Optimal Dispatch and Control Strategy of Park Micro-Energy Grid in Electricity Market

Abstract

In the existing research on the dispatch and control strategies of park micro-energy grids, the dispatch and control characteristics of controllable energy units, such as response delay, startup and shutdown characteristics, response speed, and sustainable response time, have not been taken into account. Without considering the dispatch and control characteristics of the controllable energy units, substantial deviation will occur in the execution of optimized dispatch and control strategies, resulting in economic losses in the electricity market and adverse effects on the safe operation of power systems. This paper proposes a unified model to describe the dispatch and control characteristics of various types of controlled energy units, based on which we develop a three-tier optimization dispatch and control strategy for the micro-energy grid, involving day-ahead, intra-day, and real-time stages. The day-ahead and intra-day optimization dispatch strategy is implemented to obtain the optimal reference values in the real-time stage for each controllable energy unit. In the real-time stage, a minimum variance control strategy based on d-step prediction is proposed. By considering the multi-dimensional control characteristics of controllable energy units, the real-time predictive control strategy aims to ensure that the controllable energy units can precisely follow the optimized dispatch plan. The simulation results show that when compared with the dispatching method optimized by the improved quantum particle swarm algorithm, the adoption of the optimal dispatch and control strategy proposed in this paper resulted in a 45.79% improvement in execution accuracy and a 2.38% reduction in the energy cost.

1. Introduction

The park micro-energy grid, which is composed of various forms of energy such as cooling, heating, electricity, gas, wind, and solar, is a typical form of the park’s comprehensive energy system. The energy units can be classified into energy production units (micro gas turbines, wind and solar power generation, gas boilers, absorption chillers, electric chillers, etc.), energy storage units (electrochemical energy storage systems, cold energy storage systems, etc.), and energy consumption units. Based on the characteristics of energy units, they can be classified as controllable energy units, uncontrollable energy units, and random fluctuation energy units. The controllable energy units include energy storage units, flexible controllable consumption energy units, and energy production units apart from wind and solar generation. Their output power can be dispatched and controlled. The uncontrollable energy units are mainly the rigid loads of the park enterprises, and most of energy consumption units in the park micro-energy grid are uncontrollable rigid loads. The random fluctuation energy unit is mainly the wind and solar power generation, whose output power fluctuates randomly with the change of natural resources.

In the electricity market, a park micro-energy grid can participate in the day-ahead spot market, real-time spot market, and ancillary service market. In order to maximize the trading revenue and minimize the costs, it is crucial for the controllable energy units to execute dispatch and control strategies precisely. However, due to the power prediction errors of rigid loads, wind power generation, and solar power generation, combined with multi-dimensional dispatch and control characteristics of controllable energy units, it is extremely challenging to realize precisely the execution of the park micro-energy grid. Substantial execution deviation will result in the failure of trading strategies and optimized dispatch strategies, leading to economic losses and adverse effects on the safe operation of the power system. The research on practical dispatch and control strategies that enable park micro-energy grid to achieve precise control is of utmost importance.

Scholars from both domestic and foreign institutions have conducted extensive research on the dispatch and control models and strategies for micro-energy grids and microgrids. In terms of micro-energy grid modeling, Sun et al. [1] considered the inertia of natural gas and heat and proposed a unified dynamic model of natural gas and heat systems. Geidl et al. [2] and Geidl et al. [3] modeled the micro-energy grid system as a whole and proposed the concept of the Energy Hub, which considers each unit inside the micro-energy grid as a whole and does not care about its internal structure. Wang et al. [4] constructed a general model of an electric network, a natural gas network, and a heat network and, based on this, constructed a comprehensive model of an integrated energy system in the park considering electric-gas-heat coupling. Xie et al. [5] proposed a new demand-driven intelligent perception framework, which is conducive to the construction of micro-energy networks and the modeling of each energy unit. In terms of dispatch and control strategies of the micro-energy grid, Shao et al. [6] constructed an integrated electric-gas demand response model and proposed a two-layer optimization framework, which integrated the integrated electric-gas demand response model into the electrical integrated energy system scheduling model. Ju et al. [7] constructed a day-ahead and real-time two-phase cooperative optimization scheduling model for micro-energy grids. This model addressed the impact of uncertain wind power and PV output, but it overlooked the potential execution deviations of adjustable energy units. Turk et al. [8] used a model predictive control algorithm to optimize the real-time operation of the integrated energy system, balance the real-time prediction error, and improve the economic efficiency and wind power utilization rate. Zhao et al. [9] proposed a novel intraday robust energy management framework for autonomous multi-microgrids based on the distributed dynamic tube model predictive control (DD-TMPC) approach, which ensures the stability of the microgrid operation and improves the system operation efficiency at the same time. Shaheen et al. [10] proposed an improved Marine Predator Optimization Algorithm (IMPOA), which achieves significant results in the economic dispatching problem of Combined Heat and Power (CHP). Shaheen et al. [11] proposed a novel heap-based and JellyFish Optimizer (AHJFO), which effectively improves the optimization solving accuracy and proposes a re-scheduling strategy based on AHJFO. Zhao et al. [12] proposed a computationally efficient and accurate reduced order model (ROM) for microgrid stability analysis. Zhao et al. [13] proposed a control model for grid-connected wind turbines after they are connected to a microgrid, which provides solution ideas for the control of energy units such as wind turbines in microgrids. An et al. [14] proposed a real time adaptive dynamic optimization control strategy based on deep learning. Zhang et al. [15] developed a robust optimization method to guarantee an optimal and reliable multi-energy supply under the uncertainties, which can achieve high energy utilization efficiency and high operating robustness against the uncertainties. Yang et al. [16] proposed a multi-timescale coordinated optimization framework for economic dispatch to balance the stability and prediction accuracy of the system. Luo et al. [17] proposed a multi-objective optimization operation strategy considering the distributed energy generation uncertainty, environmental factors, and self-supply rate. Zhou et al. [18] proposed a day-ahead robust optimal dispatching strategy for the park’s integrated energy system under the market of electric energy and auxiliary services, which considers the robustness and profitability of the system. Li et al. [19], Wang et al. [20], and Wang et al. [21] considered the uncertainty of electricity price, load, and new energy output in the power market and, based on the conditional value-at-risk theory, proposed the operating cost optimization strategy of the integrated energy system under the environment of the power market. Chen et al. [22] considered the uncertainty of renewable energy output and cooling, heating, and electric loads in the micro-energy grid and proposed day-ahead and intraday robust dispatch strategies for integrated demand response resources within micro-energy networks in an electricity market environment but lacked real-time regulation of adjustable loads. Zhang et al. [23] proposed a multi-objective optimization model for intelligent integrated energy systems that considers demand response and dynamic prices reflecting the preferences of multiple stakeholders, which can effectively solve the multi-objective optimization problem in micro-energy grid lands.

Although there has been extensive research on the modeling approaches and dispatch and control strategies for the micro-energy grid, there are still some unresolved issues, which have been listed in

Table 1. Current research approaches and unresolved issues.

Research Field	Current Research Approaches	Unresolved Issues
Modeling of park micro-energy grid	Including steady-state model and transient model. The steady-state model primarily used to describe the energy balance relationship of the micro-energy grid, especially the steady-state input-output relationship of energy production and storage units. The transient model is formulated for precise modeling of the micro-energy grid or individual control objects, primarily used for stability analysis.	There is a lack of a unified modeling approach that considers the dispatch and control characteristics, such as response delay, startup and shutdown characteristics, response speed, and sustainable response time, of various controllable energy units. In the park micro-energy grid, there are numerous controllable energy consumption units, and precise modeling of these units is essential for achieving precise control of the park micro-energy grid.
Optimal dispatch of park micro-energy grid	Focusing on the research of optimal dispatch models and strategies and their solution algorithms. The objective is to maximize operation efficiency, minimize cost, and lower emissions in a micro-energy grid by dispatching the energy production and storage units. The energy consumption units are always considered uncontrollable units.	It is assumed that each controllable energy unit can execute the dispatch plan perfectly without any errors. The dispatch and control characteristics of energy units are not considered in the constraint conditions. The role of controllable energy consumption units in developing the multi-time scale dispatching capability of a park micro-energy grid has not been fully demonstrated.
Real-time control of park micro-energy grid	Utilizing controllable energy units with rapid adjustment capabilities, such as battery-based energy storage devices and gas turbines, to balance the execution deviations, which may increase the investment cost and operating cost of a park micro-energy grid.	In park micro-energy grids without large-capacity rapid adjustment energy units, the challenge of achieving the precise following of dispatch plans at a low cost remains unresolved. The study of real-time predictive control based on the control characteristics of controllable energy units is highly valuable.

.

In order to solve the above problems, this paper conducts the following research on the modeling and dispatch and control of multi-type energy units in the micro-energy grid:

(1)

It proposes a unified modeling approach that considers the dispatch and control characteristics of various energy units in the park micro-energy grids, accurately describing the response delay, startup and shutdown characteristics, response speed, and sustainable response time of the controllable energy units.

(2)

Considering the dispatch and control characteristics of multi-type energy units, a multi-time scale dispatch model of the park micro-energy grids is proposed. Taking the minimum overall cost of the park micro-energy grids as a goal, a two-stage method for obtaining the optimal dispatch strategy is proposed. This method converts the mixed integer nonlinear programming problem into a mixed integer linear programming problem and efficiently solves the dispatch strategy of the park micro-energy grids.

(3)

Considering the control response characteristics of various controllable energy units, a predictive control method for controllable energy units is proposed, which can efficiently minimize the execution deviation caused by overlooking the control characteristics of controllable energy units.

2. Dispatch and Control Characteristics of Energy Units in a Micro-Energy Grid

In the park micro-energy grid, only a portion of the energy consumption units can be dispatched and controlled. These controllable consumption units do not have the rapid adjustment capability similar to energy storage units; they are classified as limited controllable units. These limited controllable units have different control response characteristics across different stages, and there are substantial differences in the characteristics of different energy units. Without considering the dispatch and control characteristics of various energy units, it is very difficult to achieve precise control of the park micro-energy grid. Therefore, this paper proposes a unified model to describe the various dispatch and control characteristics of controllable energy units. The operating process of controllable energy units can be divided into three stages: startup, operation, and shutdown. After receiving the startup, power adjustment, and shutdown command, energy units require a certain delay time before they begin to respond. Taking the startup stage as an example, after receiving the startup command, energy units need to go through a certain startup delay before entering the startup process. The operation stage and shutdown stage follow a similar pattern. The typical dispatch and control characteristic curves for the startup stage, operation stage, and shutdown stage are shown in Figure 1.

The description of dispatch and control characteristics are as follows: (1) delay characteristics: time of startup delay (TSD), time of power adjustment delay (TDD), and time of shutdown delay (TED); (2) startup-shutdown characteristics: time of startup response (TS) and time of shutdown response (TE); (3) power adjustment characteristics: power upward adjustment capability (+∆P) and power downward adjustment capability (−∆P).

Each energy unit in the micro-energy grid is regarded as a linear discrete-time system. In the three stages of startup, operation, and shutdown, the response characteristics of each energy unit are listed below:

• Startup stage: After receiving a startup command or a fixed power input, the energy unit switches from a shutdown state to an operation state (operating stably following a given power command). The entire process can be approximated as the zero-state response of a linear system.
• Operation stage: The energy unit adjusts the output power continuously upon receiving power variations commands. The entire process can be approximated as the non-zero state response of a linear system.
• Shutdown stage: After receiving a shutdown command or zero power input, the energy unit switches from an operation state to a shutdown state. The entire process can be approximated as the zero-input response of a linear system.

Based on the analysis above, the dispatch and control characteristics of energy units in different stages can be described using segmented state-space equations.

Startup stage:

$$\begin{array}{c}x\left(t+1\right)=A_{s}x\left(t\right)+B_{s}u\left(t-d_s\right)+D_{s}d\left(t\right)\\ p\left(t\right)=C_{s}x\left(t\right)\end{array}, t_0\le t\le t_0+TS-1$$

(1)

Operation stage:

$$\begin{array}{c}x\left(t+1\right)=A_{d}x\left(t\right)+B_{d}u\left(t-d_d\right)+D_{d}d\left(t\right)\\ p\left(t\right)=C_{d}x\left(t\right)\end{array}, t_0+TS\le t\le t_0+TS+TR$$

(2)

Shutdown stage:

$$\begin{array}{c}x\left(t+1\right)=A_{e}x\left(t\right)+B_{e}u\left(t-d_e\right)+D_{e}d\left(t\right)\\ p\left(t\right)=C_{e}x\left(t\right)\end{array}, t_0+TS+TR-1\le t\le t_0+TS+TR+TE$$

(3)

where $x\left(t\right)$ is the state variable vector of an energy unit, $u\left(t\right)$ is the control input variable vector, $d\left(t\right)$ is the external random disturbance variable, and $p\left(t\right)$ is the output power of the energy unit. $A_{s,d,e},$ $B_{s,d,e},$ $C_{s,d,e}, D_{s,d,e}$ is the response characteristic model parameter. $TS, TR, TE$ are the command response times for the startup, operation, and shutdown stage.

3. Three-Tier Optimal Dispatch and Control of a Micro-Energy Grid in Electricity Markets

Energy consumption units in a micro-energy grid will be affected by changes in production plans, and the output power of a wind and solar power generation system will fluctuate randomly with changes in natural resources. These have led to a large deviation between the actual power of load and the actual wind and solar power generation compared to the day-ahead predictions. In addition, each controllable energy unit has multi-time scales dispatch and control characteristics, which further increases the difficulty of precise control of the micro-energy grid.

Considering the multi-time scales dispatch and control characteristics of various energy units, this paper proposes a three-tier dispatch and control framework for the park micro-energy grid, including day-ahead optimal dispatch, intra-day rolling optimal dispatch, and real-time control at the unit level. The three-tier dispatch and control framework diagram for park micro-energy grid is shown in Figure 2.

In the day-ahead optimal dispatch stage, all controllable energy units will be pre-dispatched (including the startup-shutdown plan and operation power plan) with the goal of minimizing the costs of the park micro-energy grid. The day-ahead pre-dispatch power plan for interconnection lines published by the dispatch organization, the day-ahead prediction of wind-solar power generation, and the day-ahead prediction of rigid loads are the most influential input variables that need to be considered. In the intra-day optimal dispatch stage, based on the ultra-short-term prediction of rigid load and wind-solar power generation, the rolling optimal dispatch will be conducted hourly to obtain the power plan of each controllable energy unit for the next 4 h. In the real-time control stage, the predictive control of controllable energy units will be executed with a goal of precisely following the intra-day optimal dispatch plan.

In order to achieve precise dispatch and control of the park micro-energy grid, this paper proposes a day-ahead optimal dispatch strategy, an intraday rolling optimal strategy, and a unit-level real-time control strategy.

3.1. Day-Ahead Optimal Dispatch of a Micro-Energy Grid

Day-ahead optimal dispatch is performed on the day before the execution day. By meeting the constraint requirement, all controllable energy units will be pre-dispatched (including the startup-shutdown plan and operation power plan) with the goal of minimizing the operational costs of the park micro-energy grid. The dispatching arrangement takes 15 min as a dispatch period.

3.1.1. Power Balance Equation of Day-Ahead Dispatch

• Electric power balance equation:

$$P_{NL,t}^e-P_{PV,t}^e-P_{WT,t}^e-P_{Grid,t}=\sum _{i=1}^{N_{EG}}{P}_{G,i,t}^e-\sum _{j=1}^{N_{AL}}{P}_{AL,j,t}^e+\sum _{k=1}^{N_{ES}}(P_{S.d,k,t}^e-P_{S.c,k,t}^e)$$

(4)

2.

Cold power balance equation:

$$P_{NL,t}^c=\sum _{i=1}^{N_{CG}}{P}_{G,i,t}^c+\sum _{k=1}^{N_{CS}}(P_{S.d,k,t}^c-P_{S.c,k,t}^c)$$

(5)

3.

Thermal power balance equation:

$$P_{NL,t}^h=\sum _{i=1}^{N_{HG}}{P}_{G,i,t}^h+\sum _{k=1}^{N_{HS}}(P_{S.d,k,t}^h-P_{S.c,k,t}^h)$$

(6)

where $P_{WT,t}^e$ and $P_{PV,t}^e$ are the power of the wind and solar generation at time $t$. $P_{NL,t}^e$ and $P_{AL,j,t}^e$ are the power of the uncontrolled electric load and the j-th controlled electric load at time $t$. $P_{NL,t}^c$ and $P_{NL,t}^h$ are the cooling load and thermal load at time $t$. $P_{Grid,t}$ is the power of interconnection lines at time $t$. $P_{G,i,t}^e$, $P_{G,i,t}^c$, and $P_{G,i,t}^h$ are the output electric powers of the i-th electric energy production unit, the output cold power of the i-th cold energy production unit, and the output thermal power of the i-th thermal production unit.

$P_{S,d,k,t}^e$ and $P_{S,c,k,t}^e$ are the discharging and charging powers of the k-th electrical energy storage unit at time $t$. $P_{S,d,k,t}^c$ and $P_{S,c,k,t}^c$ are the cooling power release and cooling power storage of the k-th cold energy storage unit. $P_{S,d,k,t}^h$ and $P_{S,c,k,t}^h$ are the thermal power release and thermal storage power of the k-th thermal storage unit. $N_{EG}$, $N_{CG}$, and $N_{HG}$ are the number of production units of electrical energy, cooling energy, and thermal energy. $N_{AL}$ is the number of controlled electrical loads. $N_{EC}$, $N_{CS}$, and $N_{HS}$ are the number of storage units of electrical energy, cooling energy, and thermal energy.

3.1.2. Optimization Objective of Day-Ahead Dispatch

When there is an execution deviation between the pre-dispatch plan and the actual operational power, the park micro-energy grid will incur penalty fines for the deviation assessment. Considering the deviation assessment, the objective of day-ahead optimal dispatch of the micro-energy grid is to minimize the overall operating cost:

$$minC=min{(C}_{grid}+C_{gas}+C_{dr})$$

(7)

where $C_{grid}$ is the cost of purchasing electric energy from the power grid, $C_{gas}$ is the cost of purchasing natural gas, and $C_{dr}$ is the penalty fee for deviation assessment.

• The cost of purchasing electric energy from the power grid:

$$C_{grid}=\sum _{t=1}^T{P}_{grid,t}{R}_t^e$$

(8)

where $R_t^e$ is the spot price of electricity at time $t$ and $P_{grid}$ is the purchasing power from the power grid in time $t$.

• The cost of purchasing natural gas:

$$C_{gas}=\sum _{t=1}^T{R}_t^g(P_{GT,t}^g+P_{GB,t}^g)$$

(9)

• Penalty fee for deviation assessment:

$$C_{dr}=\sum _{t=1}^T(\max \left(0,P_{grid,t}-{\alpha }^{+}{P}_{base,t}\right)R_{dr,t}^{+}+\max \left(0,{{\alpha }^{-}P}_{base,t}-P_{grid,t}\right)R_{dr,t}^{-})$$

(10)

where ${\alpha }^{+}$ and ${\alpha }^{-}$ are the exemption proportional coefficients for positive and negative deviation. $R_{dr,t}^{+}$ and $R_{dr,t}^{-}$ are the penalty prices for positive and negative deviations during time $t$. $P_{base,t}$ is the day-ahead pre-dispatch command for the interconnection line at time $t$.

3.1.3. Constraints of Day-Ahead Dispatch

• Constraints of interconnection lines:

$$-P_{Grid,t,max}\le P_{Grid,t}\le P_{Grid,t,max}$$

(11)

where $P_{Grid,t,max}$ is the maximum power that the micro-energy grid can purchase from or sell to the external power grid at time $t$.

• Constraints of energy production units:

$${PO}_{P,t.min}^u\le {PO}_{P,t}^u\le {PO}_{P,t.max}^u$$

(12)

$$-{KD}_p^u\le {PO}_{P,t}^u-{PO}_{P,t-1}^u\le {KU}_p^u$$

(13)

$${PO}_{P,t}^{on}-(a_{P,t-1}-a_{P,t})T_{P,on}\ge 0$$

(14)

$${PO}_{P,t}^{off}-(a_{P,t}-a_{P,t-1})T_{P,off}\ge 0$$

(15)

$${PO}_{P,t}^{on}=\sum _{k=t-T_{p.on}}^{t-1}{a}_{P,k}$$

(16)

$${PO}_{P,t}^{off}=\sum _{k=t-T_{p.off}}^{t-1}(1-a_{P,k})$$

(17)

Equation (12) is the upper and lower limit constraints of the output power of the energy production unit at time $t$; Equation (13) is the power ramp constraint of the energy production units at time $t$; and Equations (14)–(17) are the startup and shutdown constraints of the energy production unit, where $T_{P,on}$ is the minimum continuous production time of the energy production unit and $T_{P,off}$ is the minimum continuous shutdown time of the energy production unit. $a_{P,k}$ is a 0–1 state variable, indicating whether the energy production unit is in the startup state at time $k$ or not, ${PO}_{P,t}^{on}$ is the length of consecutive production in energy production unit at time $t$, and ${PO}_{P,t}^{off}$ is the length of consecutive downtime in energy generation unit at time $t$.

• Constraints of energy storage units:

$$x_{S,t}^d{PI}_{S,d,t.min}^u\le {PI}_{S,d,t}^u\le {x_{S,t}^{d}PI}_{S,d,t.max}^u$$

(18)

$$x_{S,t}^c{PI}_{S,c,t.min}^u\le {PI}_{S,c,t}^u\le {x_{S,t}^{c}PI}_{S,c,t.max}^u$$

(19)

$$x_{S,t}^d+x_{S,t}^c\le 1$$

(20)

$$E_{S,t.min}^u\le E_{S,t}^u\le E_{S,t.max}^u$$

(21)

$$E_{S.T_{start}}=E_{S.T_{end}}$$

(22)

$$E_{S,t+1}^u=E_{S,t}^u\left(1-\frac{∆t}{T_S^u}{\delta }_{S.self}^u\right)+({\eta }_{S.c}^u{PI}_{S.c,t}^u-\frac{1}{{\eta }_{S.d}^u}{PI}_{S.d,t}^u)\mathsf{\Delta }t$$

(23)

Equations (18) and (19) are the constraints of the maximum discharging and charging power of energy storage units at time $t$. Equation (20) is the constraints of the discharging and charging state of energy storage units at time $t$. $X_{S,i,t}^c$ and $X_{S,i,t}^d$ are 0–1 variables, indicating the discharging and charging state of energy storage units at time $t$. Equation (21) is the constraints of the stored energy, where $E_{S,t,min}^u$ and $E_{S,t,max}^u$ are the minimum and maximum stored energy limits. Equation (22) is the constraints of stored energy at the beginning and end of a control cycle. Equation (23) is the calculation formula for calculating the energy storage capacity.

• Constraints of energy consumption units:

Operating constraints of transferable electric load:

$${PI}_{L.TS,t}=s_t^{TS}{P}_{t-u+1}^{plan}$$

(24)

$$\sum _{t=u}^{t_v+T_{TS}-1}{s}_t^{TS}=T\left(s_u-s_{u-1}\right),\forall t\in \left[t_{start},t_{end}-T_{TS}+1\right]$$

(25)

$$s_t^{TS}=0,\forall t\notin \left[t_{start},t_{end}\right]$$

(26)

$$P^{plan}=\left[P_1,\cdots ,P_n,\cdots ,P_T\right]$$

(27)

where ${PI}_{L.TS,t}$ is the actual power of the transferable electrical load at time $t$. $P^{plan}$ is the planned power of the transferable electrical load. $s_t^{TS}$ is a 0–1 variable, indicating the state of the transferable electrical load at time $t$, $s_t^{TS}=1$ indicates that the load is on operation state, and $s_t^{TS}=0$ indicates the load is on shutdown state. $u$ is the startup time of the transferable electrical load. $t_{start}$ is the earliest allowed startup time for the transferable electrical load. $t_{end}$ is the nearest allowed shutdown time for the transferable electrical load. $T_{TS}$ is the minimum continuous operating duration required for the transferable electrical load.

Constraints of interruptible electrical loads:

$${PI}_{L.IR,t}=s_t^{IR}{P}_{rated}$$

(28)

$$\sum _{t=t_{start}}^{t_{end}}{s}_t^{IR}=T_{IR}$$

(29)

$$s_t^{IR}=0,\forall t\notin \left[t_{start},t_{end}\right]$$

(30)

where ${PI}_{L.IR,t}$ is the actual power of the interruptible electrical load at time $t$. $s_t^{IR}$ is a 0–1 variable and indicates the state of the interruptible electrical load at time $t$, $s_t^{IR}=1$ indicates that the interruptible electrical load it is in the operation state, and $s_t^{IR}=0$ indicates that the interruptible electrical load it is in the shutdown state. $t_{start}$ is the earliest allowed startup time for the interruptible electrical load. $t_{end}$ is the nearest allowed shutdown time for the interruptible electrical load. $T_{IR}$ is the operation time required for the interruptible electrical load within the allowed startup and shutdown time.

Constraints of power-adjustable electrical loads:

$${PI}_{L.RG,t}=\sum _{i=1}^n{s}_{i,t}{P}_{RG,i}$$

(31)

$$\sum _{i=1}^n{s}_{i,t}=1,t\in \left[t_{start},t_{end}\right]$$

(32)

where ${PI}_{L.RG,t}$ is the actual power of the power-adjustable electrical load at time $t$. $P_{RG,i}$ is the i-th operating power value of the power-adjustable electrical load. $s_{i,t}$ is a 0–1 variable, $s_{i,t}=1$ indicates the power-adjustable electrical load in a startup state, and $s_{i,t}=0$ indicates the power-adjustable electrical load in a shutdown state. $t_{start}$ is the allowed startup time of the power-adjustable electrical load. $t_{end}$ is the allowed shutdown time of the power-adjustable electrical load.

3.1.4. Day-Ahead Optimal Dispatch Strategy

According to the energy balance equation of the day-ahead optimal dispatch, the objective function of the optimal dispatch strategy, the constraints of the interconnection line, and the constraints of the characteristics of energy units, it is evident that when the transition process of the startup-shutdown characteristics of the energy unit is neglected, the optimization problem can be considered a mixed integer linear programming (MILP) problem. Without considering the transition process of the startup-shutdown characteristics of the energy unit, the optimization problem is no longer an MILP problem. When the startup-shutdown transition process of the energy unit is disregarded, the startup and shutdown plan of each energy unit can be obtained by the method used in solving MILP problems. Following the determination of the startup-shutdown plan of each energy unit, the problem of day-ahead optimal dispatch and control can be transformed into an MILP problem. Therefore, a two-stage solution strategy was adopted to convert the original problem into two convex optimization problems: the optimization of the startup-shutdown state of the energy units and the optimization of the economic dispatch and control of the energy units. At stage 1, it was assumed that there was no transition process for the startup-shutdown state of the energy unit. By omitting the constraints on the transition process of the startup-shutdown characteristics and rewriting the constraints of the output power adjustment of the energy unit, the problem of stage 1 was solved as an MILP problem. After solving this problem, a set of feasible solutions for the startup-shutdown states of the energy unit were obtained. Consequently, the problem of stage 2 was also an MILP problem, and other decision variables were solved subsequently. The time complexity of the original problem does not change even if the power sequence of the startup and shutdown transition process is a nonlinear sequence. The problem can still be solved with high efficiency because the two-stage problem is of polynomial time complexity.

At stage 1, the startup-shutdown transition process is disregarded. As the startup-shutdown transition process refers to the transition process of the energy unit from shutdown state to operation state or from operation state to shutdown state, the solution must consider the minimum output constraint on the energy unit after startup. We can express this characteristic by omitting the constraint on startup characteristics and rewriting the output power adjustment constraint on the energy unit as follows:

$${PO}_{x,t}-{PO}_{x,t-1}\le {KU}_x{\tau }_{s,t-1}+{PO}_{x,t,min}\left({\tau }_{s,t}-{\tau }_{s,t-1}\right)+{PO}_{x,t,max}\left(1-{\tau }_{s,t}\right),x\in \left\{e,h,c\right\}$$

(33)

$${PO}_{x,t-1}-{PO}_{x,t}\le {KD}_x{\tau }_{x,t}+{PO}_{x,t,min}\left({\tau }_{x,t}-{\tau }_{x,t-1}\right)+{PO}_{x,t,max}\left(1-{\tau }_{x,t-1}\right),x\in \left\{e,h,c\right\}$$

(34)

where ${KD}_x$ is the maximum downward adjustment rate of the energy unit, ${PO}_{x,t}$ is the output power of the energy unit at time $t$, ${KU}_x$ is the maximum upward adjustment rate of the energy unit, and ${\tau }_{x,t}$ is the state variable of the energy unit at time $t$. When the energy unit is in a startup state, considering the upper and lower limit constraints on the output power, the ramp-up power is equal to the minimum technical output of the energy unit. When the energy unit is in a shutdown state, considering the upper and lower limit constraints on the output power, the ramp-down power is equal to the minimum technical output of the energy unit.

Based on the startup and shutdown plans obtained in stage 1, we assign values to the continuous variables of the input and output powers of the energy unit according to the fixed power sequence of the startup-shutdown transition process of the energy unit. Finally, the startup-shutdown plans and power plans of energy production units, energy storage units, and energy consumption units can be obtained.

3.2. Intra-Day Rolling Optimal Dispatch of a Micro-Energy Grid

During the operation day, an hour-level rolling optimal dispatch strategy is implemented. Based on the day-ahead optimal dispatch plan, we apply a rolling prediction model to obtain a more accurate ultra-short-term power prediction of rigid loads and wind-solar power generation. By meeting the operation constrains requirement, an intra-day rolling dispatch strategy is implemented on the hourly flexible controllable energy units, aiming to minimize the operational cost of the micro-energy grid. The output power plan of the controllable energy unit in the next 4 h is updated every hour.

The objective function of the intra-day optimal dispatch can be set as:

$$minC=\mathrm{m}\mathrm{i}\mathrm{n}(C_{grid}^{intra}+C_{gas}^{intra}+C_{dr}^{intra})$$

(35)

where $C_{grid}^{intra}$ is the cost of the micro-energy grid to purchase electric energy from the power grid, $C_{gas}^{intra}$ is the cost of the micro-energy grid to purchase natural gas, and $C_{dr}^{intra}$ is the deviation penalty fee to the micro-energy grid as it deviates from the dispatch plan published by the dispatch organization.

The energy balance equation and constraint conditions of the intra-day rolling optimal dispatch is the same as that of the day-ahead optimal dispatch, and the solution process of the intra-day rolling optimal dispatch strategy is also consistent with that of the day-ahead optimal dispatch strategy. The solution result is the power output plans of various controllable energy units in the next 4 h, which was used as an ideal reference value for real-time dispatch and control of each energy unit.

3.3. Real-Time Predictive Control of Energy Units for Micro-Energy Grids

Each controllable energy unit of the micro-energy grid has multi-time scale response characteristics at different operation stages, and each controllable energy unit generally has a d-step response delay. In order to achieve precise control of the controllable energy units, this paper proposes a predictive control model, which predicts the actual output power of the controllable energy units in d-steps in advance and then calculates the optimal control action $U\left(t\right)$ to compensate for the impact of random disturbances on the output power. The predictive control model takes the minimum variance between the actual power and the intraday rolling optimal dispatch plan as the optimal object and performs real-time iterative closed-loop control on a large number of controllable energy units to achieve precise control.

The flow chart of predictive control is shown in Figure 3. The input of the real-time predictive control model is the dispatch planned power from the intra-day rolling optimization dispatching. The predictive control model consists of two parts: the optimal prediction of the controllable energy unit’s output and the minimum variance control of the controllable energy unit based on the optimal prediction. By implementing the proposed predictive control model, the optimal control actions $U\left(t\right)$ for various types of controllable energy units can be obtained. The first component of $U\left(t\right)$ is implemented to the controlled object, obtaining the response of the controllable object at the next time step. With the newly obtained initial conditions, the optimal prediction of the energy unit’s output and the minimum variance control of the energy unit based on this prediction are recalculated, achieving rolling optimization.

3.3.1. Power Output Prediction of Energy Units

Each controllable energy unit in the micro-energy grid can be regarded as a linear discrete-time system, which may be described by a state space mode:

$$x\left(t+1\right)=A_{i}x\left(t\right)+B_{i}u\left(t-d_i\right)+C_{i}d\left(t\right)$$

(36)

$$p\left(t\right)=D_{i}x\left(t\right)$$

(37)

The model can be rewritten to an incremental model as

$$x\left(t+1\right)=A_{i}x\left(t\right)+B_{i}u\left(t-d_i\right)+C_{i}d\left(t\right)$$

(38)

$$x\left(t\right)=A_{i}x\left(t-1\right)+B_{i}u\left(t-d_i-1\right)+C_{i}d\left(t-1\right)$$

(39)

Equation (38) minus Equation (39):

$$∆x\left(t+1\right)=A∆x\left(t\right)+B∆u\left(t-d_i\right)+C∆d\left(t\right)$$

(40)

where

$$∆x\left(t+1\right)=x\left(t+1\right)-x\left(t\right)$$

(41)

$$∆u\left(t-d_i\right)=u\left(t-d_i\right)-u(t-d_i-1)$$

(42)

$$∆d\left(t\right)=d\left(t\right)-d(t-1)$$

(43)

The output equation can be rewritten as an incremental model as follows:

$$p\left(t\right)=D_{i}x\left(t\right)=D_i\left[x\left(t-1\right)+∆x\left(t\right)\right]=D_i∆x\left(t\right)+p(t-1)$$

(44)

After using an incremental model, the state space equation of the energy unit can be obtained as

$$∆x\left(t+1\right)=A∆x\left(t\right)+B∆u\left(t-d_i\right)+C∆d\left(t\right)$$

(45)

$$p\left(t\right)=D_i∆x\left(t\right)+p(t-1)$$

(46)

Taking the latest measurements value as the initial conditions, the control and prediction time domains were respectively set as m and n, with $m\le n$. To simplify the model, the following two assumptions were considered:

$$∆u\left(t-d_i+j\right)=0,j=m,m+1,m+2,\cdots ,n-1$$

(47)

$$∆d\left(t+j\right)=0,j=\mathrm{1,2},\cdots ,n-1$$

(48)

then,

$$∆x\left(t+1|t\right)=A_i∆x\left(t\right)+B_i∆u\left(t-d_i\right)+C_i∆d\left(t\right)$$

(49)

$$\begin{array}{c}∆x\left(t+2|t\right)=A_i∆x\left(t+1\right)+B_i∆u\left(t-d_i+1\right)+C_i∆d\left(t+1\right)\\ =A_i^2∆x\left(t\right)+A_i{B}_i∆u\left(t-d_i\right)+B_i∆u\left(t-d_i+1\right)+A_i{C}_i∆d\left(t\right)\end{array}$$

(50)

$$\begin{array}{c}∆x\left(t+3|t\right)=A_i∆x\left(t+2\right)+B_i∆u\left(t-d_i+2\right)+C_i∆d\left(t+2\right)\\ =A_i^3∆x\left(t\right)+A_i^2{B}_i∆u\left(t-d_i\right)+A_i{B}_i∆u\left(t-d_i+1\right)+B_i∆u\left(t-d_i+2\right)+A_i^2{C}_i∆d\left(t\right)\end{array}$$

(51)

$$\begin{array}{c}∆x\left(t+m|t\right)=A_i^m∆x\left(t\right)+A_i^m{B}_i∆u\left(t-d_i\right)+A_i^{m-2}{B}_i∆u\left(t-d_i+1\right)\\ +\cdots +B_i∆u\left(t-d_i+m-1\right)+A_i^{m-1}{C}_i∆d\left(t\right)\end{array}$$

(52)

$$\begin{array}{c}∆x\left(t+n|t\right)=A_i^n∆x\left(t\right)+A_i^{n-1}{B}_i∆u\left(t-d_i\right)+A_i^{n-2}{B}_i∆u\left(t-d_i+1\right)\\ +\cdots +A_i^{n-m}{B}_i∆u\left(t-d_i+m-1\right)+A_i^{n-1}{C}_i∆d\left(t\right)\end{array}$$

(53)

$P_p(t+1|t)$ was used to represent the vector of n-step output prediction and $∆U\left(t\right)$ to represent the vector of m-step control input:

$$P_p\left(t+1|t\right)\stackrel{\scriptscriptstyle\mathrm{def}}{=}{\left[p\left(t+1|t\right),p\left(t+2|t\right),\cdots ,p\left(t+n|t\right)\right]}_{1\times n}^T$$

(54)

$$∆U\left(t\right)\stackrel{\scriptscriptstyle\mathrm{def}}{=}{\left[∆u\left(t-d_i\right),∆u\left(t-d_i+1\right),\cdots ,∆u\left(t\right),∆u\left(t+1\right),\cdots ,∆u(t+m-1)\right]}_{1\times m}^T$$

(55)

From the output equation, the output power of the controllable energy unit can be obtained as

$$\begin{array}{c}p\left(t+1|t\right)=D_i∆x\left(t+1|t\right)+p\left(t\right)\\ =D_i{A}_i∆x\left(t\right)+D_i{B}_i∆u\left(t-d_i\right)+D_i{C}_i∆d\left(t\right)+p\left(t\right)\end{array}$$

(56)

$$\begin{array}{c}p\left(t+2|t\right)=D_i∆x\left(t+2|t\right)+p\left(t+1|t\right)\\ =\left({D_i{A}_i^2+D}_i{A}_i\right)∆x\left(t\right)+{(D_i{A}_{i}B}_i+D_i{B}_i)∆u\left(t-d_i\right)+\cdots \\ +D_i{B}_i∆u\left(t-d_i+1\right)+\left(D_i{A}_{i}C+D_i{C}_i\right)∆d\left(t\right)+p\left(t\right)\end{array}$$

(57)

$$\begin{array}{c}\begin{array}{c}p\left(t+m|t\right)=\sum _{j=1}^m{D}_i{A}_i^j∆x\left(t\right)+\sum _{j=1}^m{D}_i{A}_i^{j-1}{B}_i∆u\left(t-d_i\right)+\\ \sum _{j=1}^{m-1}{D}_i{A}_i^{j-1}{B}_i∆u\left(t-d_i+1\right)+\\ \cdots +D_i{B}_i∆u\left(t+m-d_i+1\right)+\sum _{j=1}^m{D}_i{A}_i^{j-1}{B}_i∆d\left(t\right)+p\left(t\right)\end{array}\\ \cdots \end{array}$$

(58)

$$\begin{array}{c}p\left(t+n|t\right)={\displaystyle \sum _{j=1}^n}{D}_i{A}_i^j∆x\left(t\right)+{\displaystyle \sum _{j=1}^n}{D}_i{A}_i^{j-1}{B}_i∆u\left(t-d_i\right)+\\ {\displaystyle \sum _{j=1}^{n-1}}{D}_i{A}_i^{j-1}{B}_i∆u\left(t-d_i+1\right)+\\ \cdots +{\displaystyle \sum _{j=1}^{n-m+1}}{D}_i{A}_i^{j-1}{B}_i∆u\left(t+m-d_i-1\right)+{\displaystyle \sum _{j=1}^n}{D}_i{A}_i^{j-1}{B}_i∆d\left(t\right)+p\left(t\right)\end{array}$$

(59)

$$P_p\left(t+1|t\right)=S_x∆x\left(t\right)+S_u∆U\left(t\right)+S_d∆d\left(t\right)+Ip\left(t\right)$$

(60)

while

$$S_x={\left[D_i{A}_i,\sum _{j=1}^2{D}_i{A}_i^j,\cdots ,\sum _{j=1}^n{D}_i{A}_i^j\right]}_{1\times n}^T$$

(61)

$$S_d={\left[D_i{B}_i,\sum _{j=1}^2{D}_i{A}_i^{j-1}{B}_i,\cdots ,\sum _{j=1}^n{D}_i{A}_i^{j-1}{B}_i\right]}_{1\times n}^T$$

(62)

$$S_u={\left[\begin{array}{ccccc}{D}_i{B}_i& 0& 0& \cdots & 0\\ {\displaystyle \sum _{j=1}^2}{D}_i{A}_i^{j-1}{B}_i& D_i{B}_i& 0& \cdots & 0\\ ⋮& ⋮& ⋮& \ddots & ⋮\\ {\displaystyle \sum _{j=1}^m}{D}_i{A}_i^{j-1}{B}_i& {\displaystyle \sum _{j=1}^{m-1}}{D}_i{A}_i^{j-1}{B}_i& \cdots & \cdots & D_i{B}_i\\ ⋮& ⋮& ⋮& \ddots & ⋮\\ {\displaystyle \sum _{j=1}^n}{D}_i{A}_i^{j-1}{B}_i& {\displaystyle \sum _{j=1}^{n-1}}{D}_i{A}_i^{j-1}{B}_i& \cdots & \cdots & {\displaystyle \sum _{j=1}^{n-m+1}}{D}_i{A}_i^{j-1}{B}_i\end{array}\right]}_{n\times m}$$

(63)

Due to model mismatch and environmental disturbances, the predicted power will deviate from the actual operating power. The errors value reflects the impact of various uncertain factors. which can be calculated as

$$e\left(t+1\right)=p_r\left(t+1\right)-p\left(t+1|t\right)$$

(64)

The prediction results of future output power can be corrected by using a time series method as

$$\tilde{P}\left(t+1|t\right)=P\left(t+1|t\right)+E\left(t+1|t\right)$$

(65)

3.3.2. Minimum Variance Control of Energy Units Based on Optimal Prediction

The ideal control reference of controllable energy units can be obtained from the intra-day rolling optimal dispatch strategy. The optimal control objective for a controllable energy unit in the real-time control stage is to achieve a minimum execution deviation and a minimum change in control variable $∆u\left(k\right)$, which can be set as

$$minJ=\sum _{i=1}^n{‖{\alpha }_{p,i}(p\left(t+i|t\right)-r\left(t+i\right))‖}^2+\sum _{i=1}^m{‖{\beta }_{u,i}∆u(t+i-1)‖}^2$$

(66)

where $r(t+i)$ is the i-th component of the ideal control reference, ${\alpha }_{p,i}$ is the weighting factor for the i-th prediction error, and ${\beta }_{u,i}$ is the weighting factor for the j-th control increment.

The objective function can be expressed in a matrix-vector form as

$$minJ={‖{\alpha }_p(P_p\left(t+1|t\right)-R(t+1\left)\right)‖}^2+{‖{\beta }_u∆U\left(t\right)‖}^2$$

(67)

The weighting matrices in the above equation are

$${\alpha }_p=diag({\alpha }_{p,1},{\alpha }_{p,2},\cdots ,{\alpha }_{p,p})$$

(68)

$${\beta }_u=diag({\beta }_{u,1},{\beta }_{u,2},\cdots ,{\beta }_{u,m})$$

(69)

The given ideal control reference sequence is

$$R\left(t+1\right)={\left[r\left(t+1\right),r\left(t+2\right),\cdots ,r(t+p)\right]}^T$$

(70)

To facilitate the solution, auxiliary variables are defined as

$$\Psi =\left[\begin{array}{c}{\alpha }_p(P_p\left(t+1|t\right)-R(t+1\left)\right)\\ {\beta }_u∆U\left(t\right)\end{array}\right]$$

(71)

Then the objective function can be expressed as

$$min{\Psi }^T\Psi ={(Az-b)}^T(Az-b)$$

(72)

where

$$A=\left[\begin{array}{c}{\alpha }_p{S}_u\\ {\beta }_u\end{array}\right],z=∆U\left(t\right),b=\left[\begin{array}{c}{\alpha }_p(R\left(t+1\right)-S_x∆x\left(t\right)-Iy\left(t\right)-S_d∆d(t\left)\right)\\ 0\end{array}\right]$$

(73)

According to the extremum condition of ${\left(Az-b\right)}^T(Az-b)$:

$$\frac{d{\Psi }^T\Psi }{dz}=2{\left(\frac{d\Psi }{dz}\right)}^T\Psi =2A^T\left(Az-b\right)=0$$

(74)

The extremum solution is obtained as

$$z^{*}={\left(A^{T}A\right)}^{-1}{A}^{T}b$$

(75)

As

$$\frac{d^2\left({\Psi }^T\Psi \right)}{d{z}^2}=2A^{T}A>0$$

(76)

$z^{*}$ is the unique extremal solution. Then, the optimal solution at time $t$ is

$$∆U^{*}\left(t\right)={\left(S_u^T{\alpha }_p^T{\alpha }_p{S}_u+{\beta }_u^T{\beta }_u\right)}^{-1}{S}_u^T{\alpha }_p^T{\alpha }_p(R\left(t+1\right)-S_x∆x\left(t\right)-Ip\left(t\right)-S_d∆d(t\left)\right)$$

(77)

Implement the first component of ${∆U}^{\mathrm{*}}\left(t\right)$ on the controlled object, and at the time $t+1$, re-predict the future output with the newly obtained initial conditions and solve the optimization problem again to achieve rolling optimization.

4. Simulation Results and Discussion

To validate the three-tier dispatch and control framework and strategy of the micro-energy grid, a simulation verification was conducted using an industrial park in Guangdong Province as a case study. The simulation platform was Python 3.7, and the CPLEX 12.10 solver was used for optimization.

4.1. Description of Simulation Scenario

The day-ahead power prediction, intra-day rolling power prediction, and actual power for wind power generation, solar power generation, and rigid load (including cooling load, thermal load, and electrical load) are shown in Figure 4. The curve of the intra-day power prediction shown in Figure 4 is formed by concatenating the hourly predictions.

The time-of-use electricity price for an industrial park in Guangdong Province is shown in

Table 2. Electricity price of an industrial park in Guangdong Province.

Period	Electricity Price (Yuan/kWh)
10:00–12:00, 14:00–19:00	1.177
08:00–10:00, 12:00–14:00, 19:00–24:00	0.704
00:00–08:00	0.285

. The price of natural gas is 3.5 yuan/cubic meter.

The industrial park is equipped with multi-type energy production units (micro gas turbines, gas boilers, absorption chillers, electric chillers, etc.), energy storage units (electrochemical energy storage, cold storage devices, etc.), and controllable energy consumption (transferable loads, power-adjustable loads, and interruptible loads). The controllable period of the controllable energy consumption units is from 12:00 to 21:00, while at other times, the controllable energy consumption units are on a shutdown state. The parameters of the simulation case are shown in

Table 3. Parameters of multi-type energy units in an industrial park in Guangdong Province.

${\mathit{P}\mathit{O}}_{\mathit{G}\mathit{T}.\mathit{m}\mathit{a}\mathit{x}}^{\mathit{e}}$	${\mathit{\eta }}_{\mathit{G}\mathit{T}}^{\mathit{e}}$	${\mathit{P}\mathit{O}}_{\mathit{G}\mathit{B}.\mathit{m}\mathit{a}\mathit{x}}^{\mathit{h}}$	${\mathit{\eta }}_{\mathit{G}\mathit{B}}^{\mathit{h}}$	${\mathit{P}\mathit{I}}_{\mathit{E}\mathit{C}.\mathit{m}\mathit{a}\mathit{x}}^{\mathit{e}}$	${\mathit{P}\mathit{I}}_{\mathit{H}\mathit{C}.\mathit{m}\mathit{a}\mathit{x}}^{\mathit{h}}$	${\mathit{P}\mathit{I}}_{\mathit{S}.\mathit{d}.\mathit{m}\mathit{a}\mathit{x}}^{\mathit{e}}$	${\mathit{P}\mathit{O}}_{\mathit{E}\mathit{H}.\mathit{m}\mathit{a}\mathit{x}}^{\mathit{h}}$
$2000 \mathrm{k}\mathrm{W}$	$7.5 \mathrm{k}\mathrm{W}/{\mathrm{m}}^3$	$2500 \mathrm{k}\mathrm{W}$	$9.72 \mathrm{k}\mathrm{W}/{\mathrm{m}}^3$	$3500 \mathrm{k}\mathrm{W}$	$2000 \mathrm{k}\mathrm{W}$	$1600 \mathrm{k}\mathrm{W}$	$2500 \mathrm{k}\mathrm{W}$
${PI}_{S.c.max}^e$	${PI}_{S.d.max}^c$	${PI}_{S.c.max}^c$	$E_{S.max}^e$	$E_{S.min}^e$	$E_{S.max}^c$	$E_{S.min}^c$	${\eta }_{EH}$
1600 kW	1000 kW	1000 kW	2560 kWh	0 k Wh	4000 kW	0 kW	0.95
${PO}_{PV.max}^e$	${\eta }_{EC}$	${\eta }_{EC}$	${PI}_{L,TS}^e$	${PI}_{L,IR}^e$	${PI}_{L,RG}^e$	$R_t^g$	$R_{dr,t}^{+}$
$2500 \mathrm{k}\mathrm{W}$	$1.2$	$1.1$	$1600 \mathrm{k}\mathrm{W}$	$1700 \mathrm{k}\mathrm{W}$	$1500 \mathrm{k}\mathrm{W}$	$2.87 \mathrm{Y}\mathrm{u}\mathrm{a}\mathrm{n}/{\mathrm{m}}^3$	$2.00 \mathrm{Y}\mathrm{u}\mathrm{a}\mathrm{n}/(\mathrm{k}\mathrm{W}·\mathrm{h})$
$R_{dr,t}^{-}$	${\alpha }^{+}$	${\alpha }^{-}$	$P_{Grid,t,max}$
$2.00 \mathrm{Y}\mathrm{u}\mathrm{a}\mathrm{n}/(\mathrm{k}\mathrm{W}·\mathrm{h})$	$1.1$	$0.9$	12,000 kW

.

The response delays and response errors of energy production units and energy storage units were disregarded due to their rapid adjustment capabilities. In this simulation case, the dispatch and control characteristics of controllable energy consumption units are mainly considered, including their response delay, startup and shutdown characteristics, response speed, and sustainable response time. In order to compare with other traditional methods, two simulation scenarios were set up:

Scenario 1: Disregarding the dispatch and control characteristics of the controllable energy units and using a traditional method to achieve a multi-time scale rolling dispatch for the micro-energy grid. The optimal dispatch strategies were obtained by using an improved quantum particle swarm intelligence algorithm.

Scenario 2: Using the three-tier dispatch and control framework proposed in this paper. By implementing day-ahead optimal dispatch and intra-day optimal rolling dispatch, the startup-shutdown plan and operation power plan of controllable energy units (including energy production units, energy storage units, and controllable energy consumption units) were determined. In the real-time control stage, model predictive control was implemented for limited controllable energy consumption units considering their multi-dimensional control response characteristics.

4.2. Analysis of Simulation Results for Scenario 1

We used the method proposed in [14] to achieve a rolling dispatch for the park micro-energy grid in Guangdong Province. The simulation results are shown in Figure 5. It is assumed that the controllable energy units are all ideal controllable objects, which can execute a dispatch plan without execution deviation.

During the periods of low electricity prices, the gas turbine is in a shutdown state, the electric power of micro-energy is mainly supplied by the power grid, the electrochemical energy storage device and the cold storage device are running in a charging state, the thermal load of micro-energy is supplied by the electric boiler and the gas boiler, and the cold load is supplied by the electric chiller. During the periods of peak electricity prices, with the gas turbine running in an operating stage, the thermal load supplied by gas turbines, and the excessive thermal energy transformed into cold energy by the absorption chiller, the insufficient cooling power of the micro-energy grid is supplied by the electric chiller and the cold storage device. The electrochemical energy storage device undergoes two charge-discharge cycles daily. The first cycle involves charging during the low-price period and discharging during the peak-price period, and the second cycle involves charging during the flat-price period and discharging during the peak-price period. The startup-shutdown plan and operation power plan of controllable energy consumption units (including transferable load, power-adjustable load, and interruptible load) are obtained by the optimal dispatch model, which considers the operation constraints.

However, the controllable energy consumption units in this industrial park have control response characteristics that could not be disregarded. By considering the control response characteristics (including response delay, startup and shutdown characteristics, response speed, and sustainable response time) of controllable energy consumption units, the actual execution power of these controllable energy consumption units can be obtained. The expected power and actual power of the controllable energy consumption units in Scenario 1 is shown in Figure 6.

4.3. Analysis of Simulation Results for Scenario 2

We used the day-ahead optimal dispatch strategy and intra-day rolling optimal dispatch strategy proposed in this paper. The simulation results are shown in Figure 7. In Scenario 2, the dispatch and control characteristics of controllable energy consumption units have been considered.

In the real-time control stage, the model predictive control of controllable energy units is executed with a goal of precisely following the optimal dispatch plan. The expected power and actual power of the controllable energy consumption units in Scenario 2 is shown in Figure 8.

By comparing Figure 6 and Figure 8, it can be observed that the adoption of the three-tier dispatch and control strategy proposed in this paper leads to a significant reduction in the execution deviation of the controlled energy unit. It is primarily due to the consideration of the multi-dimensional control response characteristics of the controlled energy units in the dispatch and control model proposed in this paper.

4.4. Comparative Analysis of Simulation Results

The comparison of the dispatch and control method used in Scenario 1 and Scenario 2 is shown in

Table 4. The comparison of the dispatch and control method used in simulation scenarios.

	Scenario 1	Scenario 2
Day-ahead optimized dispatch	√	√
Intraday rolling optimized dispatch	√	√
Real-time control strategies	×	√
Considering control response characteristics	×	√

. The dispatch and control method used in Scenario 1 is one of the traditional methods, while in Scenario 2 an innovative three-tier dispatch and control method proposed in this paper is used, which has considered in detail the control response characteristics of controllable energy units.

Based on the simulation results from Scenarios 1 and 2, the actual power of the interconnection line of the park micro-energy grid can be obtained. The comparison of the expected dispatch plan and the actual power of the interconnection line is shown in Figure 9.

The dispatch and control period of the limited controllable energy units was from 12:00 to 21:00. It can be observed that when using traditional control methods, due to the substantial execution deviations of controllable energy units, the power of the interconnection line cannot precisely follow the optimal dispatch plan, which will result in substantial assessment costs. However, the method proposed in this paper enables the controllable energy units and the power of interconnection line to precisely follow the optimal dispatch plan.

On the basis of the precise modeling of the dispatch and control characteristics (especially control response delay characteristics) of various controllable energy units, the dispatch and control strategy for park micro-energy grid proposed in this paper is more advanced and efficient than a traditional dispatch strategy. It is specifically reflected in terms of the execution accuracy and the operational cost of the park micro-energy grid, which are shown in

Table 5. The comparison of execution accuracy and operational cost for Scenarios 1 and 2.

	Scenario 1	Scenario 2
Execution accuracy (RMSE Root Mean Square Error)	850.12 kW	160.27 kW
Expected operational cost	¥647,525.73	¥647,525.73
Actual operational cost	¥685,359.45	¥654,728.86

.

The calculations for expected operational cost and actual operational cost are based on Equations (7)–(10). The calculation formula for RMSE in Table 4 is as follows:

$$RMSE=\sqrt{\frac{1}{t}\sum _{t=1}^T{(P_{grid,t,actual}-P_{grid,t,expected})}^2}$$

(78)

where $P_{grid,t,actual}$ is the actual power of the interconnection line at time t, and $P_{grid,t,expected}$ is the planned power of the interconnection line at time t.

From the above simulation comparison, it can be observed that:

• When controllable energy units in a park micro-energy grid have significant dispatch and control characteristics that cannot be disregarded, it becomes difficult for the micro-energy grid to precisely follow the dispatch planned power by using traditional day-ahead and intra-day optimal dispatch methods. The substantial execution deviation will make it challenging to effectively reduce the comprehensive operational costs of the park micro-energy grid.
• The execution deviation and operational cost of a park micro-energy grid can be efficiently reduced by implementing model predictive control on controllable energy units. The optimal object of the proposed control strategy is to minimize the variance of the execution deviations of controllable energy units, based on considering the control response delay, control response speed, and other control response characteristics of controllable energy units.
• The simulation results demonstrate that when compared with the traditional day-ahead and intra-day optimal dispatch methods for micro-energy grids, the adoption of the three-tier optimal dispatch and control strategy proposed in this paper results in a 45.79% improvement in execution accuracy and a 2.38% reduction in the energy cost.

4.5. Application Case

The optimal dispatch and control strategy for the micro-energy grid proposed in this paper is being pilot applied in an industrial park in Guangdong Province. There are solar power generation, a storage system, and production loads in the industrial park. Among production loads, there are six controllable loads, while the rest of the loads are rigid loads. In this case, data collection and control terminals are used to achieve monitoring and control of energy units. A dispatch and control system has been developed to achieve coordinated control and management of the park micro-energy grid. The implementation architecture of the pilot application case is shown in Figure 10.

Based on the application results, it has been demonstrated that with the consideration of the dispatch and control characteristics of controllable energy units, precisely following a dispatch plan can be achieved by the coordinated control of controllable energy units. The real operational data of the industrial park micro-energy grid for a given day is shown in Figure 11. In the figure, the x-axis represents time, and the y-axis unit is in megawatts. From top to bottom: The first graph is the “Real-time Response Curve.” From left to right, the legends are “Winning Time Slot,” “Actual Operating Load,” and “Baseline Load.” The two bar charts represent the results of the response execution. From left to right, the legends are “Winning Response Load,” “Actual Response Load,” and “Actual Response Coefficient.” The curve chart below depicts the execution of the plan. The legends for the curve, from left to right, are “Actual Operating Load” and “Dispatch Plan Power.” During the dispatch and control period from 13:00 to 16:00, the power of the interconnection line in the micro-energy grid precisely followed the dispatch plan, with an execution accuracy of 95.6%. The methods proposed in this paper have explored and contributed to achieving precise control of park micro-energy grids with a high proportion of controllable energy consumption units.

5. Conclusions

Disregarding the multidimensional dispatch and control response characteristics of multi-type energy units in micro-energy grids will lead to substantial execution deviation, making it difficult to run as a virtual power plant to support real-time power balance in the power system. In this paper, we mainly focus on the modeling of the multidimensional dispatch and control response characteristics of the controllable energy units in a micro-energy grid, and a three-tier dispatch and control strategy framework is proposed to achieve the unified collaborative optimal dispatch and control of a large number of controllable energy units in a micro-energy grid. The main contributions of this paper are as follows:

• Proposing a unified modeling approach that considers the response delay, startup and shutdown characteristics, response speed, and sustainable response time of various controllable energy units, for the purpose of decreasing the execution deviation of an energy unit and micro-energy system. The proposed model is a foundation for a park micro-energy grid to achieve precise dispatch and control in electricity markets.
• Developing a multi-time scales dispatch and control model for a park micro-energy grid, including a day-ahead dispatch model, an intra-day rolling dispatch model, and a real-time predictive control model, to match the multi-time scale trading varieties in electricity market. Laying the foundation for achieving a multi-time scale optimal dispatch and control of a park micro-energy grid.
• Taking the minimization of the operating cost as the optimal objective of day-ahead optimal dispatch and intra-day optimal rolling dispatch. Using a two-stage solution method, which transforms the mixed-integer nonlinear programming problem into a mixed-integer linear programming problem, to efficiently solve the optimal strategies that consider the multi-dimensional dispatch and control response characteristics of a park micro-energy grid.
• Considering the response delay characteristics of each type of controlled energy unit, a closed-loop optimal control strategy based on rolling d-step prediction is proposed to obtain the minimum variance control law. It solves the problem that controllable energy units are difficult to be controlled precisely due to the disregarding of their multidimensional dispatch and control response characteristics.

6. Future Prospects

Although the three-tier dispatch and control strategies proposed in this study can effectively reduce the execution deviation and operational cost of the park micro-energy grid, there still remain some limitations that make it unable to accurately execute the planed power without deviation. The mainly reasons are listed below:

• In order to obtain the day-ahead and intra-day optimal dispatch strategies, a two-stage solving model is implemented in this paper. To reduce the complexity of the solution, the dispatch and control characteristics of controllable energy units have been simplified in the first solving stage, which could have a negative impact on the optimality of the solution results and the execution accuracy of the strategies.
• In engineering applications, the control response characteristics of controllable energy consumption units are extremely complex, making it difficult to develop a precise model, which may lead to certain execution deviations.

In response to these challenges, the precise modeling of controllable energy units and the more efficient methods for solving optimal strategies will be studied further. The main goal of our research is to enable a park micro-energy grid to run as a true virtual power plant.