?")
addVoltmeter!(system, device; bus = "Bus 1", magnitude = 1.0)
addVoltmeter!(system, device; bus = "Bus 2", magnitude = 0.9)

@ammeter(label = "!")
addAmmeter!(system, device; from = "Branch 1", magnitude = 1.1)
addAmmeter!(system, device; to = "Branch 1", magnitude = 0.9)

@wattmeter(label = "Wattmeter ?: !")
addWattmeter!(system, device; bus = "Bus 1", active = 0.6)
addWattmeter!(system, device; from = "Branch 1", active = 0.3)

To illustrate, the voltmeter labels are defined with incremental integers as follows:

julia> device.voltmeter.labelOrderedCollections.OrderedDict{String, Int64} with 2 entries:
  "Voltmeter 1" => 1
  "Voltmeter 2" => 2

Moreover, for ammeter labels, location information is employed:

julia> device.ammeter.labelOrderedCollections.OrderedDict{String, Int64} with 2 entries:
  "From Branch 1" => 1
  "To Branch 1"   => 2

Lastly, for wattmeters, a combination of both approaches is used:

julia> device.wattmeter.labelOrderedCollections.OrderedDict{String, Int64} with 2 entries:
  "Wattmeter 1: Bus 1"         => 1
  "Wattmeter 2: From Branch 1" => 2

Retrieving Labels

Let us explore how to retrieve stored labels. Consider the following model:

system = powerSystem()
device = measurement()

addBus!(system; label = "Bus 1")
addBus!(system; label = "Bus 2")
addBranch!(system; label = "Branch 1", from = "Bus 1", to = "Bus 2", reactance = 0.12)
addBranch!(system; label = "Branch 2", from = "Bus 2", to = "Bus 1", reactance = 0.14)

addWattmeter!(system, device; label = "Wattmeter 2", bus = "Bus 2", active = 0.6)
addWattmeter!(system, device; label = "Wattmeter 1", bus = "Bus 1", active = 0.2)
addWattmeter!(system, device; label = "Wattmeter 4", from = "Branch 1", active = 0.3)
addWattmeter!(system, device; label = "Wattmeter 3", to = "Branch 1", active = 0.1)
addWattmeter!(system, device; label = "Wattmeter 5", from = "Branch 2", active = 0.1)

To access the wattmeter labels, we can use the variable:

julia> device.wattmeter.labelOrderedCollections.OrderedDict{String, Int64} with 5 entries:
  "Wattmeter 2" => 1
  "Wattmeter 1" => 2
  "Wattmeter 4" => 3
  "Wattmeter 3" => 4
  "Wattmeter 5" => 5

If we need to obtain labels in the same order as the wattmeter definitions sequence, we can use the following code:

julia> label = collect(keys(device.wattmeter.label))5-element Vector{String}:
 "Wattmeter 2"
 "Wattmeter 1"
 "Wattmeter 4"
 "Wattmeter 3"
 "Wattmeter 5"

To isolate the wattmeters located at the buses, both at the from-bus and to-bus ends of branches, users can accomplish this by employing the following code:

julia> label[device.wattmeter.layout.bus]2-element Vector{String}:
 "Wattmeter 2"
 "Wattmeter 1"
julia> label[device.wattmeter.layout.from]2-element Vector{String}:
 "Wattmeter 4"
 "Wattmeter 5"
julia> label[device.wattmeter.layout.to]1-element Vector{String}:
 "Wattmeter 3"

Furthermore, when using the addWattmeter! function, the labels for the keywords bus, from, and to are stored internally as numerical values. To retrieve bus labels, we can follow this procedure:

julia> label = collect(keys(system.bus.label));
julia> label[device.wattmeter.layout.index[device.wattmeter.layout.bus]]2-element Vector{String}:
 "Bus 2"
 "Bus 1"

Similarly, to obtain labels for branches, we can use the following code:

julia> label = collect(keys(system.branch.label));
julia> label[device.wattmeter.layout.index[device.wattmeter.layout.from]]2-element Vector{String}:
 "Branch 1"
 "Branch 2"
julia> label[device.wattmeter.layout.index[device.wattmeter.layout.to]]1-element Vector{String}:
 "Branch 1"

This procedure is applicable to all measurement devices, including voltmeters, ammeters, varmeters, and PMUs.

julia> print(device.wattmeter.label, device.wattmeter.active.mean)Wattmeter 2: 0.6
Wattmeter 1: 0.2
Wattmeter 4: 0.3
Wattmeter 3: 0.1
Wattmeter 5: 0.1

Add Device Groups

Users have the option to add measurement devices with data generated from one of the AC analyses, specifically, using results obtained from either AC power flow or AC optimal power flow. To do this, users simply need to provide the AC abstract type as an argument to one of the functions responsible for adding measurement devices:

system = powerSystem()
device = measurement()

addBus!(system; label = "Bus 1", type = 3, active = 0.5, magnitude = 0.9, angle = 0.0)
addBus!(system; label = "Bus 2", type = 1, reactive = 0.05, magnitude = 1.1, angle = -0.1)
addBus!(system; label = "Bus 3", type = 1, active = 0.5, magnitude = 1.0, angle = -0.2)

@branch(resistance = 0.03, susceptance = 0.02)
addBranch!(system; label = "Branch 1", from = "Bus 1", to = "Bus 2", reactance = 0.5)
addBranch!(system; label = "Branch 2", from = "Bus 1", to = "Bus 3", reactance = 0.1)
addBranch!(system; label = "Branch 3", from = "Bus 2", to = "Bus 3", reactance = 0.2)

addGenerator!(system; label = "Generator 1", bus = "Bus 1", active = 0.2)
addGenerator!(system; label = "Generator 2", bus = "Bus 2", active = 1.2)

analysis = newtonRaphson(system)
for iteration = 1:100
    stopping = mismatch!(system, analysis)
    if all(stopping .< 1e-8)
        break
    end
    solve!(system, analysis)
end
power!(system, analysis)
current!(system, analysis)

@voltmeter(label = "!", noise = true)
addVoltmeter!(system, device, analysis; variance = 1e-3)

@ammeter(label = "!")
addAmmeter!(system, device, analysis; varianceFrom = 1e-3, statusTo = 0, noise = true)

@wattmeter(label = "!")
addWattmeter!(system, device, analysis; varianceBus = 1e-3, statusFrom = 0)

@varmeter(label = "!")
addVarmeter!(system, device, analysis; varianceFrom = 1e-3, statusBus = 0)

@pmu(label = "!", polar = true)
addPmu!(system, device, analysis; varianceMagnitudeBus = 1e-3)

In this example, we incorporate voltmeters to all buses and ammeters to all branches on both ends of each branch. We set noise = true once in the template and once directly in the function, which means that measurement values are generated by adding white Gaussian noise with specified variances to perturb the values obtained from the AC power flow analysis.

For wattmeters, varmeters, and PMUs added to all buses and branches, we rely on the default setting of noise = false to obtain measurement values that match precisely with those obtained from the AC power flow analysis. Additionally, when including PMUs in the AC state estimation model, we opt for the polar coordinate system by setting polar = true.

User has the option to employ an alternative method for adding groups of measurements, utilizing functions that add measurements individually. This approach may offer a more straightforward process. For example, to add wattmeters similarly to the procedure outlined above, we can employ the following:

Pᵢ = analysis.power.injection.active
for (label, index) in system.bus.label
    addWattmeter!(system, device; bus = label, active = Pᵢ[index], variance = 1e-3)
end

Pᵢⱼ = analysis.power.from.active
Pⱼᵢ = analysis.power.to.active
for (label, index) in system.branch.label
    addWattmeter!(system, device; from = label, active = Pᵢⱼ[index], status = 0)
    addWattmeter!(system, device; to = label, active = Pⱼᵢ[index])
end

Update Devices

After the addition of measurement devices to the Measurement composite type, users possess the flexibility to modify all parameters as defined in the function that added these measurement devices.

Update Voltmeter

Users have the flexibility to modify all parameters as defined within the addVoltmeter! function. For illustration, let us continue with the example from the Add Device Groups section:

updateVoltmeter!(system, device; label = "Bus 2", magnitude = 0.9, noise = false)

In this example, we update the measurement value of the voltmeter located at Bus 2, and this measurement is now generated without the inclusion of white Gaussian noise.

Update Ammeter

Similarly, users have the flexibility to modify all parameters defined within the addAmmeter! function. Using the same example from the Add Device Groups section, for example, we have:

updateAmmeter!(system, device; label = "From Branch 2", magnitude = 1.2, variance = 1e-4)
updateAmmeter!(system, device; label = "To Branch 2", status = 0)

In this example, we make adjustments to the measurement and variance values of the ammeter located at Branch 2, specifically at the from-bus end. Next, we deactivate the ammeter at the same branch on the to-bus end.

Update Wattmeter

Following the same logic, users can modify all parameters defined within the addWattmeter! function:

updateWattmeter!(system, device; label = "Bus 1", active = 1.2, variance = 1e-4)
updateWattmeter!(system, device; label = "To Branch 1", variance = 1e-6)

In this case, we modify the measurement and variance values for the wattmeter located at Bus 1. The wattmeter at Branch 1 on the to-bus end retains its measurement value while only the measurement variance is adjusted.

Update Varmeter

Following the same logic, users can modify all parameters defined within the addVarmeter! function:

updateVarmeter!(system, device; label = "Bus 1", reactive = 1.2)
updateVarmeter!(system, device; label = "Bus 2", status = 0)

In this instance, we make adjustments to the measurement value of the varmeter located at Bus 1, while utilizing a previously defined variance. Furthermore, we deactivate the varmeter at Bus 2 and designate it as out-of-service.

Update PMU

Finally, users can modify all PMU parameters defined within the addPmu! function:

updatePmu!(system, device; label = "Bus 1", magnitude = 1.05, noise = true)
updatePmu!(system, device; label = "From Branch 1", varianceAngle = 1e-6, polar = false)

In this example, we adjust the magnitude measurement value of the PMU located at Bus 1. Now, this measurement is generated by adding white Gaussian noise with specified variance value to perturb the magnitude value, while keeping the bus angle voltage value unchanged. For the PMU placed at Branch 1 on the from-bus end, we retain the existing measurement values and only adjust the variance of the angle measurement. Additionally, we choose to include this measurement in the rectangular coordinate system for the AC state estimation.

Measurement Set

Once measurement devices are integrated into the Measurement composite type, we empower users to create measurement sets in a randomized manner. To be more precise, users can manipulate the status of devices, activating or deactivating them according to specific settings. To illustrate this feature, let us first create a measurement set using the following example:

system = powerSystem()
device = measurement()

addBus!(system; label = "Bus 1", type = 3, active = 0.5, magnitude = 0.9, angle = 0.0)
addBus!(system; label = "Bus 2", type = 1, reactive = 0.05, magnitude = 1.1, angle = -0.1)
addBus!(system; label = "Bus 3", type = 1, active = 0.5, magnitude = 1.0, angle = -0.2)

@branch(resistance = 0.03, susceptance = 0.02)
addBranch!(system; label = "Branch 1", from = "Bus 1", to = "Bus 2", reactance = 0.5)
addBranch!(system; label = "Branch 2", from = "Bus 1", to = "Bus 3", reactance = 0.1)
addBranch!(system; label = "Branch 3", from = "Bus 2", to = "Bus 3", reactance = 0.2)

addGenerator!(system; label = "Generator 1", bus = "Bus 1", active = 0.2)
addGenerator!(system; label = "Generator 2", bus = "Bus 2", active = 1.2)

analysis = newtonRaphson(system)
for iteration = 1:100
    stopping = mismatch!(system, analysis)
    if all(stopping .< 1e-8)
        break
    end
    solve!(system, analysis)
end
power!(system, analysis)
current!(system, analysis)

addVoltmeter!(system, device, analysis)
addAmmeter!(system, device, analysis)
addPmu!(system, device, analysis)

Activating Devices

As a starting point, we create the measurement set where all devices are set to in-service mode based on default settings. In this instance, we generate the measurement set comprising 3 voltmeters, 6 ammeters, and 9 PMUs.

Subsequently, we offer users the ability to manipulate the status of in-service devices using the status! function. For example, within this set, if we wish to have only 12 out of the total 18 devices in-service while the rest are out-of-service, we can accomplish this as follows:

status!(system, device; inservice = 12)

Upon executing this function, 12 devices will be randomly selected to be in-service, while the remaining 6 will be set to out-of-service.

Furthermore, users can fine-tune the manipulation of specific measurements. Let us say we want to activate only 2 ammeters while deactivating the remaining ammeters:

statusAmmeter!(system, device; inservice = 2)

This action will result in 2 ammeters being in-service and 4 being out-of-service.

Users also have the option to further refine these actions by specifying devices at particular locations within the power system. For instance, we can enable 3 PMUs at buses to measure bus voltage phasors while deactivating all PMUs at branches that measure current phasors:

statusPmu!(system, device; inserviceBus = 3, inserviceFrom = 0, inserviceTo = 0)

The outcome will be that 3 PMUs are set to in-service at buses for voltage phasor measurements, while all PMUs at branches measuring current phasors will be in out-of-service mode.

Deactivating Devices

Likewise, we empower users to specify the number of devices to be set as out-of-service rather than defining the number of in-service devices. For instance, if the intention is to deactivate just 2 devices from the total measurement set, it can be achieved as follows:

status!(system, device; outservice = 2)

In this scenario 2 devices will be randomly deactivated, while the rest will remain in in-service status. Similar to the previous approach, users can apply this to specific devices or employ fine-tuning as needed.

Activating Devices Using Redundancy

Furthermore, users can take advantage of redundancy, which represents the ratio between measurement devices and state variables. For example, if we wish to have the number of measurement devices be 1.2 times greater than the number of state variables, we can utilize the following command:

status!(system, device; redundancy = 1.2)

Considering that the number of state variables is 5 (excluding the voltage angle related to the slack bus), using a redundancy value of 1.2 will result in 6 devices being set to in-service, while the remainder will be deactivated. As before, users can target specific devices or adjust settings as needed.