A hydroelectric power plant real-time monitoring system (1;1') comprising i) a real-time data acquisition system (11;11') connected to dedicated sensors positioned in a hydroelectric power plant and configured to acquire in real-time real-time measured power plant data, said real-time measured power plant data comprising - real-time measured simulation inputs (111;111'), ii) a real-time simulation system (12;12') iii) and a real-time diagnostic system (13;13'), characterized - in that said real-time simulation system (12;12') is configured to receive said real-time measured simulation inputs (111;111') from said real-time data acquisition system (11;11'), - in that a real-time simulation software (121;121') is stored in a computer comprised in said real-time simulation system (12;12'), said real-time simulation software (121;121') being configured to simulate in real-time a transient behavior of the hydroelectric power plant based on said real-time measured simulation inputs and to provide in real-time real-time simulated power plant data related to said transient behavior of the hydroelectric power plant, - in that said real-time simulated power plant data comprise at least one real-time simulated monitored quantity (123;123'), said real-time simulated monitored quantity (123;123') corresponding to a simulated quantity of a non-measured power plant quantity or of a non-measurable power plant quantity - and in that said real-time diagnostic system (13;13') is configured - to compare in real-time said real-time simulated monitored quantity (123;123') with a predetermined threshold to trigger, when said real-time simulated monitored quantity (123;123') exceeds said predetermined threshold, an alarm identifying a power plant transient behavior problem - and/or to compute in real-time at least one output related to said real-time simulated monitored quantity (123;123') and compare in real-time said output with a predetermined threshold to trigger, when said output exceeds said predetermined threshold, an alarm identifying a power plant transient behavior problem. i) a real-time data acquisition system (11;11') connected to dedicated sensors positioned in a hydroelectric power plant and configured to acquire in real-time real-time measured power plant data, said real-time measured power plant data comprising - real-time measured simulation inputs (111;111'), - real-time measured simulation inputs (111;111'), ii) a real-time simulation system (12;12') iii) and a real-time diagnostic system (13;13'), - in that said real-time simulation system (12;12') is configured to receive said real-time measured simulation inputs (111;111') from said real-time data acquisition system (11;11'), - in that a real-time simulation software (121;121') is stored in a computer comprised in said real-time simulation system (12;12'), said real-time simulation software (121;121') being configured to simulate in real-time a transient behavior of the hydroelectric power plant based on said real-time measured simulation inputs and to provide in real-time real-time simulated power plant data related to said transient behavior of the hydroelectric power plant, - in that said real-time simulated power plant data comprise at least one real-time simulated monitored quantity (123;123'), said real-time simulated monitored quantity (123;123') corresponding to a simulated quantity of a non-measured power plant quantity or of a non-measurable power plant quantity - and in that said real-time diagnostic system (13;13') is configured - to compare in real-time said real-time simulated monitored quantity (123;123') with a predetermined threshold to trigger, when said real-time simulated monitored quantity (123;123') exceeds said predetermined threshold, an alarm identifying a power plant transient behavior problem - and/or to compute in real-time at least one output related to said real-time simulated monitored quantity (123;123') and compare in real-time said output with a predetermined threshold to trigger, when said output exceeds said predetermined threshold, an alarm identifying a power plant transient behavior problem. - to compare in real-time said real-time simulated monitored quantity (123;123') with a predetermined threshold to trigger, when said real-time simulated monitored quantity (123;123') exceeds said predetermined threshold, an alarm identifying a power plant transient behavior problem - and/or to compute in real-time at least one output related to said real-time simulated monitored quantity (123;123') and compare in real-time said output with a predetermined threshold to trigger, when said output exceeds said predetermined threshold, an alarm identifying a power plant transient behavior problem.