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This warning says that the iteration method used to calculate the part-load ratio of the hot water coil failed to find an answer. I thought most of these problems have been corrected. Which version of EnergyPlus are you using? You can upload your input file here or send that file to the help desk (support@energyplus.helpserve.com) and someone will look at the root cause and correct this problem.

In your case, the algorithm could not even start to find a solution since the warning says "Bad hot part-load ratio limits". This means that a solution cannot be found.

At other times the warning may say "iteration limit exceeded." For this failure type, there is one way to address this using V8.8. There is a new object in V8.8 that allows the user to choose the solution algorithm used during iterations. This new object is called HVACSystemRootFindingAlgorithm. You can read about this object in the documentation. The default method used during the iterative solution is RegulaFalsi. This is a secant based solution method and has difficulty finding very small part-load ratios or solutions for coil performance that is highly non-linear. The Bisection method will always find an answer however it takes longer since it uses the method of half-stepping (e.g., try 0.5, then try 0.25, then try 0.125, etc.) to the answer. This new object is unique in that it can switch between Bisection and RegulaFalsi to find the solution faster. For example, choosing BisectionThenRegulaFalsi with Number of Iterations Before Algorithm Switch set to 4 will use both solution methods and switch between them every 4 iterations.

HVACSystemRootFindingAlgorithm,
       \memo Specifies a HVAC system solver algorithm to find a root
       \unique-object
  A1 , \field Algorithm
       \type choice
       \key RegulaFalsi
       \key Bisection
       \key BisectionThenRegulaFalsi
       \key RegulaFalsiThenBisection
       \default RegulaFalsi
  N1 ; \field Number of Iterations Before Algorithm Switch
       \note This field is used when RegulaFalsiThenBisection or BisectionThenRegulaFalsi is
       \note entered. When iteration number is greater than the value, algorithm switches.
       \type integer
       \default 5

This warning says that the iteration method used to calculate the part-load ratio of the hot water coil failed to find an answer. I thought most of these problems have been corrected. Which version of EnergyPlus are you using? You can upload your input file here or send that file to the help desk (support@energyplus.helpserve.com) and someone will look at the root cause and correct this problem.

In your case, the algorithm could not even start to find a solution since the warning says "Bad hot part-load ratio limits". This means that a solution cannot be found.found. The first warning shown is for 01/31 and the next is for 04/25. So this is not happening many times during the simulation. What was the total number reported at the end of the err file? If the number of times this occurs is low, you can usually disregard these warnings as they do not greatly affect the annual energy use. You would still want to report this so it can be fixed.

At other times the warning may say "iteration limit exceeded." For this failure type, there is one way to address this using V8.8. There is a new object in V8.8 that allows the user to choose the solution algorithm used during iterations. This new object is called HVACSystemRootFindingAlgorithm. You can read about this object in the documentation. The default method used during the iterative solution is RegulaFalsi. This is a secant based solution method and has difficulty finding very small part-load ratios or solutions for coil performance that is highly non-linear. The Bisection method will always find an answer however it takes longer since it uses the method of half-stepping (e.g., try 0.5, then try 0.25, then try 0.125, etc.) to the answer. This new object is unique in that it can switch between Bisection and RegulaFalsi to find the solution faster. For example, choosing BisectionThenRegulaFalsi with Number of Iterations Before Algorithm Switch set to 4 will use both solution methods and switch between them every 4 iterations.

HVACSystemRootFindingAlgorithm,
       \memo Specifies a HVAC system solver algorithm to find a root
       \unique-object
  A1 , \field Algorithm
       \type choice
       \key RegulaFalsi
       \key Bisection
       \key BisectionThenRegulaFalsi
       \key RegulaFalsiThenBisection
       \default RegulaFalsi
  N1 ; \field Number of Iterations Before Algorithm Switch
       \note This field is used when RegulaFalsiThenBisection or BisectionThenRegulaFalsi is
       \note entered. When iteration number is greater than the value, algorithm switches.
       \type integer
       \default 5