------
## 最终结论
```python
def sum_three_smallest_nums(numbers):
    positive_numbers = [num for num in numbers if num > 0]
    positive_numbers.sort()
    return sum(positive_numbers[:3])

# Test cases
assert sum_three_smallest_nums([10,20,30,40,50,60,7]) == 37
assert sum_three_smallest_nums([1,2,3,4,5]) == 6
assert sum_three_smallest_nums([0,1,2,3,4,5]) == 6
```