Pi-model admittance parameter

examples/ieee14bus/buildexample.jl

@@ -20,16 +20,16 @@ buses=OrderedDict(
     "bus14"=> PQAlgebraic(P=-0.149, Q=-0.05));
 
 branches=OrderedDict(
-    "branch1"=> PiModelLine(from= "bus1", to = "bus2",y=4.999131600798035-1im*15.263086523179553, y_shunt_km=0.0528/2, y_shunt_mk=0.0528/2),
-    "branch2"=> PiModelLine(from= "bus1", to = "bus5",y=1.025897454970189-1im*4.234983682334831, y_shunt_km=0.0492/2, y_shunt_mk=0.0492/2),
-    "branch3"=> PiModelLine(from= "bus2", to = "bus3",y=1.1350191923073958-1im*4.781863151757718, y_shunt_km=0.0438/2, y_shunt_mk=0.0438/2),
-    "branch4"=> PiModelLine(from= "bus2", to = "bus4",y=1.686033150614943-1im*5.115838325872083, y_shunt_km=0.0340/2, y_shunt_mk=0.0340/2),
-    "branch5"=> PiModelLine(from= "bus2", to = "bus5",y=1.7011396670944048-1im*5.193927397969713, y_shunt_km=0.0346/2, y_shunt_mk=0.0346/2),
-    "branch6"=> PiModelLine(from= "bus3", to = "bus4",y=1.9859757099255606-1im*5.0688169775939205, y_shunt_km=0.0128/2, y_shunt_mk=0.0128/2),
+    "branch1"=> PiModelLine(from= "bus1", to = "bus2",Y=4.999131600798035-1im*15.263086523179553, Y_shunt_km=0.0528/2, Y_shunt_mk=0.0528/2),
+    "branch2"=> PiModelLine(from= "bus1", to = "bus5",Y=1.025897454970189-1im*4.234983682334831, Y_shunt_km=0.0492/2, Y_shunt_mk=0.0492/2),
+    "branch3"=> PiModelLine(from= "bus2", to = "bus3",Y=1.1350191923073958-1im*4.781863151757718, Y_shunt_km=0.0438/2, Y_shunt_mk=0.0438/2),
+    "branch4"=> PiModelLine(from= "bus2", to = "bus4",Y=1.686033150614943-1im*5.115838325872083, Y_shunt_km=0.0340/2, Y_shunt_mk=0.0340/2),
+    "branch5"=> PiModelLine(from= "bus2", to = "bus5",Y=1.7011396670944048-1im*5.193927397969713, Y_shunt_km=0.0346/2, Y_shunt_mk=0.0346/2),
+    "branch6"=> PiModelLine(from= "bus3", to = "bus4",Y=1.9859757099255606-1im*5.0688169775939205, Y_shunt_km=0.0128/2, Y_shunt_mk=0.0128/2),
     "branch7"=> StaticLine(from= "bus4", to = "bus5",Y=6.840980661495672-1im*21.578553981691588),
-    "branch8"=> Transformer(from= "bus4", to = "bus7", y=0.0-1im*4.781943381790359, t_ratio=0.978),
-    "branch9"=> Transformer(from= "bus4", to = "bus9", y=0.0-1im*1.7979790715236075, t_ratio=0.969),
-    "branch10"=> Transformer(from= "bus5", to = "bus6", y=0.0-1im*3.967939052456154, t_ratio=0.932),
+    "branch8"=> Transformer(from= "bus4", to = "bus7", Y=0.0-1im*4.781943381790359, T_ratio=0.978),
+    "branch9"=> Transformer(from= "bus4", to = "bus9", Y=0.0-1im*1.7979790715236075, T_ratio=0.969),
+    "branch10"=> Transformer(from= "bus5", to = "bus6", Y=0.0-1im*3.967939052456154, T_ratio=0.932),
     "branch11"=> StaticLine(from= "bus6", to = "bus11",Y=1.9550285631772604-1im*4.0940743442404415),
     "branch12"=> StaticLine(from= "bus6", to = "bus12",Y=1.525967440450974-1im*3.1759639650294003),
     "branch13"=> StaticLine(from= "bus6", to = "bus13",Y=3.0989274038379877-1im*6.102755448193116),

examples/ieee14bus/grid.json

@@ -166,83 +166,83 @@
     {
       "name": "branch1",
       "params": {
-        "y": {
+        "Y_shunt_km": 0.0264,
+        "Y_shunt_mk": 0.0264,
+        "from": "bus1",
+        "Y": {
           "re": 4.999131600798035,
           "im": -15.263086523179553
         },
-        "from": "bus1",
-        "y_shunt_mk": 0.0264,
-        "y_shunt_km": 0.0264,
         "to": "bus2"
       },
       "type": "PiModelLine"
     },
     {
       "name": "branch2",
       "params": {
-        "y": {
+        "Y_shunt_km": 0.0246,
+        "Y_shunt_mk": 0.0246,
+        "from": "bus1",
+        "Y": {
           "re": 1.025897454970189,
           "im": -4.234983682334831
         },
-        "from": "bus1",
-        "y_shunt_mk": 0.0246,
-        "y_shunt_km": 0.0246,
         "to": "bus5"
       },
       "type": "PiModelLine"
     },
     {
       "name": "branch3",
       "params": {
-        "y": {
+        "Y_shunt_km": 0.0219,
+        "Y_shunt_mk": 0.0219,
+        "from": "bus2",
+        "Y": {
           "re": 1.1350191923073958,
           "im": -4.781863151757718
         },
-        "from": "bus2",
-        "y_shunt_mk": 0.0219,
-        "y_shunt_km": 0.0219,
         "to": "bus3"
       },
       "type": "PiModelLine"
     },
     {
       "name": "branch4",
       "params": {
-        "y": {
+        "Y_shunt_km": 0.017,
+        "Y_shunt_mk": 0.017,
+        "from": "bus2",
+        "Y": {
           "re": 1.686033150614943,
           "im": -5.115838325872083
         },
-        "from": "bus2",
-        "y_shunt_mk": 0.017,
-        "y_shunt_km": 0.017,
         "to": "bus4"
       },
       "type": "PiModelLine"
     },
     {
       "name": "branch5",
       "params": {
-        "y": {
+        "Y_shunt_km": 0.0173,
+        "Y_shunt_mk": 0.0173,
+        "from": "bus2",
+        "Y": {
           "re": 1.7011396670944048,
           "im": -5.193927397969713
         },
-        "from": "bus2",
-        "y_shunt_mk": 0.0173,
-        "y_shunt_km": 0.0173,
         "to": "bus5"
       },
       "type": "PiModelLine"
     },
     {
       "name": "branch6",
       "params": {
-        "y": {
+        "Y_shunt_km": 0.0064,
+        "Y_shunt_mk": 0.0064,
+        "from": "bus3",
+        "Y": {
           "re": 1.9859757099255606,
           "im": -5.0688169775939205
         },
-        "from": "bus3",
-        "y_shunt_mk": 0.0064,
-        "y_shunt_km": 0.0064,
         "to": "bus4"
       },
       "type": "PiModelLine"
@@ -262,39 +262,39 @@
     {
       "name": "branch8",
       "params": {
-        "y": {
+        "from": "bus4",
+        "Y": {
           "re": 0.0,
           "im": -4.781943381790359
         },
-        "t_ratio": 0.978,
-        "from": "bus4",
-        "to": "bus7"
+        "to": "bus7",
+        "T_ratio": 0.978
       },
       "type": "Transformer"
     },
     {
       "name": "branch9",
       "params": {
-        "y": {
+        "from": "bus4",
+        "Y": {
           "re": 0.0,
           "im": -1.7979790715236075
         },
-        "t_ratio": 0.969,
-        "from": "bus4",
-        "to": "bus9"
+        "to": "bus9",
+        "T_ratio": 0.969
       },
       "type": "Transformer"
     },
     {
       "name": "branch10",
       "params": {
-        "y": {
+        "from": "bus5",
+        "Y": {
           "re": 0.0,
           "im": -3.967939052456154
         },
-        "t_ratio": 0.932,
-        "from": "bus5",
-        "to": "bus6"
+        "to": "bus6",
+        "T_ratio": 0.932
       },
       "type": "Transformer"
     },

src/lines/PiModel.jl

@@ -1,6 +1,6 @@
 """
 ```Julia
-    PiModel(y, y_shunt_km, y_shunt_mk, t_km, t_mk)
+    PiModel(Y, Y_shunt_km, Y_shunt_mk, T_km, T_mk)
 ```
 Implementation of the unified branch model with our sign conventions.
 See also the Chapter 2 in
@@ -9,17 +9,17 @@ Assumptions:
 * the line admittance is symmetric
 
 # Arguments
-- `y`: line admittance
-- `y_shunt_km`: shunt admittance at the end connected to node `k`
-- `y_shunt_mk`: shunt admittance at the end connected to node `m`
-- `t_km`: transformer ratio at the end connected to node `k`
-- `t_mk`: transformer ratio at the end connected to node `m`
+- `Y`: line admittance
+- `Y_shunt_km`: shunt admittance at the end connected to node `k`
+- `Y_shunt_mk`: shunt admittance at the end connected to node `m`
+- `T_km`: transformer ratio at the end connected to node `k`
+- `t_mk`: Transformer ratio at the end connected to node `m`
 """
-function PiModel(y, y_shunt_km, y_shunt_mk, t_km, t_mk)
+function PiModel(Y, Y_shunt_km, Y_shunt_mk, T_km, T_mk)
     Π = zeros(Complex{Float64}, 2, 2)
-    Π[1, 1] = - abs2(t_km) * (y + y_shunt_km) # Our sign convention is opposite for the source of the edge
-    Π[1, 2] = conj(t_km) * t_mk * y # Our sign convention is opposite for the source of the edge
-    Π[2, 1] = - conj(t_mk) * t_km * y
-    Π[2, 2] = abs2(t_mk) * (y + y_shunt_mk)
+    Π[1, 1] = - abs2(T_km) * (Y + Y_shunt_km) # Our sign convention is opposite for the source of the edge
+    Π[1, 2] = conj(T_km) * T_mk * Y # Our sign convention is opposite for the source of the edge
+    Π[2, 1] = - conj(T_mk) * T_km * Y
+    Π[2, 2] = abs2(T_mk) * (Y + Y_shunt_mk)
     Π
 end

src/lines/PiModelLine.jl

@@ -1,6 +1,6 @@
 @doc """
 ```Julia
-    PiModelLine(from, to, y, y_shunt_km, y_shunt_mk)
+    PiModelLine(from, to, Y, Y_shunt_km, Y_shunt_mk)
 ```
 A line modelled according to the PI-Model.
 
@@ -10,21 +10,21 @@ See also the Chapter 2 in
 # Arguments
 - `from` : node `k`
 - `to` : node `m`
-- `y`: admittance of line between `k` and `m`
-- `y_shunt_km`: shunt admittance at the end connected to node `k`
-- `y_shunt_mk`: shunt admittance at the end connected to node `m`
+- `Y`: admittance of line between `k` and `m`
+- `Y_shunt_km`: shunt admittance at the end connected to node `k`
+- `Y_shunt_mk`: shunt admittance at the end connected to node `m`
 - `t_km`: transformer ratio at the end connected to node `k`
 - `t_mk`: transformer ratio at the end connected to node `m`
 
 # Assumptions:
 - the line admittance is symmetric
 """
-@Line PiModelLine(from, to, y, y_shunt_km, y_shunt_mk) begin
-    Y = PiModel(y, y_shunt_km, y_shunt_mk, 1, 1)
+@Line PiModelLine(from, to, Y, Y_shunt_km, Y_shunt_mk) begin
+    Π = PiModel(Y, Y_shunt_km, Y_shunt_mk, 1, 1)
 end begin
     # If current is flowing away from the source, it is negative at the source.
     voltage_vector = [source_voltage,destination_voltage]
-    current_vector = Y * voltage_vector
+    current_vector = Π * voltage_vector
 end
 
 export PiModelLine

src/lines/Transformer.jl

@@ -1,6 +1,6 @@
 """
 ```Julia
-    Transformer(from, to, y, t_ratio)
+    Transformer(from, to, Y, T_ratio)
 ```
 
 assuming an ideal transformer in series with an admittance.
@@ -9,26 +9,26 @@ The representation uses the Π model.
 # Mathematical Representation
 The voltage transforms as:
 ```math
-    u_{to} = t_{ratio} u_{from}
+    u_{to} = T_{ratio} u_{from}
 ```
 
 # Arguments
 
 - `from` : start node
 - `to` : end node
-- `y`: transformer admittance
-- `t_ratio`: transformation ration
+- `Y`: transformer admittance
+- `T_ratio`: transformation ration
 
 # Assumptions
 
 The admittance is here taken to be on the high-voltage side.
 """
-@Line Transformer(from, to, y, t_ratio) begin
+@Line Transformer(from, to, Y, T_ratio) begin
 
     # If current is flowing away from the source, it is negative at the source.
     voltage_vector = [source_voltage,destination_voltage]
-    Y = PiModel(y, 0, 0, t_ratio, 1)
-    current_vector = Y * voltage_vector
+    Π = PiModel(Y, 0, 0, T_ratio, 1)
+    current_vector = Π * voltage_vector
 end
 
 export Transformer

src/operationpoint/power_flow.jl

@@ -218,18 +218,18 @@ function make_branch_ac!(data::Dict{String,Any}, dict::Dict{Any, Int}, line::Tra
     branch_dict = _make_branch_ac_header(data, dict, line)
     branch_dict["transformer"] = true
     branch_dict["tap"] = line.t_ratio
-    branch_dict["br_r"] = real(1 / line.y)
-    branch_dict["br_x"] = imag(1 / line.y)
+    branch_dict["br_r"] = real(1 / line.Y)
+    branch_dict["br_x"] = imag(1 / line.Y)
 end
 
 function make_branch_ac!(data::Dict{String,Any}, dict::Dict{Any, Int}, line::PiModelLine)
     branch_dict = _make_branch_ac_header(data, dict, line)
-    branch_dict["g_fr"] = real(line.y_shunt_km)
-    branch_dict["b_fr"] = imag(line.y_shunt_km)
-    branch_dict["br_r"] = real(1 / line.y)
-    branch_dict["br_x"] = imag(1 / line.y)
-    branch_dict["g_to"] = real(line.y_shunt_mk)
-    branch_dict["b_to"] = imag(line.y_shunt_mk)
+    branch_dict["g_fr"] = real(line.Y_shunt_km)
+    branch_dict["b_fr"] = imag(line.Y_shunt_km)
+    branch_dict["br_r"] = real(1 / line.Y)
+    branch_dict["br_x"] = imag(1 / line.Y)
+    branch_dict["g_to"] = real(line.Y_shunt_mk)
+    branch_dict["b_to"] = imag(line.Y_shunt_mk)
 end
 
 

test/common/PowerGrid.jl

@@ -9,11 +9,11 @@ using OrderedCollections: OrderedDict
 
 @testset "permutation tests array constructor" begin
     nodes_1 = [SlackAlgebraic(U=1), SwingEqLVS(H=1, P=-1, D=1, Ω=50, Γ=20, V=1), SwingEqLVS(H=1, P=1, D=1, Ω=50, Γ=20, V=1)]
-    lines_1 = [StaticLine(from=1, to=2, Y=5im),PiModelLine(;from=2, to=3, y = 1/(0.1152 + im*0.0458), y_shunt_km = 0.,  y_shunt_mk = 0.)]
+    lines_1 = [StaticLine(from=1, to=2, Y=5im),PiModelLine(;from=2, to=3, Y = 1/(0.1152 + im*0.0458), Y_shunt_km = 0.,  Y_shunt_mk = 0.)]
     power_grid_1 = PowerGrid(nodes_1,lines_1)
 
     nodes_2 = [SlackAlgebraic(U=1), SwingEqLVS(H=1, P=-1, D=1, Ω=50, Γ=20, V=1),SwingEqLVS(H=1, P=1, D=1, Ω=50, Γ=20, V=1)]
-    lines_2 = [PiModelLine(;from=2, to=3, y = 1/(0.1152 + im*0.0458), y_shunt_km = 0.,  y_shunt_mk = 0.),StaticLine(from=1, to=2, Y=5im)]
+    lines_2 = [PiModelLine(;from=2, to=3, Y = 1/(0.1152 + im*0.0458), Y_shunt_km = 0.,  Y_shunt_mk = 0.),StaticLine(from=1, to=2, Y=5im)]
     power_grid_2 = PowerGrid(nodes_2,lines_2)
 
     @test collect(edges(power_grid_1.graph))[1]==collect(edges(power_grid_2.graph))[1]
@@ -24,7 +24,7 @@ using OrderedCollections: OrderedDict
     @test sum(abs.(op1[:]-op2[:]))<=1*10-6
 
     nodes_3 = [SwingEqLVS(H=1, P=-1, D=1, Ω=50, Γ=20, V=1),SlackAlgebraic(U=1), SwingEqLVS(H=1, P=1, D=1, Ω=50, Γ=20, V=1)]
-    lines_3 = [PiModelLine(;from=1, to=3, y = 1/(0.1152 + im*0.0458), y_shunt_km = 0.,  y_shunt_mk = 0.),StaticLine(from=1, to=2, Y=5im)]
+    lines_3 = [PiModelLine(;from=1, to=3, Y = 1/(0.1152 + im*0.0458), Y_shunt_km = 0.,  Y_shunt_mk = 0.),StaticLine(from=1, to=2, Y=5im)]
     power_grid_3 = PowerGrid(nodes_3,lines_3)
     op3 = find_operationpoint(power_grid_3)
     @test isapprox(op2[3],op3[1],atol=1e-8)
@@ -34,11 +34,11 @@ end
 
 @testset "permutation tests OrderedDict constructor" begin
     nodes_1 = OrderedDict("bus1"=>SlackAlgebraic(U=1), "bus2"=>SwingEqLVS(H=1, P=-1, D=1, Ω=50, Γ=20, V=1),"bus3"=> SwingEqLVS(H=1, P=1, D=1, Ω=50, Γ=20, V=1))
-    lines_1 = OrderedDict("line1"=>StaticLine(from="bus1", to="bus2", Y=5im),"line2"=>PiModelLine(;from="bus2", to="bus3", y = 1/(0.1152 + im*0.0458), y_shunt_km = 0.,  y_shunt_mk = 0.))
+    lines_1 = OrderedDict("line1"=>StaticLine(from="bus1", to="bus2", Y=5im),"line2"=>PiModelLine(;from="bus2", to="bus3", Y = 1/(0.1152 + im*0.0458), Y_shunt_km = 0.,  Y_shunt_mk = 0.))
     power_grid_1 = PowerGrid(nodes_1,lines_1)
 
     nodes_2 = OrderedDict("bus1"=>SlackAlgebraic(U=1), "bus2"=>SwingEqLVS(H=1, P=-1, D=1, Ω=50, Γ=20, V=1),"bus3"=> SwingEqLVS(H=1, P=1, D=1, Ω=50, Γ=20, V=1))
-    lines_2 = OrderedDict("line1"=>PiModelLine(;from="bus2", to="bus3", y = 1/(0.1152 + im*0.0458), y_shunt_km = 0.,  y_shunt_mk = 0.),"line2"=>StaticLine(from="bus1", to="bus2", Y=5im))
+    lines_2 = OrderedDict("line1"=>PiModelLine(;from="bus2", to="bus3", Y = 1/(0.1152 + im*0.0458), Y_shunt_km = 0.,  Y_shunt_mk = 0.),"line2"=>StaticLine(from="bus1", to="bus2", Y=5im))
     power_grid_2 = PowerGrid(nodes_2,lines_2)
 
     @test collect(edges(power_grid_1.graph))[1]==collect(edges(power_grid_2.graph))[1]
@@ -49,7 +49,7 @@ end
 
 
     nodes_3 = OrderedDict("bus1"=>SwingEqLVS(H=1, P=-1, D=1, Ω=50, Γ=20, V=1),"bus2"=>SlackAlgebraic(U=1), "bus3"=> SwingEqLVS(H=1, P=1, D=1, Ω=50, Γ=20, V=1))
-    lines_3 = OrderedDict("line1"=>PiModelLine(;from="bus1", to="bus3", y = 1/(0.1152 + im*0.0458), y_shunt_km = 0.,  y_shunt_mk = 0.),"line2"=>StaticLine(from="bus1", to="bus2", Y=5im))
+    lines_3 = OrderedDict("line1"=>PiModelLine(;from="bus1", to="bus3", Y = 1/(0.1152 + im*0.0458), Y_shunt_km = 0.,  Y_shunt_mk = 0.),"line2"=>StaticLine(from="bus1", to="bus2", Y=5im))
 
     power_grid_3 = PowerGrid(nodes_3, lines_3)
     op3 = find_operationpoint(power_grid_3)

test/faults/NodeShortCircuit.jl

@@ -18,15 +18,15 @@ nodes = [
   CSIMinimal(; I_r = complex(0.4988, -0.4988)),
 ]
 
-y = complex(1.736, -208.326)
+Y = complex(1.736, -208.326)
 
-SL = StaticLine(; from = 1, to = 2, Y = y)
+SL = StaticLine(; from = 1, to = 2, Y = Y)
 PL = PiModelLine(;
     from = 1,
     to = 2,
-    y = y,
-    y_shunt_km = 0.0,
-    y_shunt_mk = 0.0,
+    Y = Y,
+    Y_shunt_km = 0.0,
+    Y_shunt_mk = 0.0,
   )