Excessive carbon emissions lead to global warming and threaten human survival. On November 13, 2021, at the United Nations Climate Change Conference, all parties completed the implementation details of the Paris Agreement. The agreement is signed by 178 parties around the world. The long-term goal is to limit the increase in global average temperature to less than 2 °C compared with the pre-industrial period, and strive to limit the increase in temperature to less than 1.5 °C. So far, the “carbon peaking and carbon neutrality” (“double carbon”) strategy with the goal of reducing carbon dioxide emissions has become the consensus of all mankind.

1.1 Energy Efficiency Is the Number One Fuel

The use of fossil energy sources such as coal, natural gas and oil is a major source of carbon dioxide. In order to reduce the use of fossil energy, we need green and efficient energy production for power generation systems; for energy consumption systems, we need energy conservation and high energy efficiency.

The International Energy Agency (IEA) believes that “energy efficiency is the first fuel” and will make the greatest contribution to the climate goals of the Paris Agreement.

Energy efficiency peak is the technical support for “carbon peak”!

1.2 Energy Saving Is One of the Important Purposes of Electrical Control

The purpose of electrical control and automation control is to replace labor, improve production and precision, and create a safe and comfortable environment. In the case of completing the same task, reducing energy consumption and improving energy efficiency are also one of its important purposes.

In addition to saving production costs, energy saving can also improve the living environment of human beings and reduce carbon dioxide emissions.

During the COVID-19 pandemic, our random survey of 501 secondary water supply pum** stations in an international metropolis (with a population of more than 20 million) showed that the average power waste is 54%. That is to say, if the energy efficiency optimization design method and the energy efficiency optimization control method are adopted, the power consumption of 200,000–300,000 sets of secondary water supply pum** stations in the city can be reduced by 54%!

1.3 Energy Saving Needs Are Everywhere

During the development of human society, various devices have been invented to help people use and change nature, including electric motors, transformers, diesel engines, steam engines, gas engines, water pumps, fans, ships, generators, automobiles, trains, airplanes, motor vehicles, steam turbines, boilers, etc.

In various fields of the national economy, including industry, agriculture, transportation, municipal administration, construction, etc., as long as energy is needed to maintain operation, energy conservation must be faced.

1.3.1 Single Device Energy Saving

As an individual device, according to its efficiency function, its energy saving status can be determined. The point of maximum efficiency corresponds to the optimum load. Taking a car as an example, the economic speed corresponds to the maximum efficiency point, which is the most fuel-efficient working point. It is easy to judge the energy saving status. The key issue is to obtain the efficiency curve of the equipment.

For energy-consuming objects such as human beings or man-made machines, each has an efficiency function, and its shape is generally shown in Fig. 1.1.

Fig. 1.1
A line graph of eta versus beta plots a concave-down increasing trend for eta of beta with the projection lines of eta e, beta e, and beta m.

The efficiency function η

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In Fig. 1.1, β is the load and η is the efficiency function. ηe is the maximum efficiency value corresponding to the optimal load βe, and βm is the maximum load.

For generator sets, if the load β is water intake or coal intake, each has an efficiency function whose shape is generally shown in Fig. 1.2.

Fig. 1.2
A line graph of eta versus beta plots a concave-down increasing trend for eta of beta that starts from beta 0 and ends at beta m, with the projection lines of eta e and beta e.

The efficiency function η

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In Fig. 1.2, β is the power generation load, η is the efficiency function at rated speed, β0 is the input load when electric energy starts to be generated, ηe is the maximum efficiency value corresponding to the optimal load βe, and βm is the maximum load.

According to the efficiency curve, we can judge whether the current load is optimal.

1.3.2 Multi-unit System Energy Saving

In reality, many systems are composed of multi-unit devices, called multi-unit systems. Judging the energy saving status of such a multi-unit system is not simple and intuitive (Figs. 1.3, 1.4 and 1.5).

Fig. 1.3
Two photographs. On the left is an aerial view of a large dam and the flow of water through its spillways. On the right is a power plant with multiple cooling towers that emit steam.

Power stations

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Fig. 1.4
Two photographs. On the left is an electrical substation with transformers and high-voltage power lines. On the right is a substation with several power lines.

Power transmission

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Fig. 1.5
Two photographs. On the left is a building with highlighted sparks and light. On the right is a high-speed train that travels on a railway track.

Energy consumption

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  1. (1)

    A hydropower station has multiple hydroelectric generating units. According to the flow and head of the river, how to schedule the number of operating units and how to control the load rate of each operating unit to obtain the maximum power generation?

  2. (2)

    There are multiple transmission lines supplying power in a region. Given the total load in the region, how to dispatch the transmission lines to maximize the overall efficiency of the power supply system?

  3. (3)

    Given the total load in a power system with multiple transformers, how can these transformers be distributed to maximize the overall efficiency of the power system?

  4. (4)

    A pum** station consists of multiple pumps. According to the required flow and head, how to arrange the number of operating units and how to adjust the water volume of each operating pump to maximize the overall efficiency of the pum** station?

  5. (5)

    A fan station consists of multiple fans. According to the required flow rate and pressure, how to arrange the number of running fans and how to adjust the flow rate of each running fan to maximize the overall efficiency of the fan station?

  6. (6)

    A high-speed train is driven by multiple motors. Under given conditions, how to control the number of operating motors and adjust the output torque of each operating motor to minimize the overall power consumption?

  7. (7)

    An electric car is driven by multiple motors, how to control the number of units running the motors and how to distribute the output torque of each running motor to minimize the power consumption and get the longest range?

  8. (8)

    The propeller of a ship is driven by multiple motors. Facing a given situation, how to control the number of motors running and how to adjust the output torque of each motor to minimize power consumption and obtain the longest cruising distance?

  9. (9)

    There are multiple boilers in the heating system, how to distribute the load of each boiler to maximize the overall efficiency of the system?

  10. (10)

    Multiple motors drive a long conveyor, how to distribute the output torque of each motor so that the overall power consumption is the lowest?

As long as multiple devices or multiple people are required to cooperate to complete a job, there must be an energy saving problem, which is the overall efficiency optimization problem.

If you are given on-site operating data and equipment parameters, can you provide the optimal operating efficiency and the control method to achieve this efficiency? Obviously, this is not an easy job to do. Otherwise, the “carbon peaking” work will not be so tangled.

1.4 R&D Overview of Energy Efficiency Optimization

People always want to do the most work with the least cost, which is the origin of the efficiency optimization problem, and the way to achieve this goal is the efficiency optimization method.

If the optimization variables are independent parameters and do not change with time, for such a system, it is called a static optimization problem or a parameter optimization problem. The main task is to solve the extremum function. This optimization includes three basic elements, namely variables, objective function and constraints. The optimization process is to change and finally determine the optimization variables under the condition of satisfying the constraints, so that the objective function has a minimum or maximum value [1].

If the objective function is a linear function of the optimization variables, and the constraints are linear equations or inequalities of the optimization variables, then such optimization is classified as a linear programming problem [2]. If the objective function or constraints contain a nonlinear function of one or more optimization variables, it is classified as a nonlinear programming problem [3]. In nonlinear programming, if the objective function is a quadratic function of the optimization variables and the constraints are linear functions of the optimization variables, then the optimization problem is called a quadratic programming problem [4]. If the objective function is a convex function and the constrained feasible region is a convex set, it is called a convex optimization problem [5]. A notable feature of convex optimization is that the local optimal solution is the global optimal solution.

The most commonly used method to solve extreme value problems is the classic differential method in advanced mathematics [6, 7]. The optimal solution is obtained by taking the partial derivative of the objective function with respect to each variable so that it is zero.

If the objective function of a nonlinear optimization problem is too complex to be solved analytically, then we can resort to numerical methods [8]. In order to improve the computational efficiency on the basis of versatility, people have developed engineering numerical optimization methods [9, 51,52,53,54], heat power system optimization and energy saving [55,56,57,58,59,60], power system optimization and energy saving [61,62,63,64,65], motor system optimization and energy saving [66,67,68,69], transportation optimization scheduling system [70,71,72], etc. It can be said that as long as energy is used, there is a problem of optimizing energy saving.

A lot of overall optimal problems in human society, most of them are a combination of static optimization and dynamic optimization. For example, for a large-scale water supply system, the water supply of the water plant is randomly determined by a lot of users, and the water quantity and water pressure that meet the process requirements may change at any time, which requires dynamic optimization. If the water supply and water pressure are stable over a period, it is necessary to use a static optimization method to solve the problem. Large-scale gas transmission systems are similar. Under the influence of acceleration, deceleration, uphill, downhill, wind speed, passenger capacity and other factors, EMUs will also have static optimization and dynamic optimization problems. These systems have multiple motors to provide power, so the optimization of power switching also needs to be considered. For some fluid systems, it is still difficult to give an accurate mathematical model, and the characteristics of the equipment are mostly given in the form of discrete data or curves. For these complex systems, there are not only the problems of combining static optimization and dynamic optimization, but also the problems of how to extract the mathematical model of the system and how to establish the objective function.

At present, there is no unified conclusion on the optimization method for the universality of biological and artificial machines in nature. Another problem is that many typical control methods that are widely used cannot be said to be optimal, but people have not found out what the optimal control method is. For example, for pump systems that account for 20–25% of the world’s electricity consumption, the conventional operation method is to use a single closed-loop control method to achieve control that meets process requirements, collect the actual values of process parameters, and compare them with the set values. Increase or decrease the speed of the pump, that is, adjust the load of the speed-regulating pump, and increase or decrease the number of running pumps according to the actual process parameters at full speed or zero speed. Although this method is adopted all over the world, it is not optimal. Because this method does not consider the energy consumption problem in the control process, it is impossible to naturally realize the operation with the lowest energy consumption under the process conditions. Even the South-to-North Water Diversion Project, the largest water conservancy project in the world, did not conduct acceptance checks on operational energy efficiency when the pum** stations were put into operation.

For the classical differential method of static optimization, the partial derivative of each variable is calculated, and it is equal to zero, and the optimal result is solved. However, due to the fact that some of the variables in the actual system are real numbers, such as the load borne by each device, and some are positive integers, such as how many devices or people are used or which device is used, etc., the optimal solution for integer variables may be real numbers with decimals, which doesn’t match reality. Another problem is that for a total load required by the system and certain existing equipment, the optimal point of its total efficiency is not necessarily the point where the derivative is zero, but the best one among all the schemes that can be realized. Another problem is that many optimization methods have non-unique solutions, that is, the optimization results of this arrangement and that arrangement are the same. For many complex systems, because it is difficult to give an accurate mathematical description or mathematical model, it is sometimes difficult to give an accurate mathematical expression of the optimization problem whether it is a dynamic optimization method or a static optimization method.

1.5 Problems of Existing Energy Efficiency Optimization Methods

  1. 1.

    For a complex system, its accurate mathematical model is mostly a multi-variable, nonlinear, time-varying function. For such system, it is still difficult to obtain an accurate mathematical model or state equation, and its characteristics are usually provided by discrete data or curves.

  2. 2.

    Many practical optimization problems are a combination of static optimization and dynamic optimization. For example, for a large-scale urban water supply system, the water volume is randomly determined by urban residents, and the water pressure should maintain a demand value that changes with the change of water volume, which requires dynamic optimization. Static optimization is suitable if the water volume and pressure are fixed over time.

  3. 3.

    Many practical optimization problems are multi-objective. the above-mentioned water supply system must meet two objectives. the first objective is to maintain pressure, and the second objective is to save energy.

  4. 4.

    Many typical control methods, such as PID, are widely used in practical applications. However, they only meet the goals of process requirements and are not optimal because they do not consider the energy consumption of the system.

  5. 5.

    For the static optimization of the classical differential method, the partial derivative is calculated for each variable, and it is equal to 0 to obtain the optimal solution. However, some variables can only be positive integers, such as the number of operating equipment or the number of people, etc., if the optimal result of the variable is a real number with decimals, which is inconsistent with the reality.

  6. 6.

    Many optimization methods do not have a unique solution, which means that different schedules will get the same optimization results.

  7. 7.

    In the field of efficiency optimization, there is no unified general optimization method for human being and machines.

1.6 Quantum Optimization Method and Energy Efficiency Prediction Theory

The essence of energy saving is to keep a regulated system in the overall high efficiency area. When the overall efficiency is the highest value that can be achieved, we say that the system has been running in the most energy-saving state, so the essence of energy saving is to improve the overall operating efficiency of the system.

There are a lot of various systems in the industry, and the variables and solution methods involved in the efficiency optimization are different from what we have talked about in advanced mathematics in the past. One of the differences is that some of the variables are real numbers and some are positive integers. The real numbers are the load borne by each device, and the integers are how many devices or people are used, which device is used, etc. For the derivative of an integer variable, the optimal point may be a real number with decimals. It is obviously unrealistic. The second difference is that for a total load required by the system and certain existing equipment, the optimal point of its total efficiency is not necessarily the point where the derivative is zero, but the best one among all the schemes that can be realized. Another difference is that there are non-unique solutions at many optimization points, that is, the optimization results of this arrangement and that arrangement are the same.

Since the energy efficiency function is nonlinear and has a limit on the maximum input value, this is a nonlinear optimization problem with constraints. The number of optimized operating units is an integer, the optimal load distribution value is a real number, which is also an integer-real-number mixed optimization problem.

We call the method of solving such an efficiency optimization problem as the quantum optimization method.

Aiming at the existing problems, this book presents a quantum optimization method applicable to general-purpose devices, which is based on:

  1. 1.

    The efficiency function can be approximately regarded as a concave function passing through the origin, and the second derivative of the efficiency function is less than zero.

  2. 2.

    Assume the load rate of each working equipment is greater than zero, calculate partial derivatives for multiple variables, and deduce the optimal control method for each operating equipment.

  3. 3.

    Based on graphics, deduce the optimal switching method. When the total load increases, determine the optimal switching point of n and k1 operating equipment, and when the total load decreases, determine the optimal switching point of n and k2 operating equipment.

We call this theory to solve energy efficiency optimization as energy efficiency predictive theory.

This theory and related theorems proved in this book have been successfully applied to nearly a thousand pum** stations in the fields of building secondary water supply, urban water supply, steel, petrochemical, pharmaceutical and other fields.

It should be reminded that some control methods in this book are protected by patent laws in the United States, Japan, Germany and China.

Since participating in the research of “Simple Three-phase AC Motor Speed Regulating Device” in 1988 [73], the author has been paying great attention to energy efficiency optimization work, and has carried out some research and application work on actual energy saving optimization [74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,100,101,102,103,104,105,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129].