equations. Each equation accounts for the unbalance in the pressure loss equation due to incorrect values of flowrate. The equation includes the contribution for a particular path as well as contributions from all other paths which have pipes common to both paths. Gradient techniques are used to formulate these equations. For path j, the pressure change required to balance the pressure loss equation is expressed in terms of the flow change in path j (△Wj) and the flow changes in adjacent paths (△Wk) and is given as:
equations. Flat Modelica can be conceptually mapped to a set of equations consisting of differential, algebraic and discrete equations of the following form (see Table 3 for brief description of the used symbols): 5xxxx://xxxxxx.xxxxxx.xx/project/rcn/111584_en.pdf , (Nov, 2015). 6E.g., the semantics of operators likenoEvent(), orreinit()is not covered. Symbol Description pparameters and constants ⊆ pB parameters and constants of typeBoolean,p B p ttime x(t) vector of dynamic variables of typeReal,i.e., variables that appear differentiated at some place ˙x(t) differentiated vector of dynamic variables y(t) vector of other variables of typeRealwhich do not fall into any other category (= algebraic variables) m(te) vector of discrete-time variables of typediscrete Real,Boolean,In- teger,String. Change only at event instantst e ⊆ mB(te) vector of discrete-time variables of typeBoolean,m B(te) m(t e). Change only at event instantst e mpre(te) values ofmimmediately before the current event at event instantt e m B pre (te) values ofm B immediately before the current event at event instantt e, pre mB (te)⊆m pre(te) c(te) vector containing all Boolean condition expressions,e.g., if-expressions v(t) vector containing all elements in the vectorsx(t),˙x(t),y(t), [t],m(t e), mpre(te),p Table 3: Notation used in the Modelica hybrid DAE representation.
