How to model flow balance equation in Pyomo?

Question

I need to specify the following equation in my Pyomo model:

w[t]=w[t-1]+y[t]+z[t]-v[t]

t is a time step, and w, y, z and v are variables that change over time steps. Should I model it as a constraint? I appreciate any example of how similar equations (maybe not exactly the same) are modeled.

Answer 1

Yes, you should model this as a constraint. Here is a small example to help you get started:

m.t = Set(initialize=[1,2,3,4])
m.w = Var(m.t)
m.y = Var(m.t)

def _flow_rule(m, t):
   if t == 1:
      return Constraint.Skip
   return m.w[t] == m.w[t-1] + m.y[t]
m.flow = Constraint(m.t, rule=_flow_rule)