清华大学 汽车安全与节能国家重点实验室, 北京 100084
收稿日期：2016-09-30
基金项目：上海汽车工业科技发展基金会项目（1530）
作者简介：谢海明(1984—), 男, 博士研究生
通信作者：黄勇, 高工, E-mail:huangyev@tsinghua.edu.cn
摘要：为在保证动力性的条件下提高增程式城市客车的燃油经济性，提出了一种基于电池荷电状态（SOC）消耗管理和功率分配的能量分段跟踪优化方法。该方法通过在每个控制周期内构建一个短期的需求功率预测序列，并设计参考曲线以实现SOC消耗管理的方式，建立了以费用最小为目标的动力系统功率分配的阶段性优化模型。引入模型预测控制方法，滚动优化并调整功率分配策略。基于该方法，一辆12 m增程式城市客车在中国城市公交工况下的100 km油耗为21.8 L，电耗为25.4 kWh，优于CDCS策略的结果（100 km油耗24.1 L，电耗25.4 kWh）。该方法能通过防止SOC在行程中被过早耗尽并使其在行程结束时降到最低，保证增程式城市客车的动力性并提高燃油经济性。
关键词：能量优化电量消耗管理跟踪优化模型预测控制增程式电动汽车
Piecewise tracking energy optimization approach for an extended-range electric city bus
XIE Haiming, LIN Chengtao, LIU Tao, TIAN Guangyu, HUANG Yong
State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China
Abstract: A piecewise tracking energy optimization approach was developed to manage the battery state of charge (SOC) consumption and the splitting power to improve the fuel economy of extended-range electric city buses while ensuring their performance. The approach established a stage power splitting optimization model for each control period by constructing a power demand prediction sequence and designing a reference curve to manage the SOC consumption. Model predictive control was introduced for rolling optimization and strategy adjustment. For the Chinese city bus driving cycle, this approach enables a 12 meters extended-range electric city bus to use only 21.8 L fuel and 25.4 kWh electricity per 100 km, which are better than CDCS strategy based results (24.1 L fuel and 25.4 kWh electricity per 100 km). The results show that by preventing the SOC from running out during the route but only reaching its minimum, this approach ensures the dynamic performance and improves the fuel economy.
Key words: energy optimizationstate of charge (SOC) consumption managementtracking optimizationmodel predictive controlextended-range electric vehicle
纯电动汽车的行驶里程受到车载动力电池组容量的限制。目前，动力电池存在能量密度低、材料价格贵等问题，单纯依靠增大电池容量来提高行驶里程，会大幅增加汽车的自重和制造成本，增程式电动汽车(extended-range electric vehicles，E-REV)应运而生。E-REV利用能量辅助单元(auxiliary power unit, APU)为车辆提供电能补充，延长行驶里程[1]。图 1为一种增程式电动汽车的动力系统结构示意图。APU由发动机与发电机组成，通过整流装置(AC/DC)与动力电池组耦合。该动力系统具有纯动力电池组驱动、APU和动力电池组混合驱动、制动能量回收和外接充电等多种能量流动模式[2-3]。APU和动力电池组构成的双能量源为E-REV的能量管理提供了更多的灵活性，同时也带来了挑战。
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| 图 1 增程式电动汽车动力系统结构与能量流动 |
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E-REV与混合动力汽车(hybrid electric vehicles，HEV)、插电式混合动力汽车(plug-in hybrid electric vehicles，PHEV)的能量管理策略相似。然而，E-REV的发动机功率较小，APU不能单独满足车辆的大功率需求，在动力电池组的电量耗尽时，车辆的动力性会受到影响。因此，E-REV的能量管理策略需要考虑管理动力电池组的SOC消耗，防止行驶过程中提前耗尽电量；同时，又要在行程结束时消耗完电量，以充分利用E-REV可以外接充电的优势。常见的能量策略包括基于规则的(rule-based)和基于优化的(optimization-based)策略两大类[4-8]。前者通过设定逻辑门限值或者模糊规则来控制动力系统部件的输出功率[9-12]，后者通过建立并求解能量优化问题的数学模型来优化功率分配策略。LIN等[6]最先将确定性动态规划算法(deterministic dynamic programming，DDP)用来求解HEV的能量优化分配问题。DDP算法依赖于完整的工况信息，然而在实际行驶过程中，车辆未来的需求功率是未知的。针对这一问题，LIN等[13]建立了需求功率的Markov预测模型，提出了基于随机动态规划的HEV能量管理策略，摆脱了对完整工况信息的依赖。近年来，基于模型预测控制(model predictive control，MPC)的能量管理策略在HEV[14-18]和PHEV[19]上得到了应用，相关的研究工作多是基于已知工况展开的。随机模型预测控制(stochastic model predictive control，SMPC)[20]方法的出现，使得MPC方法在用于能量管理时，不再依赖于完整的工况信息[21]。
E-REV能量管理的实质是在保证车辆动力性的前提下，合理分配APU与动力电池组的输出功率，从而提高整车的燃油经济性。本文以一辆12 m增程式城市客车为研究对象，针对其行驶路线相对固定、一天行驶里程可估计的特点，利用分段优化的方法，将全行程的整车能量优化问题转化为瞬时的阶段性优化问题，主要工作包括：1) 统计工况信息，建立需求功率的Markov预测模型，基于需求功率的当前值，预测其未来N-1步的值；2) 实时估计车辆在剩余里程中的能量需求，将行程结束时期望的SOC值转化为阶段性的终端约束条件，并结合需求功率的预测序列，设计SOC消耗的参考曲线；3) 以费用最小为目标，同时引入跟踪SOC消耗参考曲线的惩罚项，建立动力系统瞬时功率分配的阶段性优化模型；4) 引入模型预测控制方法，在每个控制周期内，更新工况信息，重新预测需求功率序列，利用改进的DDP算法对优化模型进行求解，滚动优化并调整功率分配策略，降低需求功率的预测误差对能量管理效果的影响。
1 动力系统建模基于控制周期ΔT，对动力电池组、APU、驱动电机以及整车进行离散化建模。
动力电池组的SOC按式(1) 演化[22]，
| ${\rm{SOC}}\left( {k + 1} \right) = {\rm{SOC}}\left( k \right)-\frac{{{I_{{\rm{bat}}}}\left( k \right)}}{{{Q_{{\rm{bat}}}}}}\frac{{\Delta T}}{{3{\rm{ }}600}}.$ | (1) |
| ${I_{{\rm{bat}}}}\left( k \right) = \frac{{{V_{{\rm{ocv}}}}\left( k \right)-\sqrt {V_{{\rm{ocv}}}^2\left( k \right)-4{R_{{\rm{bat}}}}\cdot1{\rm{ }}000{P_{{\rm{bat}}}}\left( k \right)} }}{{2{R_{{\rm{bat}}}}}}.$ | (2) |
| ${V_{{\rm{ocv}}}}\left( k \right) = {V_{{\rm{ocv}}}}({\rm{SOC}}\left( k \right)).$ | (3) |
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| 图 2 基于发动机效率图的APU工作点设计 |
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表 1 APU各工作点对应的输出功率和燃油消耗率
| 工作点 | APU输出功率/kW | 燃油消耗率/ (g·(kWh)-1) |
| 1 | 0 | 0 |
| 2 | 11.50 | 208.69 |
| 3 | 15.13 | 196.47 |
| 4 | 19.19 | 206.41 |
| 5 | 20.35 | 237.28 |
| 6 | 24.10 | 199.17 |
| 7 | 25.60 | 234.38 |
| 8 | 28.99 | 208.42 |
| 9 | 32.24 | 198.28 |
| 10 | 35.30 | 203.97 |
| 11 | 37.60 | 225.45 |
| 12 | 39.92 | 223.40 |
| 13 | 42.20 | 227.49 |
| 14 | 44.50 | 242.69 |
| 15 | 48.50 | 222.68 |
| 16 | 50.80 | 212.60 |
| 17 | 53.20 | 225.56 |
| 18 | 55.97 | 235.44 |
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| ${{\dot m}_{{\rm{f, steady}}}} = {{\dot m}_{{\rm{f, steady}}}}\left( {{P_{{\rm{APU}}}}\left( k \right)} \right).$ | (4) |
| ${P_{{\rm{APU}}}}\left( k \right) + {P_{{\rm{bat}}}}\left( k \right) = {P_{{\rm{req}}}}\left( k \right).$ | (5) |
车辆的能量消耗E和位移d分别为：
| $E\left( {k + 1} \right) = E\left( k \right) + {P_{{\rm{req}}}}(k)\frac{{\Delta T}}{{3{\rm{ }}600}}, $ | (6) |
| $d\left( {k + 1} \right) = d\left( k \right) + {u_{\rm{a}}}(k)\frac{{\Delta T}}{{3600}}.$ | (7) |
由式(5) 给定的约束条件可知，当给定未来需求功率的预测序列时，控制APU的输出功率可实现动力系统的功率分配。定义系统的输入为u(k)=PAPU(k)，输出为y(k)=Pbat(k)，状态量为x(k)=[SOC(k) d(k) E(k)]T，它们分别满足如下约束：
| $\mathit{\boldsymbol{X}} \buildrel \Delta \over = {\rm{\{ }}\mathit{\boldsymbol{x}}:{\rm{SO}}{{\rm{C}}_{{\rm{min}}}} \le {x_1} \le {\rm{SO}}{{\rm{C}}_{{\rm{max}}}}\}, $ | (8) |
| $U \buildrel \Delta \over = \left\{ \begin{array}{l}0, {\rm{ }}11.50, {\rm{ }}15.13, {\rm{ }}19.19, {\rm{ }}20.35, {\rm{ }}24.10, \\25.60, {\rm{ }}28.99, {\rm{ }}32.24, {\rm{ }}35.30, {\rm{ }}37.60, {\rm{ }}39.92, \\42.20, {\rm{ }}44.50, {\rm{ }}48.50, {\rm{ }}50.80, {\rm{ }}53.20, {\rm{ }}55.97\end{array} \right\}, $ | (9) |
| $Y \buildrel \Delta \over = \{ y:{P_{{\rm{bat}}, {\rm{min}}}} \le y \le {P_{{\rm{bat, max}}}}\} .$ | (10) |
2 未来需求功率预测2.1 Markov预测模型车辆在行驶过程中，需求功率Preq受到交通拥堵情况和司机驾驶习惯等因素的影响，具有随机性。基于文[13]的工作，需求功率序列为一个齐次Markov链，即下一个时刻需求功率的状态值Pj，只与当前状态值Pi有关。
| $\begin{array}{l}P\{ {P_{{\rm{req}}}}\left( {k + 1} \right) = {P_j}|{P_{{\rm{req}}}}\left( k \right) = {P_i}\} = {\pi _{i, j}}, \\\;\;\;\;\;\;\;\;\;\sum\limits_{j = 1}^s {{\pi _{i, j}} = 1} .\end{array}$ | (11) |
| $\mathit{\boldsymbol{ \boldsymbol{\varPi} = }}{{\rm{(}}{\pi _{i, j}})_{s \times s}}.$ | (12) |
2.2 转移概率矩阵估计转移概率矩阵П的估计方法如下：
1) 基于仿真工况，计算需求功率序列。
本文中，需求功率Preq定义为驱动电机输入端的功率，其与轮边需求功率Pwh的关系为
| ${P_{{\rm{req}}}} = \left\{ \begin{array}{l}\frac{{{P_{{\rm{wh}}}}}}{{{\eta _{\rm{T}}}{\eta _{\rm{M}}}}}, \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{P_{{\rm{wh}}}} \ge 0;\;\\{P_{{\rm{wh}}}}{\eta _{\rm{T}}}{\eta _{\rm{M}}}\left( {1-\beta } \right){\beta _{{\rm{elc}}}}, \;\;{P_{{\rm{wh}}}} < 0.\end{array} \right.$ | (13) |
| ${P_{{\rm{wh}}}} = \frac{{Gf{u_{\rm{a}}}}}{{3{\rm{ }}600}} + \frac{{{C_{\rm{D}}}Au_{\rm{a}}^{^3}}}{{76{\rm{ }}140}} + \frac{{\delta m{u_{\rm{a}}}}}{{3{\rm{ }}600}}a.$ | (14) |
2) 将需求功率的取值范围划分为s个状态区间，每个状态区间对应的需求功率的状态值Pj(j=1, 2, …, s)用落在该状态区间的所有需求功率的平均值表示。
3) 统计需求功率序列中从状态i转移到状态j的频数fi, j(i=1, 2, …, s；j=1, 2, …, s)，并在统计结束后，计算需求功率的转移概率,
| ${\pi _{i, j}} = {f_{i, j}}/\sum\limits_{j = 1}^s {{f_{i, j}}} .$ | (15) |
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| 图 3 中国城市公交工况下的车速 |
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| 图 4 中国城市公交工况下的需求功率 |
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| 图 5 需求功率序列的状态转移概率 |
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2.3 需求功率序列预测基于图 5的转移概率矩阵和当前需求功率的状态，利用文[21]中的极大似然估计方法，构建一条未来需求功率的预测序列，相关定义说明如下：
1)
2) pre(Ti)：Ti在预测序列
3) succ(Ti, j)：Markov链中，需求功率的状态Ti能够到达的下一个状态j，j∈1, 2, …, s。
4)
5) πTi：预测序列中，从T1到达Ti的概率。
3 SOC消耗参考曲线设计本文采用MPC方法对阶段性的功率分配问题进行滚动优化。在每个控制周期内，基于需求功率的预测序列，设计一条SOC消耗参考曲线{SOCrefi(k)|i=1, 2, …, N}，k为当前控制周期数。以预测时域长度N=5为例，图 6给出了3个相邻控制周期内SOC消耗参考曲线的示例。考虑到每个控制周期内优化得到的N个控制量只会执行第1个，将第k个控制周期内SOC消耗参考曲线的初值SOCref1(k)设定为第k-1个控制周期内SOC消耗参考曲线上第2个点的值[23]。
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| 图 6 SOC消耗参考曲线设计原理示例 |
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车辆平均每km能量消耗e为
| $\bar e\left( k \right) = \left\{ \begin{array}{l}{{\bar e}_0}, \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;d\left( k \right) = 0;\\\max \left\{ {\frac{{E\left( k \right)}}{{d\left( k \right)}}, {{\bar e}_0}} \right\}, d\left( k \right) > 0.\end{array} \right.$ | (16) |
| ${E_{{\rm{rest}}}}\left( k \right) = \bar e\left( k \right)\left( {{d_0}-d\left( k \right)} \right).$ | (17) |
| $\begin{array}{l}\Delta {\rm{SOC}}_{{\rm{ref}}}^{^i}\left( k \right) = \\\frac{{{\rm{SOC}}_{{\rm{ref}}}^{^1}\left( k \right) - {\rm{SO}}{{\rm{C}}_{{\rm{ref,end}}}}}}{{{E_{{\rm{rest}}}}\left( k \right)}}\sum\limits_{j = 1}^{i - 1} {\left( {\frac{{\Delta T}}{{3{\rm{ }}600}}{P_{{\rm{req,}}j}}} \right)} .\end{array}$ | (18) |
| $\begin{array}{l}{\rm{SOC}}_{{\rm{ref}}}^{^i}\left( k \right) = {\rm{SOC}}_{{\rm{ref}}}^{^1}\left( k \right)-\Delta {\rm{SOC}}_{{\rm{ref}}}^{^i}\left( k \right), \\\;\;\;\;\;\;\;\;\;\;\;\;\;\;i = 2, {\rm{ }}3, \cdots, {\rm{ }}N.\end{array}$ | (19) |
| $ {\rm{SOC}}_{{\rm{ref}}}^{^1}\left( k \right) = \left\{ \begin{array}{l}{\rm{SO}}{{\rm{C}}(1)}, \;\;\;\;\;\;\;\;\;\;k = 1;\\{\rm{SOC}}_{{\rm{ref}}}^2\left( {k-1} \right), k > 1.\end{array} \right. $ | (20) |
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| 图 7 SOC消耗参考曲线 |
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4 整车能量管理的分段优化建模以预测序列{PT1, PT2, …, PTN}中每个需求功率出现的概率为加权因子，对系统的单步费用进行概率累加，从而构建以总费用最低为目标的瞬时功率分配最优化模型。为了简化符号的表述，在优化模型中，所有的Ti将简化为i来表示，即用xi，Preq, i，PAPU, i，Pbat, i，πi，pre(i)来分别表示xTi，PTi，PAPU, Ti，Pbat, Ti，πTi，pre(Ti)。模型如下：
| $\begin{array}{l}\min \;J = \sum\limits_{i \in \mathcal{J}\backslash \mathcal{S}} {{\pi _i}\alpha } P_{{\rm{bat}},i}{\left( {{\eta _{{\rm{bat}}}}} \right)^{-{\rm{sign}}\left( {{P_{{\rm{bat}}, i}}} \right)}}\frac{{\Delta T}}{{3{\rm{ }}600}} + \\\sum\limits_{i \in \mathcal{J}\backslash S} {{\pi _i}\beta {{\dot m}_{\rm{f}}}} \left( {{P_{{\rm{APU, }}i}}} \right){P_{{\rm{APU, }}i}}\frac{{\Delta T}}{{3{\rm{ }}600}}\frac{1}{{{\rho _{{\rm{fuel}}}}}} + \\\sum\limits_{i \in \mathcal{J}\backslash \{ {T_1}\} } {{\pi _i}\gamma |{\rm{SOC}}{_i}-{{\rm{SOC}}_{{\rm{ref,}}k}^i}|} .\end{array}$ | (21) |
| $\begin{array}{l}{\mathit{\boldsymbol{x}}_1} = \mathit{\boldsymbol{x}}\left( k \right), \\{P_{{\rm{req}}, 1}} = {P_{{\rm{req}}}}\left( k \right), \\{u_{{\rm{a}}, 1}} = {u_{\rm{a}}}\left( k \right), \\{\mathit{\boldsymbol{x}}_i} = {\left[{{\rm{SO}}{{\rm{C}}_i}\;\;{d_i}\;\;{E_i}} \right]^{\rm{T}}}.\\{\rm{SO}}{{\rm{C}}_i} = {\rm{SO}}{{\rm{C}}_{{\rm{pre}}\left( i \right)}} -\frac{{{I_{{\rm{bat, pre}}\left( i \right)}}}}{{{Q_{{\rm{bat}}}}}}\frac{{\Delta T}}{{3{\rm{ }}600}}, \\{d_i} = {d_{{\rm{pre}}\left( i \right)}} + {u_{{\rm{a}}, {\rm{pre}}(i)}}\frac{{\Delta T}}{{3{\rm{ }}600}}, \\{d_i} = {d_{{\rm{pre}}\left( i \right)}} + {u_{{\rm{a}}, {\rm{pre}}(i)}}\frac{{\Delta T}}{{3{\rm{ }}600}}, \\{E_i} = {E_{{\rm{pre}}\left( i \right)}} + {P_{{\rm{req}}, {\rm{pre}}(i)}}\frac{{\Delta T}}{{3{\rm{ }}600}}, \\{P_{{\rm{bat}}, i}} = {P_{{\rm{req}}, i}} -{P_{{\rm{APU}}, i}}, \;\forall i \in \mathcal{J}\backslash \mathcal{S}, \\{\mathit{\boldsymbol{x}}_i} \in \mathit{\boldsymbol{X}}, \forall i \in \mathcal{J}\backslash \{ {T_1}\}, \\{P_{{\rm{APU}}, i}} \in \mathit{\boldsymbol{U}}, \forall i \in \mathcal{J}\backslash \mathcal{S}, \\{P_{{\rm{bat}}, i}} \in \mathit{\boldsymbol{Y}},\forall i \in \mathcal{J}\backslash \mathcal{S}.\end{array}$ |
5 仿真计算和结果分析利用模型预测控制方法对由式(21) 给定的优化问题进行滚动优化，预测时域长度为N=20。在每一个控制周期内，利用DDP算法来求解式(21) 所示的优化问题。为了降低求解的难度，本文对上述优化问题进行了如下简化：当APU需要升功率时，只允许其向相邻高功率点调节；当APU需要降功率时，只允许其向相邻低功率点调节或者进入怠速状态，以此达到限制APU动态调节的幅度来降低发动机动态调节过程的油耗，同时减少DDP中遍历状态的个数以降低算法的复杂度。针对由中国城市公交工况构造的200 km循环工况，计算得到了12 m增程式城市客车的纯油耗为21.8 L/(100 km)，电耗为25.4 kWh/(100 km)，仿真结束时，动力电池组SOC值为0.250 9。图 8为前1 500 s的需求功率和优化得到的APU输出功率。基于改进的DDP算法，APU的输出功率没有出现频繁的调节。图 9中展示了此过程中动力电池组SOC曲线的变化趋势，电池组SOC曲线较好地跟随了SOC消耗参考曲线，虚线由每个控制周期内SOC消耗参考曲线上第1个点的值组成，即
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| 图 8 能量分段跟踪优化方法的APU输出功率 |
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| 图 9 基于能量分段跟踪优化方法的SOC演变曲线 |
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| $\left\{ {{\rm{SOC}}_{_{{\rm{ref}}}}^{^1}\left( k \right)|k = 1, {\rm{ }}2, \cdots, 1{\rm{ }}500} \right\}.$ |
6 结论针对车辆在行驶过程中未来需求功率未知的情况，为了既保证增程式城市客车的动力性又提高燃油经济性，本文提出了一种基于电池SOC消耗管理和功率分配的整车能量分段跟踪优化方法。该方法通过在每个控制周期内构建一个需求功率预测序列和设计一条SOC消耗参考曲线，将全程的能量优化问题转化为一系列的阶段性优化问题，然后利用模型预测控制方法对功率分配策略进行滚动优化，并在中国城市公交工况下对该方法的燃油经济性进行了仿真验证，得到结论如下：
1) 利用模型预测控制方法对功率分配策略进行滚动优化，可以减少需求功率预测误差的影响，能够使得实际SOC曲线较好地跟随SOC消耗参考曲线。
2) 通过防止电池SOC在行程中被过早耗尽，并使其在行程结束时降到最低，能够在保证动力性的前提下提高增程式城市客车的燃油经济性。
为进一步改善车辆燃油经济性，未来将研究利用工况辨识技术来提高需求功率预测准确度的方法。
参考文献
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