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You can model curved slats using the venetian blind shading layer type in WINDOW (enter a non-zero value for rise) to model your venetian blinds:

You can then model the whole window with the shading layer in an exterior or interior position, also including the glazing and frame, in WINDOW and export an idf fragment containing a ComplexFenestrationState object describing the window and a FrameAndDivider object describing the frame.
In the Window library, choose Report, then select Report Type: "EnergyPlus BSDF Idf File". The exported idf fragment includes the BSDF matrices required to model the optical properties of the shading layer and glazing. If you include the WINDOW idf fragment in your main idf file, you can then refer to the complex fenestration and frame objects in your FenestrationSurface:Detailed objects (make sure you match the names output by WINDOW):

in the idf fragment generated by WINDOW:

    WindowProperty:FrameAndDivider,
        NAME_OF_FRAME_OBJECT,  !- Name
        0.038395,                !- Frame Width {m}
        ,                        !- Frame Outside Projection {m}
        ,                        !- Frame Inside Projection {m}
...

    Construction:ComplexFenestrationState,
        NAME_OF_CFS_OBJECT, !- Name
        LBNLWindow,              !- Basis Type
        None,                    !- Basis Symmetry Type
        ThermParam_NAME,  !- Window Thermal Model
        CFS_NAME_Basis,  !- Basis Matrix 
...

in main idf - the Construction Name should be the name of the ComplexFenestrationState object, and the Frame and Divider name should be the name of the FrameAndDivider object:

    FenestrationSurface:Detailed,
    Block1_Zone1_East_Wall_0_0_1_Win,  !- Name
    Window,                  !- Surface Type
    NAME_OF_CFS_OBJECT, !- Construction Name
    Block1_Zone1_East_Wall,  !- Building Surface Name
    ,                        !- Outside Boundary Condition Object
    AutoCalculate,           !- View Factor to Ground
    NAME_OF_FRAME_OBJECT,  !- Frame and Divider Name
    1,                       !- Multiplier
    4,                       !- Number of Vertices
    3.356958552,7.80691071,.6,  !- X,Y,Z ==> Vertex 1 {m}
    3.356958552,9.90691071,.6,  !- X,Y,Z ==> Vertex 2 {m}
    3.356958552,9.90691071,2.1,  !- X,Y,Z ==> Vertex 3 {m}
    3.356958552,7.80691071,2.1;  !- X,Y,Z ==> Vertex 4 {m}
...