diff --git a/src/core/objective.jl b/src/core/objective.jl
index 046437c5..aca4167d 100644
--- a/src/core/objective.jl
+++ b/src/core/objective.jl
@@ -123,6 +123,38 @@ function objective_min_fuel_and_flow_cost_polynomial(pm::AbstractPowerModel; kwa
     end
 end
 
+"""
+    _pow(x, i)
+
+A type-unstable version of `x^i` becaues using the base `x^i` for JuMP variables
+has some unusual behavior:
+
+```julia
+julia> model = Model();
+
+julia> @variable(model, x)
+x
+
+julia> typeof(x^1)
+QuadExpr (alias for GenericQuadExpr{Float64, VariableRef})
+
+julia> typeof(x^1.0)
+NonlinearExpr
+```
+"""
+function _pow(x, i)
+    if i == 0
+        return 1
+    elseif i == 1
+        return x
+    elseif i == 2
+        return x^2
+    else
+        return x^Float64(i)
+    end
+end
+
+
 ""
 function _objective_min_fuel_and_flow_cost_polynomial_linquad(pm::AbstractPowerModel; report::Bool=true)
     gen_cost = Dict()
@@ -131,31 +163,19 @@ function _objective_min_fuel_and_flow_cost_polynomial_linquad(pm::AbstractPowerM
     for (n, nw_ref) in nws(pm)
         for (i,gen) in nw_ref[:gen]
             pg = sum( var(pm, n, :pg, i)[c] for c in conductor_ids(pm, n) )
-
-            if length(gen["cost"]) == 1
-                gen_cost[(n,i)] = gen["cost"][1]
-            elseif length(gen["cost"]) == 2
-                gen_cost[(n,i)] = gen["cost"][1]*pg + gen["cost"][2]
-            elseif length(gen["cost"]) == 3
-                gen_cost[(n,i)] = gen["cost"][1]*pg^2 + gen["cost"][2]*pg + gen["cost"][3]
-            else
-                gen_cost[(n,i)] = 0.0
-            end
+            gen_cost[(n, i)] = JuMP.@expression(
+                pm.model,
+                sum(v * _pow(pg, d - 1) for (d, v) in enumerate(reverse(gen["cost"]))),
+            )
         end
 
         from_idx = Dict(arc[1] => arc for arc in nw_ref[:arcs_from_dc])
         for (i,dcline) in nw_ref[:dcline]
             p_dc = sum( var(pm, n, :p_dc, from_idx[i])[c] for c in conductor_ids(pm, n) )
-
-            if length(dcline["cost"]) == 1
-                dcline_cost[(n,i)] = dcline["cost"][1]
-            elseif length(dcline["cost"]) == 2
-                dcline_cost[(n,i)] = dcline["cost"][1]*p_dc + dcline["cost"][2]
-            elseif length(dcline["cost"]) == 3
-                dcline_cost[(n,i)] = dcline["cost"][1]*p_dc^2 + dcline["cost"][2]*p_dc + dcline["cost"][3]
-            else
-                dcline_cost[(n,i)] = 0.0
-            end
+            dcline_cost[(n, i)] = JuMP.@expression(
+                pm.model,
+                sum(v * _pow(p_dc, d - 1) for (d, v) in enumerate(reverse(dcline["cost"]))),
+            )
         end
     end
 
@@ -275,7 +295,7 @@ function _objective_min_fuel_and_flow_cost_polynomial_nl(pm::AbstractPowerModel;
             pg = sum( var(pm, n, :pg, i)[c] for c in conductor_ids(pm, n))
             gen_cost[(n,i)] = JuMP.@expression(
                 pm.model,
-                sum(v * pg^(d-1) for (d, v) in enumerate(reverse(gen["cost"]))),
+                sum(v * _pow(pg, d-1) for (d, v) in enumerate(reverse(gen["cost"]))),
             )
         end
 
@@ -285,7 +305,7 @@ function _objective_min_fuel_and_flow_cost_polynomial_nl(pm::AbstractPowerModel;
             p_dc = sum( var(pm, n, :p_dc, from_idx[i])[c] for c in conductor_ids(pm, n))
             dcline_cost[(n,i)] = JuMP.@expression(
                 pm.model,
-                sum(v * p_dc^(d-1) for (d, v) in enumerate(reverse(dcline["cost"]))),
+                sum(v * _pow(p_dc, d - 1) for (d, v) in enumerate(reverse(dcline["cost"]))),
             )
         end
     end
@@ -316,16 +336,10 @@ function _objective_min_fuel_cost_polynomial_linquad(pm::AbstractPowerModel; rep
     for (n, nw_ref) in nws(pm)
         for (i,gen) in nw_ref[:gen]
             pg = sum( var(pm, n, :pg, i)[c] for c in conductor_ids(pm, n) )
-
-            if length(gen["cost"]) == 1
-                gen_cost[(n,i)] = gen["cost"][1]
-            elseif length(gen["cost"]) == 2
-                gen_cost[(n,i)] = gen["cost"][1]*pg + gen["cost"][2]
-            elseif length(gen["cost"]) == 3
-                gen_cost[(n,i)] = gen["cost"][1]*pg^2 + gen["cost"][2]*pg + gen["cost"][3]
-            else
-                gen_cost[(n,i)] = 0.0
-            end
+            gen_cost[(n, i)] = JuMP.@expression(
+                pm.model,
+                sum(v * _pow(pg, d - 1) for (d, v) in enumerate(reverse(gen["cost"]))),
+            )
         end
     end
 
@@ -345,7 +359,7 @@ function _objective_min_fuel_cost_polynomial_nl(pm::AbstractPowerModel; report::
             pg = sum( var(pm, n, :pg, i)[c] for c in conductor_ids(pm, n))
             gen_cost[(n,i)] = JuMP.@expression(
                 pm.model,
-                sum(v * pg^(d-1) for (d, v) in enumerate(reverse(gen["cost"]))),
+                sum(v * _pow(pg, d - 1) for (d, v) in enumerate(reverse(gen["cost"]))),
             )
         end
     end
diff --git a/test/docs.jl b/test/docs.jl
index e7b6eb89..7338be12 100644
--- a/test/docs.jl
+++ b/test/docs.jl
@@ -31,6 +31,7 @@
         #print(pm.model)
 
         @test JuMP.num_nonlinear_constraints(pm.model) == 0
+        @test JuMP.num_constraints(pm.model, JuMP.NonlinearExpr, JuMP.MOI.EqualTo{Float64}) == 12
         @test JuMP.num_variables(pm.model) == 28
 
         result = optimize_model!(pm, optimizer=JuMP.optimizer_with_attributes(Ipopt.Optimizer, "print_level"=>0))
diff --git a/test/model.jl b/test/model.jl
index c301e41c..68d719c1 100644
--- a/test/model.jl
+++ b/test/model.jl
@@ -16,6 +16,7 @@
         pm = instantiate_model("../test/data/matpower/case5.m", ACPPowerModel, PowerModels.build_opf, jump_model=m)
 
         @test JuMP.num_nonlinear_constraints(pm.model) == 0
+        @test JuMP.num_constraints(pm.model, JuMP.NonlinearExpr, JuMP.MOI.EqualTo{Float64}) == 28
         @test JuMP.num_variables(pm.model) == 49
 
         @test pm.model[:my_var] == x