Coordinated Frequency Control Of Power Systems Based On Differential Games Theory

There are a large number of various controllers running in electric power systems, e.g., frequency controller, voltage controller, PSS and FACTS, etc. They are designed for different objectives, e.g., frequency stability, voltage stability, tie-line power exchange plan, etc. With power systems being increasingly huge, complicated and smart, more and more new controllers are being introduced into systems. In some case, where the different controllers and their controlled are electric-connected, we have to combine the policy-making problems for all controllers into one multi-controller multi-objective policy-making problem. While developing the control commands for controllers in this case, effective coordination is necessary for the controllers to play their designed roles. The "coordination" in this paper has two levels of meanings:the first is globally considering all controllers rather than individually developing their commands, so as to prevent the controllers from conflicting and weakening mutually; the second is ensuring that the commands are persuasive to every single controller (i.e., none of the controllers has the desire to deviate from command), so as to prevent the controllers from violating commands in secrecy and resulting in the system insecurity. For the first time, this paper introduced the differential games theory to solve multi-controller multi-objective coordinated policy-making problem in power systems, and employed the proposed method on two problems in the field of frequency control.The first problem is the coordination between secondary frequency controllers in multi-areas. In the secondary frequency control, the units in different areas are responsible for compensating the internal power mismatch in common case. Besides, they are also supposed to provide temporary supports via the tie-line, while certain area disturbs the system frequency due to the lack of control capacity. The process of power support imposes extra regulation burden on the helping areas and leads to certain costs which are hard to quantify or compensate, such as the wear and tear of units. The control areas in Chinese power systems are usually supervised by a parent company and economically independent to certain extent. They pursue common objectives (e.g., the stability of interconnection frequency) and contradictory objectives (e.g., the minimum of regulation costs) at the same time. In this coordination problem, one target is to make the areas cooperate for their common frequency; the other target is to allocate the persuasive shares of power support for all areas.The second problem is the coordination between primary and secondary frequency control. The primary frequency control is aimed at reducing the frequency error as soon as possible, while the secondary frequency control is aimed at eliminating the frequency error and maintaining the tie-line power exchanges at their planned value. The primary frequency control adjusts the valve position of turbine, while the secondary frequency control adjusts the power output of boiler. These two control loop usually work together, determining the power outputs of units. With different control method and control objective, they conflict with each other occasionally, causing the waste of fuels and meaningless wear and tears of units. In this coordination problem, one target is to reduce the conflict and to stabilize the frequency quickly; the other target is to ensure that the commands are persuasive to the two control loops.This paper established the linear quadratic differential game models for above two problems, and proposed three algorithms for non-cooperative feedback nash equilibrium, overall individual rationality based cooperative equilibrium and dynamic individual rationality based cooperative equilibrium, respectively.We employed the proposed method to resolve the coordination problems between secondary frequency controllers in a two-area interconnected power system and a two-area interconnected power system, and compared the DGs based control scheme with proportional-integral control scheme and optimal control scheme. The simulation showed the following results. Due to the lack of consideration of coordination, the proportional-integral control scheme causes the conflicts between areas. The optimal control scheme achieves the coordination at the first level. By punishing the control actions in the objective function, it can reduce the conflict and deeply exploit the control capabilities of all areas. Nevertheless, the optimal control method faces a tough challenge which is how to select a proper weight for different objectives without a mature theory. The DGs based control scheme is able to act in the similar way with optimal control scheme in terms of reducing the conflict, while avoiding the problem about weight. Moreover, it achieves the coordination at the second level, i.e., ensuring that all areas implement the commands faithfully because the commands are persuasive. Depending on whether the persuasion can maintain over time, the equilibrium solution could be time inconsistent, weakly time consistent, or strongly time consistent. The feedback nash equilibrium and the dynamic individual rationality based cooperative equilibrium are strongly time consistent and weakly time consistent, respectively. The overall individual rationality based cooperative equilibrium might be either time inconsistent or weakly time consistent.We also employed the proposed method to resolve the coordination problems between primary frequency controller and secondary frequency controller in a two-area interconnected power system, and compared the DGs based control scheme with classical proportional-integral control scheme, enhanced proportional-integral control scheme and optimal control scheme. The simulation showed the similar results and conclusions with that of the coordination problems in the above paragraph.Taking two coordination problems in the field of frequency control for example, this paper demonstrated that it is feasible and fruitful to solve the multi-controller multi-objective coordinated policy-making problems in power systems by the differential games theory. Using this tool, the controllers can be treated as multiple decision-making subjects who obtain the equilibrium solution through self-organize competition, with no need to select a weight. To varying degrees, the non-cooperative equilibrium and the cooperative equilibrium achieve the coordination at both two levels, i.e., reducing the conflict between controllers and meanwhile ensuring the persuasions of commands. This paper introduced the differential games theory into the multi-controller multi-objective coordinated policy-making problems in power systems for the first time, proposing a brand new solution.