/
transient_expression.jl
173 lines (164 loc) · 6.63 KB
/
transient_expression.jl
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
"density derivative"
function expression_density_derivative(gm::AbstractGasModel, nw::Int, nw_prev::Int)
var(gm, nw)[:density_derivative] = Dict{Int,Any}()
for i in ref(gm, nw, :non_slack_junction_ids)
var(gm, nw, :density_derivative)[i] = (var(gm, nw, :density, i) - var(gm, nw_prev, :density, i)) / gm.ref[:it][gm_it_sym][:time_step]
end
for i in ids(gm, nw, :slack_junctions)
var(gm, nw, :density_derivative)[i] = 0
end
end
"density derivative for storage reservoir"
function expression_reservoir_density_derivative(
gm::AbstractGasModel,
nw::Int,
nw_next::Int;
num_discretizations::Int = 4,
report::Bool = true,
)
var(gm, nw)[:reservoir_density_derivative] = Dict{Int,Any}()
for storage_id in ids(gm, nw, :storage)
var(gm, nw, :reservoir_density_derivative)[storage_id] = (
var(gm, nw_next, :reservoir_density, storage_id) -
var(gm, nw, :reservoir_density, storage_id)
) / gm.ref[:it][gm_it_sym][:time_step]
end
report && sol_component_value(
gm,
nw,
:storage,
:reservoir_density_derivative,
ids(gm, nw, :storage),
var(gm, nw)[:reservoir_density_derivative],
)
end
"net nodal injection"
function expression_net_nodal_injection(gm::AbstractGasModel, nw::Int; report::Bool = true)
q = var(gm, nw)[:net_nodal_injection] = Dict{Int,Any}()
for (i, junction) in ref(gm, nw, :junction)
var(gm, nw, :net_nodal_injection)[i] = 0
for j in ref(gm, nw, :dispatchable_receipts_in_junction, i)
var(gm, nw, :net_nodal_injection)[i] += var(gm, nw, :injection, j)
end
for j in ref(gm, nw, :dispatchable_transfers_in_junction, i)
var(gm, nw, :net_nodal_injection)[i] -= var(gm, nw, :transfer_effective, j)
end
for j in ref(gm, nw, :dispatchable_deliveries_in_junction, i)
var(gm, nw, :net_nodal_injection)[i] -= var(gm, nw, :withdrawal, j)
end
for j in ref(gm, nw, :nondispatchable_receipts_in_junction, i)
var(gm, nw, :net_nodal_injection)[i] += ref(gm, nw, :receipt, j)["injection_nominal"]
end
for j in ref(gm, nw, :nondispatchable_transfers_in_junction, i)
var(gm, nw, :net_nodal_injection)[i] -= ref(gm, nw, :transfer, j)["withdrawal_nominal"]
end
for j in ref(gm, nw, :nondispatchable_deliveries_in_junction, i)
var(gm, nw, :net_nodal_injection)[i] -= ref(gm, nw, :delivery, j)["withdrawal_nominal"]
end
for j in ref(gm, nw, :storages_in_junction, i)
var(gm, nw, :net_nodal_injection)[i] += var(gm, nw, :storage_flow, j)
end
end
report && sol_component_value(
gm,
nw,
:junction,
:net_injection,
ids(gm, nw, :junction),
q,
)
end
"net nodal edge flow out"
function expression_net_nodal_edge_out_flow(
gm::AbstractGasModel,
nw::Int;
report::Bool = true,
)
q = var(gm, nw)[:net_nodal_edge_out_flow] = Dict{Int,Any}()
for (i, junction) in ref(gm, nw, :junction)
var(gm, nw, :net_nodal_edge_out_flow)[i] = 0
for j in ref(gm, nw, :pipes_fr, i)
var(gm, nw, :net_nodal_edge_out_flow)[i] += (var(gm, nw, :pipe_flux_fr, j) * ref(gm, nw, :pipe, j)["area"])
end
for j in ref(gm, nw, :compressors_fr, i)
var(gm, nw, :net_nodal_edge_out_flow)[i] += var(gm, nw, :compressor_flow, j)
end
for j in ref(gm, nw, :pipes_to, i)
var(gm, nw, :net_nodal_edge_out_flow)[i] -= (var(gm, nw, :pipe_flux_to, j) * ref(gm, nw, :pipe, j)["area"])
end
for j in ref(gm, nw, :compressors_to, i)
var(gm, nw, :net_nodal_edge_out_flow)[i] -= var(gm, nw, :compressor_flow, j)
end
end
report && sol_component_value(
gm,
nw,
:junction,
:net_nodal_edge_out_flow,
ids(gm, nw, :junction),
q,
)
end
"non slack affine derivative"
function expression_non_slack_affine_derivative(
gm::AbstractGasModel,
nw::Int;
report::Bool = true,
)
var(gm, nw)[:non_slack_derivative] = Dict{Int,Any}()
for i in ref(gm, nw, :non_slack_junction_ids)
var(gm, nw, :non_slack_derivative)[i] = 0
derivative_indices = ref(gm, nw, :non_slack_neighbor_junction_ids, i)
for j in derivative_indices
pipe_info = ref(gm, nw, :neighbor_edge_info, j)[i]
id = pipe_info["id"]
is_compressor = pipe_info["is_compressor"]
pipe = is_compressor ? ref(gm, nw, :compressor, id) : ref(gm, nw, :pipe, id)
x = pipe["length"] * pi * pipe["diameter"]^2 / 4.0
if (is_compressor && pipe["fr_junction"] == j && pipe["to_junction"] == i)
var(gm, nw, :non_slack_derivative)[i] += (
x *
var(gm, nw, :compressor_ratio, id) *
var(gm, nw, :density_derivative, j)
)
else
var(gm, nw, :non_slack_derivative)[i] += (x * var(gm, nw, :density_derivative, j))
end
end
for (j, neighbor) in ref(gm, nw, :neighbor_edge_info, i)
id = neighbor["id"]
is_compressor = neighbor["is_compressor"]
pipe = is_compressor ? ref(gm, nw, :compressor, id) : ref(gm, nw, :pipe, id)
x = pipe["length"] * pi * pipe["diameter"]^2 / 4.0
if (is_compressor && pipe["fr_junction"] == i && pipe["to_junction"] == j)
var(gm, nw, :non_slack_derivative)[i] += (
x *
var(gm, nw, :compressor_ratio, id) *
var(gm, nw, :density_derivative, i)
)
else
var(gm, nw, :non_slack_derivative)[i] += (x * var(gm, nw, :density_derivative, i))
end
end
end
end
"compression power"
function expression_compressor_power(gm::AbstractGasModel, nw::Int; report::Bool = true)
comp_power = var(gm, nw)[:compressor_power_expr] = Dict{Int,Any}()
for (i, compressor) in ref(gm, nw, :compressor)
alpha = var(gm, nw, :compressor_ratio, i)
f = var(gm, nw, :compressor_flow, i)
m = (gm.ref[:it][gm_it_sym][:specific_heat_capacity_ratio] - 1) /
gm.ref[:it][gm_it_sym][:specific_heat_capacity_ratio]
W = 286.76 * gm.ref[:it][gm_it_sym][:temperature] / gm.ref[:it][gm_it_sym][:gas_specific_gravity] / m
var(gm, nw, :compressor_power_expr)[i] = JuMP.@expression(gm.model, W * abs(f) * (alpha^m - 1.0))
end
report && sol_component_value(
gm,
nw,
:compressor,
:power_expr,
ids(gm, nw, :compressor),
comp_power,
)
end