Narrative:

During cruise we began deviations for thunderstorms off of our clearance. We requested mem dct sgf dct ZZZ [destination] for routing through the weather. As we moved closer to our route the weather shifted north and we needed to begin deviations to find our way around a severe line of weather. Our deviation took us right of course and we had been getting any deviation right of course we needed to cross the weather with memphis center. As we crossed the tops of a line running southwest to northeast memphis cleared us fam dct slver dct ZZZ 'when able'. We crossed the top of the weather and rounding to top of a large cell we began a 10 degree turn to the south back towards our previously cleared route; I announced (pilot monitoring) our intentions to ATC and was alerted to traffic at our same altitude moving inside our 12.5 mile TCAS ring. He told us to stop the turn; turn back right and comply with the clearance which we were still unable due to the west edge of severe weather laying over our new routing. We immediately turned back to the right and the traffic passed off our left approximately 10 miles to the left according to the TCAS display. The controller then questioned our turn to the left asking why we turned left if our clearance was routing north. I stated that we had been given deviations as necessary right of course and then fam slver ZZZ 'when able' and we were not able that clearance. He requested we begin a descent and 'handed' us off to ZKC. ZKC then proceeded to continue to force us back towards the weather over our new routing. We requested alternate routing over delma to give us time to descend to which we were denied because we were 'too high'. We eventually were able to make a turn back towards our routing and landed with no further event. ATC in my opinion was very vague in their clearances based on our deviations. We were making our turns based on deviating 'right of course' with the intention that we could work our way back to our course between mem and sgf. Our new clearance of fam slver was not accepted as we were not 'able' and had not proceeded on that clearance. If ATC needs us to not turn in a certain direction because of traffic; we need more specific clearance.I think there was some confusion between deviations 'right of course' or 'to the right'. We were under the impression we could deviate anywhere on the right side of our course. We had not accepted our new clearance yet since it was issued 'when able'. Factors to the event were severe weather including a convective SIGMET in our area. We were very aware of our surroundings and saw the traffic prior to ATC notifying us of it. We appreciate the ability to 'stay high' over the weather prior to descending after it. We would prefer to take further routing west then be forced back into weather to facilitate a descent. ZKC's ability to manage traffic descending into the area with weather around is always an issue and they are very unwilling to help. This includes their desire to force us back towards severe weather in order to get us onto their preferred arrival routes and descents. We would have gladly stayed over our requested routing over sgf and will state that next time. We planned to have extra fuel for weather deviations anyways.

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Original NASA ASRS Text

Title: CL30 Flight Crew reported misunderstanding a clearance to deviate right of course around weather at FL450. A TCAS TA is generated and ATC is advised. ATC orders a right turn to avoid the traffic and indicates the crew was not cleared to turn left even though they were still right of their original course.

Narrative: During cruise we began deviations for thunderstorms off of our clearance. We requested MEM DCT SGF DCT ZZZ [Destination] for routing through the weather. As we moved closer to our route the weather shifted north and we needed to begin deviations to find our way around a severe line of weather. Our deviation took us right of course and we had been getting any deviation right of course we needed to cross the weather with Memphis center. As we crossed the tops of a line running southwest to northeast Memphis cleared us FAM DCT SLVER DCT ZZZ 'when able'. We crossed the top of the weather and rounding to top of a large cell we began a 10 degree turn to the south back towards our previously cleared route; I announced (Pilot Monitoring) our intentions to ATC and was alerted to traffic at our same altitude moving inside our 12.5 mile TCAS ring. He told us to stop the turn; turn back right and comply with the clearance which we were still unable due to the west edge of severe weather laying over our new routing. We immediately turned back to the right and the traffic passed off our left approximately 10 miles to the left according to the TCAS display. The controller then questioned our turn to the left asking why we turned left if our clearance was routing north. I stated that we had been given deviations as necessary right of course and then FAM SLVER ZZZ 'when able' and we were not able that clearance. He requested we begin a descent and 'handed' us off to ZKC. ZKC then proceeded to continue to force us back towards the weather over our new routing. We requested alternate routing over DELMA to give us time to descend to which we were denied because we were 'too high'. We eventually were able to make a turn back towards our routing and landed with no further event. ATC in my opinion was very vague in their clearances based on our deviations. We were making our turns based on deviating 'right of course' with the intention that we could work our way back to our course between MEM and SGF. Our new Clearance of FAM SLVER was not accepted as we were not 'ABLE' and had not proceeded on that clearance. If ATC needs us to not turn in a certain direction because of traffic; we need more specific clearance.I think there was some confusion between deviations 'right of course' or 'to the right'. We were under the impression we could deviate anywhere on the right side of our course. We had not accepted our new clearance yet since it was issued 'when able'. Factors to the event were severe weather including a convective SIGMET in our area. We were very aware of our surroundings and saw the traffic prior to ATC notifying us of it. We appreciate the ability to 'stay high' over the weather prior to descending after it. We would prefer to take further routing west then be forced back into weather to facilitate a descent. ZKC's ability to manage traffic descending into the area with weather around is always an issue and they are very unwilling to help. This includes their desire to force us back towards severe weather in order to get us onto their preferred arrival routes and descents. We would have gladly stayed over our requested routing over SGF and will state that next time. We planned to have extra fuel for weather deviations anyways.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.